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sprint abilizer

April 2011
ISSN 1211—877X
CZECH
AEROSPACE
Proceedings
LETECKÝ
zpravodaj
In this issue:
J OURN A L
FOR
C Z ECH
A EROS P A CE RESE A RCH
Feasibility tests of
friction welding of high
melting temperature
materials in VZLÚ
Simulation of level
of quasistatic
microaccelerations
on-board of a spacecraft
Small aircraft ECS
optimization using 1D
tool
Microaccelerometer
Error Analysis
Analysis of dynamic
characteristics of gas
turbine
Kinetic analysis of
oxidizing decomposition
of carbon fiber
reinforced epoxy
composite
Analysis of options for
calibration of micro
accelerometer MAC
No. 1 / 2011
CZECH
CZECH
AEROSPACE
Proceedings
J OURN A L
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FOR
C Z ECH
A EROS P A CE RESE A RCH
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Czech AEROSPACE Proceedings
Letecký zpravodaj
1/2011
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Contents / Obsah
2
Feasibility tests of friction welding of high melting temperature materials in VZLÚ, Plc.
Zkoušky proveditelnosti třecího svařování materiálů s vysokou teplotou tání realizované ve VZLÚ, a.s.
Ing. Petr Bělský / VZLÚ, Plc., Prague
7
Experimental modal and FEM analysis of space instrument DUMMY
Experimentální modální a MKP analýza kosmického přístroje DUMMY
Ing. Vladimír Dániel, Ph.D., Ing. Tomáš Jamróz, Ing. Jiří Had /VZLÚ, Plc., Prague
10
Simulation of level of quasistatic microaccelerations on-board of a spacecraft
Modelování úrovně mikrozrychlení na palubě kosmického prostředku
Ing Viktor Fedosov Ph.D. /VZLÚ, Plc., Prague
16
The influence of structural damping on flutter characteristics of a small sport aircraft
Vliv strukturálního tlumení na flutterové charakteristiky malého sportovního letounu
Ing. Martin Zejda / Aerospace Research Centre, FME CTU in Prague; Ing. Aleš Kratochvíl / Aerospace
Research Centre, FME CTU in Prague; Doc. Ing. Svatomír Slavík, CSc. / Czech Technical University in
Prague, Faculty of Mechanical Engineering, Department of Aerospace Engineering
20
Small aircraft ECS optimization using 1D tool
Optimalizace ECS malých dopravních letadel pomocí 1D simulačního nástroje
Ing. Jiří Hejčík, Ph.D. / Institute of Aerospace Engineering, Brno University of Technology
Prof. Ing. Miroslav Jícha, CSc. / Department of Thermodynamics and Environmental Engineering, Brno
University of Technology
23
Development of series production technology for stator and rotor blades
Vývoj technologie výroby statoru a rotoru pro opakovanou výrobu.
Ing. Karel Barák; Ing. Michal Řehák/ Department of Aerospace Engineering
25
Microaccelerometer Error Analysis
Rozbor chyb mikroakcelerometru
Ing. Milan Chvojka
31
Analysis of dynamic characteristics of gas turbine
Analýza dynamických vlastností spalovací turbíny
Tomáš Jamróz, Jiří Had, Vladimír Dániel / VZLÚ, Plc., Praha
34
Kinetic analysis of oxidizing decomposition of carbon fiber reinforced epoxy composite
Kinetická analýza oxidačního rozkladu uhlíkového epoxidového kompozitu
Ing. Zdeněk Mašek
40
Analysis of options for calibration of micro accelerometer MAC
Analýza možností kalibrace mikroakcelerometru MAC
RNDr. Vojtěch Zadražil / VZLÚ, Plc., Prague
47
Worst Case Analysis Methods Implementation in an Accelerometer Measuring Loop Analysis
Aplikace postupů Analýzy nejhoršího případu (WCA) při analýze měřicí smyčky akcelerometru
Jozef Zakucia, Milan Merkl / VZLÚ, Plc., Prague
54
Experimental Assessment of the Fragments Effect to the Fuselage of the Aircraft
Experimentální určení účinku střepin na drak letounu
Ing. Miroslav Lošťák, Doc. Ing. Miloslav Petrásek CSc. VUT Brno
C z e c h A e r o s pa c e P r o c e e d i n g s 2
Feasibility tests of friction welding of high
melting temperature materials in VZLÚ, Plc.
Zkoušky proveditelnosti třecího svařování materiálů s vysokou
teplotou tání realizované ve VZLÚ, a.s.
Ing. Petr Bělský / VZLÚ, Plc., Prague
The paper provides information about first feasibility tests of FSW and FSSW of high melting temperature materials in the territory of Czech Republic by VZLÚ, Plc in November 2010. Experiments were focused on friction welding of microalloyed steel USIBOR 1500 P intended mainly for the use in the automobile industry. Tested subjects
consisted of four types of materials for working parts of welding tools (pure tungsten, W25Re2HfC alloy, silicon
nitride and PCBN). In addition, the influence of welding parameters on mechanical properties and macroscopic
pattern of the weld joints had been studied.
Příspěvek stručnou formou informuje o prvních zkouškách třecího svařování materiálů s vysokou teplotou tání
realizovaných na území České republiky ve VZLÚ, a.s. v listopadu 2010. Uskutečněné experimenty byly zaměřeny
na kontinuální a bodové třecí svařování mikrolegované oceli USIBOR 1500 P určené především pro použití v automobilovém průmyslu. Během těchto testů byly testovány 4 druhy materiálu pro pracovní části svařovacích nástrojů (čistý wolfram, slitina W25Re2HfC, nitridová keramika a kubický nitrid bóru). Zkoumán byl vliv svařovacích
parametrů na mechanické vlastnosti a makrostrukturu svarových spojů.
Keywords: Friction stir welding, USIBOR 1500, microalloyed steel, PCBN, silicon nitride, tungsten rhenium
Introduction
The solid state welding processes known as friction stir
welding (FSW) and friction stir spot welding (FSSW) are
relatively new when compared to fusion welding methods.
Principle of FSW technology was invented and patented in
1991 by The Welding Institute (TWI) in Cambridge UK [1].
The process uses a non-consumable rotating tool to generate frictional heat in the work piece. The conventional friction stir tool consists of a pin and a shoulder. The pin is
plunged into the material to be joined and stirs the material
at the joint interface. The shoulder remains in contact with
the top surface of the material to be joined and generates
additional heat while constraining the plasticized material.
The FSSW is a variant on the friction stir welding process that does not involve any lateral movement along the
work piece. During FSSW process a rotating tool with probe
is plunged into two overlapped blanks to be jointed. The
rotating tool generates friction heat in the specimens. The
heated and softened material close to the tool plastically
deforms and a bond is made between the upper and lower
sheet.
FSW and FSSW offer many advantages over conventional
fusion welding processes because of their low heat input
and absence of melting and solidification process. It results
in better material properties, fewer weld defects, low residual stresses and improved dimensional stability. In the past,
commercial applications of FSW and FSSW have been limited to lower melting temperature materials, e.g. aluminium,
zinc, lead etc. The joining methods have proven very beneficial in these applications, but these materials represent less
than 10% of the welded products in the world. On the other
hand, steels and other high melting temperature materials
(HMTM) represent greater than 80% of the welded product
worldwide. Thus, the economic impact of FSW and FSSW
in HMTM could markedly dwarf that of lower melting temperature materials. For example automotive industry represents huge opportunity for the next dissemination of the
promising methods. Recently, the increasing use of advanced high strength steels (AHSS) for occupant protection and
potential weight savings in high productivity manufacture
has encouraged the development and adoption of new joining technologies capable of meeting the quality, reliability
and cost requirements in the sector. There is a possible question whether FSW and FSSW methods could be utilized for
welding of the AHSS steels and fulfil automotive industry
requirements.
The automotive industry at the territory of the Czech
Republic has a long tradition of engineering and production.
At the present time czech automotive manufacturers produce over most 1 million vehicles per year. The motor industry
covers roughly 20% of the total exports and about 21% of
the Czech exports to EU. The success was not possible to
achieve without continuous innovations and cooperation of
the industry with technical universities and R&D institutes.
One of the most extensive production cycles in automotive
manufacturing is joining, particularly welding. That way
any innovation in the area can have big impact on resulting
price and competitiveness. FSW and FSSW are very promising joining methods that could to find utilization in czech
automotive industry.
VZLÚ, Plc. officially started FSW research activities in
2005 in frame of the project ARC-B2 (Aerospace Research
Centre) supported by the Czech Ministry of Education,
Youth and Sports. A lot of various studies focused on butt,
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1/2011
cimens. The specimens for continuous FSW tests consisted
of two plates 200x110 mm. Specimens for FSSW tests
were realized by using two coupons 45x150 mm with a
45x50 mm overlap in case of lap-shear specimens and two
coupon 50x150 mm with a 50x50 mm overlap in case of
cross-tension specimens. All specimens were degreased
prior to welding using a household cleaner and alcohol.
FSW and FSSW Tools
Friction stir welding of high melting temperature materials such as steels require a tool material that possesses a
combination of properties including high strength, toughness, high-temperature thermal stability, hot hardness,
high temperature oxidation resistance, and a decreased
affinity to the weld materials. During the feasibility studies in VZLÚ, Plc. were tested 4 tool materials:
Fig. 1 - Continuous FSW of USIBOR 1500 steel sheets
lap, spot and T-welds of aluminium alloys and other low
melting temperature materials were performed through the
years 2005-2009. Research activities focused on friction stir
welding of high melting temperature materials such as steel,
titan and nickel base alloys are next very important milestone for understanding all possibilities of the modern joining
technology. The paper gives short information about first
feasibility tests of FSW and FSSW of advanced high strength steel realized at the territory of the Czech Republic by
VZLÚ, Plc in November 2010.
Table 1 – Chemical composition and basic mechanical
properties of USIBOR 1500 steel
Material
The test material used in the feasibility tests were sheets
with thickness 1,5 mm made of Al-Si pre-coated quenchenable micro-alloyed steel 22MnB5, well known with the
commercial name of USIBOR 1500 P [2]. The steel is
intended mainly for use in automobile structural and safety
components. USIBOR 1500 P is designed to be heat treated and then quenched during the hot stamping process.
The mechanical properties of the final part make significant weight savings possible (up to 50% compared to standard high yield strength steel). The very high yield strength of the steel after heat treatment and hot stamping make
it suitable for anti-intrusion components (fender beams,
door reinforcements, B-pillars, windscreen uprights, floor
and roof reinforcements, etc.). The material strength is
propagated by adding a small fraction of boron to the carbon, manganese and chromium composition. Therefore
this steel grade is also called “boron steel”, in colloquial
terms. The nominal chemical composition and basic
mechanical properties are listed in Table 1.
The sheets were delivered in soft-annealed condition
from Benteler Automotive Rumburk s.r.o. and cut into spe-
Fig.2 – FSW and FSSW tools
Pure Tungsten
Pure tungsten is a steel-gray to tin-white metal. Very pure
tungsten can be cut with a hacksaw, forged, spun, drawn, and
extruded. The impure metal is brittle and can be worked only
with difficulty. Tungsten metal has excellent high temperature mechanical properties and the lowest expansion coefficient
of all metals. Pure tungsten has the highest melting point
(3422°C) of all metals, and at temperatures over 1650oC has
the highest tensile strength. The metal oxidizes in air and
must be protected at elevated temperatures. Pure tungsten
semifinished products in form of rods are quite easily obtainable on the market.
W24.5%Re2%HfC alloy
Historically W25%Re alloy has been produced into wire
for the thermocouple market. The use of pure tungsten in
thermocouple applications, as the positive element, posed
a problem when heating tungsten above its recrystallization temperature (about 1200°C). This causes the wire to
become brittle when reintroduced to room temperature.
The addition of rhenium increases the recrystallization
temperature, the ductility, and the ultimate tensile strength
of the material. Also the hafnium carbide addition is very
C z e c h A e r o s pa c e P r o c e e d i n g s beneficial - it markedly increases strength of the alloy at
high temperature levels above 1300°C. The excellent material produced by Rhenium Alloys, Inc has recrystallization
temperature about 1900oC, elastic modulus 400 GPa and
the ultimate tensile strength at room temperature greater
than 1400 MPa. The major advantage of the alloy is the
high strength at elevated temperatures (250 MPa at 1926°C)
[3].
Silicon Nitride
Silicon nitride is a ceramic-based material characterized by
high hardness, high thermal conductivity and low thermal
expansion coefficient that give better thermal shock resistance than other ceramic materials. Silicon nitride is
mostly used in high-endurance and high-temperature applications, such as gas turbines, car engine parts, bearings and
metalworking and cutting tools. A disadvantage may be the
limited fracture toughness. The working parts of welding
tools used for feasibility tests in VZLÚ, Plc were made of
ceramic semifinished products from CERATIZIT Austria
G.m.b.H (rods made of ceramic material SNC1).
PCBN
Polycrystalline Cubic Boron Nitride (PCBN) is a highly
efficient cutting material from a polycrystalline substance
of a cubic boron nitride grain. PCBN is produced by sintering at high temperature and high pressure. Since PCBN is
a very hard, wear resistance material, it seems to be an
optimal material for friction stir welding of steel. But premature cracking and high costs could be limiting factors
for its application. PCBN welding tools used in the study
were realized in frame of cooperation VZLÚ, Plc and
Bonar, a.s.
Two different engineering designs of the welding tools
were used (see Fig.x). The first design utilized short bar
working parts (parts made of tungsten and Si3N4) inserted
into shank holder and secured with locking bolts. The
second tool construction consisted of a working tip, a locking collar, and a shank. The collar coupled the torque
from the shank to the working tip by means of hexagonal
connection. Position of collar and working tip was secured
with locking bolts. The second tool design was used for
PCBN and WReHfC alloy tips. Bodies of the tool holders,
locking collars and shanks were made of nickel alloy Hastelloy X. All working parts of the tools have standard concave shoulder with diameter of 13 mm and concavity angle
7°. Also pin geometry was the same for all the welding
tools. It had shape of truncated cone. The cone pin had
base diameter of 5 mm and top angle 40°. Pin length was
1.27 mm for FSW tools and 2.45 mm for FSSW tools.
4
3) combination of ceramic spray ToolProtect and separation pad made of Phlogopite Mica or paper
Welding Procedures
All the continuous FSW tests of USIBOR 1500 steel
were carried out on the manual knee-type milling machine
FGU40 with 11 kW spindle drive motor. This old milling
machine is characterized by good stiffness and sufficient
power (spindle speed range: 35-1800 rpm, max torque:
2000 Nm). At the beginning of each weld the rotation tool
slowly plunged into the joint line between two plates
200x110 mm. After attainment of full plunge 0.4 mm tool
dwelled at the place about 5 seconds. Then followed accelerating (40 mm/min to distance 10 mm) and transition to
planned welding speed. The tool rotational speed and welding speed were varied, which were 710 and 900 rpm, and
80, 160 and 224 mm/min, respectively. The welding tools
were tilted 2.5° from the plate normal direction and inert
gas (Ar) shroud was utilized for shielding which prevented
base metal surface oxidation.
Next experiments were focused on friction spot welding
of the same material. They were conducted with NC bed-type milling machine FSG80-A2 under displacement control. The tool rotational speed and tool plunge rate were
varied, which were 1800, 2500 and 3200 rpm, and 0.7 and
2 mm/s, respectively. Plunge depth was held constant at
2.65 from the specimen surface. Note that this plunge
depth corresponds to 87% of the combined thickness (3.04
mm) of the overlapping strips. Since the pin length was
2.45 mm, this means that the tool shoulder plunged approximately 0.2 mm into the specimen during welding. Quasi-dwell of 1.5 s was applied at the end of each weld program. The dwell was accomplished by creating a two-step
welding program that involved first plunging to nearly the
full desired depth followed by further plunging the final
0.3 mm of depth at a slower rate 0.2 mm/s. Total time of
welding cycle for plunge rates 0.7 and 2 mm/s was c. 5 and
3 s respectively.
Heat protection of welding fixture
During friction stir welding of steels is achieved very
high temperature (above 900°C). It is necessary to protect
the welding fixture from the welding heat and sticking of
the weld test sheets to the fixture. Three types of protection
of welding fixture and sticking prevention were tested:
1) backing bar made of 15 mm thick high speed steel
Böhler S790 Microclean hardened to 66 HRC
2) backing bar made of pure oxide ceramic DISAL 100
(99% Al2O3)
Fig. 3 - Time-transient temperature evolution
Temperature field measurement
During welding transient temperatures were measured
with 6 thermocouples placed in two cross-sections in the
middle of the welded sheets (see Fig.x). The thermocouples were of the k-type using wires 0.19 mm with a
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1/2011
welded ball junction of about 0.5 mm. The CC High Temperature Cement based on Zirconium Silicate was used for
fixation of the thermocouples. Data were acquired and
saved using the USB external measurement system meM-Adfo BPL-16 from BMC Messsysteme GmbH. Examples
of temperature records for CMT welds and sample FSW 2
are shown in Fig.2. At the figure is shown that temperature
on the advancing side is markedly higher in comparison
with the retreating side. The temperature difference of
maximums measured with thermocouple 1 and 2 is c. 165
°C. Maximum temperature measured in distance 9 mm
from weld axis reached to 490 °C.
Results and discussion
Feasibility of continuous FSW of high melting temperature material was successfully demonstrated. Fully consolidated butt welds of USIBOR 1500 sheets were produced
when lower welding speed was applied. No surface or
internal defects were evident when welding speed was up
to 80 mm/min at 710 rpm or up to 160 mm/min at 900 rpm.
Higher welding speed led to problems and defects formation (see Fig.x b).
Three types of protection of welding fixture and sticking
prevention were tested during the feasibility tests. Single
backing bar made of high speed steel Böhler S790 hardened to 66 HRC turned out to be insufficient due to the test
plate sticking. Also backing bar made of 99% Al2O3 was
tested, but it was damaged during the first welding test,
obviously due to the brittleness and too high temperature.
Combination of ceramic release agent applied on backing
bar made of Böhler S790 and separation pad made of Phlogopite Mica or paper was tested with very good results.
Drawback was the ceramic powder or flogopit remnants at
the weld root face.
All welded panels were cut and metallographic analyses
and tensile tests were carried out. The main objective of the
metallographic examination was assessment macroscopic and
microscopic pattern of the weld joints. The weld zones were
compared with unaffected base material using optical
microscope. A typical as-welded defect free microstructure is
illustrated in Fig.x a). Four distinct regions were identified in
the USIBOR1500 friction stir weld: 1) a coarse grained predominantly martensitic stir zone (CGSZ) located in the centre
of SZ, 2) shoulder affected SZ (SASZ) with fine martensite
located closely below shoulder, 3) a heat affected zone (HAZ)
as transition region between the SZ and base material, and 4)
base material with ferritic-pearlitic microstructure with carbide precipitations. The aluminium coating was stirred during
FSW, producing aluminium inclusions randomly distributed
along or inside the stir zone. In some cases the aluminium
inclusions partially blocked consolidation of welded material
and decreased tensile strength of the welds.
All tensile tests were performed on a 500-kN TIRAtest
28500 testing machine at a constant crosshead displacement
rate of 2 mm/min. Continuous FSW specimens without
defects welded at lower welding speed failed outside the
weld joint in base material. Ultimate tensile strength of the
specimens was over most 541 MPa (joint efficiency over most
91%).
Fig. 4 - Examples of macrographs for FSW welds:
a) Si3N4 tool, 80 mm/min, 710 rpm; b) Si3N4 tool,
224 mm/mm, 710 rpm
Joint strength of FSSW welds were evaluated by tensile
shear and cross-tensile testing in accordance with standards ČSN EN ISO 14272 and ČSN EN ISO 14273. In case
of the tensile shear test shims of the same thickness as the
test specimens were used when gripping the samples to
induce pure shear and to avoid the initial realignment
during testing. The relationships between tensile shear failure load, tool rotational speed and plunge rate, are represented in Fig.x. It can be seen that the tensile shear strength increases with increasing rotational speed. It can be
also clearly observed that higher tensile shear strength was
achieved at lower plunge rate. Maximum tensile shear failure load 7.3 kN was measured for specimens welded at
rotational speed c.2500 rpm and plunge rate 0.7 mm/s.
Macrographs of the weld joints with the highest and lowest
tensile shear strength are illustrated in Fig.x.
Figure x shows the cross tension results as they vary by
tool rotation speed and plunge rate. Analogous to tensile
shear strength also cross tension strength increases with
increasing rotational speed. Effect of plunge rate is not so
clear because cross tension strength is higher for lower
plunge rate 0.7 mm/s up to c. 2300 rpm and above the
value the strength is higher for higher plunge rate. Maximum cross-tensile strength 3.65 kN was achieved for high
rotational speed 3200 rpm and plunge rate 2 mm/s.
As mentioned above, four types of material for working
parts of welding tools were tested. Although fully consolidated welds was possible to realize by the means of all the
tools, they markedly varied in toughness at high temperature, wear rate and chemical interaction between tool material and USIBOR 1500 steel sheets. Tools made of pure
tungsten showed a tendency to wear rapidly and to change
pin geometry in consequence to high loading (especially
during plunging) and weldment material sticking. Average
pure tungsten tool life during friction spot welding was
only about 8 spot welds because of high deformation of pin.
Fig. 5 - Tensile shear failure load as a function of
rotational speed and plunge rate
Fig. 7 - Cross tensile strength as a function of
rotational speed and plunge rate
W25Re2HfC alloy tools appeared to be markedly more
resistant to wear than tools made of pure tungsten but problem with weldment material sticking occurred too. It is
not clear if the problem was caused by chemical interaction
between tool and weldment material or by increased surface roughness (lathe-turning was used for final manufacturing operation). W25Re2HfC alloy is possible to classify as very robust tool material that can tolerate incorrect
set-up and it does not require high precision FSW machine.
Silicon nitride (Si3N4) and PCBN tools were characterized by very high hardness, excellent high temperature
strength, low wear rate and high geometry stability. No
problems with weldment material sticking occurred. On
the other side catastrophic failure threatened if set-up welding conditions was incorrect. Tool life of PCBN tools was
surprisingly lower than for Si3N4. During the welding tests
radial cracks occurred in the PCBN tool shoulder.
during the feasibility tests. Combination of ceramic release
agent applied on backing bar made of Böhler S790 and
separation pad made of Phlogopite Mica or paper turned
out as the best solution.
3) Fully consolidated continuous FSW butt welds of
USIBOR 1500 sheets were produced when lower welding
speed was applied. Maximum tensile shear strength was
achieved when welding speed was up to 80 mm/min at 710
rpm or up to 160 mm/min at 900 rpm. Higher welding
speed led to problems and defects formation.
4) Higher shear tensile and cross-tensile strength of friction spot welds (FSSW) was achieved for higher rotational
speed (above 2500 rpm). Effect of plunge rate is not so
clear because tensile shear strength was higher for lower
plunge rate but dependence of cross tensile strength on
plunge rate changed with rotational speed. Maximum
cross-tensile strength 3.65 kN was achieved for high rotational speed 3200 rpm and plunge rate 2 mm/s.
Conclusions
Feasibility tests of FSW and FSSW of high melting temperature materials were successfully performed using USIBOR 1500 steel. During the tests were tested four types of
material for working parts of welding tools (pure tungsten,
W25Re2HfC alloy, Silicon Nitride and PCBN). The influence of welding parameters on mechanical properties and
macroscopic pattern of the weld joints has been studied. As
a result, the following conclusions were achieved.
1) Silicon nitride
(Si3N4) appears to be
the best material for
working part of FSW
and FSSW tools. It is
characterized by balanced performance ratio,
high hardness, excellent
high temperature strength, low wear rate and
chemical inertness.
2) Three types of protection of welding fixture and sticking prevention were tested
Fig. 6 - Examples of macrographs for FSSW welds with
the highest (a) and lowest (b) shear tensile strength
Acknowledgements
These R&D activities were carried out in the ARC supported by the Czech Ministry of Education, Youth and
Sports. The author would like to thank Rhenium Alloys,
Inc for supply of W25Re2HfC sample and information
about the excellent material. The author also gratefully
acknowledges cooperation of BONAR a.s., CERATIZIT
Austria G.m.b.H. and Benteler Automotive Rumburk s.r.o.
References
[1] Thomas, WM; Nicholas, ED; Needham, JC; Murch,
MG;Temple-Smith, P;Dawes, CJ.Friction-stir butt welding,
GB Patent No. 9125978.8, International patent application
No. PCT/GB92/02203, (1991)
[2] Alberto Turetta: Investigation of thermal, mechanical and
microstructural properties of quenchenable high strength
steels in hot stamping operations, doctoral thesis,
University of Padua, January 2008.
[3] Leonhardt T. Processing and Properties of Tungsten
25%Rhenium with and without Hafnium Carbide, Journal
of The Minerals, Metals and Materials Society, Volume 61,
Number 7, page 68-71, TMS, July 2009.
[4] Mishra R.S., Ma Z.Y.: Friction stir welding and processing
(part 6. Material specific issues), Materials Science and
Engineering, Volume 50, p.1–78, August 2005.
7
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Experimental modal and FEM analysis of
space instrument DUMMY
Experimentální modální a MKP analýza kosmického přístroje DUMMY
Ing. Vladimír Dániel, Ph.D., Ing. Tomáš Jamróz, Ing. Jiří Had /VZLÚ, Plc.,
Prague
The paper focuses on the dynamic characteristics of the space instrument DUMMY. This is a substitute of flight
hardware. It must also met the dynamic requirements for payload goals. The goal of the work was to compare
results of experiment modal analysis (OMA) and FEM model data. The modes almost correspond to experimental
modes. Frequency analysis was also performed and the results are compared with experiment parameters.
Disagreements are the modes with a nonlinear contact vibration and modes with a significant geometric similarity.
Článek se zabývá studií kosmického přístroje DUMMY. Jedná se o náhradu letového hardwaru. Tato náhrada
musí také splňovat dynamické požadavky kladené na užitečný náklad. Cílem práce je porovnat výsledky experimentální modální analýzy (OMA) a MKP modelu. Modální analýzou byly nalezeny vlastní tvary kmitání. Tyto
tvary odpovídají většině vlastních tvarů zjištěných experimentem. Dále je provedena frekvenční analýza a výsledky
jsou porovnány s experimentem. Neshody jsou u tvarů s nelinearitou tvořenou kontaktem a u tvarů kmitání s vysokým stupněm geometrické podobnosti.
Keywords: space instrument, modal analysis, frequency analysis, OMA, FEM sten rhenium
Introduction
Vibration properties of space instrument are significant
in respect to design of the instrument. During the launch
the instruments are affected by rocket engine, dynamic
shock of solid booster burn out, stage and fairing separation and resonances incurred in the rocket. For evaluating
the effects of vibration to instrument the modal analysis is
fundamental. Experimental modal analysis is method for
description of vibration and modal properties of instrument
[2]. For experimental evaluation of modal properties more
methods exists. In this work the operation modal analysis
(OMA) was used. This method based on transfer function
[1]. For designing the instrument parts the FEM are used.
The modal analysis determines the modes and frequency
analysis determines the transfer function or the frequency
response function.
number of modes in frequency range to 2000Hz was evaluates with using the function Multivariant MIF and SUM.
The modes are in table (Fig. 2). In TestLab software the
AutoMAC criteria were calculated for all modes. Modes 6
and 7 and the group of modes 9 to 13 has significant geometric similarity. Lower geometric similarity has modes 2
and 3 and 17 and 18.
Experimental modal analysis - OMA
Operational Modal Analysis was used for determine the
modal parameters of interest space instrument – Dummy.
The structure was drive by broadband noncorrelating random signal. The response was measured in 63 points. The
purpose of experiment was to evaluate modal parameters in
frequency range from 20 to 20000Hz. More the experiment
checks the functionality of interconnection of systems
LMS TestLab [3] and PRODERA.
The instrument hangs on elastic rope during the test to
simulate the free support (Fig. 1). The system was excited
by three dynamic forces in three perpendicular dimensions.
The excitation was realised by electro-dynamic drivers
PRODERA. The stochastic independent broadband stationary random signals were used. The value of force was not
measured.
The modes were found by method Time MDOF. First the
Fig. 1 - Experimental modal analysis
Fig. 2 - AutoMAC criteria describes geometric similarity
FE model
The finite element model of Dummy and vibration
adapter was prepared. The Dummy is done as 3D geometry
and vibration adapter is done as 2D shell. The quadratic
tetrahedron and quadratic rectangular was used. The screw
connections between walls of Dummy are done as rigid
connection. The sides are connects to the base only in three
point. The sidewall can vibrate in transverse direction. In
vertical direction this connection crates the nonlinear
behaviour. The model contains slot in this place to allow
transverse vibration. Nonlinear behaviour is impossible in
frequency analysis [4]. The results of several first modes
can be fault. The connection between disc adapter and
Dummy is done as rigid by RBE2 elements. Model has free
support. The mesh is on Fig. 3.
Fig. 4 - Modal analysis – comparison of experiment
end model, mean deviation is 16.4%
Fig. 3 - Mesh of Dummy a disc adapter
All parts are made from Duralumin 7075 T651 (www.
matweb.com). Many steel screws are on Dummy. They
increase the weight of Dummy in respect to model. More
some electronic parts are inside the Dummy. Therefore the
density is higher than in common Duralumin. This simplification spread the weight of screws equivalent to all
Dummy structure. The adapter is full of hole which does
not change the stiffness, but change the weight. The simplification above was used here too.
Modal results
The modal analysis was done. The comparison of calculated modes end experiment is in Fig. 4. The graphic result
is on Fig. 5.
The model has higher frequencies of modes. Average rate of
frequencies between model end experiments is 83.51%. Some
modes founded by TestLab were not found by modal analysis.
The missing modes correspond to AutoMAC criterion (Fig. 2.)
calculated by TestLab. Graphic representation of first mode is
in Fig. 6. First mode represents nonlinear behaviour when the
sidewalls with base panel forms contact which open and close
in time.
In TestLab software the modal dumping coefficients (Fig.
7.) were calculated for each mode. The reverse FFT method
was used.
Fig. 5 - Modal analysis – comparison of model
and experiment
Fig. 6 - First mode getting from experiment OMA method
(left) and FEM model (right) - ahead to back oscillation
Fig. 7 - Calculated modal dumping coefficients by
TestLab software for each mode
9
1/2011
Frequency analysis
The frequency analysis on model of Dummy and adapter
was done. The excitation places were comparable with
experiment. The excitation was realized by harmonic sinus
signal with amplitude 0.5mms-2. The excitation was realized in all three axes together. The material damping coefficient was used of value 0.01.
The results are showed only in interested places. They
correspond to position of accelerometers used on experiment. Calculated crosspower spectrum of acceleration unit
is g2/Hz. For calculating the crosspower spectrum two
point results were used. Because we don't know the value
of excitation force, we cannot compare the model end
experiment. We will discuss only the rate of measured end
experimental data.
The Fig. 8 shows crosspower spectrums obtained from
experiment and frequency analysis of mesh point 39159, it
correspond to point 15p from OMA analysis which is the
top corner of Dummy.
The Fig. 9 shows crosspower spectrums obtained from
experiment and frequency analysis of mesh point 28425, it
correspond to point 48p from OMA analysis which is the
centre of base plate of Dummy.
Fig. 9 - Comparison of crosspower spectrum of Dummy –
centre of base plate
The experimental modes from no. 9 to no. 13 are similar.
The model is not so affected by adapter vibration - first
adapter mode no. 14 has resonance frequency 1388Hz.
Conclusion
The frequency shift between experiment and model
modes is 16.5%. Some experiment modes were not found
out by FEM analysis at all. These are shapes with high
similarity as evidenced AutoMAC criteria.
High frequency shift appears at nonlinear modes. The
nonlinear behaviour is not possible to compute by frequency analysis.
Frequency results present crosspower spectrums. They
agree with experimental data in meaning of frequency. The
amplitudes are not comparable in absolute value, because
the experiment force value was not measured. The relative
amplitude values agree with experiment except the range
around first mode of disc adapter (1100Hz).
Acknowledgment
This work was supported by the Czech Ministry of Education, Youth and Sports, by the Grant No. 1M0501.
Fig. 8 - Comparison of crosspower spectrum of
Dummy – top corner of unite
The results on figures are frequency shift of value 16.5%
as a result from modal analysis of deviation between experiment and model.
We can draw up the calculated frequency shift correspond to measured data. The best agreement of model end
experiment is between 600Hz and 1300Hz. Under frequency 600Hz the results are affected by nonlinear behaviour of
Dummy side walls. The nonlinear vibration is not possible
to compute by frequency analysis. The side walls are not in
contact with the base plate, the penetration shift the resonance frequency below the measured resonance.
The Fig. 9 shows the results of base plate vibration. Over
frequency 1300Hz the resonance peaks are shifted to
higher frequencies. This frequency shift is affected by rigid
screws used for connecting Dummy and adapter. The influence of rigid connection rise with frequency.
As we note above we can compare only relative changes
of amplitude. The big difference is mainly between 1000Hz
and 1300Hz. It describes the first mode of disc adapter.
References
[1] Černý, O.: Teorie a praxe modálních zkoušek konstrukcí
letadel; VZLÚ zpráva R – 2689/92
[2] Miláček, S.: Modální analýza mechanických kmitů;
Vydavatelství ČVUT, ISBN 80-01-02333-8
[3] LMS TestLab polyMax Modal Analysis, Software.
[4] MSC.Software, MSC.Nastran: Reference Guide; 2005.
Simulation of level of quasistatic
microaccelerations on-board of a spacecraft
Modelování úrovně mikrozrychlení na palubě kosmického prostředku
Ing Viktor Fedosov Ph.D. /VZLÚ, Plc., Prague
This paper introduces the simulation methods of residual quasistatic microaccelerations on board of a spacecraft.
On base of equations describing spacecraft orbital motion and perturbations acting on a spacecraft the main components of microaccelerations field were analysed. Some simulation results relating to orbit flight of different spacecrafts with allowance for drag are also provided.
Článek uvádí do problému modelování úrovně zbytkových kvazistatických mikrozrychlení na palubě kosmického
prostředku. Hlavní komponenty mikrozrychlení jsou analyzovány na základě rovnic popisujících orbitální pohyb
kosmického prostředku a popisu negravitačních rušivých sil působících na satelit. Článek prezentuje výsledky
modelování mikrozrychlení pro některé případy orbitálního letu kosmického prostředku s ohledem na odpor
svrchní atmosféry.
Keywords: quasistatic microaccelerations, orbital motion, simulation, drag
Introduction
Purpose of using of a high sensitivity microaccelerometer developing in the VZLÚ is measurement of low frequency (< 1 Hz) quasistatic microaccelerations on-board of
an orbiting spacecraft. Nature of these accelerations is
defined on base following reasoning. Let a spacecraft be a
rigid body which has center of mass (CoM) in point C and
let a point C’ be fixed with its frame. The difference
between the gravitational field strength at the point C’ and
the absolute acceleration of this point is called a residual
acceleration at the point C’ (Figure 2). Base sources of the
residual accelerations are: firstly, non-gravitational (non-conservative) forces such as high atmosphere drag, (in-)
direct solar pressure, Earth Albedo and Earth infrared
radiation which should be described with respect to spacecraft angular motion (may be active/stabilized or passive)
and secondly, there are internal factors as movement and
working of the spacecraft internal parts or, mainly, vibrations of the spacecraft structure during flight. In general,
frequency spectrum of residual acceleration lies into wide
range from ultra low frequencies to hundreds of Hz. The
first group of residual accelerations sources has character
of low frequency quasistatic accelerations (< 1Hz), the
second - lies in range above 1 Hz. Primarily, effect of quasistatic residual accelerations has important impact to
(bio-)technological experiments in orbit (Tab 1) or during
missions orientated on improvement of near-earth space
models (thermosphere density, Earth gravitational and
magnetic fields and other). In conclusion of the brief introduction we have to define used reference frames (Figure
1). OXYZ is Equatorial or Inertial (Absolute Celestial)
Coordinate System. Its center is taken at the Earth’s center.
The X-axis of this system is directed towards the vernal
equinox. The Z-axis is directed parallel to the Earth’s polar
axis towards the North Pole of the Earth and the Y-axis is
directed so as to form a right/handed coordinate system.
Fig. 1 - Relative orientation of IRF (OXYZ), orbital RF
(CXoYoZo) and SC RF (Cxyz)
Datum point of Orbital Coordinate System CXoYoZo is
taken at the Centre of Mass (CoM) of a spacecraft. X-axis
(CXo) is directed parallel to the vector of angular momentum (A) of an orbiting spacecraft. Z-axis (CZo) is directed
from the Earth’s center to the Zenith through spacecraft’s
CoM the Y-axis is directed so as to form a right/handed
coordinate system. Generally, the next coordinate system
11
- Spacecraft reference frame Cxyz - is defined by satellite
manufacturer. In the paper, unless otherwise indicated, we
use spacecraft structural coordinate system such that its
axes are oriented parallel to the Xo, -Yo and –Zo axes.
Back and forth transformations between mentioned coordinate systems can be expressed by rotational angles (Direction Cosine Matrix) or by quaternion functions. These
transformations are described in extensive literature (for
example, [2], [3]).
a (r ) = α r
1/2011
of a local vertical
Denote by vector a (r ) acceleration of any point into V. This
acceleration is equal to difference between absolute acceleration α r of the point and a (r ) at the point of the V:
(2)
a (r ) = α r − g (r ), (∀∆r ∈ V )
In addition, suppose that triaxial accelerometer is mounted
at the point (for example, C’) into V. In this case, namely acceleration describing by (2) will be measured by the instrument.
With respect to (1) and (2) the acceleration at the spacecraft
CoM
( ∆r ∈
=V
0)) is equal to sum of external non-gravitational
− g (r ), (∀
accelerations acting to the spacecraft:
Seeing that absolute acceleration of any points of the V is
described as
•
α (r ) = aC + ω × ∆r + (ω × ∆r ) × ω
we can express quasistatic microacceleration at the point of
the V as following:
(3)
•
a (r ) = ΓC + ω × ∆r + (ω × ∆r ) × ω + aG , (∀∆r ∈ V )
aGG = g C − g (rC + ∆r ) is an acceleration due to
•
gravitational gradient at the point C’, ω , ω are vectors of
where
Tab. 1 - Base perturbations and related accelerations
acting on-board of Russian Space technological
systems [1],* - specialized small space platforms
angular velocity and acceleration of the spacecraft.
Whereas that ([5]):
Analytical expression of the residual quasistatic
accelerations
Suppose that a spacecraft orbital motion is described
by following differential equation:
d 2 rC
= g + Γ , where:
dt
C
2
(1)
C
We suppose that spacecraft’s CoM lies in internal space of
a spacecraft (payload area V, see Fig 2) so we can approximate U (r ) as following:
µ
,where
is a gravitational parameter of a centre
of attraction (for example for Earth = GEM, where GE is the
Earth’s Gravitation Constant and M is Earth’s mass). Hence
for any point C’ (figure 1) we can define its position vector as
r = rC + ∆r (∆r ∈ V , ∆r / rC < 1) and g (r ) = − µr / rC 3
e.g., for the point C’ g (r ) = −
rC
3
[3(e ⋅ ∆r )e − ∆r ]
We can express quasistatic acceleration at the point C’ as
•
g C = − gradU (r ) r = rC
rC
µe
a (r ) = ΓC + ω × ∆r + (ω × ∆r ) × ω +
rC is a position vector of spacecraft CoM, ΓC is a perturbative
acceleration due to non-gravitational perturbations acting to
a spacecraft, g C is a field force with potential U (r ) and
U (r ) = −
aGG =
µ
r
2
er where er =
r
is an ort
r
µe
rC
3
(4)
[3(e ⋅ ∆r )e − ∆r ]
This formula is principal expression allowing us to simulate quasistatic acceleration at any point on-board of an
orbiting spacecraft.
•
In case, if parameters of spacecraft angular motion ( ω , ω )
are known we are able to define quasistatic acceleration at the
point C’ situated at distance ∆r from spacecraft CoM taking
into account non-gravitational perturbations ( Γ ) acting to
CoM.
How it was noted above the microaccelerometer mounted at
the point C’ (any point of the V) will measure accelerations
described by (4). We can use experimental data obtained by
the accelerometer and data predicted by (4) in following way.
We can reconstruct the spacecraft motion by spacecraft telemetry (for example, using data from on-board magnetometers,
star-camera or by angular velocity sensors) and calculate the
acceleration along the reconstruction by formula (4) in the
C z e c h A e r o s pa c e P r o c e e d i n g s point of accelerometer location. Comparison the calculation
results with the results of processed acceleration measurements in the same time interval defines method how to verify
the accelerometer during flight.
12
The main perturbation at this orbit is drag therefore we can
consider that:
Γ = aD
Perturbation due to atmosphere drag ( aD ) is possible to calculate as
1
C D ρAV 2 , where:
2m
aD =
C‘ ∆r
C
V
CD is aerodynamic drag coefficient, for the simulation case it
is equal to 2.2
A is an effective cross-sectional area = ¼ of the spacecraft
surface area
is thermosphere (high atmosphere) density, for the simulation case is calculated by using of the thermosphere model
TD88 in relation to reference environmental condition (solar
flux and geomagnetic parameter) and spacecraft orbital parameters. TD88 detailed description is given in [6].
V is the spacecraft velocity relative to atmosphere rotation, for
the simulation case it is possible to define high atmosphere as
statically and V is equal to the spacecraft absolute velocity.
Simulation time is equal to one orbit. Values of the atmosphere density and spacecraft acceleration (in spacecraft coordinate system) due to drag are shown in Figure 3.
Fig. 2 - Payload space V
Simulation
The formula (4) was derived for a general situation without
any frequency restrictions. But if the spacecraft attitude motion is like as motion of a rigid body (this motion is usually very
slow), then formula (4) gives only a quasi-steady acceleration
component, i.e., a part of a real acceleration that has frequencies within the range from 0 to 0.1 Hz. On this account, thereinafter, we will study spacecraft free motion as motion of
rigid-body. Two cases of the motion are presented: spacecraft
torque-free motion and motion under external moments of
perturbations (gravitation moment is considered).
1. Suppose, that a spacecraft which is characterized by size
(0.5 x 0.5 x 0.7 (m)) and mass (80 kg) moves at orbit with
following parameters:
-
orbit period – 100 minutes;
-
circular orbit;
-
altitude – 450 km;
-
inclination – 98,8 o ;
-
perigee argument – 66,5 o
-
eccentricity – 0,00112
Fig. 3 - Accelerations due to drag
Rotation motion of the spacecraft (as rigid –body) relative to
its CoM is simulated by dynamic Euler equation in matrix
form:
J
dω
+ (ω
×)( J ⋅ ω ) = M
dt
(5)
where:
J is an inertia tensor of the spacecraft (in the spacecraft refe•
rence frame), ω ,isωa vector of spacecraft angular velocity, M is
•
a vector of external moments acting to the spacecraft and (ω ,X)
ω
is a skew-symmetric matrix of spacecraft angular velocity:
13
 0

(ω×) =  ω z
− ω y

− ωz
0
ωx
1/2011
ωy 

− ωx 
0 
Let the spacecraft inertia tensor is
0
0 
4,93

J = 0
4,93 0 
 0
0
3,33
And initial values of x, z, z -components of satellite angular
velocity vector are (rad/s):
Fig 5 Components of angular acceleration vector M
(external moments) = 0
ω x  1e − 3
ω = ω y  = 1e − 3
ω z  1e − 2
Figures 4 and 5 show diagrams of vector components of spacecraft angular velocity and accelerations obtained by solution
(5) at M = 0.
Fig 6 Quasistatic accelerations along to X axis of the
spacecraft reference frame (symmetrical spacecraft)
2. The case 1 describes torque-free motion of the symmetrical
rigid body. Now we will consider unsymmetrical spacecraft
motion. Suppose the spacecraft orbit, mass, its sizes and initial
values of x, y, z -components of satellite angular velocity vector are the same as defined in case 1.
Fig 4 Components of angular velocity vector M
(external moments) = 0
Let the spacecraft inertia tensor is following:
In this situation, simulated angular motion of the spacecraft
corresponds with motion of free symmetric gyroscope (z is a
spin axis) – its nutational oscillations. Describable case is useful for validation of the applied simulation method because
makes it possible to compare results of simulation (
with well known dynamical phenomena.
•
ω ,ω )
Figure 6 shows diagrams of accelerations in x spacecraft direction at the spacecraft CoM (equivalent to the drag) and at the
point with 2 mm offset from CoM along the axis
 6.86 0.03 5.9 
J = − 0.03 8.66 − 9.5
 − 5.9 9.5
5.4 
Figures 7 and 8 demonstrate diagrams of spacecraft angular
velocity and accelerations vectors components obtained by
solution (5).
Figure 10 demonstrates level of accelerations in x spacecraft
direction at the spacecraft CoM (equivalent to the drag) and at
the point with 2 mm offset from CoM along the axis in the spacecraft structural coordinate system for initial angular velocity
components [1e-4; 1e-4; 1e-3(rad/s)] (green curve relates to the
symmetrical spacecraft, red – to the unsymmetrical).
Fig 7 Components of angular velocity vector
(unsymmetrical spacecraft)
Fig 10 Quasistatic accelerations along to
X axis of the spacecraft reference frame
Experiment
Fig 8 Components of angular acceleration vector
(unsymmetrical spacecraft)
Figure 9 shows plots of accelerations in x spacecraft direction
at the spacecraft CoM (equivalent to the drag) and at the point
with 2 mm offset from CoM along the axis (green curve reflects
situation when Mx = 0 and red graph for case abs(Mx) > 0).
Fig 9 Quasistatic accelerations along to X axis of the
spacecraft reference frame (unsymmetrical spacecraft)
We have had opportunity to verify reviewed method of quasistatic accelerations estimation by analysis of data obtained by
accelerometer during orbit flight. The accelerometer has been
placed on board of Russian spacecraft Tatyana/ Univerast – 2.
This small platform was designed for flight testing of new tri-axial stabilization system with low level of produced microaccelerations. Orbit parameters of the Universat-2 are following:
circular sun-synchronous, inclination – 98 degrees and altitude
is 820 km. Satellite was launched on September 2009. Unfortunately, after spacecraft separation from the launcher upper stage
the satellite stabilization system did not work correctly (infrared
Earth sensor failed). Communication with the spacecraft was
interrupted after one month operation of the satellite in orbit.
For analysis of the accelerometer flight data we have to take
into account this real platform situation in combination with
existence of displacement of the accelerometer relative to the
center of mass of the satellite. The proof mass offset will cause
that not only accelerations due to the non-conservative forces
but also accelerations due to gravitational forces and angular
motion act on the proof mass. Hence, the measurement model
we can describe according to formula (4).
As we have possibility (on base of telemetry data) to reconstruct parameters of spacecraft attitude motion (components of
satellite angular velocities) than we can estimate the magnitude
of microaccelerations at instrument position and compare it
with measured data. It has been confirmed that during observa-
15
tion windows the character of the spacecraft angular motion
was primary component influencing accelerometer measurements. So, maximum predicted values of non-gravitational
accelerations acting along each axis of the satellite reference
frame should not be more than 3.5x10-8 ms-2, for accelerations
rising due to gravitational gradient – 0.64x10-8 ms-2. The level
of computed values of accelerations rising due to spacecraft
rotation was defined as two order bigger (+3x10-6 ms-2). The
Fig. 11 and Fig. 12 show typical observing window plots of raw
data of the accelerometer (green, ms-2) versus angular velocities
along X and Y satellite axes (blue, rad/s).
Finally the Fig. 14 demonstrates model (red) describing
dependence of measured smoothed data (blue) on angular velocities of stabilization system (high level interventions to stabilize the spacecraft along direction to Earth) and temperature
registered at sensor. Green curve reflects absolute values of
residuals of model predictions related to measured data. The
time resolution on all figures is one minute.
1/2011
Fig 14 Accelerometer measurements as function
of components of angular velocity and sensor
temperature (during one revolution)
Conclusion
The paper describes estimation method of level of quasistatic
accelerations on board of a spacecraft. Performed simulations
demonstrate variation of accelerations level in dependence on
dynamical characteristics of the spacecraft and its angular motion. This method has been validated by analysis of microaccelerometer data received during space flight on board of the Russian spacecraft Universat-2. The base expression (4) for microaccelerations calculation can be applied for non-gravitational
accelerations
determination from measurements (aM)
obtained by microaccelerometer mounted at the point C’
(C’ (x, y, z) of V).
•
ΓC = aM − (ω × ∆r + (ω × ∆r ) × ω +
µe
rC
3
[3(e ⋅ ∆r )e − ∆r ])
In the case, uncertainties relating to accuracy of the sensor
accelerometer location and spacecraft angular velocity determination should be analyzed.
Fig 12 Spacecraft angular velocity along X axis and
accelerometer measurements (one revolution)
References
[1] Polezhaev, V.I. and other: Konvektivnyje processy v nevesomosti.
Moscow, Nuaka, publishing of Russian Academy of Sciences, 1991
[2] Herrick, S.: Astrodynamics. Orbit determination, Space navigation
and Celestial Mechanics University of California, Los Angeles,1971
[3] Narimanov, G.S.: Osnovy teorii poleta kosmicheskych apparatov,
Mashinostroenie, Mocsow, 1972
[4] Beliakov, I., Borisov, D.: Osnovy kosmicheskoy technologii.
Moscow, Mashinostroenie, 1985
[5] Polezhaev, V.I., Ermakov, M.K, Nikitin, N.V., Nikitin, S.A,
Yaremchuk, V.P.: The Use of Microaccelerations Data
for Convection Modeling & Analysis of the Microaccelerations
Limits, 7th Annual Microgravity Environment Interpretation
Tutorial, V.2, Section 24, 2004
[6] Sehnal L., Pospisilova, L.: Thermospheric Model TD88.
Astronomical Institute Czechoslovak Academy of sciences.
Preprint N67.
[7] Beletsky, V.: Motion of an Artificial Satellite about its Center
of Mass. Moscow, 'Nauka', 1965 (in Russian), English translation:
Israel Program for Scientific Translation, Jerusalem, 1966
Fig 13 Spacecraft angular velocity along Y axis and
accelerometer measurements (one revolution)
[8] Preresty, R., Chvojka, M., Fedosov, V.: Use of the high sensitive
electrostatic accelerometer for orbit perturbation effects
investigation on board of LEO spacecraft. Proceedings of
International Astronautics Congress 2010, Prague 2010
The influence of structural damping on flutter
characteristics of a small sport aircraft
Vliv strukturálního tlumení na flutterové charakteristiky malého
sportovního letounu
Ing. Martin Zejda / Aerospace Research Centre, FME CTU in Prague; Ing.
Aleš Kratochvíl / Aerospace Research Centre, FME CTU in Prague; Doc.
Ing. Svatomír Slavík, CSc. / Czech Technical University in Prague, Faculty
of Mechanical Engineering, Department of Aerospace Engineering
Authors present the basic mathematical models of damping and principles of experimental determination of
structural damping from the system frequency response. The specific method was applied on measurements of few
types of small sport aircraft. The flutter calculation of tail surfaces with consideration of structural damping influence is shown. The applicability of the used method is discussed for the need of further flutter calculations.
Jsou představeny základní matematické modely tlumení a experimentální zjišťování velikosti strukturálního tlumení z frekvenční odezvy systému. Vybraná metodika byla aplikována na měření několika typů letounu. Je uveden
příklad výpočtu flutteru ocasních ploch s uvážením vlivu strukturálního tlumení. Je diskutována aplikovatelnost
použité metodiky pro potřeby aeroelastického výpočtu.
Keywords: structural damping, logarithmic decrement, flutter analysis, half-power point method
Introduction
One of the research topics of Aerospace Research Centre
at Department of Aerospace Engineering – Faculty of
Mechanical Engineering, CTU in Prague is focused on a
flutter characteristics analysis of small sport aircrafts, with
maximal take-off weight up to 600 kg. The calculation
model, which is used for flutter test, is based on standard
“p-k” model where the damping characteristics and frequency are dependent on speed [4]. Thus, the actual real
value of damping for each mode of the airplane structure is
very desirable physical quantity to know.
Damping as one of the structural property significantly
influences the aeroelastic behaviour of airplane structure.
This characteristic can be substituted by appropriate mathematical model, when practical calculations are needed, or
it can be directly gained from ground frequency tests. The
shown method is based on determination of structural damping from FRF (Frequency response function) of the forced
structure. The values of damping are collected to obtain an
adequate database of how the typical airplane structure
behaves under dynamic loading.
Structural damping
Damping of mechanical structures can be approximately
divided into these three categories
• material damping – related to the molecular structure of the material
• structural damping – usually caused by friction
between parts of the structure
• external damping – caused by interaction between
the structure and environment
We can see that relations between damping and its
causes make it more problematic to measure. As a result
the indirect methods are often used, to determine the value
of system damping. Considering the influence of structural
damping in computation of dynamical structural behaviour
is usually accomplished by usage of the simpler model
where is expressed by suitable mathematical expression.
The damped motion is more frequently described by these
mathematical models.
The simplest one is the viscous, where the damping forces are linearly dependent to velocity of the motion. The
governing equation of motion is
mx + bx + kx = F
or
x + 2ζΩx + Ω 2 x =
F
m
where Ω means the undamped natural frequency and is
the damping ratio defined by
Ω2 =
k
b
; 2ζΩ =
m
m
Hysteresis mathematical model is used for cases, where
damping force is proportional to elastic force. The phase
shift between forces is π/2. The motion of system is
described with equation
mx + (1 + jη )kx = F
17
Using the expression for Ω leads to
x + (1 + jη )Ω 2 x =
F
m
F
2
x + (1 + jη )Ω
x=
The term in brackets
represents
the complex stiffm
ness.
If the value of damping is proportional to stiffness and
mass of the structure, the reasonable mathematical model
to use is a proportional model, characterized by governing
equation
1/2011
The practical evaluation of damping is very tough and
therefore this method can be recommended only as a control tool.
The half-power point method is reasonable, when FRF
(Frequency response function) of structure is measured.
Method is based on relationship between the damping ratio
and position of half-power points. The half-power points
are those in a FRF diagram in which the amplitude decays
1
to
of a peak value (Fig. 2).
2
m + (a1m + a2 k )x + kx = F
(
)
x + a1 + a2 Ω 2 x + Ω 2 x = F
The terms a1 and a2 represents the coefficients of proportional damping.
Mathematical models are described in more details in [1].
Experimental evaluation of structural damping
The classical approach, how to evaluate the structural
damping of the system, is to determine the decay of amplitudes, from time flow of the oscillating motion. Assuming
the linear behaviour of the system applies to ratio of two
successive amplitudes
Figure 2
x(t +T ) / xt = e −ζ ΩT
Structural damping can be simply expressed in form of
logarithmic decrement – shown in the Fig.1.
This results to be the half peak value in power spectra
diagram, so that’s why the half-power points. Assuming a
linear behaviour and small damping the relation is
ω2 − ω1 = 2Ωζ
ω2 − ω1
=ζ
2Ω
The main advantage of this method is the possibility to
determine the value of structural damping directly from measured frequency response function. The results are valid only
for modes with linear behaviour and sufficient frequency shift
differing them from other modes. The method is discussed in
more details in [3].
Data acquisition
Figure 1
x 
2πζ
= ϑ´= const
ln 2  =
1− ζ 2
 x1 
In most cases the value of logarithmic decrement is assu
med to be
, so than we can write
ϑ = 2πζ
Data were gathered during the ground frequency tests of
several small aircrafts. The measurement system consisted of
an 11 channel analyser TL-5412_CDD, 2 electrodynamics
exciters, 2 channel signal generator and power amplifiers. The
piezoelectric accelerometers of IEPE standards were used.
The measured data were analysed in ME scope software which
analyses frequency characteristics by means of Fast Fourier
Transformation of signal data from a time domain in to a frequency plane.
The airplane with fixed control surfaces was softly hung on
adjustable frame, when natural frequencies of body were measured. Vice versa the modal parameters of the control surfaces
were measured, when body structure was fixed.
C z e c h A e r o s pa c e P r o c e e d i n g s Contr.
surf.
HT
Wing
mode
type
18
type of airplane
SD - 4 Viper
f [Hz]
d [-]
PiperSport
f [Hz]
d [-]
VL-3 Sprint
f [Hz]
d [-]
Samba
f [Hz]
TL-3000 Sirius
d [-]
f [Hz]
d [-]
Skylane
f [Hz]
d [-]
1. sym. bending
11,2
0,072
11,3
0,055
8
0,040
5,8
0,075
10,8
0,115
12,1
0,104
1. sym. torsion
49,4
0,092
40,8
0,114
31,1
0,195
31,6
0,069
21,6
0,109
34,1
0,184
1. antisym. bending
13,45
0,113
23,7
0,172
19,7
0,103
15,6
0,212
17,3
0,089
19,4
0,210
1. antisym. torsion
48,3
0,084
39,6
0,043
30,5
0,206
31,9
0,057
30,4
0,151
34,8
0,253
1. sym. bending
18,8
0,167
22,9
0,217
17,7
0,125
16,1
0,176
13,3
0,083
33,6
0,178
1. antisym. bending
15,9
0,100
13,1
0,144
13,5
0,183
14,2
0,121
12,2
0,129
11,8
0,295
FRE*
30,6
0,386
20,1
0,328
25,2
0,536
6,06
0,476
19,2
0,278
15,6
0,550
FRA**
20,4
0,482
14,4
0,486
25,6
0,508
7,25
0,597
11,4
0,579
14,9
0,591
* Fundamental rotation of elevator
** Fundamenta rotation of ailerons
Tab. 1 - Frequencies and values of logarithmic decrement
Tab. 1 - Frequencies and values of logarithmic decrement
The structure was excited by two shakers. These were
powered by a sweep sine signal with corresponding or opposite phase, to obtain symmetric or antisymmetric excitation. The
frequency range was set from 2 to 100 Hz. Natural frequencies
were specified by means of amplitude values in real and imaginary components.
Results
The values of structural damping were measured on six
types of sport aircrafts. These were all-metal low-wing monoplanes, composite low-wing monoplanes and strut braced
high-wing monoplanes. Frequency test were performed with a
complete equipped airplanes at the light-mass test configuration, so it means that only one light pilot and empty fuel tanks
were simulated. The half-power point method was used to
determine the logarithmic decrement of typical modes of both
structure and control surfaces. Modes were chosen according
to conditions of used method, to obtain significant results.
These are shown in Table 1. For each mode the frequency and
negative logarithmic decrement are given.
Fig. 3 – Map of logarithmic decrement vs. frequency
for modes of structure and control surfaces
The methodology FAR 23.629 allows to use the damping
value of g = +0,03 as an inherent structural damping. This is
adequate to value of negative logarithmic decrement d = 0,1.
However, this value should be used with caution if the damping of the mode decreases very rapidly with an increase in
airspeed.
On the Figure 3 the relationship between frequency “f” and
value of negative logarithmic decrement “d” is shown. As we
can see, there are four areas corresponding to modes of the
structure or control surfaces. As a benchmark the value of
damping according to FAR 23.629 is given. Modes of the
structure more or less correspond to the value given by FAR
23.629, with average value of d=0,122 for wing modes and
d=0,160 for horizontal tail modes. The modes of control surfaces show considerably higher values of damping d=0,483 in
average, which is nearly five times higher than FAR 23.629
value.
Example of calculation
The example calculation was performed on all-metal
down-wing airplane of foreign manufacturer with design
speed of VD = 275km/h see Fig. 4 – 5.
Fig. 4
19
The modes of tail structure, rudder and elevator were calculated. Force effects of a pilot were simulated by 1kg of mass,
placed on a control stick. Flutter equations were based on
Lagrange’s energy equations of a structure elastic system with
control surfaces. The “p-k” computational model was used to
find eigenvalues of complex flutter matrix. The structural
damping values were added into generalized stiffness matrix
[4]. The results are presented in Fig. 6 - 8 which show the
dependence of damping (in form of negative logarithmic
decrement) and frequency versus equivalent air speed. The
degrees of freedom stand with five eigenmodes of primary
structure with fixed elevator and rudder and three eigenmodes
of elevator with fixed stabilizer and fin.
1/2011
In the second case (see Fig. 7), respecting FAR 23.629, the
value d=0,1 was used for all eigenmodes of control surfaces
and primary structure. The speed VFL=267,1km/h and speed
ratio VFL/VD=0,971 lead to the same conclusion as in the previous case.
d [1]
d [1]
VEAS [km/h]
f [Hz]
VEAS [km/h]
f [Hz]
VEAS [km/h]
Fig. 7 – V-d and v-f diagrams
(Structural damping according to FAR 23.629)
VEAS [km/h]
In the last figure (Fig. 8) the real measured structural damping of critical mode d=0,512 was added to the computation.
The critical second mode of elevator still shows a decline of
damping at speeds over 170km/h but the flutter speed goes
above 1,2VD. The result is, that the tail structure was said to be
flutter free, respecting the real structural damping. In addition
to improve the inherent flutter stability, the manufacturer was
advised to rebalance the elevator.
(Without structural damping)
d [1]
In Fig. 6 the structural damping was not used in calculation.
The second mode of elevator is supposed to be critical. The
value of negative logarithmic decrement falls to zero at speed
of VFL=170,6km/h, which is the critical flutter speed and gives
the speed ratio VFL/VD=0,620. Considering the inherent
structural damping of d=0,1 , given by FAR 23.629, the flutter
speed goes up to approximately VFL=273,6km/h and the speed
ratio raises to VFL/VD=0,995. According to FAR 23.629 the
airplane structure should be flutter free up to 1,2VD, Therefore
it is supposed that some undamped dynamical effects can be
observed.
VEAS [km/h]
C z e c h A e r o s pa c e P r o c e e d i n g s f [Hz]
VEAS [km/h]
(Measured structural damping)
Conclusion
The values of structural damping were evaluated for typical
eigenmodes of six aircraft structures. The half-power point
method was used. The results show that modes of control surfaces are always remarkably higher damped than modes of
primary structure. The possible causes of this phenomenon
could be the effect of control system path especially its stiff-
20
ness and friction between rotating and moving elements. The
question is how the structure behaves, when effects of real
pilot are considered. This should be the topic of subsequent
research. Although the half-power point method seems to be
very useful for determination of structural damping, it is valid
only for linear eigenmodes with sufficient frequency shift
from other modes, otherwise it gives incorrect results. This is
a main disadvantage, since the airplane structure modes can be
generally complex with characteristics of nonlinearity.
The effects of structural damping were shown on example
flutter calculation of tail structure. It was proved, that
knowledge of real damping values is very reasonable, especially for control surfaces modes, which are supposed to be the
most critical.
References
[1] Miláček, S.: Měření a vyhodnocování mechanických veličin;
Vydavatelství ČVUT, Praha 2001. ISBN 80-01-02417-2.
[2] Stejskal, V., Okrouhlík, M.: Kmitání s Matlabem;
Vydavatelství ČVUT, Praha 2002. ISBN 80-01-02435-0.
[3] Bilošová, A.: Experimentální modální analýza; VŠB Technická univerzita Ostrava, Ostrava [200?]
[4] Slavík, S.: Flutter calculation model with isolated modal
characteristics of control surfaces for small sport airplanes;
Czech aerospace proceedings, Vol. 2, 2008, ISSN 1211-877X.
Small aircraft ECS optimization using 1D tool
Optimalizace ECS malých dopravních letadel pomocí 1D simulačního
nástroje
Ing. Jiří Hejčík, Ph.D. / Institute of Aerospace Engineering, Brno University
of Technology; Prof. Ing. Miroslav Jícha, CSc. / Department of
Thermodynamics and Environmental Engineering, Brno University of
Technology
The paper details evaluations of a heat exchanger performance influence on a small airplane and/or helicopter
ECS. The ECS performance platform’s operation under different pressure losses and heat exchanger effectiveness
is numerically simulated using a multi-domain 1D simulation tool LMS Imagine.Lab AMESim.
Příspěvek se zabývá studií vlivu parametrů tepelného výměníku na výkon klimatizačního systému malých letounů
a vrtulníků, na základě provedených numerických 1D simulací chování klimatizačního systému, s využitím simulačního nástroje LMS Imagine.Lab AMESim.
Keywords: ECS, Heat exchanger, Air conditioning
Introduction
The Environmental Control System (ECS) is a key component for flight safety. It is basically an air conditioning
system, which main task is to deliver air at the required
pressure, temperature and humidity to the cockpit and
cabin. It has to work during all phases of flight and for any
occupancy. The ECS is also responsible for the cabin pre-
ssurization control with the possibility to regulate pressurization speed (time required for cabin pressure increase or
decrease) in case of an aircraft with a cruising ceiling of
over 3000 m. Since the benefit of the ECS to flight safety
is undisputable, it is also being installed to small aircrafts,
but only when the reliability, efficiency and weight of the
ECS fulfill designer’s requirements.
21
1/2011
Environmental Control System
ECS behaviour simulation
The ECS is in principle different from air-conditioning
systems known from the automobiles or household appliances because it works with no refrigerant. Only air is used
in the ECS either as a coolant or a heating medium.
Because of the required high overpressure (the pressure in
the cabin is up to 62 kPa above ambient) and huge volume
of the delivered air to the ECS the ventilating air is delivered from the aircraft’s or auxiliary power units (APU’s)
engines [1]. This “bleed” air cannot be used directly for
ventilation because it is too hot (about 200 °C) hence it is
necessary to cool it down to a suitable temperature before
it enters the cockpit or the cabin.
The balance between heat exchanger, turbine and compressor parameters is mandatory for the effective ECS
performance. Probably the easiest way to reach the parameter balance is to tune up heat exchanger parameters,
because its design is more flexible than that of the others.
The 1D model of the system shown in Fig. 1 was created
in a multidisciplinary 1D simulation tools LMS Imagine.
Lab AMESim (Fig. 2) to understand how the ECS behaviour is influenced by the heat exchanger parameters. This
model is based on some of experimental data e.g. turbine
and compressor characteristics, power losses in bearings
and temperature drops in connecting pipes, so that it simulates commercially available ECS system behaviour.
Commercial Aircraft’s ECS is a quite complicated device where the bleed air goes through an ozone converter,
cooling unit and water separator to the mixing chamber
where it is mixed with the recirculating air. Subsequently,
the required air temperature and humidity is set and ventilating air enters to the distribution system. On the other
hand the small aircraft’s and helicopter’s ECS is quite
simple and it usually contains an air cooler and water separator only. It is caused by the lower ceiling and flying
range of small aircrafts so that some parts are not necessary (e.g. ozone converter, air recirculation etc.), and the
directly treated bleeding air is suitable for effective cabin
ventilation.
And how does the small aircraft’s ECS work? The bleed
air from the engine goes through the cooling unit - usually
an air to air heat exchanger - which pre-cools the bleed air
by ambient air. After that it flows to the expansion turbine
where it is finally cooled. Certain amount of the bleed air
is added afterwards to set the required air temperature. The
last operation before the air is distributed to the cabin or
cockpit is moisture removing. The simplest arrangement of
cooling units, as it is used in small planes, is shown in Fig.
1.
Fig. 2 ECS model in Amesim
The heat exchanger efficiency and pressure drops were used
as simulation inputs. The obtained values of the bleed air and
ambient air parameters (flow rate, temperatures and pressures
at specific points), turbine and compressor RPM and power
losses in bearings were the outputs.
The simulation were done for two operational regimes (see
Table 1) with heat exchanger parameters varying in the range
of 50 to 100 % for the heat exchanger efficiency and for the
relative pressure drops from 0,9 to 9 % for the bleed air and
from 0,5 to 12 % for the ambient air.
Table 1 ECS regimes
Fig. 1 ECS of small aircraft or helicopter
Although there are no all control valves depicted in Fig.
1, it is evident that the thermal performance of small ECS
is set by the bleed air flow rate, expansion turbine + compressor characteristics and heat exchanger parameters.
Regime 1
Bleeding Air
Inlet pressure
331 900 Pa
Inlet temperature
165,6 °C
Expansion pressure
110 300 Pa
Ambient Air
Inlet pressure
95 100 Pa
Inlet temperature
16,4 °C
Table 1. ECS regimes
Regime 2
300 500 Pa
190,9 °C
109 700 Pa
95 100 Pa
43,9 °C
Conclusion
Probably the most important value for the cooling part
of the ECS is the expansion turbine outlet temperature.
This is shown in Fig. 3, where there is the influence of the
outlet temperature on the operational regime and pressure
drops or heat exchanger efficiency (constant pressure
drops). The simulation results confirm the expectation that
the heat exchanger efficiency has the greatest influence on
the outlet air temperature. On the contrary, the most surprising was the finding that the pressure drops on the bleed air
side of heat exchanger have only minor influence on the
outlet temperature, where the 10 times higher pressure
drops of the bleed air caused the outlet temperature change
about 5 °C. Further analysis of results shows that this is
due to the turbine characteristic, where the expansion is
changing in accordance to the air mass flow.
The influence of the ambient air pressure drops seems to
be negligible on the Fig. 3, where for the constant heat
exchanger efficiency and constant pressure drops of the
bleed air the outlet temperature from the expansion turbine
is almost constant. But one has to take into account that the
heat exchanger efficiency is the input for the simulation
and the mass flow rate of the ambient air is almost 2 times
greater than for the bleed air, hence the bleed air temperature at the outlet of the heat exchanger is constant. It shows
the weak point of simulations, because there is no dependency between mass flows and heat transfer (heat exchanger efficiency).
The simulations show the basic influence of the ECS
behaviour on the heat exchanger parameters. However they
show the procedure is good enough to compare different
ECS but not for their optimisation, because input parameters are independent what is not true in reality.
Fig. 3 Heat exchanger influence on ECS behaviour
The improved ECS model containing the thermal hydraulic behaviour of the heat exchanger is currently under
development. Because this improved model is more complex than the described one, it should be used not only for
the ECS optimization but also as an input generator for the
CFD simulation of cabin air quality.
Acknowledgement
This work was supported by CLKV (task A6 Prediction
of indoor environment in aeroplane cabin) and by MPO
project FI-IM5/217 Air conditioning system for helicopters and small airplanes.
References
[1] HUNT, Elwood H., et al. Commercial Airliner Environmental
Control System : Engineering Aspects of Cabin Air Quality
[online]. c1995-2009 [cit. 2009-05-10], <http://www.boeing.com/
commercial/cabinair/ecs.pdf>.
Intentionally left void.
23
1/2011
Development of series production technology
for stator and rotor blades
Vývoj technologie výroby statoru a rotoru pro opakovanou výrobu.
Ing. Karel Barák; Ing. Michal Řehák/ Department of Aerospace Engineering,
Czech Technical University in Prague, Faculty of Mechanical Engineering
This paper relays the soundness of technology pretaining to the structural componants of a fan propulsion demonstrator developed for small airplanes. This demonstration was intended for experimental verification of constructional and technological solution and acquiring data for subsequent construction optimization.
The paper‘s intent is especially focused on the technologies for the production of the composite rotor blades and
stature of ducted fan propulsion for repeated production.
Příspěvek se zabývá technologií výroby částí demonstrátoru ventilátorového pohonu, určeného pro experimentální
ověřování konstrukčních a technologických řešení pohonu a získávání dat pro následnou optimalizaci konstrukce.
Příspěvek je zaměřen zejména na vývoj technologie výroby kompozitních součástí rotorového systému a předstatoru pro opakovanou výrobu.
Keywords: UL aeroplanes, cold jet, ducted fan, ultra light rotor technology, composites material.
Introduction
1 Rotor blade
Demonstrator of fan propulsor is a system that serves for
verification of correct function of a new propulsion unit
with canal fan. This propulsor is developed for small airplanes. This test equipment was described in articles published in lit [1]. Construction of original rotor blades and
stator was described in lit [2].
The described parts of fan propulsor are made of glass
fiber and carbon fiber composit with foam cores. This
makes possible to achieve high stiffness.
Rotor blade of fan propulsor is composite sandwich
structure based on low viscosity polymer resin, carbon
fibers and a light-weight foam. On the basis of provided
information was done the balance of vacuum infusion processing (see figure 1). Generally this technology is suitable
for making of smaller products, whose shape is complicated, requiring high geometric precision and surface quality
[2]. Selected technology meets all requirements for series
production.
The part was made in three-parts mould. This one allowed to make leading edge of the blade without mould joint
(especially in term of aerodynamics).
Visual analysis was made after curing of each of single
specimen. Then eventually changed characteristics of
infusion process for improve surface quality by removal of
air voids (of defects). In the figure is fifth sample of rotor
blade after curing and removal out of the mould (see figure
2).
The goal was rotor blade with minimum defects mainly
caused by air voids and with approved structure.
Conception of the rotor blade
The rotor blade consists of foam core with titanium
bushing for a hinge, carbon flange and a coat. The shell of
the blade is made from carbon reinforcement that is assimilated to transfer of load (tensile load and torsion) from the
blade to the titanium bushing [1].
In the figure is three-dimensional CAD part of the blade
(see figure 3).
Materials
The offer of epoxy systems, that are primarily used for
vacuum infusion process,is large. Two component epoxy
C z e c h A e r o s pa c e P r o c e e d i n g s resin was chosen after previous experience in producing
simple flat table parts.
Carbon reinforcements was used in blade making. For
the flanges of the blade is used high strength unidirectional
carbon fabric (see figure 4). The shell of the blade is manufactured from balanced high strength carbon fabric with
plain weave (see figure 5).
The foam core was made from one - component polyurethane foam. Its dentsity is about 25 kg/m3.
Manufacturing moulds
The blade was made with using of composite mold, that
was assimilate to vacuum infusion technology. The rotor
vane mold was made with using of milled duraluminium
model (see figure 6). This one was made by NC tooling.
Own composite mold was made by contact lamination
on positive master model. The materials of the mould are
glass fabric and basic epoxy resin. Predefine chosen technology does not pose claim to thermal resistivity of resin
system.
At the beginning of making mould was used gelcoat. A
gelcoat is a material used to provide a high-quality finish
on the visible surface of the mold. Then the surface is also
hardier to mechanical damage. The gelcoat eminently
affected final quality of blade surface.
The mould was equipped with steel bushings and quidepins for easier right assembling of all its parts. Compagination mold parts was realized by screws and nuts (see
figure 7).
Sealing of the mold was maked through vacuum bag and
sealing tape. Sharp ends of screws was necessary cover up
with silicone rubber before vacuum processing, in order to
not for vacuum leakage (see figure 8).
Molds of blade cores were made on milled duralumin
model. The moulds were casted from silicone rubber (see
figure 9).
2 STATOR
Stator is located at the end of entry duct. Load of stator
blades is minimal. The load is carried by the curved entry
duct. The original stator consists of these basic parts: outer
ring, inner ring and fourteen blades (see figure 10). Any
part consists of fourteen parts.
24
Whole stator was made from 42 parts. This number of parts
made production and assembly lengthy. It also makes difficult
to fix or exchange stator. For these reasons, we were looking
for the possibility of simplifying the production technology.
For simplified design was chosen solution which integrates
the three essential elements of the original stator to the one
elements. Stator segment is composed of the stator blade and
part of the inner and outer ring. Stator assembled from these
segments can be glued directly to the airplane structure. If
there is need to replace the entire stator, it can provide seating
face. Seating face can be made in separate mould. For assembling segments there are shaped lock on edge of rings (see
figure 11).
Composite mould
For making mould of this difficult shape of rotor segment was made master model with rapid prototyping
method (see figure 12). The stator three-part mould was
made by contact lamination on positive master model. The
materials of the mould are glass fabric and basic epoxy
resin (see figure 13). The three-part mould allowed a
manufacturing of this difficult shape of rotor segment.
Dividing of the mould was designed for easy product
removal from the mould.
Making of the stator is provided by contact lamination in
negative forms. For manufacturing was selected epoxy
resin MGS L285 with hardener L285. Individual parts of
stator are formed by glass fiber surface layer. Firstly is
made blade part of the stator, then are assembled individuals parts of mould and finish glass fiber surface layer (see
figure 14). For joining blade parts was used laminating
epoxy with cotton flake filler as is usual in practices. Weight of stator segment is 65g. Curing was with the increased
temperature with slow start-up. Total time curing cycle
with the slow start-up to 40 °C was 5.5 hours. Net time
required to produce one segment stator is 1.5 hours, total
production of one segment takes 8 hours.
Simple preparation was made where are individual segments of stator placed together. For easy placing is the preparation equipped by hinges. Bushings for hinges in ring parts of
segment are in them already from production in forms (see
figure 15).
25
1/2011
up the production and reduce production costs.
The designed manufacturing process of stator and its
composition was successfully verified. Designed technology reduced the time required for stator production about
30%. Weight savings of over 18% and reduced difficulty
of manufacture.
3 Conclusion
The right manufacturing process leading to elimination
air voids from surface of the blade was found, thereby quality progression of blade surface was achieved during prototyp production.
Production productivity was satisfactory. Five blades
have been manufactured with one set of molds in ten days,
thus one rotor blade in two days.
Design concept and selected materials are suited to serial production. The quality of three-part mold surface was
preserved after curing of six specimens as well as moulds
for cores.
For the next development is supposed adjustment and
simplification of mold sealing system. In term of serial
production more suitable mold sealing system could speed
References
[1] Barák K.: Sendvičová kompozitní lopatka ventilátoru pro pohonnou
jednotku malých letadel; Sborník TRANSFER, č. 11/2010, 2010,
p. 50-57
[2] Martaus F.: Aplikace technologie RTM při vývoji kompozitního
vrtulového listu; Sborník TRANSFER, č. 5/2007, 2007, p. 5-12
[3] Barák K., Malásek T., Brabec J.: Ducted Fan Power Unit
Demonstrator for Ultralight Airplanes — Part Three; Czech
AEROSPACE Proceedings, No.3/2008, 2008, p. 7-9
[4] Růžička, P. Ducted Fan Power Unit Demonstrátor for Ultra Ligh
tweight Airplanes. Czech Aerospace Proceedings, Letecký
zpravodaj. November 2007, No3/2007, p. 49-52. ISSN 1211-877x
Microaccelerometer Error Analysis
Rozbor chyb mikroakcelerometru
Ing. Milan Chvojka
Completed cosmic microaccelerometer cannot be fully tested on ground due to its extreme sensitivity. Its final
parameters must be calculated from data measured on discrete blocks. Article describes results of accelerometers
blocks measurements and on this basis it estimates the expected random error of the complete device. Article evaluates contributions of separate blocks to the overall random error and sketches out fundamental ways of future
improvement.
Kosmický mikroakcelerometr nelze otestovat jako celek v pozemních podmínkách. Výsledné parametry musí být
určeny výpočtem z dat naměřených na dílčích blocích. Článek popisuje výsledky měření jednotlivých bloků kosmického mikroakcelerometru a na jejich základě odhaduje náhodnou chybu celého přístroje. Porovnává příspěvky
jednotlivých bloků k celkové náhodné chybě a nastiňuje nejdůležitější oblasti jeho dalšího vývoje.
Keywords: Cosmic microaccelerometer, error estimation, ground testing, sources of errors, random and systematic errors, ways of improvement.
Introduction
Basic parameter of each measurement device is its relative resolution. It is the ratio of its own noise divided by
measurement range, expressed usually in percentage. By
explicandum (defined notion) own noise we understand
sum of random disturbances of the device output measurements not caused by the change of input measured phenomena through the whole frequency range. Own noise is
usually defined as
parameter of the Gaussian curve of
measurement results when measurement device measures
zero (or constant) input value. Two sigma criterion is used
in the ESA projects. This criterion covers about 95% of
measured values. Some other applications can use different
criterion derived from the nature of the purpose.
Most of measurements described in this article were
done on the blocks or boards prepared for the microaccelerometer version 4, model PFM (abbreviation MAC). Completed device without right and upper wall is visible on the
Figure 1.
Review of tests
Figure 1 - View to inside electronics of MAC-04 PFM Model.
On the left side there are the electronic boards; on the right
side there is the sensor covered by position detectors.
Microaccelerometer short description
This chapter serves to clarify the terms used in this
article. Microaccelerometer block diagram is visible on the
Figure 2. Microaccelerometer is based on the glass cubic
proof mass placed in the glass cubic cavity with six pairs of
electrodes. One pair is placed on each wall. The proof mass
is kept by the electrostatic servomechanism in the centre of
the cavity. Block diagram shows the fundamental functional
blocks. Mechanical details except the sensor are not included. But their behaviour, especially temperature deformations, has significant influence to the microaccelerometer
parameters. Output voltages from the position detectors are
marked P11, P12, P21, P22, P31 and P32. They are proportional to the deviation of the cubic proof mass from the
geometrical centre of the sensor cavity. Position control
voltages, which are applied to the cavity electrodes are
marked A11, A12, A21, A22, A31 and A32. These control
voltages are proportional to the external acceleration which
acts to the cavity. It is due to the fact that electrodes area,
cube mass and gap length between the electrodes and the
cubic proof mass are practically constant. Deviations of the
proof mass cube for the centre of the cavity are less than
1% of the gap length when feedback loop is working. Cubic
sensor has six degree of freedom that is why the control
loops are six. This sensor doesn’t measure the gravitational
acceleration, because this acceleration acts with the same
intensity to the proof mass and also to the cavity and all
others parts of the device.
Figure 2 - Microaccelerometer Block Diagram
All tests described in this article are concentrated to the
estimation of parameters of the microaccelerometer. From
the sensitivity analyses we know that the biggest influence
to the low frequency noise have position detectors
POSDETs, based on the capacitive principle. From the previous projects we also know that these position detectors
have two major external sources of disturbances. Temperature is the first and about second one the big discussion was
several times. Part of experts had hypothesis that this external influence is humidity, part of them had hypothesis that
this part of bias is caused by electronics long term instability, without external influence. Analysis of used components and sensitivity analysis of schematics of the POSDETs
result in the most probable hypothesis that this second
major influence is the humidity. There fore the combined
test was realized. This test confirms this hypothesis. Results
of this test are plotted on the Graph 1. Position detectors
POSDETs needs except supply voltages also two auxiliary
voltages Sin230k and PLDCLK for their function. Auxiliary POSDET testing device POSDET Testing Jig is necessary for their testing. This POSDET Testing Jig (abbreviation
PTJ) includes also two preamplifiers for the amplification
of two POSDET output voltages. These amplifiers have
amplification factor 18x. The output voltages of POSDET
are eighteens smaller than the values plotted in the Graph 1
Graph 1 - Amplified output voltage of position detector
POSDET after humidity change from 70% to 20%
(at 5100 sec. time) and after temperature change
from 25°C to 30°C (at 8700 sec. time)
Result of this test significantly changes the view of management staff to the way of next tests. Commonly was
accepted idea, that precise tests of microaccelerometer
(MAC) electronics boards, especially position detectors
POSDETs, must be realized in vacuum conditions. After
this initial test there were realized these following tests:
Test of the long term stability of POSDET, test of the temperature bias of POSDET, test of the own noise of A/D
converters and their supportive circuits, test of the temperature dependence of A/D converters and their auxiliary circuits, test of the influence of temperature changes of the
distance between POSDET boards and MAC cover, test of
27
Relation between POSDET and complete sensor
error
Position detector POSDET has two outputs for each axe:
Translation output voltage proportional to the translation
deviation of the cubic proof mass from the central position
and rotational output voltage proportional to the rotational
deviation of the cube. If the translational POSDET output
voltage has error
then complete sensor has error
which is expressed by the Equation 1.
Equation 1
Voltage (V)
Where:
C
m
Pv0.04
D
0.02
0
Lps
-0.02
Thermo-vacuum test was realized, with temperature time
profile simulating temperature cycling of microaccelerometer on the satellite during several orbits. POSDET board
was equipped by the four temperature sensors T5, T6, T7
and T8 in the corners. Temperature time profile measured
by these sensors is plotted on the Graph 2. The POSDET
board outputs were trimmed to zero before this test.
Translation and rotation output voltages of the POSDET
board during this test are plotted on the Graph 3.
POSDET temperature sensors time profile
50
40
30
Temperature (deg C)
the influence of temperature dependence of Sin230kHz
auxiliary sine voltage to the POSDET output voltages and
test of the influence of the temperature dependence of the
phase between PLDCLK synchronization voltage and the
Sin230kHz sine voltage to the POSDET outputs. All these
tests checks external influences to the microaccelerometer
systematic and random errors..
is the absolute measurement error in translation channel (in ms-2)
is the capacitance between one
electrode nad the cube (in pF)
Linear and rotational channel voltages
is the mass of cubic proof mass (in kg)
is the polarization voltage (in V)
is the distance between electrode and
the cube wall in central position (in m)
is the offset error of the POLDET
position detector in transl. channel (in V)
is the sensitivity of the POSDET in
translation channel (in m/V)
Where
r
Lpr
Jcube
C,Pv,D
10
T5, top left
T6, top right
T7, bottom left
T8, bottom right
-10
-20
22/05/2007
12:00:00
23/05/2007
00:00:00
23/05/2007
12:00:00
24/05/2007
00:00:00
24/05/2007
12:00:00
25/05/2007
00:00:00
25/05/2007
12:00:00
26/05/2007
00:00:00
Date and time
Graph 2 - Temperature time profile during
the POSDET thermo-vacuum test
Rotational channel
Linear channel
Linear and rotational channel voltages
0.04
If the rotational POSDET output voltage has error
-0.06
UDRot then the complete sensor has error
which is expressed by Equation 2.
23/05/2007
00:00:00
23/05/2007
12:00:00
24/05/2007
00:00:00
24/05/2007
12:00:00
25/05/2007
00:00:00
25/05/2007
12:00:00
Date and Time
is the absolute measurement error in rotation
channel (in rad.s-2)
is arm of force (in m) r = 7.294 52.10-3 m
is the sensitivity of the POSDET in rotation
channel (in rad/V) = 1.370 89 . 10-3 rad/V
is the moment of inertia of the proof mass
cube
is the offset error of the POLDET position
detector in rotation channel (in V)
symbols indicates the same physical
quantity as in the previous Equation
Results of ground tests
Initiatory tests were concentrated to the POSDET parameters checking. For POSDET board testing was designed
electronic auxiliary device named POSDET Testing Jig
(abbreviation PTJ) and mechanical testing jig simulating
the mechanics of microaccelerometer sensor and its cover.
0.02
0
26/05/2007
00:00:00
Voltage (V)
Equation 2
20
0
-0.04
-0.08
22/05/2007
12:00:00
1/2011
Rotational chann
Linear channel
-0.02
-0.04
-0.06
-0.08
22/05/2007
12:00:00
23/05/2007
00:00:00
23/05/2007
12:00:00
24/05/2007
00:00:00
24/05/2007
12:00:00
25/05/2007
00:00:00
25/05/2007
12:00:00
26/05/2007
00:00:00
Date and Time
Graph 3 - POSDET output voltag during
the thermo-vacuum test
Significant are the jumps in both channels during lowest
temperature cycling. Origins of these steps are the rigid
connections of the capacitor trimmers to the printed circuit
board (PCB). In next version of POSDET there were these
rigid connections replaced by the soft elastic ones. Graph 4
shows dependence between temperature and POSDET
translation output voltage and Graph 5 shows this dependence for the rotational output of POSDET.
Significant are the jumps in both channels during lowest
temperature cycling. Origins of these steps are the rigid
connections of the capacitor trimmers to the printed circuit
board (PCB). In next version of POSDET there were these
rigid connections replaced by the soft elastic ones. Graph 4
shows dependence between temperature and POSDET
translation output voltage and Graph 5 shows this dependence for the rotational output of POSDET.
Graph 6 - Temperature dependence of auxiliary sinus
voltage Sin230kHz. Red curve comes from MAC-03.
Blue curve: Improved generator on MAC-04. Green
line is the linear approximation.
Graph 4 - Translational POSDET output voltage
vs. temperature during temperature cycling
Graph 5 - Rotational POSDET output voltage
vs. temperature during temperature cycling
Graph 7 - Temperature dependence of phase
between PLDCLK and Sin230kHz on MAC-04
microaccelerometer model.
Outputs from PTJ on the left axes are recalculated to the
POSDETs output voltages (divided by factor 18). On the
Graph 4 we see the phase shift between temperature cycling and the translational output of the POSDET. Its cause
is the fact that translation measurement has origin in the
opposite electrodes, which have significant distance. This
fact causes in significant temperature gradient between
them. Rotational measurement is derived from adjacent
electrodes, which are close each to other. In this case the
phase shift is significantly reduced. Temperature biases of
both POSDET outputs derived from the Graphs 4 and 5 are:
Another source of microaccelerometer error is long term
instability of POSDET outputs. In the ground conditions is
very difficult collect some representative data. Graph 8
shows results of the measurements, where external terrestrial influences were relatively highly reduced. Fluctuation of
translation channel is about
and in rotation channel
about
during 14 hours. Adequate errors in acceleration channels calculated according Equation 1 and 2 are:
Temperature bias of translation output is:
Temperature bias of translation output is:
Temperature bias of rotational output is:
Temperature bias of rotational output is:
29
POSDET Output Voltage Time Stability
4
3
POSDET Output Voltage [mV]
2
1
0
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
-1
-2
-3
-4
POSDET Output Voltage Time Stability
-5
4
3
On the Graph 10 there are plotted outputs of A/D converters when the input voltages and external conditions are constant and only own noise of A/D converters and their auxiliary circuits is significant. Statistical analysis of the data plotted on the Graph 10 shows that dispersion of the translation
data recalculated to the voltage A11 is
and for
the rotational data expressed as voltage A12
Sensitivities of microaccelerometer with respect to input voltages of A/D converters in translation and rotation channels
are:
for translation channel and
Time [sec]
Tran Output
Rotat Output
for rotation channel.
POSDET Output Voltage [mV]
Graph 28: Long term outputs of POSDET board with stabilized input and external conditions
1
1/2011
Graph 8 - Long term outputs of POSDET board
with stabilized input and external conditions
Latest significant source of microaccelerometer disturbances is the own noise of A/D converters with
Resolution is usually defined as
dispersion of summa0
their auxiliary
the random
part
temperature
dependence
of45000
these circuits.
A/D
0 circuits
5000 and 10000
15000
20000of the
25000
30000
35000
40000
50000
rized
noise.
Then
own
noise
of
A/D
converters
converted to
converters -1Latest
are the Sigma-Delta
types.
These types
have output word 24 bitesdisturbances
long, but lowest 4 bites
significant
source
of microaccelerometer
are noisy, resolution is about 20 bits. Full measurement range of the converters is from 0.0 to +5.0the
V. adequate acceleration is:
is -2the own noise of A/D converters with their auxiliary circuits
Graph 9 represents the response of A/D converters together with their auxiliary circuits to the
and-3 the
part
thewith
temperature
dependence
of these cirtemperature
jumprandom
from 30.8°C
to of
11.4°C
constant input
voltage P11=P12=+0.2V.
P11 is the
for translation channel and
translational output of the POSDET measuring X axes. P12 is its rotational output. A11 is the output
cuits.
A/D converters are the Sigma-Delta types. These types
-4
of translational output of the X axes position control circuit. A12 is rotational output of it.
have output word 24 bites long, but lowest 4 bites are noisy,
resolution is about 20 bits. Full measurement range of the converters
is term
fromoutputs
0.0 toof +5.0
V.board
Graph
9 represents
theexternal
response
of Temperature dependences of A/D converters including their
Graph
8: Long
POSDET
with stabilized
input and
conditions
A/D converters together with their auxiliary circuits to the tem- auxiliary circuits derived from data plotted on the Graph 9
Latestperature
significant source
microaccelerometer
disturbances
is the
own noiseinput
of A/D voltage
converters with
and expressed as adequate accelerations are:
jumpoffrom
30.8°C to 11.4°C
with
constant
their auxiliary circuits and the random part of the temperature dependence of these circuits. A/D
P11=P12=+0.2V.
P11 is
thetypes
translational
output
of the
converters
are the Sigma-Delta types.
These
have output word
24 bites
long,POSDET
but lowest 4 bites
are noisy,
resolution is
20 P12
bits. Full
rangeoutput.
of the converters
fromoutput
0.0 to +5.0 V.
measuring
Xabout
axes.
is measurement
its rotational
A11 isisthe
Graph 9 represents the response of A/D converters together with their auxiliary circuits to the
of translational
output
of the
Xconstant
axes position
control
circuit. A12
temperature
jump from 30.8°C
to 11.4°C
with
input voltage
P11=P12=+0.2V.
P11 is the for translation channel and
translational output of the POSDET measuring X axes. P12 is its rotational output. A11 is the output
is rotational output of it.
-5
Time [sec]
Tran Output
Rotat Output
of translational output of the X axes position control circuit. A12 is rotational output of it.
Graph 9: Response of A/D converters outputs to the temperature jump with constant input
voltage.
Temperature dependence is systematic error and can be partly
reduced by calibration of this dependence and its mathematical
extraction.
Summarized microaccelerometer error
Each device has random and systematic errors. Each systematic error, for example like temperature dependence, has
deterministic and random part. For estimation of the random part of all temperature dependencies it is necessary to
know what the error of the temperature measurements is
Graph 9:Graph
Response 9
of -A/D
converters outputs
to the
temperature jump
with constant
Response
of A/D
converters
outputs
to input and how much percent of systematic error is its random
voltage.constant input voltage.
the temperature jump with
part. These values depend on concrete conditions in each
project. Here we will suppose that random part is 30% of
systematic error and the random error of temperature measurements is
= 0.5°C. Under these conditions the most
significant accelerometer errors are:
Random errors:
1. Long term instability of POSDETs
2. Own noise of A/D converters and their auxiliary circuits
Systematic errors:
3. POSDETs outputs Temperature bias
4. Influence of temperature depen-
dence of Sin230k amplitude to POSDETs outputs
5. Influence of temperature depen-
dence of phase between Sin230k
and PLDCLK to POSDETs outputs
Graph 10:
Noise of10
A/D-converters
outputs
constant input
voltage and
temperature.
6. Temperature dependence of A/D Graph
Noise of
A/Dwithin
converters
outputs
within
On the Graph 10 there are plotted outputs of A/D converters when the input voltages and external
converters
and their auxiliary circuits
constant input voltage and temperature.
conditions are constant and only own noise of A/D converters and their auxiliary circuits is
significant. Statistical analysis of the data plotted on the Graph 10 shows that dispersion of the
translation data recalculated to the voltage A11 is  = 5.29 V and for the rotational data expressed
as voltage A12 is  = 4.21 V. Sensitivities of microaccelerometer with respect to input voltages of
A/D converters in translation and rotation channels are:
Estimation of overall random error of the complete microaccelerometer based on the results of tests of basic microaccelerometer blocks and taking into account the conditions described in the beginning of this chapter is summarized in the Table 1.
development
of electronic
circuits.converters
In the microaccelerometer
data we also find some few
Outputs
of A/D
duringoutput
thermo-vacuum
small jumps. See Graph 11. Big jumps like ones on the Graph 3 were steamed off by the redesign of
tests trimmer
Smallconnection.
jumps Very
in small
output
caused
the also
flash
capacitive
jumps,data,
visible on
the Graphby
11, have
origin in the
behaviour of the mechanics. That is the reason, why it is necessary to redesign partly also the
mechanical
tension
releasing
mechanics of the microaccelerometer, especially fixing elements of the glass sensor inside the cover.
Outputs of A/D converters during thermo-vacuum tests
Small jumps in output data, caused by the flash mechanical tension releasing
Error
No.
2 Errors
expressed
in Volts
Systematic Errors
expressed in
acceleration
2 Random errors
expressed in
acceleration
1
Long Term POSDET stability
Translation
20 V
---
5.732 . 10-10 m.s-2
1
Long Term POSDET stability
Rotation
70 V
---
1.002 . 10-7 rad.s-2
2
Own Noise of A/D Converters
Translation
10.58V
---
1.102 . 10-9 m.s-2
2
Own Noise of A/D Converters
Rotation
8.42 V
---
4.383 . 10-8 rad.s-2
3
POSDET Output Temperature Bias
Translation
376V/K
1.078 . 10-8 m.s-2/K
1.617 . 10-9 m.s-2
3
POSDET Output Temperature Bias
Rotation
686V/K
9.821 . 10-7 rad.s-2/K
1.473 . 10-7 rad.s-2
4
Influence of Temperature Dependence Amplitude
of Sin230kHz
Translation
46.39 V/K
1.330 . 10-9 m.s-2/K
1.995 . 10-10 m.s-2
4
Influence of Temperature Dependence Amplitude
of Sin230kHz
Rotation
Negligible
---
---
5
Influence of Temperature Dependence of Phase
between Sin230k and PLDCLK
Translation
36.5V/K
1.046 . 10 m.s /K
5
Influence of Temperature Dependence of Phase
between Sin230k and PLDCLK
Rotation
36.5V/K
-8
6
Temperature Dependence of A/D converters Tra
417V/K
4.345 . 10-8 m.s-2/K
6.518 . 10-9 m.s-2
6
Temperature Dependence of A/D converters Rot
422V/K
2.197 . 10-6 rad.s-2/K
3.296 . 10-7 rad.s-2
-9
-2
1.569 . 10-10 m.s-2
-2
-9
5.223 . 10 rad.s /K
7.835 . 10 rad.s
-2
Overall Random Error of Translation
1.017 . 10-8 m.s-2
Overall Random Error of Rotation
6.288 . 10-7 rad.s-2
Graph 11: Outputs of A/D converters during thermo-vacuum tests (variable temperature)
Graph 11 - Outputs of A/D converters during
thermo-vacuum
tests
All the fixing elements
of the glass sensor
must(variable
be statically temperature)
determinate or elastic with permanent
contact. Fulfilment of these two conditions significantly reduces the internal forces in the mechanics
caused by temperature changes and gradients.
Conclusion
All the fixing elements of the glass sensor must be statically
Initial estimation of 2random error for microaccelerometer version 4 in translation channel was
determinate
or elastic with permanent contact. Fulfilment of
1.364 . 10-8 m.s-2. See [2]. Calculation based on the test results of realized blocks gave value
these
significantly
reduces
the-2 for
internal
forces
1.017
. 10-8two
m.s-2 conditions
for the translation
channels and 6.288
. 10-7 rad.s
the rotation
channels. This
The estimation given in [2] of the translation channel error made at the beginning of the
shows that anticipated results were reached. On the other hand these tests disclosed several
microaccelerometer version 4 design was that 2error will be 1.364 . 10 m.s . Recent result, based results
in the mechanics caused by temperature changes and gradion the
test of
developed and realized
aboutof
25% the
less than
initial estimation.
From this it small insufficiencies, especially influence of mechanical construction to electronics. This new
The
estimation
givenblocks,
in is[2]
translation
channel
experience
ents. show the way of future redesign.
follows that parameters of newly developed blocks satisfy established goal.
error made at the beginning of the microaccelerometer ver-8
Main
errors
reduction
future
design
m.s-2. References
sion 4sources
designof
was
that and their
error
will be in
1.364
. 10
Conclusion
From the Table 1 results, that most significant are two sources of errors: Instability and temperature [1]
Chvojka,estimation
M. T.: Analýza zdrojů
nestabilit kosmického
mikroakcelerometru;
Recent
result,
based
on
the
test
of
developed
and
realized
Initial
of chyb a random
error for
microaccele-Výzkumná
dependence of position detector POSDET and own noise and noise and temperature dependence of
zpráva R-4862, VZLÚ, a.s., Praha – Letňany 2010
A/D
converters
and
their
auxiliary
circuits.
There
are
two
most
significant
ways
of
future
blocks, is about 25% less than initial estimation. From this rometer version 4 in translation channel was 1.364 . 10-8
development of electronic circuits. In the microaccelerometer output data we also find some few
-2
it follows
of newly
developed
blocks
. SeeM.[2].
Calculation
based
test results
of reali-VZLÚ, a.s.,
small
jumps. See that
Graph parameters
11. Big jumps like ones
on the Graph
3 were steamed
off by thesatisfy
redesign of [2]m.sChvojka,
T.: ACC
Performance Analysis
Ver.on
2.6;the
Výzkumná
zpráva VZL-AC-0003,
capacitive trimmer connection. Very small jumps, visible on the Graph 11, have also origin in the
-2
established
goal.
Praha
– Letňany
2009
for
the
translation
zed
blocks
gave
value
1.017
.
10-8
m.s
behaviour of the mechanics. That is the reason, why it is necessary to redesign partly also the
mechanics of the microaccelerometer, especially fixing elements of the glass sensor inside the cover.
channels and 6.288 . 10-7 rad.s-2 for the rotation channels.
Main sources of errors and their reduction in future This results shows that anticipated results were reached. On
Outputs of A/D converters during thermo-vacuum tests
design
the other hand these tests disclosed several small insufficiSmall jumps in output data, caused by the flash mechanical tension releasing
From the Table 1 results, that most significant are two encies, especially influence of mechanical construction to
sources of errors: Instability and temperature dependence electronics. This new experience show the way of future
of position detector POSDET and own noise and noise and redesign.
temperature dependence of A/D converters and their auxiliary circuits. There are two most significant ways of future
development of electronic circuits. In the microaccelerometer output data we also find some few small jumps. See
References
Graph 11. Big jumps like ones on the Graph 3 were stea[1] Chvojka, M. T.: Analýza zdrojů chyb a nestabilit kosmického
med off by the redesign of capacitive trimmer connection.
mikroakcelerometru; Výzkumná zpráva R-4862, VZLÚ, a.s.,
Praha – Letňany 2010
Very small jumps, visible on the Graph 11, have also origin
in the behaviour of the mechanics. That is the reason, why
[2] Chvojka, M. T.: ACC Performance Analysis Ver. 2.6; Výzkumná
it is necessary to redesign partly also the mechanics of the
zpráva VZL-AC-0003, VZLÚ, a.s., Praha – Letňany 2009
microaccelerometer, especially fixing elements of the glass
sensor inside the cover.
Table
1 - Estimation
of Overall
Random
Table 1: Estimation
of Overall Random
Microaccelerometer
Error
Microaccelerometer Error
-8
-2
31
1/2011
Analysis of dynamic characteristics of gas
turbine
Analýza dynamických vlastností spalovací turbíny
Tomáš Jamróz, Jiří Had, Vladimír Dániel / VZLÚ, Plc., Praha
The research conducted explains the dynamic analysis of a generator rotor that is loaded and its relation to stress
under excessive vibration. The generator rotor consists of a gas turbine, compressor, and steam turbine. A connection of the compressor and of the steam turbine lead to a structural modification to the original construction. In
the article we are shown basic calculations of dynamical properties of a new construction of the generator rotor (in
particular to critical speed and its speed dependance, and its sensitivity analysis for unbalance).
Článek se zaobírá dynamikou rotorového soustrojí, které je namáháno nadměrnými vibracemi. Rotorové soustrojí
se skládá z plynové turbíny, kompresoru a parní turbíny. Spojení kompresoru a parní turbíny vedlo ke konstrukční změně původního návrhu. V článku jsou uvedeny základní výpočty dynamických vlastností konstrukčně upravené soustavy (kritické otáčky a jejich závislost na otáčkách a citlivostní analýza na nevývahu).
Keywords: turbomachinery; critical speed; unbalance
Fig. 1 - 3D projection of FEM model of the Generator rotor
Introduction
Generator rotor is running at operating speed of 7650
min-1. The Generator rotor consists of a gas turbine, a compressor, a steam turbine, a gearbox and a generator. Dynamic model of this system involves only the gas turbines,
the compressors and the steam turbine part. Above mentioned parts of the generator rotor for the dynamic analysis
are supported by three sliding bearings. Radial bearing of
gas turbine (L6), radial bearing of compressor (L5) and the
combined radial-axial (L4r-L4a) bearing of compressor.
Steam turbine is supported by two radial and one axial
bearing (L3 - combined and L2- radial). The parts are
connected by coupling. The gas turbine and the compressor
is connected by a cone ring coupling and between the compressor and the stream turbine is used a gear coupling. The
rotor system is loaded by an excessive vibration especially
in position L5. Dynamic calculation of rotor system was
performed to find out whether the system does not work
near critical speed and to find the cause of excessive vibration.
Model
For the purposes of the dynamic characteristics calculation in the software MSC.Nastran is necessary the Generator rotor is discredited into finite elements.
The model consists of beam elements modeling the
shaft. Disk of gas turbine is done by shell elements. Blades
of compressor was not modeled in details but was included
in the model of the compressor rotor. Hubs coupling at the
compressor rotor were done as point masses with the mass
and inertia effects. Stiffness and mass was modelled separately. The stiffness of the rotor was done by the beam
elements. Mass points distributed along the rotor system
define the mass and inertia effects of the each parts of the
rotor system.
Compressor rotor and rotor of the Gas turbine are connected by beam elements and rigid elements (RBE2) that
replace screw connection. The beam elements transmit
axial moment. This simplification replaces of a Cone ring
coupling.
Compressor rotor and rotor of the Steam turbine are
connected only rigid element (RBE2) that replaces function of a Gear coupling.
Rotor is supported on four points which are numbered
L3-L6. The supports are shown in Figure 1.
The shaft supports (L6, L5, L4r and L3r) enable free
motion with exception of radial displacement.
The bearings are modelled with 1D elements with asymmetric stiffness properties.
C z e c h A e r o s pa c e P r o c e e d i n g s Calculation
Critical speed
Dynamic properties of the bearing depend on external
parameters, namely angular velocity of the rotor ω . That’s
why is necessary to perform calculations of dynamic
properties in entire operating range of speeds. The result of
calculation of the natural frequencies is sets of complex
eigenvalues that were calculated for various operating
speed. Each complex eigenvalue consists of imaginary part
Ωm (represents the natural frequency of rotating shaft with
angular velocity ω ) and the real part δm (represents a damping)
32
stability, ie. for all ω > ωk. The values of critical speed and the
logarithmic decrement are shown in table 1. The damping is
described by a logarithmic decrement
To evaluate of danger of the critical speeds was used a
methodology according to the American standard API. There
is defined an Amplification Factor, which is proportional to the
theoretical maximum value of excess vibrations in the critical
speed. The value of AF is defined by its own decay and natural
frequencies
By connecting corresponding natural frequencies Ωm computed for various shaft speed ω get curves expressing dependence of natural frequencies on the speed of the shaft ω called
Campbell diagram. Critical speeds ωk of the rotor are speeds
at which natural frequencies curves Ωm( ω ) cross the rotation
frequency curve Ω( ω ).
Table 1 - Critical speed of the rotor
and the Amplification factor
If the value of AF in critical speed meets the requirement
0<AF<2.5, according to the standard the critical speed ω k is
over damped and it is not considered as critical speed. Between
2.5<AF<5.0 the critical speed is very attenuate and for AF>5.0
is critical speed less attenuate.
Operating rotor speed is 127.5Hz. This value is between two
critical speeds with very less attenuation.
Fig. 2 - Campbell diagram
One of the important information needed to assess of danger
of critical speed is the value of decay δm ( ω k) in the critical
speed. The critical speed will be stable if decay
is δm (ω k) > 0.
The results of the calculation of natural frequencies show
that the first and third critical speed are unstable ie. δm
( ω k)<0. In these cases the most important influence on stability has bearings. The characteristics of sliding bearing show
that the rotor motion will be unstable for all the speed limits of
Fig. 3 - Amplification factor
33
1/2011
Fig. 4 - Natural frequencies modes of rotor shapes of 1th, 3th, 5th and 7th.
Sensitivity analysis for unbalance
Several planes were chosen to define of unbalance. The
first two planes were defined at faces of the compressor
and the other two were placed in coupling. Due to the operation mode shape only planes with couplings has been
tested.
In a hub of the Gear coupling on the compressor rotor
was added a mass 0.08kg, 0.16kg and 0.24kg of 87.5mm
radius. These unbalances gradually formed torques
7E-3kgm, 14E-3kgm and 24E-3kgm.
that was defined above.
The Figure 5 shows that unbalance is only sensitive to
the critical speed of the Gear coupling around 8500[min-1].
The sensitivity analysis of the unbalance in the Cone
ring coupling was solved as well as in case of the sensitivity analysis for the Gear coupling.
In a hub of the Cone ring coupling on the rotor of the
Gas turbine was added a mass 0.16kg, 0.24kg and 0.32kg
of 110mm radius. These unbalances gradually formed
torques 17E-3kgm, 26E-3kgm and 35E-3kgm.
Fig. 5 - Sensitivity to unbalance on the Gear coupling
Fig. 6 - Sensitivity to unbalance
on the Cone ring coupling
In the Figure 5 is shown a significant increase of the
vibration in natural frequencies without mass point for an
unbalance. The second part draws sensitivity to unbalance
In the Figure 6 is shown a significant increase of the
vibration in natural frequencies without mass point for an
unbalance. The second part draws a sensitivity to unbalance
C z e c h A e r o s pa c e P r o c e e d i n g s that was defined above.
The Figure 6 shows that unbalance is only sensitive to
the critical speed of the Cone ring coupling and then it is
quickly damped. See to table 1. mode 5.
Conclusion
Dynamic analysis of rotor system unfortunately did not
identify the exact cause of an excessive vibration in the
bearing housings.
According to analysis results to find the critical speed, it
was found that rotor system is working in proximity to one
of the natural frequencies. This critical shape has an important damping ratio and thus it is not cause excessive vibration in bearing housing.
The excessive vibration could be caused by instability of
the first two natural frequencies. In future measurements
will be made to prove or disprove whether the issue of oil
whip or oil whirl.
Another cause of excessive vibrations could be unbalance in couplings. An influence of the Gear coupling on
vibration can reduce by a structural adjustment by reducing
34
the shaft end.
There could be another reason of the excessive vibration
and that is coaxial support of compressor rotor and the
Steam turbine rotor at a standstill. This situation would
cause misalignment of rotors in support of single parts at
the heat state of generator rotor. An effect of misalignment
of support will be dealt with in the future.
References
[1] Brepta, R., P;st, L., Turek, F.: Mechanické kmitání, Sobotáles,
Praha, 1994.
[2] Slavík, J., Stejskal, V., Zeman, V.: Základy dynamiky strojů,
ČVÚT, Praha, 1997.
[3] Krämer, E.: Dynamics of Rotors and Foundtions, Springer Verlag,
Berlin, 1993.
[4] Muszynska, A.: Rotordynamics, Taylor & Francis Group, 2005.
Kinetic analysis of oxidizing decomposition of
carbon fiber reinforced epoxy composite
Kinetická analýza oxidačního rozkladu uhlíkového epoxidového
kompozitu
Ing. Zdeněk Mašek
The kinetic oxidizition and decomposition epoxy composite was studied. Temperature decomposition was studied
on a laboratory sample at the temperature upto 550oC in an oxidized atmosphere. The kinetic-diffusion model
was proposed, following the measured values. The shape of thin composite plates of the sample was calculated.
Byla studována kinetika oxidačního rozkladu epoxydového kompozitu. Tepelný rozklad byl studován na laboratorním vzorku při teplotách do 550 0C. v oxidační atmosféře. Byl navržen kineticko-difúzní model na základě experimentálních údajů. Model počítá s tvarem tenkých kompozitních desek.
Keywords: Epoxy composite, carbon fiber, thermo gravimetric analysis (TGA), kinetic equation,
activation energy.
1 Introduction
The tempering of carbon composites concludes to
exhausted gases evaporation. The production of exhausted
gases is followed by mass decreasing of combusted material. The description of mass decreasing caused by heating
is the object of thermo gravimetric analysis (TGA). In this
work a TGA analysis of carbon fiber reinforced sample of
epoxy composite was done. The sample was heated in the
air region by the controlled temperature trend. The measured values aimed were analyzed at the base of reaction
kinetic. During the thermal decomposition the production
of basic combusted gases was observed. During the heating
the temperature directly on the surface of the sample was
measured. The measurement of temperature on the surface
and of the hot air can detect the exothermic reaction appearance. The values measured were compared with equations
of kinetic and diffusion processes proposed. The first
rough process estimate involved a description with correlation according to a speed equation of Prout-Tompkins :
d dt =
. The whole process was divided into
35
several parts and the parameters of activation energy, pre-exponential factor and exponents of velocity equation was
calculated for each part. The next approximation involved
a three-step model including a kinetic of pyrolytic decomposition in the first part, surface oxidizing reaction and a
diffusion in the second part and the oxidizing reaction in
the third part.
2 Experimental arrangement
2.1 Processing material
The tempering of carbon composites concludes to
exhausted gases evaporation. The production of exhausted
gases is followed by mass decreasing of combusted material. The description of mass decreasing caused by heating
Epoxy composite plates of weight around 200 g and with
thickness of 3 – 5 mm were tested. There is a difference compared with the classical TGA, which goes with several gram-weight samples. The plates were manufactured by RTM
technology and fibre reinforcement was aligned in equal direction. The weight ratio of carbon fibers was about 50 %.
2.2 Experimental equipment
Experimental equipment developed for composite degradation was used. The reacting chamber has a volume of 240
dm3 and is heated by electrical elements. The chamber is
not hermetically closed and small negative pressure is kept
inside by sucking of exhausted gasses. Sucking of exhausted gasses enables to keep an oxidizing atmosphere inside
the reacting chamber. The program for temperature control
is adjusted with regards to optimal yield and quality of
processed carbon fibers composites. The curve of the temperature increase is shown on the graph 1. The speed of
temperature increase is not constant. The temperature is
monitored by thermo electrical thermometer fixed closely
above the surface. The plate is put at the iron grind in the
horizontal level.
2.3 Experimental procedure
Thermogravimetric analysis (TGA) is a method often
used for studying of thermal behaviour of materials. The
material is heated and a mass decreasing is plotted with
temperature changing depending on the time. Kinetic parameters of thermal degradation are determined from the
measured values.
2.4 Analysis of results
Data files of temperature trends and mass decreasing
were taken and converted into table processor Excel. All
numeric calculations and graphs were provided by this
means.
3 Theoretical background
3.1 The velocity equation
It is obvious that the chemical kinetic equations are written in this form:
Velocity of conversion = Velocity constant . velocity function
•
•
•
1/2011
Velocity of conversion: d /dt is a time derivative of
extent of process that is a number between 0 and 1.
Velocity constant K=A.exp(E/RT) is Arrhenius equation which express the dependence of velocity constant
on the temperature. A is called a pre-exponential factor, E is a activation energy, R is universal gas constant
and T is absolute temperature in Kelvin.
Velocity function f( ) is a function of the extent of
process its shape is derived from the reacting mechanism.
Many authors referred about expressing of kinetic parameters and several methods were described. The experimental methods are obviously based on the linear temperature increasing because the linear temperature dependence
makes the counting easier. There are a integral and a differential approach how to solve the kinetic equations. The
integral approach provides the kinetic parameters for all
reach of checked values, though the differential approach
can get the kinetic parameters from the one point of gravimetric analysis. The integral approach is more robust,
gives more reliable values and is more protected against
the influence of distant values. The differential approach is
more sensitive to the distant values, but can detect the
changes of reacting mechanism at specified temperature
reach.1 In this paper is discussed about using of kinetic
equation d /dt = A(1- )n m. This equation gives a good
condition for process description. There was referred in
papers2,3 about suitability of this equation for description
of epoxy system degradation.
3.2 The regression task
The essence of the regression task is finding of function
(t) which fits to measured vales mostly. The regression
task concludes to finding of the minimum of optimizing
function. The optimizing function is obviously defined as a
summa of squares of differences taken from measured
values and values of the optimizing function. The minimum of optimizing function is looked for 4 variables: Apre-exponential factor, E-activation energy of degradation
reaction, n,m – parameters of the velocity function.
3.3 Diffusion process
The kinetic equations are obviously used for homogeneous reaction description which go through all bulk of
reacting site and are independent of diffusion processes.
The degradation process contrary runs on the specific defined surfaces and is slowed by transporting processes. In
the three-steps model given a diffusion processes are calculated and some simplifying presumptions are used.
Diffusion processes are described by Fick laws.
4 Kinetic model of thermal decomposition
On the beginning the one-step model of decomposition
was solved as a regression task with searching of parameters of the equation.
The measured values
of extent of reaction were numerically smoothed with
using of regress polynomials of order 3. For this intention
the measured values of TGA were divided into several
periods and each period was smoothed by regression poly-
nomial yi = ati2 + bti + c, where (ti, yi) is smoothed value yi
at the time ti. As a extent of conversion value was taken
value mi/M, where mi is actual mass of the sample at the
time ti and M in initial mass of the sample. For numerical
calculations was the equation set up to make numerical
calculation easier:
ted parameters for each part are shown in the figure1. 


TheDegree
process
of degradation
wasfrom
divided
into adecomposition
sequenceof
Graph1
of conversion
and temperature curve
thermal oxidative
epoxy
resin
of parts according to the shape of the conversion curve. The
The process of degradation
was divided
a sequence
according to theThe
shape of
the
regression
was done
in theintoeach
partof parts
degradation.
calconversion curve. The regression was done in the each part degradation. The calculated
culated
for each
part are shown in the figure1.
parametersparameters
for each part are shown
in the figure1.
Temperature reach 0C A(1010 s-1) E activation energy (105J.mol-1)
n
m
268 – 325
4,20
1,35
5,48 0,50
325 – 347
2,66
1,35
3,59 0,61
347 – 379
2,68
1,35
10
0,87
379 – 409
2,68
1,50
7,91 0,20
409-553
5,90
2,17
0
-3,65
553
5,81
2,21
0
-1
553-502
5,9
2,17
-0,14 -3,26
Figure1 Kinetic parameters for a sequence of temperature intervals 

Figure 1 - Kinetic parameters for a sequence
From the figure1 we can conclude that the model can distinguish at least two different
of temperature intervals
processes, the first one with the activation energy 135 kJ.mol-1 in the reach of temperatures
268 – 400 0C and the second one with activation energy 217 kJ.mol-1 above the temperature
0
0
400
C. From
calculated values
of theconclude
parameters n,m
at the
temperature
we can
From
thethefigure1
we can
that
the
model553
canC distin-
The optimizing function then gives the shape:
Where the summation goes through the selected time interval, yi are values of smoothing polynomial at the time ti and
are values of derived smoothing polynomial at the time ti.
The function S is now taken as a function of 4 variables
S=S(A,E,n,m) and its minimum is searched. The necessary
condition for the minimum is zero value of partial derivatives
of S function after checked parameters:
guish at least two different processes, the first one with the
activation energy 135 kJ.mol-1 in the reach of temperatures 268
– 400 0C and the second one with activation energy 217 kJ.
mol-1 above the temperature 400 0C. From the calculated
values of the parameters n,m at the temperature 553 0C we can
conclude that that process is ruled by the diffusion, thus
f( ) = -1. This function is obviously referred as a velocity
function for the diffusively ruled process4.
5 Three-steps process model
5.1 Model schema
The weak point of kinetic model is that that doesn’t operate with diffusion processes. The following text is an
attempt to establish a quantitative kinetic process model,
The numerical calculation was done by iteration method
which would include diffusion. The model is represented
where the approximation of the next step was taken the relatiby a plastic plate of composite carbon fiber reinforced
on:
material. The matrix is a kind of epoxy resin. The plate is
put at the grind in the reacting chamber and the reacting
chamber is slowly heated. Inside the chamber is very
slowly motion of the hot gas. The concentration of the oxyThe numerical calculation was done by iteration method where the approximation of the next
gen is approximately equal to the normal oxygen concentstep was taken the relation:
S ( x n )
ration. The temperature of the plate is balanced with the
x n Where
1  xn 
S (, x n )are values of optimizing function derived after temperature inside the chamber. The characterizing shape
checked parameter.
of the plate is the thickness. The exhausted gases go out
Where S  , S  are values of optimizing function derived after checked parameter.
from
the
plate.
the thermal
is
conclude
that that
processThe
is ruledrun
by theof
diffusion,
thus f(-1.decomposition
This function is obviously
referred as a velocity function for the diffusively ruled process4.
described by 3 following processes.
5 Three-steps process model
5.2
Process I – quick pyrolytic decomposition
5.1 Model schema
The
weak point of
kinetic model is that
that doesn’tgoes
operatesimultaneously
with diffusion processes.in
Thethe
Thermal
degradation
reaction
following text is an attempt to establish a quantitative kinetic process model, which would
all
bulk
of
the
plate.
The
combusted
gases
go
out
through
include diffusion. The model is represented by a plastic plate of composite carbon fiber
reinforced material. The matrix is a kind of epoxy resin. The plate is put at the grind in the
the
surface of the plate and block the acting of oxidative
reacting chamber and the reacting chamber is slowly heated. Inside the chamber is very
slowly motion of the
hot gas.
The concentration
of the oxygen
approximately
to the
atmosphere.
This
process
is finished
by iscreating
ofequal
porous
normal oxygen concentration. The temperature of the plate is balanced
0 with the temperature
structure
at the
temperature
around
C and
the plate
inside the chamber.
The characterizing
shape of
the plate is410
the thickness.
The exhausted
gases go out from the plate. The run of the thermal decomposition is described by 3 following
looses
around
25%
of
the
initial
mass.
The
carbon
fibers
processes.
are not revealed during this process, they are surrounded
5.2 Process I – quick pyrolytic decomposition
degradation
reaction
goesthe
simultaneously
the all bulk of the plate. The
combusted
byThermal
a porous
char
with
rests ofinhigh-molecular
hydrocargases go out through the surface of the plate and block the acting of oxidative atmosphere.
0
bon
compounds.
The
regression
for around
this 410
process
C and
This stable
process is finished
by creating of
porous
structure at the task
temperature

the plate looses around 25% of the initial mass. The carbon fibers are not revealed during this
was
solved
for
temperature
reach
until
the
temperature


process, they are surrounded by a porous char with the rests of high-molecular hydrocarbon
Graph1 Degree of conversion and temperature curve from thermal oxidative decomposition
of 0compounds.
stable
The regression
task for this process
solved at
for temperature
reach until
410
C. Calculated
parameters
are was
shown
the Figure2
0
Graph 1 - Degree of conversion and temperature curve
epoxy resin
the temperature 410 C. Calculated parameters are shown at the Figure2
from thermal oxidative decomposition of epoxy resin
The process of degradation was divided into a sequence of parts according to the shape of the
reach
conversion curve. The regression was done in the each part degradation. The calculated Temperature
0
C
The process
of are
degradation
was divided into a sequence of
parameters
for each part
shown in the figure1.
parts according to the shape of the conversion curve. The
0
10 -1 each part degradation.
-1 calcularegression reach
was done
in the
The
Temperature
C A(10
s ) E activation energy (105J.mol
)
n
m
268 – 325
325 – 347
347 – 379
379 – 409
4,20
2,66
2,68
2,68
1,35
1,35
1,35
1,50
5,48
3,59
10
7,91
0,50
0,61
0,87
0,20
A(1010 s-1)
E activation energy (105J.mol-1)
268 - 409
2,0
1,25
Figure2 Kinetic parameters of Process I
n
m
1,6
0
Figure 2 - Kinetic parameters of Process I
5.3 Process II – Oxidative decomposition with diffusion
The motion of exhausted gases then doesn’t block the diffusion motion into the plate. The
porous char core is oxidized and the carbon fibers are being revealed. The porous char core is
oxidized on the plane boundary that matches with the plate surface. The plane boundary of
oxidizing is being moved inside the plate and a layer of revealed fibers is growing. The
growing thickness of the revealed fibers increases the diffusion resistance and decreases the
37
5.3 Process II – Oxidative decomposition with
diffusion
The motion of exhausted gases then doesn’t block the
diffusion motion into the plate. The porous char core is
oxidized and the carbon fibers are being revealed. The
porous char core is oxidized on the plane boundary that
matches with the plate surface. The plane boundary of oxidizing is being moved inside the plate and a layer of revealed fibers is growing. The growing thickness of the revealed fibers increases the diffusion resistance and decreases
the velocity of oxidizing. The important simplifying presumption is that the layer of porous carbon char and fibers
have a sharp boundary. The micro-porous layer creates a
kind of solid core of the plate and the thickness of the solid
plate is decreasing. The process is started about temperatures around 410 0C. The plate looses approximately 21% of
its initial mass. The simplifying schema of the process II is
shown on the Picture2. In the region out of the plate is a
slowly motion of the hot air. The left boundary is meant to
be impermeable. The boundary of the plate is surrounded
by the thin diffusion air layer where the mass transport
runs. The diffusion layer of revealed carbon fibers follows.
The oxidizing process goes on the boundary between the
carbon fiber layer and micro porous char core. Following
those presumptions we can formulate equations describing
the surface oxidation and diffusion.
1/2011
cA is molar concentration of oxygen, De is an effective
diffusivity coefficient of oxygen in the air and porous layer
of revealed carbon fibers, variable r is a distance from the
left boundary of the plate and variable t is a time. The
equation (1) is solved in quasi-steady-state, where
is equal to zero and the reacting surface is in the distance
rC from the left boundary of the plate. Then the equation
(1) goes to equation (2)
(2)
where r goes from rC to R, R is the thickness of the plate.
The solution of equation (2) must fill those boundary conditions:
(3)
On the surface of the char core runs the reaction:
A(g) + b.B(s) - > products
This expresses the value of mass flux of oxygen from the
region into the plate surface, where the coefficient kAg is
mass transfer coefficient, cAg is concentration of oxygen in
the region of the reacting chamber and cAs is concentration
of oxygen on the surface of the plate.
where A is gas reacting component, B is reacting solid
phase.
The field of oxygen concentration is described by equatiA(g) + b.B(s) -> products
on:
(4)
rA  k AC c AC  A  e  E / RmT  c AC
where A is gas reacting component, B is reacting solid phase.
The field of oxygen concentration is described by equation:
De
 2 c A c A

r 2
t
(1)
(1)
This expresses the value of mass flux of oxygen into the
solid reacting core, where the coefficient kAC is velocity
constant of surface reaction and cAC is a concentration of
oxygen on the char core surface.
Simultaneously must be filled that the flux of the oxygen
is continuous, including the phase boundaries:
Picture2 Schema of Process II
Picture 2 - Schema of Process II
cA is molar concentration of oxygen, De is an effective diffusivity coefficient of oxygen in the
air and porous layer of revealed carbon fibers, variable r is a distance from the left boundary
of the plate and variable t is a time. The equation (1) is solved in quasi-steady-state, where
c A
is equal to zero and the reacting surface is in the distance rC from the left boundary of
t
(5)
From the equation (5) can be expressed the unknown
variable cAs on the plate surface:
(9)
(6)
that expresses the moving of reacting boundary plane rC
with using of extent of the reaction , can the whole equation be expressed as
(10)
After integration of equation (3) the variable cAs can be
substituted from equation (6) and put into integration form
of (3) and then can be expressed the variable cAC on the
reacting core surface.
(5)
This equation involves the material’s constants and the
shape parameter R, the thickness of the plate. The equation
was solved numerically. The temperature dependence of
material constants was respected.
For diffusion coefficient value of oxygen in the air was
used the relation:
(11)
With using of equation (5) can be expressed the reaction
rate of the surface reaction with acting of variables cAC and
constant of reaction rate on the core surface kAC.
[mol.m-2.s-1]
(6)
The velocity of mass decrement of solid phase B, char
solid core, can be expressed with using of extent of reaction ,
[mol.m-2.s-1]
[m2.s-1]
(12)
(7)
where is a molar density of char solid core and R is a
thickness of the plate.
With respect to relation between rA a rB
Where DAB is a molecular diffusivity, kB is Boltzmann
constant, NA is Avogadro number, MA and MB are molecule
masses of Oxygen and Nitrogen, T is a absolute temperature in Kelvin and dA and dB are efficient diameters of oxygen and nitrogen molecule. Because the gas diffusion goes
through the region of thin carbon fibers, the efficient
diffusion coefficient was approximated by this equation5:
(8)
Where is a porosity of material environment and
is
a particle tortuosity, which is a kind of structural factor
that relates to the ratio of real and ideal trajectory of molecules given by the porous structure. Particle tortuosity has
a value 1,0 – 100. For the ideal cylinder is assumed the
accurate value of as 1. The influence of Knudsen diffusion was neglected, as the real dimension of pores is of order
but Knudsen diffusion is counted in dimensions of
order 10 nm. For the numerical calculation those numbers
were approximated:
=0,35 and
=1,4. The temperature dependence of molar concentration of oxygen cA was
derived from the gas state equation:
where b is a molar coefficient, and with application of
relation
[mol.s-3]
(12)
There was assumed that the parameters R, thickness of the plate, De , diffusivity and c Ag ,
concentration of oxygen can be used with better accuracy than the parameters b and
 B , that are in the connection with molar compounding of oxidized solid phase. Value of
39
The velocity constant of the surface reaction was supposed as the Arrhenius equation:
[m-1s-1]
(14)
L ewhere
tec
ý zwith
pr
a vrelationship
o d a j to the
1/2011
k As was approximated after Figure1,
thekvalue
most
temperature 410 0C was taken. (At this temperature the Process II starts and the diffusion
resistance is not efficient).
cal
simulation of equation 15 was done respecting that this
The results of the simulation of parameter’s influences are shown in Figure3. The values of
 B /b, graphical
which include
parameters were
taken according
to the
valuessample
except the parameter
process
includes
21 %
ofreal
total
mass. The
the unknown molar density and stoichiometric number b. Thus, this factor was used to filling
simulation was usedalso
for searching the acceptable trend

the simulation
condition
(15)review
a graphical
simulation
of equation
 t dt =1.
of
the curve.
The
ofSimultaneously
parameters
gained
by this
gra15
was
done
respecting
that
this
process
includes
21
%
of
total
sample
mass.
The
graphical
phical
simulation
is
pictured
in
the
figure
3.
simulation was used also for searching the acceptable trend of the curve. The review of
parameters gained by this graphical simulation is pictured in the figure 3.
R
(mm)
In the equation (10) are used parameters that can be
counted only with the limited accuracy. There are next
limited occurrences. Parameter R is defined as a half of
plate thickness. (A half thickness of plate convention is
from symmetry reason). Though the thickness of the plate
is changing during the process and the volume of the gapes
is increasing. Then the conditions for diffusion are changing too. The value of coefficient kAg can be calculated
very difficulty and not accurately and the value of surface
velocity constant kA is unknown. The molar density of
can be estimated also very roughly. For first approximation
can be assumed that the char material is a carbon with a
specific ratio of high-molecular hydrocarbons. The equation (10) cannot be filled with accurate constants and parameters, but it is an expression of trend that can be fitted to
simulate the process of decomposition. Then the simulation with different parameters can conclude to the creation
of semi-empiric model.
A(108m.min-1)
E
(105Jmol-1)
kAg
(m.min-1)
4
2,0
1,44
0,014
Figure3 Review of simulation results


 B /b(mol.m-3)
0,35
1,4
1600

1

dt
t
Figure 3 - Review of simulation results
5.4 Process III – oxidizing decomposition without diffusion
5.4 Process III – oxidizing decomposition without
diffusion
In this process the porous layer of char is oxidized and
only the reaction on the surface of the fibers goes. This
process on the fibers surface goes more slowly than diffusion of oxygen, thus the diffusion isn’t assumed and the
process is ruled by the kinetic of oxidation only. The process goes partially simultaneously with process II. The
extent of this process is increasing proportionally to the
extent of process II. When the process II is finished then
the process III goes only. The oxidizing of carbon fibers
goes according the equation C + O2 = CO2 on the fibers
surface.
The simply kinetic equation for this process is proposed:
Simulation
The base for simulation is the equation (15). This equation was integrated for different values of parameters. Only
those parameters can be acceptable that give a value of the
integral equal to 1. This condition says that extent of the
reaction described is 1. The integration root was between
temperatures T1=410 0C and T2=550 0C regarding the integrating variable time t.
(15)
This
equation
expresses
assumption
theonvelocity
In this
process
the porous
layer of char the
is oxidized
and only thethat
reaction
the surface of the
fibers goes. This process on the fibers surface goes more slowly than diffusion of oxygen,
of
the
surface
reaction
is
slowing
proportionally
to the
thus the diffusion isn’t assumed and the process is ruled by the kinetic of oxidation only. The
process goes
simultaneously
withthe
process
II. The extent of of
this oxygen
process is increasing
extent
of partially
the reaction
while
concentration
is
proportionally to the extent of process II. When the process II is finished then the process III
constant.
For
searching
of
parameters
of
the
kinetic
equagoes only. The oxidizing of carbon fibers goes according the equation C + O2 = CO2 on the
fibers surface.
tion
an extra experiment with pure virgin carbon fibers was
The simply kinetic equation for this process is proposed:
run and parameters from regression task were calculated.
/R T
The
decomposition
of the virgin carbon fiber is
 tcurve
 Ae  Eof
(1 ) 
This equation
the assumption
the velocity
of thethe
surface
reaction
slowing
shown
on expresses
the Picture
3. Asthatcan
be seen,
trend
ofis the
proportionally to the extent of the reaction while the concentration
of oxygen is constant. For
0
curve
changes
at
the
temperature
550
C.
The
regression
searching of parameters of the kinetic equation an extra experiment with pure virgin carbon
fibers was
and parameters
regressionoftask
were calculated. The
curve
of
task
wasrunsolved
for 2from
intervals
temperatures.
The
results
decomposition of the virgin carbon fiber is shown on the Picture3. As can be seen, the trend
0
of
the
regression
shown550
onC.the
TheFigure
regression4.
task was solved for 2 intervals
of the
curve
changes at theare
temperature
m
of temperatures. The results of the regression are shown on the Figure4.
There was assumed that the parameters R, thickness of
the plate, De , diffusivity and cAg, concentration of oxygen
can be used with better accuracy than the parameters b and
, that are in the connection with molar compounding of
oxidized solid phase. Value of kAS was approximated after
Figure1, where the value with most relationship to the temperature 410 0C was taken. (At this temperature the Process
II starts and the diffusion resistance is not efficient).
The results of the simulation of parameter’s influences
are shown in Figure3. The values of parameters were taken
according to the real values except the parameter
/b,
which include the unknown molar density and stoichiometric number b. Thus, this factor was used to filling the simulation condition (15)
=1. Simultaneously a graphi-
Temperature reach 0C A(1010 m.min-1) E activation energy (105J.mol-1)
140 – 552
Regression impossible
552
5,8
2,15
Figure4 Kinetic parameters for thermal decomposition of virgin carbon fiber
Figure 4 - Kinetic parameters for thermal
6. Analysis of the
results
decomposition
of virgin carbon fiber
From the Table1 is evident that the processes with activation energy around 140 kJ.mol-1 go
0
until the temperature 410 C. That is the reason that the following regression task was
recalculated for this particular temperature interval. The values of parameters are summarized
in the Figure2. The values of parameters n and m are then at expected levels.
6 Analysis
ofII the
results
The process
was modeled
with kinetic reaction and diffusion. The model was tested
b were taken
with
real values
well known
parameters with
From
theofTable1
is parameters.
evident The
thatunknown
the processes
B and acti-
-1 as a tuning parameters of the model
/ b which
was used
as a semi-empiric
vation
energyparameter
around B140
kJ.mol
go until the temperature
during 0the simulation. The appropriate option of this semi-empiric parameter results to a
410
C.
That
is
the
reason
that
the
following
regression
model that has an acceptable behavior during the simulation.
The simulation
result of the
model was
is shown
on the Figure3. During
the simulation
weretemperature
varied these parameters
that
task
recalculated
for this
particular
intercannot be expressed accurately: efficient diffusivity, which includes the next parameters and
val.
valuesof of
are summarized
inand
the
andThe
the thickness
the parameters
plate R, which changes
during the process
theFigure
mass transfer
coefficient
kAg.
2.
The values
of parameters n and m are then at expected
For the process III was proposed a kinetic model without diffusion. The proposed
levels.
kinetic equation was compared with real values from the decomposition of virgin carbon
fiber.
The process
curve of the II
decomposition
of virgin carbon
gives a reaction
remarkable break
The
was modeled
with fiber
kinetic
andat the
temperature 550 0C. The most acceptable explanation is in an influence of fiber sizing and the
diffusion.
The
model
was
tested
with
real
values
of
well
process of destruction of sizing or there is a kind of surface structure that has a better
durability against the destruction. As a real kinetic parameters were taken these which rule the
process at the temperature 550 0C.
7. Conclusion
During the thermal analysis of the process was used a method of non-linear regression. This
C z e c h A e r o s pa c e P r o c e e d i n g s known parameters. The unknown parameters
and b were
taken as a semi-empiric parameter
/ b which was used
as a tuning parameters of the model during the simulation.
The appropriate option of this semi-empiric parameter
results to a model that has an acceptable behavior during
the simulation. The simulation result of the model is shown
on the Figure 3. During the simulation were varied these
parameters that cannot be expressed accurately: efficient
diffusivity, which includes the next parameters and and
the thickness of the plate R, which changes during the process and the mass transfer coefficient kAg.
For the process III was proposed a kinetic model without
diffusion. The proposed kinetic equation was compared
with real values from the decomposition of virgin carbon
fiber. The curve of the decomposition of virgin carbon
fiber gives a remarkable break at the temperature 550 0C.
The most acceptable explanation is in an influence of fiber
sizing and the process of destruction of sizing or there is a
kind of surface structure that has a better durability against
the destruction. As a real kinetic parameters were taken
these which rule the process at the temperature 550 0C.
7. Conclusion
During the thermal analysis of the process was used a
method of non-linear regression. This method can gain all
parameters of kinetic equations. The proposal of the process was created involving a part of quick pyrolysis with
40
activation energy about 135 kJ.mol-1 which runs until temperature 410 0C. Then the next part of the process follows
involving diffusion and oxidation of porous char solid
phase with activation energy 144 kJ.mol-1. The reaction
rate of oxidation is comparable with the velocity of
diffusion. This process runs at temperatures 410 – 550 0C.
The third process has the activation energy around 215
kJ.mol-1. The reaction rate of oxidation is lower than
diffusion of oxygen into the region of revealed carbon
fibers. The TGA curve of degradation of virgin carbon
fiber has a break in the velocity of oxidation. According to
this observation there is a reason to assume that the activation energy decreases after some time of temperature exposition.
References
[1] Slovák, V.: Thermochimika Acta 372(2001), pp.175-182
[2] Paterson-Jones, J.C.: J Appl. Polym. Sci. 1975, 19: pp.1539-47
[3] Puglia, D.; Manfredi, L.B.; Vazquez, A.; Kenny, J.M.: Polymer
Degrad. and Stab. 73 (2001), pp.521-527
[4] Pielichowski, K.; Njuguna, J.: Thermal Degradation of Polymeric
Materials; Rapra Technology 2005, pp.38 - 40
[5] Missen, R.W.; Mims, C.A.; Saville, B.A.: Introduction to Chemical
Reaction Engineering and Kinetics; John Wiley & Sons, Inc.,1999 ,
University of Toronto, pp. 200 - 201
Analysis of options for calibration of micro
accelerometer MAC
Analýza možností kalibrace mikroakcelerometru MAC
RNDr. Vojtěch Zadražil / VZLÚ, Plc., Prague
The options for calibration of a MAC micro accelerometer instrument has been analysed from the point of view of
the level of assembly of the instrument. The following levels of assembly of the instrument had been considered at
a component level, board level, and the level of a fully assembled instrument. Additionally, all necessary miscellaneous characterization and calibration procedures have been also considered. The component level characterization and calibration covers essential adjusting capacitor trims, key fixed capacitors, analogue to digital converters,
and the proof mass. The board level characterization and calibration covers position of detection boards, translational/rotational actuators, science data measuring boards, house-keeping data measuring, and auxiliary signals
generating board. The level of fully assembled instrument covers the alignment characterization, the thermal vacuum chamber characterization, calibration of the temperature sensors, and of the science data acquisition channels.
The miscellaneous characterization and calibration procedures cover control electrodes, wall stops, prisms, and the
dynamic transfer function of the entire control loop of the instrument.
Byly analyzovány možnosti kalibrace přístroje mikroakcelerometru MAC z hlediska úrovně sestavení přístroje.
Byly zvažovány následující úrovně sestavení přístroje: úroveň komponent, úroveň desek plošných spojů a úroveň
úplně sestaveného přístroje. Navíc byly též zvažovány všechny nezbytné rozmanité charakterizace a kalibrace.
Charakterizace a kalibrace na úrovni komponent pokrývá nezbytné seřizovací kondenzátorové trimry, klíčové
pevné kondenzátory, analogově digitální konvertory a referenční těleso. Charakterizace a kalibrace na úrovni
desek plošných spojů pokrývá desky detekce polohy, desky translačních a rotačních regulátorů a měření vědeckých
dat a desku měření pomocných veličin a generátorů pomocných signálů. Úroveň úplně sestaveného přístroje
pokrývá charakterizaci geometrie čidla a charakterizaci a kalibraci teplotních čidel a akvizičních kanálů vědeckých dat v tepelně vakuové komoře. Rozmanité charakterizační a kalibrační procedury pokrývají řídící elektrody,
stěnové zarážky, hranoly a dynamickou přenosovou funkci úplné řídící smyčky přístroje.
Keywords: micro accelerometer, calibration, assembly level
41
1 Preface
This treatise pertains to the MAC04 Micro-Accelerometer space instrument built at VZLÚ for the orbital mission
to orbit the Earth at altitudes of 450 to 550 [km] in roughly circular near polar orbits. This Micro-Accelerometer
instrument has been designed to measure at the same time
both translational and rotational accelerations of small
magnitudes that can be encountered at the projected altitudes of the mission.
This Micro-Accelerometer instrument has been designed
to cover with certain margin (18 %) the measuring range of
(−1*10 −4 ;+1*10 −4 )[m / s 2 ] equal in all three linear channels of Cartesian coordinates of translational acceleration
vector and the range of (−0.0096;+0.0096)[rad / s 2 ] again
equal in all three angular channels of Cartesian coordinates
of rotational acceleration vector.
2 Introduction
The process of calibration of a unique scientific measuring instrument encompasses a procedure whereby relationship is established between the instrument output data
and the measured quantity. This relationship shall reflect
both static and dynamic characteristics of the instrument.
Regarding this particular instrument that is designed to
measure very small accelerations in comparison to the gravitational acceleration in the rest reference frame on the
surface of the Earth it is very difficult to facilitate empirical calibration of the electro mechanical part of the instrument namely that of the sensor proper, i.e., the mechanical
motion behaviour of the proof mass as it is subjected to the
electrostatic forces and the measured or emulated mechanical acceleration. For this reason the projected calibration
utilizes for this particular part of the feedback loop chain
just calculations using abstract theoretical model with just
few complementary practical measurements.
3 Principle of operation of the micro accelerometer
instrument
The principle of operation of the accelerometer instrument consists in sensing the position of cubical proof mass
relative to cubical cavity in which the proof mass is located
and in controlling the position of the cubical proof mass in
the cubical cavity in all translational as well as rotational
degrees of freedom of motion of the cubical proof mass in
all three Cartesian axes.
The cavity is only 200 micrometers wider than the cubical proof mass on each side.
The entire surface of the measuring cube (cubical proof
mass) is completely coated with metal (Chromium) so that
any two points on its surface are in galvanic (metallic, conductive) connection to each other. No electrical or mechanical connection exists between the cubical proof mass and
the cubical cavity during normal operation of the instrument except for brief periods of discharging the electrical
charge that may have accumulated on the measuring cube
due to incoming stream of particles of mainly protons and
electrons. During this discharge period of few seconds the
1/2011
feedback loops keeping the centre of the cubical proof
mass very close to the centre of the cubical cavity are switched off allowing the cubical proof mass to move freely
and eventually drift to come into mechanical and electrical
contact with wall stops. There are four wall stops at each
wall of the cubical cavity located close to the four corners
of each wall of the cubical cavity. These wall stops are 180
micrometers high protrusions of the walls of the cubical
cavity that are connected to analogue electrical ground.
Most of the remainders of the walls of the cubical cavity
are coated with metal (Chromium) in such a way that on
each wall there is a pair of electrodes. As the interaction
force between two electrodes of a plate capacitor charged
with nonzero charge is always attractive the control voltages including base polarization and additional control
polarizations for translational as well as rotational degrees
of freedom of motion are applied to each of these electrodes by means of feedback loops as to keep the cubical
proof mass as much aligned with the cubical cavity as
possible. The sensing of the translational and rotational
positions of the cubical proof mass is facilitated by means
of very stable sinusoidal (harmonic) voltage superimposed
onto each of the electrode control voltages. The alternating
harmonic electric currents passing through each of the pair
of control electrode – cubical proof mass (electrode) are
dependent on the capacitance of the electrode pair that in
turn is dependent on the distance between the electrodes of
the electrode pair. This distance is dependent on the actual
translational as well as rotational position of the cubical
proof mass. The harmonic electric currents passing through
two pairs of electrodes that are opposite to one another are
then subtracted via magnetic flux of a core of a transformer
whose two primary windings are energized by these two
currents. The secondary windings of this subtracting transformer provide harmonic voltages whose amplitudes are
proportional to the difference of the sensing currents. See
Diagram 1 below. The harmonic voltage that is the result of
the position detection is then sampled synchronously with
the excitation voltage to derive DC signal proportional to
the deviation in the corresponding detected position. Distribution unit generates the appropriate control voltages
applied to each of the four control electrodes of the cubical
cavity to keep the cubical proof mass as closely aligned
with the cubical cavity as governed by the strength of this
feedback loop in one particular dimension. Further two
distribution units (matrices) are used to close the feedback
loop in the other two dimensions.
It could be demonstrated by detailed analysis that both
the equilibrium position displacement and the corresponding additional equilibrium polarization control voltages
are directly proportional to the acting apparent translational or rotational acceleration to a very high degree.
The input signal to the proportional-derivative amplifier-controller is measured as signal that is directly proportional to position and the output signal from the first stage of
the two-stage proportional-derivative amplifier-controller
is measured as signal that is directly proportional to apparent acting acceleration.
See References [1] and [2].
C z e c h A e r o s pa c e P r o c e e d i n g s Diagram 1 - Circuit schematics of the core of the position detection board
42
43
4 Characterization and calibration of the micro
accelerometer instrument
The calibration is the process of estimation of parameters characterizing the instrument that are necessary and
sufficient to establish the relationship between the instrument measurement data output and the value of the measured physical quantity.
These parameters facilitate this relationship between the
measured quantity and the instrument measurement data
output by means of an algorithm that processes the data
output using these characterization and calibration parameters as one of its (parametric) inputs.
The characterization is either direct measurement of the
parameters, analysis of the measurements or purely theoretical analysis, if need be, if it is the only viable or plausible
way to determine the parameters.
The characterization and calibration of the micro accelerometer instrument shall cover the behaviour of the instrument over specified range of temperatures from -20[oC] to
+ 60[oC] . Additionally the characterization and calibration
shall include the static and optionally the dynamic behavior of the instrument. The dynamic behavior may optionally
cover both temporal dynamics of the analog electronics
proper and the effects of variation of temperature in time
domain as well as in 2D or 3D space domain on the analog
electronics proper.
See References [3] and [4].
5 Levels of characterization of the micro
accelerometer instrument
There are several levels of characterization of the micro
accelerometer instrument that shall be considered, namely
Component level characterization and calibration, Board
level characterization and calibration, Instrument level
characterization and calibration, and Miscellaneous characterization and calibration. These levels of characterization and calibration are treated one by one in the following
subchapters.
1/2011
the three position detection boards is just optional. The
characterization and calibration of an adjusting capacitor
trimmer consists in measuring its static characteristic that
maps the relationship between the angle of rotation of the
rotor of the trimmer and its capacitance. A well defined and
conveniently reproducible angular reference position of the
rotor shall be adopted. Preferably that of the rotor fully
screwed into the trimmer by a specified torque that is safe
to apply to the component. These data are necessary for the
complete characterization and calibration of the accelerometer instrument because these trimmers are used to emulate various fixed translational and rotational positions of
the proof mass cube of the instrument by setting them
appropriately. The change in the angular setting of the
rotor of the trimmer is related via the gathered data to the
change in the capacitance which in turn is related to the
change in the distance between the plates of the plate capacitor formed by a side of the proof mass cube and the adjacent control electrode on the inner surface of the measuring
cavity of the instrument. This relationship is calculated
from theoretical description of the system of electrodes.
The following Figure 1 depicts the relationship between
the capacitance change corresponding to angular position
change of plus one revolution and the rotor initial angular
position, i.e. the rotor angular position before the angular
position is changed by +1 revolution. This characteristic
has been measured and is plotted in the figure repeatedly
thirty times for one and the same sample of the adjusting
capacitor trimmer just to ascertain the precision and reproducibility of such measurements. The figure graphically
shows the high degree of reproducibility that can be achieved in carefully prepared and executed measurements.
Numerical analysis of the gathered data yields a value of
standard deviation calculated from the repeated 30 measurements and subsequently averaged over all 181 measuring
points of approximately 0.2 [fF] which is twice the resolution of the measuring instrument used to gather the data.
5.1 Component level characterization and
calibration
For the component level characterization and calibration
of the micro accelerometer instrument the following components are considered: adjusting capacitor trimmers, additive fixed capacitors, analogue to digital converters, and
the proof mass cube. The characterization and calibrations
of these components are treated in the following subchapters of second level one at a time.
5.1.1 Characterization and calibration of the
adjusting capacitor trimmers
There are four adjusting capacitor trimmers per each of
the three position detection boards that should be characterized and calibrated although an approach to the overall
characterization and calibration of the accelerometer
instrument may be adopted for which only one of them at
chosen fixed position has to be necessarily characterized
and calibrated. The characterization and calibration of the
remaining three adjusting capacitor trimmers per each of
Figure 1 - Capacitance change per one revolution
− ∆C (ϕ ) versus rotor initial angular position:
(1)
∆C (ϕ ) = C (ϕ + δ ) − C (ϕ ), δ = +2π [rad ] = +1[revolution], ϕ ∈< 0;9 > [revolution]
C z e c h A e r o s pa c e P r o c e e d i n g s The following Figure 2 shows the standard deviation of
capacitance change per one revolution calculated from 30
repeated measurements plotted for various rotor initial
angular positions.
44
manufacturer assuming homogeneity of the material of the
item.
5.2 Board level characterization and calibration
For the board level characterization and calibration of
the micro accelerometer instrument the following boards
are considered: the three position detection boards X, Y
and Z, the three translational and rotational actuator and
science data measuring boards X, Y, and Z, the house keeping data measuring and auxiliary signals generating
board. The characterizations and calibrations of these
boards are treated in the following subchapters of second
level one at a time.
position detection boards
Figure 2 - Standard deviation of capacitance change per
one revolution versus rotor initial angular position calculated from 30 repeated measurements of one and the
same sample of capacitor trimmer
additive fixed capacitors
The capacitances of the additive fixed capacitors to be
populated on the position detection boards shall be measured in order to able to find pairs of them that have capacitances as close to one another as possible because it is
desirable to populate the position detection boards with
these pairs of matched capacitors so that the consequent
necessary trimming is as small as possible.
analogue to digital converters
The calibration of the analogue to digital converters
essentially consists in verifying its linearity. This operation
is optional. During the operation a known voltage precisely
measured by another independent instrument is applied to
the analogue input of the converter and subsequently data
are read out of the converter. The relationship between the
data read out of the converter and the voltage read out of
the independent precise measuring instrument constitutes
the static characteristic of the converter. For good converters this relationship is practically linear with deviations
from the linearity of the order of few parts per million.
5.1.4 Characterization of the proof mass cube
The characterization of the proof mass cube consists in
establishing its mass and moment of inertia. Proper care
should be taken to account for buoyancy correction as mass
measurements are usually done at ambient conditions
including ambient atmospheric pressure while the calibration weights used to calibrate the balance have specific
density, usually 8.00 [g/cm3], generally different from the
average density of the item weighted. The moment of inertia is calculated using the established mass and known
geometry and dimensions of the item guaranteed by the
The characterization and calibration of the position
detection board consists in establishing the relationships
between the translational and rotational output voltages of
the board as the dependent variables and the four capacitances parallel to each of the four control electrodes as
independent variables. Because this relationship is practically linear to a very high degree and because, taking into
account parasitic capacitances of all elements of the circuit, it is not possible to determine the capacitance parallel to
particular control electrode absolutely so only the coefficients of partial sensitivities:
(2)
∂U T
, i ∈ {1,2,3,4}
∂Ci
and
(3)
∂U R
, i ∈ {1,2,3,4}
∂Ci
are determined. Here UT and UR represent translational and
rotational voltages respectively and C1 , C2 , C3 , C4 represent
capacitances parallel to electrodes E1 , E2 , E3 , E4 respectively.
translational and rotational actuator and science
data measuring boards
This step represents establishing the static relationships
between the translational and rotational input voltages as
two independent variables and the four output voltages on
the four control electrodes as four dependent variables and
also the static relationships between the translational and
rotational input voltages as two independent variables and
the two digital output data readings from the two analogue
to digital converters as two dependent variables.
The above mentioned acquired relationships can then be
transformed into relationships between the two digital output data readings from the two analogue to digital converters as two independent variables and the four output vol-
45
1/2011
tages on the four control electrodes as four dependent
variables. All of the above mentioned relationships are
usually practically linear to a very high degree.
and the science channels. These two distinct data acquisition channel categories are treated in the following subchapters of third level one at a time.
Additionally the characterization and calibration of the
translational and rotational actuator and science data measuring board also entails establishing the time delays of
propagation of low frequency signals through the anti aliasing filters that are part of the board structure.
5.3.2.1 Characterization and calibration of the
temperature sensors
housekeeping data measuring and auxiliary signals
generating board
This characterization and calibration represents establishing the relationships between the auxiliary quantities
(namely three linear positions detected by the position
detection boards X, Y, and Z, three angular positions detected by the position detection boards X, Y, and Z, two temperatures at two temperature sensors per each of the three
position detection boards X, Y, and Z, one temperature at
one temperature sensor per each of the following six
boards: power source board, CPU board, the tested housekeeping data measuring and auxiliary signals generating
board itself, and the translational and rotational actuator
and science data measuring boards X, Y, and Z and ten
auxiliary voltages) versus the corresponding reading from
the analogue to digital converter. The aim of this characterization and calibration is also to measure and set the
proper phase relationship between the detected 230400
[Hz] sine wave signal and the detecting rectangular signal
of the same frequency of duty cycle ratio 1:1.
5.3 Instrument level characterization and
calibration
For the instrument level characterization and calibration
of the micro accelerometer instrument the following tests
of the completely assembled micro accelerometer instrument are considered: the Alignment test, and the Thermal
vacuum chamber test. These tests are treated in the
following subchapters of second level one at a time.
5.3.1 Alignment characterization
The aim of the alignment characterization is to establish
the angular relationship between the direction of normals
to the specified surfaces of the optical reference alignment
cube and the principal directions of the instrument defined
by the normals to the internal surfaces of the measuring
cavity expressed as transformation matrix. Additionally the
radius vector of the centre of the measuring cavity relative
to the mechanical reference frame is established during
this characterization.
5.3.2 Thermal vacuum chamber characterization
and calibration
For the thermal vacuum chamber characterization and
calibration of the micro accelerometer instrument the
following two distinct data acquisition channel categories
of the completely assembled micro accelerometer instrument are separately considered: the temperature sensors,
This characterization and calibration establishes the
relationship between two temperatures at two temperature
sensors per each of the three position detection boards X,
Y, and Z as independent variables versus the corresponding
readings from the analogue to digital converter as the
dependent variables using etalon measurement of temperatures. This measurement is complimentary to that carried
out during tests described in subchapter 5.2.3. The actual
calibration procedure implements a sophisticated method
of accounting for and eliminating the effects of the dissipation of the electronics of the micro accelerometer instrument itself.
5.3.2.2 Characterization and calibration of the
science channels
This characterization and calibration represents establishing the relationships between the science quantities
(namely three translational accelerations X, Y, and Z, and
three rotational accelerations X, Y, and Z) versus the readings from the corresponding analogue to digital converters
including temperature effects in these relationships. These
temperature effects can be classified into two categories:
short-term effects and long-term effects.
5.4 Miscellaneous characterization and calibration
This chapter covers the characterization and calibration
of the following topics: control electrodes, wall stops,
cavity forming prisms, and analytical characterization of
the dynamic transfer function of the entire control loop.
These topics are treated in the following subchapters of
second level one at a time.
5.4.1 Characterization of the control electrodes
The characterization of the control electrodes entails
establishing the size of the area of the electrode and the
position within the plane of the electrode of its two-dimensional centre.
5.4.2 Characterization of the wall stops
The characterization of the wall stops entails establishing their heights to which they protrude above the
corresponding surface of the prism comprising the measuring cavity. This height must conform to stringent limits
imposed on them.
5.4.3 Characterization of the prisms comprising the
measuring cavity
The characterization of the prisms comprising the measuring cavity entails establishing the measure of flatness of
the working surfaces thereof.
5.4.4 Analytical characterization of the dynamic
transfer function
This characterization entails the calculation of the dynamic transfer function of the entire control loop beginning
at the analogue input signals of accelerations, continuing
via the proof mass cube translational and rotational mechanics, via the position detection board (input circuits, preamplifiers, and amplifiers, synchronous detectors, output
circuits), via the PD (Proportional Derivative) regulator
first stage amplifier, then continuing in the loop to the PD
regulator second stage amplifier, via the distribution unit
closing the control loop at the control electrodes back at
the proof mass cube, and also including the branch outside
the control loop at the PD regulator first stage amplifier
output to the anti aliasing filter and ending at the analogue
to digital converter that performs the actual measurements
and delivers the digital output signal measuring the science data.
Denoting the input signal x(t) and the output signal y(t)
we have the following definition of the transfer function
T(s) of a linear time invariant system of single input and
single output.
The transfer function T(s):
T (s) =
(4)
L{ y (t )}( s )
, s = σ + iω , σ ∈ R, ω ∈ R, R = {Set _ of _ all _ real _ numbers}
L{x(t )}( s )
6 Conclusion
The options for calibration of the micro accelerometer
instrument MAC have been analyzed with the emphasis on
the level of assembly of the instrument. The structure of
the calibration options on each assembly level has been
elaborated detailing significant calibration steps that may
be applied for actual calibration process. In addition to
calibration procedures carried out in previous projects this
work specifies methods that extend the repertoire of applicable methods and are completely new. See subchapters
5.1.1, 5.1.3, 5.2.1, 5.3.1, 5.3.2.1, and 5.4.4. So far these
methods have not been used either for their exacting
demands on instrumentation, experimental laboratory setup
and the actual execution of the process of calibration or
because they have not been previously even considered.
These new methods enhance the possibilities of the calibration of the instrument to previously unforeseen levels.
The application of these new methods may result in substantial improvements of precision and reliability of calibration parameters derived from the calibration data gathered during the calibration measurements. This results in
overall improvement and enhancement of the calibration
process. Hence the performance of the micro accelerometer instrument MAC itself is enhanced.
References
Where the unilateral Laplace transform L(s) is defined
by the following formula:
(5)
∞
L{ f (t )}( s ) = ∫ f (t ). exp(− s.t ).dt
[2] Chvojka, M.: ACC Instrument Technical Description, Issue 2.0;
VZLU, Prague, February 9, 2010
[3] Zadrazil, V.: ACC Characterization and Calibration Test Procedure,
Issue 1.3; VZLU, Prague, April 2, 2010
0
[1] Chvojka, M.: ACC Performance analysis, Issue 2.7; VZLU, Prague,
April 2, 2010
(6)
[4] Zadrazil, V.; Vondrak, M.: Alignment Test Procedure, Issue 1.1;
VZLU, Prague, March 25, 2010
This is usually denoted as F ( s ) = L{ f (t )}( s )
47
1/2011
Worst Case Analysis Methods Implementation
in an Accelerometer Measuring Loop Analysis
Aplikace postupů Analýzy nejhoršího případu (WCA) při analýze
měřicí smyčky akcelerometru
Jozef Zakucia, Milan Merkl / VZLÚ, Plc., Prague
Worst case analysis belongs to the most important in the analysis section that is performed to document space product quality assurance. It is important from the viewpoint that WCA procedures were described in the most concise way together with provision of a guide to its successful implementation linked to other analyses of product assurance documents system. The objective of the presented article is that such description is reliable in both a general and at an implementation level.
V oblasti analýz kosmického vybavení prováděných k průkazu zajištění jakosti produktu patří analýza nejhoršího
případu k nejdůležitějším. Proto je důležité, aby její postupy byly popsány způsobem co nejvýstižnějším a zároveň
poskytujícím návod pro její úspěšné provedení v návaznosti na ostatní analýzy systému dokumentů pro zajištění
produktu. Cílem prezentovaného článku je takovýto popis v rovině obecné i implementační.
Keywords: WCA, tolerance, sensitivity, RSS, MCA, accelerometer, product assurance.
1 Introduction
The purpose of the WCA analysis in general is to serve
as a tool for design centering, i.e. modifying of nominal
system design to receive optimum system parameters [1].
Particular WCA target is providing an assurance by analysis that system design complies with requirements. The
article describes WCA implementation for assessment of
accelerometer measuring loop design. General principles
of acceleration measuring with an electrostatic accelerometer system were described by Fontana in [4]. Basic
information to the problems of tolerance analysis presents
Géher in Chapter 4 of his monograph [2].
Three different methods of the tolerance effects analysis are generally named as:
• Extreme Value Analysis (EVA);
• Root-Sum-Square (RSS) Analysis;
• Monte Carlo Analysis (MCA).
The RSS Timing (and Delay) Analysis is performed side
by side with classical WCA procedure for digital electronics circuits.
Analyzing of an instrument circuits generally points to
interfaces analysis using EVA and RSS methods, and MCA
method is preferred in case of signal path analysis. In this
article we confine to WCA methods description on an
example of the signal path analysis and we compare results
received using both RSS and MCA method.
The worst case analysis works with the circuit structure,
tolerances of component characteristics, their temperature
changes and time and radiation consequence changes.
Grouping of tolerances from individual sources and detail
tabular comparison of the three different WCA methods is
presented in [5]. It is suitable for WCA to use a specialised
methodology with computer program support. It combines
processes of tolerance and sensitivity analyses to complete
the task. The methods published by Robert R. Boyd in [3]
are very useful for completing the task.
1.1 Acronyms and abbreviations
AKTRAD
ECSS
EVA
FMECA
GNRHSK
MC
MCA
POSDET
RSS
WCA
One of the three identical electronic boards of accelerometer with sensor
moving part position control as the main function
European Cooperation for Space Standardization
Extreme Value Analysis
Failure Modes Effects and Criticality Analysis
Electronic board of accelerometer with precision amplitude sinusoidal generator
and polarization voltage source (besides other functions)
Monte Carlo (method)
Monte Carlo Analysis
One of the three identical electronic boards of accelerometer with sensor
moving part position detection as the main function
Root Sum Squared, (Root Sum of the Squares)
Worst Case Analysis
1.2 Standards
Space systems design WCA is supported by standards that describe its methods with different
level of detail. Initial information to WCA could be found in Task 206 of MIL-STD-785B
standard [6] (formerly cancelled). The task is placed there to the Configuration analyses group
SpaceFMECA
systems
design
WCA
is The
supported
bythere
standards
containing
and Sneak
circuit analysis
as well.
analysis is named
as
Electronic parts/circuits tolerance analysis.
1.2 Standards
that describe its methods with different level of detail. IniThe list
of active and discontinued
ECSS Standards
the WCAin
standard
[7] as
tial
information
to WCA
could presents
be found
Task
206 of
discontinued with requirements transferred to [8] and the remaining data to [9]. The standard
MIL-STD-785B
[6] in (formerly
refers to an ECSS technicalstandard
memorandum ([10],
WG draft version cancelled).
to the date only) forThe
aging data and to [9] for the WCA methodology.
task
is placed there to the Configuration analysis group
Other relevant ECSS
standards are
placed
in Spacecircuit
Engineering
region [11],as
[12].
End-of-life
containing
FMECA
and
Sneak
analysis
well.
The
parameters important for the WCA implementation were presented in [13] that was formerly
replaced withis
derating
standards
(the actual
of which is [14])parts/circuits
without EoL parameters.
As an
analysis
named
there
as Electronic
toleranaccessible source of EoL data could be used instead a valid DoD handbook [15] that is free
ce
analysis.
available.
The detail WCA guidelines are contained in Appendix B of Jet Propulsion Laboratory
handbook
[16]. The
is to perform the
analysisStandards
before the designpreis
The list
of standard
activerecommendation
and discontinued
ECSS
frozen. The analysis should comprise all functionally important circuits of the equipment and
it shouldthe
consider
AC, DC,
and transients.
sents
WCA
standard
[7] as discontinued with require-
ments transferred to [8] and the remaining data to [9]. The
2 WCA Methodology
standard
refers to an ECSS technical memorandum ([10],
2.1
Extreme
Value
Analysis (EVA)
in WG draft version
to the date only) for aging data and to
EVA procedure [16] starts with total parametric variation calculation for every used
part:for the WCA methodology.
[9]
1+dP = (1+dX)(1+dS)(1+dT)(1+dE)(1+dR)
(1)
where
the individual
parametric
variations
(normalizedare
to 1,placed
i.e. 1%  in
0.01)
denote: EngiOther
relevant
ECSS
standards
Space
dP
total parametric variation
dX
part initial
tolerance
neering
region
[11], [12]. End-of-life parameters important
dS
aging and drift variation
for the WCA implementation were presented in [13] that
was formerly replaced with derating standards (the actual
of which is [14]) without EoL parameters. As an accessible
source of EoL data could be used instead a valid DoD
handbook [15] that is free available.
The detail WCA guidelines are contained in Appendix B
of Jet Propulsion Laboratory handbook [16]. The standard
recommendation is to perform the analysis before the
design is frozen. The analysis should comprise all functionally important circuits of the equipment and it should
consider AC, DC, and transients.
2 WCA Methodology
2.1 Extreme Value Analysis (EVA)
EVA procedure [16] starts with total parametric variation calculation for every used part:
1
1 + dpf
 1
1 + dpf
Q=
 


1
 1
1 

1 


 

 1 + dpf 
Step 6:
Perturbate consecutively each time one from part parameters / input values using counter p:
(3)
(4)
(1)
Vrp = G(c1 • Qp,1, c2 • Qp,2, ..., cN • Qp,N)
1+dP = (1+dX)(1+dS)(1+dT)(1+dE)(1+dR)
where the individual parametric variations (normalized to
) denote:
dP
total parametric variation
dX
part initial tolerance
dS
aging and drift variation
dT
temperature influence variation (in worst case
direction)
dE
variation due to applied voltage
dR
variation due to radiation degradation
After the cycling of p = 1.. N receive the vector:
Vr = [Vr1 , Vr2 , ..., VrN]
Step 7:
EVA procedure in steps:
(details see in R. R. Boyd: Tolerance Analysis of
Electronic Circuits [3], the procedure is modified here)
Step 1:
Specify nominal input values and nominal part parameters.
Step 2:
Specify nominal output value as function G(c1, c2, ..., cN)
of nominal input values and nominal part parameters. N
free variables in total.
Step 3:
Assign the function to output variable Vo.
Step 5:
Set up
Q = dpf I + 1,
where:
I is unit (diagonal) matrix;
dpf is directional perturbation factor;
Q is perturbation matrix with dimension N x N.
(2)
(6)
 Vrp  1
Sen p = 
− 1
 Vo
 dpf
and set up the vector:
(7)
Sen = [Sen1, Sen2, ..., SenN].
Step 8:
Assign tolerances to part parameters using data sheets
and create the tolerance array T with the dimension 2 x N:
Step 4:
Create p = 1..N as counter of input values and part parameters.
(5)
 −Tr
T = 1
 Tr1
(8)
−Tr2  −TrN 
Tr2  TrN 
Step 9:
Create the new tolerance array M with tolerances
swapped in the columns which parameter sensitivity values
are negative:
(9)
1 − sgn( Sen1 ) ⋅ Tr1 1 − sgn( Sen2 ) ⋅ Tr2  1 − sgn( SenN ) ⋅ TrN 
M =

1 + sgn( Sen1 ) ⋅ Tr1 1 + sgn( Sen2 ) ⋅ Tr2  1 + sgn( SenN ) ⋅ TrN 
49
Step 10:
1/2011
Standard deviation of the R1 resistor for normal (Gaussian)
distribution and tolerance T1 of the resistor is:
(10)
Receive:
Vevk = G(c1 • Mk,1, c2 • Mk,2, ..., cN • Mk,N) for extreme values
using row index k = 1, 2
(11)
σR =
1
(14)
R1 ⋅ T1
3
Let us denote:
The column vector with dimension 2 x 1:
(15)
∆Vrs = 3σ Vo
Vev 
Vev =  1 
Vev2 
Then we can derive (see [3]) next general equation that
will be refined in the next steps:
is the result of extreme value analysis (EVA)
and the relation:
(16)
(12)
∆Vrs = Vo ⋅
Vev − Vo 
∆Vev = Vev − Vo =  1

Vev2 − Vo 
N
∑ ( Sen
p =1
p
⋅ Tp )
2
RSS procedure in steps:
Step 11a:
For symmetric tolerances and row index k (=1, 2) compute (for Senp values use steps 1 to 7 of the EVA part of the
procedure or determine the sensitivities analytically):
is valid for deviations from the nominal output.
2.2 Root-Sum-Square (RSS) Analysis
For variations with random component, every variation
consists from two parts. One of them presents bias with
predictable direction, the other is the random component
contribution [16]. Biased portions are summarized to resultant bias. Random components are processed in an RSS
procedure and the result is added to resultant bias to receive the resultant output value variation. For detail description of such procedure see [5].
RSS definition: Variance (root sum squared, dispersion)
of any function is described by the relation (see [3],
Appendix: Derivation of the RSS Equation):
∆Vrssk = ( −1) ⋅ Vo ⋅
k
N
∑ ( Sen
p =1
p
⋅ Tk , p )
Step 11b:
For asymmetric tolerances and row index k:
σ 2 (Vo ) = ∑ 
2
where:
Xi ... characteristic parameter of the i-th component,
σ 2 = Var(Xi) ... variance,
σ ... standard deviation.
 −Tr
Ta =  11
 Tr12
2
 ∂Vo 
2
 ⋅σ ( X i )
i =1  ∂X i 
N
(18)
(13)
 ∂Vo 
Var (Vo ) = ∑ 
 ⋅ Var ( X i )
i =1  ∂X i 
or
N
2
Go to step 13.
(17)
−Tr21  −TrN 1 
Tr22  TrN 2 
create the new matrix swapping the tolerance row position
values at places with negative sensitivities:
( −u ⋅ Tr + v ⋅ Tr )
Ma - 1 =  1 11 1 12
( +u1 ⋅ Tr12 − v1 ⋅ Tr11 )
where:
(u
(u
p
p
( −u2 ⋅ Tr21 + v2 ⋅ Tr22 )
( +u2 ⋅ Tr22 − v2 ⋅ Tr21 )
= 1, v p = 0 ) for Sen p ≥ 0,
= 0, v p = 1) for Sen p < 0,


(19)
( −uN ⋅ TrN1 + vN ⋅ TrN 2 )
,
( +uN ⋅ TrN 2 − vN ⋅ TrN1 )
for Senp values use steps 1 to 7 of the EVA part of the procedure or determine the sensitivities analytically.
Step 12:
Receive the respective RSS deviation from the formula:
∆Vrssk = ( −1) ⋅ Vo ⋅
k
N
∑  Sen ⋅ ( Ma − 1)
p =1
p
(20)

k, p 
2
Step 13:
Create the deviation 2x1 column matrix:
(21)
 ∆Vrss1  Vrss1 − Vo 
∆Vrss = 
=
 = Vrss − Vo
 ∆Vrss2  Vrss2 − Vo 
or output limits 2x1 column matrix:
(22)
Vrss1 
Vo + ∆Vrss1 
Vrss = 
=


Vrss2 
Vo + ∆Vrss2 
The column vector with dimension 2 x 1 is the result of root
sum square (RSS) analysis.
2.3 WCA – Monte Carlo Method
One of the most realistic estimation of the worst case
performance is Monte Carlo analysis. Inputs for MCA are
probabilistic distributions of the part values variability.
And output of the MCA is probability distribution of circuit output values. The result of the MCA is commonly presented in the form of a histogram.
The commonly used probability distribution of the
circuit components parameters are:
• Uniform distribution function (the most conservative
for parameter variations).
• Gaussian distribution function (the most realistic for
parameter variations).
• In the next we will show, in step by step procedure,
how to perform MCA [3].
Step 4:
Specify N – number of samples, and generate N Gaussian (or Uniform) random numbers (with mean = 0 and standard deviation = 1) for each of the M components.
Assume that the numbers are spread between -3 and 3
(99.74% of the numbers lie in this range).
Step 5:
Consider:
upper total tolerance of the part = +up%
lower total tolerance of the part = -lo%
range = 3-(-3) = 6
Tm – tolerance multiplier
z – single random number from N
than
Tm =
( up − ( −lo ) ) 100
range
( z + 3) +
(23)
( −lo ) + 1
100
Convert the N random numbers (from step 4) to random
tolerance multipliers Tmi for each of the M components
using equation (23).
Step 6:
Create N random values of each component in its given
tolerances (by multiplying nominal value of the component
and N random tolerance multipliers).
Step 7:
Calculate N random output values for the N random
values of each component.
Step 8:
Create histogram of the output values.
3 Example solution
Accelerometer measuring loop analysis:
MCA and RSS analysis were performed on measuring
loop of the accelerometer. Simplified block scheme of the
accelerometer feedback loop, created for the WCA purposes, is shown in Figure 1.
Step 1:
Define nominal circuit component values (M components).
Step 2:
Create the circuit (transfer) function (or matrix) and calculate nominal output of this function.
Step 3:
Create an array with tolerance of each part.
Figure 1 Block scheme of accelerometer measuring loop
Input for the feedback system presented in the Figure 1 is
acceleration Γ and output is voltage UT. General formula for
acceleration was derived in the form (meanings of the symbols
51
are described below):
Γ =
(24)
C0 D  U 42
U 32 
−


m  ( D + x )2 ( D − x )2 
Next simplified formula was derived for translation
acceleration value computation from the known sensor
parameters and both internal and measured characteristic
values of accelerometer:
Γ =
(25)
4C0 
x 2 1 2
2 
 PVU T −  PV + U 0 + U T  
mD 
D
2

Substituting for x from the relation presented in explanation
of UT in Table 1 into equation (25) we receive the resultant
simplified equation:
PV
U 0
C0
ACNTR
LPS
polarization voltage between the sensor electrodes; (+11) Pv = fde (U10)
[V]
amplitude of sensing sinusoidal voltage with 230.4 kHz frequency; (1.0)
[V]
capacitance of an control electrode-cube electrode pair with cube placed in the central position;
[F]
(13.1•10-12)
AKTRAD amplifier’s gain; (8)
[-]
POSDET transfer from displacement to output
voltage; (105)
LPS = fp (Kca, Kfa, …..)
[Vm-1]
Functions fd1, fd2, fde, fp present simplified notations of the
functional relations of their arguments. Detail insight into the
system functions and equations is not introduced (it is comprised into computations) because of the limited length of this
presentation. Above mentioned description of the system suffices for our considerations in this paper.
3.1 EVA
The procedure works with the simplified formula for
acceleration (26) value.
Γ =

4C0
1
U T  PV −
mD
DACNTR LPS

(26)
 2 1 2
2 
 PV + 2 U 0 + U T  

Neglecting x2 against D2 in start of treatment of the precision formula (24) that led to receiving of formula (25) implies
acceleration value error not over 2 % of the precise value and
simplifies essentially the next computations for RSS analysis.
Formula (26) was applied for both EVA and RSS computation.
The precise formula (24) was applied for the MCA computation.
Meanings of the symbols in Equations (24) to (26) and
Figure 1 are listed in Table 1.
Table 1 Explanations of symbols used in Equations (24) to
(26)
translation component of on board non-gravitational
acceleration
[ms-2]
equilibrium translation of cube position from the central position caused by constant non-gravitational acceleration
[m]
gap between electrodes when the sensor cube is placed in the central position; (2 •10-4)
[m]
sensor electrode No. 3 control composite voltage
U3 = fd1 (UT, PV, UT, Ri) [V]
sensor electrode No. 4 control composite voltage
U4 = fd2 (UT, PV, UT, Rj) [V]
translation component of regulation voltage between the sensor electrodes
U T ( x ) = x ⋅ ACNTR ⋅ LPS
[V]
(27)
Γ = F{xi } = F{C0 , PV ,U 0 ,U T , ACNTR , LPS },
Both sensor mass m and gap distance D are supposed to be
constant, translation x, and consequently UT voltage are taken
as parameters and the EVA computation is performed for one
of the parameter possible values (x = 3.1•10-6 m, UT = 2.48 V).
Individual independent variables are functions of circuit elements, mainly of pertinent POSDET and AKTRAD circuit
boards elements.
(28)
n
dx
dF
= d (ln F ) = ∑ 1S Γ xFi i ; where xi ∈ {C0 , PV , U 0 , U T , ACNTR , LPS }
F
xi
i =1
and where we evaluate the relative differential first order
sensitivities generally according the formula:
Γ
x
D
U3
U4
UT
1/2011
S Γ xF =
1
(29)
∂ ln F ( X , P )
x
∂F ( x, p )
=
⋅
F ( x, p )
∂ ln X
∂x
without considering dependence on complex frequency p in
our case. The relative differential sensitivities were determined
both analytically in the next procedure (procedure of the hand
computation is presented below and the results are in the
fourth column of Table 2) and according the Steps 1 to 7 of
EVA procedure in 2.1 clause (results of the sensitivities computation performed in Mathematica are in the fifth column of
Table 2).
The relative acceleration tolerance expressed using relative
differential sensitivities of the determined acceleration value
to individual circuit element values:
C z e c h A e r o s pa c e P r o c e e d i n g s n
dx
∆Γ
= ∑ 1S Γ xFi i =
Γ
xi
i =1
=
52
3.2 RSS
(30)
,
dC0
+
C0
dP
dU 0
1
{( PV DACNTR LPS − 2 PV2 ) V − U 0 2
1
PV
U0


PV DACNTR LPS −  PV2 + U 0 2 + U T 2 
2



1

  dU T  2 1 2
 dA
+  PV DACNTR LPS −  PV2 + U 0 2 + 3U T 2  
+  PV + U 0 + U T 2  CNTR +
2
2

 U T 
 ACNTR

For the next acceleration RSS tolerances evaluation:
We will use the results of particular RSS symmetric tolerances evaluations (see the Table 2).
The root of sum of quadratic terms is extracted from the
Table 2 data according to an RSS template Step 11a and
Step 13:
1

 dL
+  PV2 + U 0 2 + U T 2  PS }
2

 LPS
5
We will replace dUT/UT with expression gained by differentiation the formula for UT (see Table 1):
U T = x ⋅ LPS ⋅ ACNTR
⇒
(31)
dU T dx dLPS dACNTR
=
+
+
UT
x
LPS
ACNTR
and we will receive after a sequence of simplifications and
substituting nominal parameter values from the Table 2:
∑ ( Sen ⋅ T )
i =1
i
i
2
(34)
� 3.14 ⋅10−1 [ % ] + 3.72 ⋅10−7 [ % ] + 8.57 ⋅10−7 [ % ] +
2
2
2
+ 2.37 [ % ] + 9.76 [ % ] � 12.444 [ % ] � 12.4 [ % ]
2
2
2
2
The result for relative tolerance value of Γ is:

 ∆Γ 

 = ±
 Γ  RSS

∑ ( Sen ⋅ T )
i
i
i
2
(35)

 � ± 3.53%

(32)
3.3 MCA
n
∑
i =1
S Γ xFi
1
dxi
dC
dU
dP
� 1 ⋅ 0 − 6.1 ⋅10−4 ⋅ 0 + 9.26 ⋅10−1 V +
xi
C0
U0
PV
+ (1.07 − 1.83 ⋅10−3U T 2 )
dA
dx
+ (1.07 − 1.22 ⋅10−3U T 2 ) CNTR +
x
ACNTR
+ (1.07 − 1.22 ⋅10−3U T 2 )
dLPS
dC
dU
� 1 ⋅ 0 − 6.1 ⋅10−4 ⋅ 0 +
LPS
C0
U0
+ 9.26 ⋅10−1
Ti approximate
value [%]
Relative
tolerance
symbol
C0
C0
U 0
U0
PV
PV
ACNTR
ACNTR
LPS
LPS
x
x
dPV
dA
dL
dx
+ (1.07 ) + (1.07 ) CNTR + (1.07 ) PS
PV
x
ACNTR
LPS
Source of
tolerance data /
Comment
accelerometer
performance
Seni approximate
value – see (32)
Seni approx. value
– RSS proc. in
steps (clause 2.2)
1
1
1
accelerometer
performance
-6.110-4
-6.1310-4
0.001
accelerometer
performance
9.2610-1
9.3010-1
1.44
accelerometer
detail analysis
1.07
1.07
0.56
3.2 RSS
We will proceed with Steps 8 to 12 for the next EVA comFor the next acceleration RSS tolerances evaluation:
We
will use theand
results
of particular
evaluations
(see the
Table 2).
putations
receive
in RSS
the symmetric
end thetolerances
following
relative
toleranThe root of sum of quadratic terms is extracted from the Table 2 data according to an RSS
ces forStep
the11aacceleration:
template
and Step 13:
5
2
i
i
2
1
7
2
7
2
 2.37  %  9.76  % � 12.444  % � 12.4  %
2
2
The result for relative tolerance value of  is:
 ∆2  

  
i   � 3.53%=

      Seni  T
  RSS
  EVA
 i
Γ
Γ
2
 −5.16 % 
 +5.30 % 


2
(33)
(34)
(35)
3.3 MCA
MCA was performed on measuring loop of the accelerometer. Simplified block scheme of the
accelerometer feedback loop, created for the WCA purposes, is shown in Figure 1. MCA
considers the tolerances of substantial resistors in the signal measuring path and particular
(35)
Γ = f (U T ( x ) )
accelerometer
1.07
1.07
detail analysis
we suppose x as
0
being a
0
0
parameter
We will proceed with Steps 8 to 12 for the next EVA computations and receive in the end the
followingTable
relative tolerances
for thetolerances
acceleration:
2 Relative
and corresponding
 5.16 % 
  
sensitivities
values

(33)



   EVA  5.30 % 
i 1
where
2.92
  Sen  T  � 3.14 10 %  3.72 10 %  8.57 10 % 
MCA was performed on measuring loop of the accelerometer. Simplified block scheme of the accelerometer feedback loop, created for the WCA purposes, is shown in
Figure 1. MCA considers the tolerances of substantial
resistors in the signal measuring path and particular
POSDET units.
Input for this feedback system, presented in the Figure 1
is acceleration Γ and output is voltage UT. The aim of this
analysis is to compute tolerances of the acceleration Γ .
Mentioned system is described by the function
(36)
U T ( x ) = x ⋅ ACNTR ⋅ LPS
corresponding with (24) where x (parameter) is the position of the sensor cube (see Table 1 for other details).
MCA was performed following the step by step procedure presented in clause 2.3.
The computation was realized by running MATLAB
script.
Inputs for the script were array of the accelerometer
part tolerances and function of the system stated in clause
3.
The result of this computation (for parameter x set to
e.g. 3.1 µm) is histogram of the acceleration Γ shown in
Figure 2. The 2 σ value of the final acceleration distribution stands for 4.24% tolerance of the acceleration value.
U T3 x x  ACNTR  LPS
(36)
5
corresponding with (24) where x (parameter) is the position of the sensor cube (see Table 1
for other details).
(37)
MCA was performed following the step by step procedure presented in clause 2.3.
The computation was realized by running MATLAB script.
Inputs for the script were array of theMCA
accelerometer part tolerances and function of the system
stated in clause 3.
2σ
= 4.24 %
A histogram of the acceleration Γ was created and comThe result of this computation (for parameter x set to e.g. 3.1 µm) is histogram of the
puted
forΓ shown
eachin value
a ofset
of the
parameter
(in
itsfor
acceleration
Figure 2. xThefrom
2σ value
the final
acceleration
distribution
stands
4.24% tolerance
of the acceleration
value. between voltage U T and acceworking
range).
Dependence
2
 4.24 %
(37)
leration Γ with its probabilistic distribution is presented
A histogram
acceleration
Γ was4created
and and
computed
each value x from a setreof the
in
Figureof 3theand
Figure
in 3D
2Dforrepresentation
parameter (in its working range). Dependence between voltage UT and acceleration Γ with its
spectively.
probabilistic distribution is presented in Figure 3 and Figure 4 in 3D and 2D representation
MCA
respectively.
600
-2
+2
Number of samples
500
1/2011
4 Conclusions
Comparison of used WCA methods illustrates, that EVA/
RSS methods present data with great effort even in the case
of using dedicated software. MCA method encores graphical outputs as a bonus for better presentation of the results.
For presented example of accelerometer measuring feedback loop the resulting tolerance values for the three used
methods are:
EVA {-5.16 %, +5.30 %}; RSS {-3.53 %, +3.53 %};
MCA {-4.24, +4.24 %}.
Regardless of the results differences, all the methods
give well corresponding results and their parallel using
supports assurance of the results correctness.
400
300
References
200
100
0
-1.5
-1.45
-1.4
-2
[ms ]
-1.35
-1.3
-1.25
[1]
Novák, M.: Theory of Network Tolerances. Academia Praha 1987,
(published in Czech: Teorie tolerancí soustav) 340 pp.
[2]
Géher, K., Theory of Network Tolerances. Akadémiai Kiadó,
Budapest 1971, 184 pp.
[3]
Boyd, R.R.: Tolerance analysis of electronic circuits using
MATLAB. CRC Press, 1999, 147 pp.
[4]
Fontana, G.: High Performance Electrostatic Sensors and Actuators for LISA Proof Mass Control. University of Trento, 2002,
57 pp., http://arxiv4.library.cornell.edu/ftp/physics/papers
/0111/0111006. pdf
-4
x 10
Figure 2 Histogram of acceleration PDF in 2D
Figure 2 - Histogram of acceleration PDF in 2D
[5] Worst Case Circuit Analysis (WCCA). System Reliability Center,
http://src.alionscience.com/pdf/WorstCaseCircuitAnalysis.pdf,
2004 Alion Science and Technology.
Figure 3 - Three-dimensional view of acceleration
PDF histograms for variable UT value
[6]
MIL-STD-785 Reliability program for systems and equipment
development and production
[7]
ECSS-Q-30-01A, First issue, Worst case circuit performance
analysis. 31. March 2005, Discontinued Requirements transferred
to ECSS-Q-ST-30C, remaining material to ECSS-Q-HB-30-01A
[8]
ECSS-Q-ST-30C Space product assurance – Dependability.
6 March 2009, 54 pp.
[9]
ECSS-Q-HB-30-01A (working draft)
[10] ECSS-Q-TM-30-12C (working draft)
[11] ECSS-E-ST-10-04C Space Engineering - Space Environment.
15 November 2008, 198 pp.
[12] ECSS-E-ST-10-12C (15 November 2008) Space Engineering Methods for the calculation of radiation received and its effects,
and a policy for design margins
[13] ECSS-Q-60-11A (7 September 2004) Space product assurance –
Derating and end-of-life parameter drifts – EEE components
[14] ECSS-Q-ST-30-11C Space product assurance – Derating – EEE
components. 31 July 2008, 59 pp.
[15] MIL-HDBK-1547A (06 July 1998): DoD Handbook – Electronic
Parts, Materials, and Processes for Space and Launch Vehicles;
253 pp.
[16] JPL D-5703, Reliability Analyses Handbook. NASA JPL,
Jul 1990,169 pp.
Figure 4 - Acceleration PDF for variable UT value
in 2D with colour scale of probability density
Experimental Assessment of the Fragments
Effect to the Fuselage of the Aircraft
Experimentální určení účinku střepin na drak letounu
Ing. Miroslav Lošťák, Doc. Ing. Miloslav Petrásek CSc. VUT Brno
The article is focused on the assessment of the most probable way of an attack to the civilian aircraft. The assessment of the effect of this attack and capability of the aircraft to continue flight after damage. The attack with
missile with a fragmentary warhead was assessed as the most dangerous one. The influence of this attack can be
simulated using finite element method and the validation for its functionality of this model was performed using a
suitable shooting experiment. The specimen was made as a semi-monocoque skin panel and it was impacted by the
fragments of known mass, velocity and direction of the stroke to the impacted area. The experiment proved that
single fragment causes only minor damage and has a little influence to the capability of the panel to carry loads.
Also more fragments, with proper distance between each other, damage more single parts, but they don’t cause
significant damage to the panel which can be explained as a sum of partial influences of single fragments. The
results of this experiment were used for the improvement of the numerical calculation of the damage.
Předkládaný příspěvek je zaměřen na stanovení nejpravděpodobnějšího způsobu útoku na civilní letadlo, na hodnocení jeho důsledků a schopnosti letounu pokračovat po poškození v letu. Jako nejnebezpečnější způsob útoku
byl vyhodnocen útok tříštivou bojovou hlavicí rakety. Důsledky takového útoku byly simulovány s využitím metody
konečných prvků, pro ověření funkčnosti tohoto modelu byl proveden vhodný střelecký experiment. Zkušební vzorek byl vyroben jako poloskořepinový potahový panel a byl ostřelován jednotlivými střepinami se známou hmotností, rychlostí a směrem dopadu na zasaženou plochu. Experimentem se prokázalo, že jednotlivá střepina způsobí
jen velmi malé poškození a má malý vliv na schopnost panelu přenášet zatížení. I více střepin dostatečně vzdálených od sebe poškodí spíše jednotlivé prvky, ale nevedou k většímu poškození, které by se dalo vyjádřit jako součet
dílčích účinků jednotlivých střepin. Výsledky experimentu byly následně použity ke zpřesnění numerického výpočtu poškození.
Introduction
We can meet with more and more international terrorism
in today news media. There are also attacks to the targets
very vulnerable which are mostly civil transport aircrafts.
Whatever attack to the aircraft has mostly tragic results. If
there is a crash of the aircraft then it results in a massive
loss of lives and also in big material losses.
This article is focused on the assessment of the dangerous effects of the terroristic attack. Terroristic attacks
could be divided from the point of view of the execution
into two categories. The first category includes attacks on
the board of the aircrafts which can be made using firearms
or explosives. The second category then represents attacks
made to the aircrafts from the outside. Into this category
have been put attacks with firearms of the bigger caliber
and with warheads of the missiles. If there are used missiles then it is mostly missiles with fragmentation warhead
which are commonly used as anti-aircraft weapons in the
most of the war conflicts.
The security of the airports was significantly increased
after last terroristic attacks on the boards of the civil aircrafts. Therefore there has been recently no successful
terroristic attack on the board of the aircraft. For this reason we have assessed as the most dangerous one attack to
the aircraft from the outside.
Analysis of the mechanism of damage of the aircraft by
the firearm and by the fragmentation warhead shows that
these mechanisms are very similar. The projectile from the
firearm affects the airframe of the aircraft by its kinetic
energy and causes damage with it. By the fragmentation
warhead the damage is caused by the effect of bigger
amount of the fragments which are made by the stretching
of the skin of the warhead. These fragments use their kinetic energy for the damage of the airframe too. The character of the damage with single fragment could be different
then damage caused by one projectile. This is caused mainly by the shape of the fragments. Effects of the damage of
airframe to the immediate static strength are, with comparison of damage with single projectile and with single
fragment, the same. If we are talking about damage with
fragmentation warhead then of course it is damage made
by multiple fragments.
The effect of shooting the aircraft with the fragmentation warhead could be divided into three categories according to the range of the damage. The first category is direct
stroke to the aircraft. Here a fatal damage of the structure
could be expected which leads to the catastrophe of the
aircraft. In the second case the warhead explodes in the
distant to the aircraft smaller then critical distance. That
means continuous damage of the airframe by the very thick
group of the fragments and the result is similar to the previous case. If the aircraft is impacted in the area with no
crucial parts of the structure it is possible to continue in
flight with partial operation limitation. In the third case the
warhead explodes in the distance bigger then critical
distance so there will be only partial damage of the structure caused by the single fragments. It is being assumed that
single fragment is not able to completely destroy part of
primary structure of the airframe.
It is useless to define range of the damage in the first
55
case. It is absolute. In the second case it will be possible to
relatively easily localize area of the continuous damage of
the airframe, to assess its range and to estimate degree of
the structure damage. In the third and the last case a deeper analysis must be made to assess the range and the effect
of the damage. This was theoretically made before here
presented experiment. It was discovered by the theoretical
analysis that for the assessment of this problem is the most
suitable analysis the one which uses finite element method
for simulation of the damage process. We chose typical
structure part of airframe which is in this case reinforced
skin panel and simplified model of the fragment. Then was
assessed interaction between panel and moving model of
the fragment.
Experiment preparation and realization
No theoretical solution could be held as correct if it is
not at least partially validated by the experiment. Therefore we prepared and realized experiment which should validate our theoretical expectations. The most suitable and the
most realistic would be an experiment with the real
warhead and the part of the civil aircraft. This solution
brought a lot of security and financial complications. There
would be also limited possibilities for detail description of
the damage caused by the particular fragments by this
experiment because it would not be possible to define their
exact shape, mass and velocity and therefore their kinetic
energy. The variant of the experiment was chosen with
shooting to the specimen with projectiles. These projectiles simulate effect of the fragments and their parameters
are known.
The part of the real structure of the aircraft was finally
not chosen as the specimen because it would be difficult to
obtain exact material characteristics of this structure. Therefore the new specimen was manufactured for this experiment. It fulfills all required parameters. Designed and
manufactured specimen corresponds with the structure
solution of the modern civil aircrafts, for example aircrafts
made by company Airbus. It is part of the semi-monocoque
1/2011
The base of the specimen was the skin sheet with dimensions 1000x1000mm. Four stringers and perpendicular to
them two frames were riveted on this skin. The frames are
connected with stringers and the skin with connection elements. This structure design allows using frames with
undivided flanges. We used cross section shape of the letter
Z for the frames and the stringers. Completed specimens
are shown on fig. 1.
The space structure form L profiles were also manufactured. To this structure the specimen was connected
during the experiment.
There were used specially designed projectiles for the
shooting. These projectiles very exactly simulate single
fragments. It was steel projectiles FSP12,7 with mass
13,39±13g. Their shape is on fig. 2.
The experiment was made on the shooting assembly
which consists of several parts. The base is shooting stand
where the weapon is fixed. There are two measure points
for measuring of the velocity in the trajectory of the fragment. Using these two velocities we were able to calculate
final impact velocity of the fragment. The last part of the
shooting assembly was the specimen. As the weapon was
used ballistic barrel with caliber 12,7mm. Complete shooting assembly is shown on fig. 3.
As noted before, the experiment consists of shooting of
the single fragments to the specimen. At the single attempts
specimen was impacted with various velocities. We tried to
hit also various combinations of the structure parts of the
specimen. Various angles of the fragments strokes to the
impacted area were also used. The base position was one
when trajectory of the fragment was perpendicular to the
plane of the specimen. For some shots were specimen
turned 30 and 60 degrees. The impact velocity alternate by
the different amount of gunpowder in the cartridge case
from 609m/s to 1645m/s.
Results of the experiment
There were hit various node points of the structure with
various velocities and directions of the strokes during the
Figure 1 - The specimen
Figure 3 - The shooting assembly
structure which consists of skin reinforced by the stringers
and frames. As a material still the most commonly used
material in aircraft design was chosen, duralumin.
experiment. Then were compared degrees of the structure
damage. On the fig.4 is shown full penetration of the panel
skin. There is obvious that fragment affected only small
C z e c h A e r o s pa c e P r o c e e d i n g s area at this damage. Velocity which is expected by the real
terroristic attack (700m/s) was used at this attempt. The
size of the opening is equal to the size of the fragment.
Also deformed area around the impact is very small.
The next part that was intentionally hit by the fragment
was the stringer. Flange of the stringer riveted to the skin
was hit at this attempt. The result is similar to the one on
the fig.7 also here. In the skin is opening equal to the size
of the fragment and in the flange of the stringer but the
damage is little bit bigger. This could be made by the influence of the material that is ripped out from the skin by the
fragment. Affected area has now the size of three diameters
of the fragment. There is destroyed and divided one flange
of the stringer. The web of this stringer and the second
flange remains untouched. The stringer was not completely
damaged and it didn´t lost all its capabilities to carry
loads.
The similar damage as in the previous case could be
observed also by the hit of the other structure parts as is
shown on fig. 5. The penetration of the connection element
and the frame is shown on this figure. Also only directly hit
structure parts are damaged here. There is almost no influence to the rest of the structure caused by this fragment.
The affected areas and degree of the damage are small.
We discovered interesting phenomenon at the one
attempt which we did not realized by the previous numerical calculation. This phenomenon is on fig. 6. Almost clear
penetration of the various structure parts can be seen here.
However, there is also damaged flange of the frame that
was not directly hit by the fragment. This damage was
caused by the material that was ripped out from the skin by
the fragment. We can call this material as secondary fragment. This effect is very random. This has to be also incorporated in the range of the damage assessment.
The experiment caused greatest damage to the structure
by the hits of the beam webs (frames or stringers) at the
first sight. This damage is on fig. 7. But it is only damage
of the directly hit parts of the structure. There is no bigger
damage of the other parts in this figure. Therefore it is the
same type of the damage as in the previous cases.
One of the tested parameters which influence impact of the
fragments was velocity of the fragments in the moment of the
stroke. Fig. 8 shows damage made by the fragments with the
biggest velocity which allows our test equipment. The velocity
was 1645m/s. If we compare this damage with the one shown
on the fig. 5 (fragment velocity 822m/s) we can observe here
obviously much bigger damage of the parts that are hit after
the penetration of the skin. More severe damage was caused by
bigger amount of the material ripped out of the skin and its
bigger velocity obtained by this material from the fragment. If
we compare these two damages from the point of view which
describes ability of the structure to carry loads, we can conclude that the influences of the damages are basically the same.
The flanges of the beams were destroyed in both cases. The
other parts of the structure are untouched and they didn’t lose
their ability to carry loads.
Comparison with numerical model
The results of the experiment were compared with the
56
numerical model created using finite element method. We
improved numerical model using our experimental data.
The visualization of the calculation result is on fig. 9. This
example shows calculation of the skin penetration. If we
compare this figure with fig. 7 there is obvious coincidence. The model shows opening with size similar to the size
of the fragment and relatively small affected area around
the penetration. With the coincidence of the calculated
result with the experimental result we can say that the
numerical model is sufficiently correctly made. The experimentally proved coincidence between theory and reality
gives us guarantee of the correct calculation which will be
with this model realized.
Figure 9 - The Finite element model
Conclusion
During this experiment was proved that single fragment
causes only very small damage and has only small effect to
the ability of the structure to carry loads. Also more fragments which have impacted in some distance to each other
damage more single parts. This doesn’t cause bigger
damage that would result in aircraft crash. With the arrangement of the single fragments was proved that overall
damage cannot be solved by the superposition of the partial
damages of the single fragments. There was also discovered that range of the damage does not depend on the velocity of the fragments. However, degree of the damage
always depends on the area of the impact and distance
between impacted area and the warhead explosion. These
parameters determine if there is continuous damage or
separated damages made by single fragments.
Results of this experiment were used for the improvement of the numerical calculation of the damage when big
coincidence between theory and experiment was proved.
References
[1] Ludvík, F. - Konečný,P.: Rakety, VA Brno, 1998
[2] Ball, R.E.: The Fundamentals of Aircraft Combat Survivability
Analysis and Design, AIAA Education Series, 1985.
Experimental Assessment of the Fragments
Effect to the Fuselage of the Aircraft
Colour illustrations to the article published on pages 54 to 56.
Figure 2 - The fragment
Figure 6 - The secondary fragments
Figure 4 - The damage of the skin
Figure 7 - The Damage of the structure
Figure 5 - The damage of the frame
Figure 8 - The maximum fragment velocity
Development of series production
technology for stator and rotor blades
Colour illustrations to the article published on pages 23 to 25.
Fig. 2 - sample of rotor blade after curing
and removal out of the mould
Fig. 3 - three-dimensional CAD
part of a blade
Fig. 5 - high strength carbon
fabric with plain weave
Fig. 4 - unidirectional carbon fabric
Fig. 6 - The rotor vane mold
Fig. 7 - Compagination mold
Fig. 10 - Original stattor parts
Fig. 9 - silicone rubber
Fig. 11 - Model of stator segment
© A s s o c i at i o n o f t h e
A v i at i o n M a n u fac t u r e r s

sprint abilizer

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