modelling and testing smart aileron servo tabs: developing simulation tools for smart materials

158 Pages·2015·3.86 MB·English

by  Velaphi Msomi

MODELLING AND TESTING SMART AILERON SERVO TABS: DEVELOPING
SIMULATION TOOLS FOR SMART MATERIALS

VELAPHI MSOMI

Submitted in partial fulfilment of the requirements for the degree
of
DOCTOR OF TECHNOLOGY IN MECHANICAL ENGINEERING

at the

CAPE PENINSULA UNIVERSITY OF TECHNOLOGY

May, 2015
To my wife, Simphiwe Nancy, who supported and encouraged me
To my son, Ayabonga, who motivated me
To my daughter, Jesunathi, who brought smile to my face
ACKNOWLEDGEMENTS
As this dissertation represents the culmination of lifetime spent learning, it seems
inappropriate to begin by acknowledging anyone other than my Creator and the
Lord Jesus Christ for strengthening me during tough times.
Many thanks go to my advisor, Professor G.J. Oliver for the directions he gave
me during this difficult level of study. I would like most of all his patience with me
during the hard time of my life and his tolerance is incomparable. I would also like
to thank my co-supervisor, Associate Professor O. Philander, for opening this
study opportunity and the confidence he had on me. I would also like to thank
Professor J. Gryzagoridis for his encouraging words and the facts that he gave
me during the no-hope moments. I am thankful to the CPUT Mechanical
Engineering Workshop staff by their support they provided to me. I am thankful to
Mr Vuyani Moni (Senior Technician) for allowing and assisting me in performing
the experiments of this thesis.

Ngithi ngasekugcineni angibonge umndeni wami obungeseka njalo nokungipha
isibindi sokuqhubeka nalapho ithemba seliphela. Ikakhulukazi unkosikazi wami
obehlezi engipha amazwi enduduzo uma isimo salomsebenzi singabonakali.
Ngingelibala umama wethu, M.Z. Msezane, obehlezi evuma ngasosonke
isikhathi uma kukhona esikucelayo kuye.

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Disclaimer
I would also like to thank Airbus Company for their financial support and for
initiating the project. It should be noted that there are no experimental or
numerical data in this work verified by Airbus Company.

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MODELLING AND TESTING SMART AILERON SERVO TABS: DEVELOPING
SIMULATION TOOLS FOR SMART MATERIALS.
Supervisor: Professor G.J. Oliver
Co-supervisor: Associate Professor O. Philander
ABSTRACT
This dissertation addresses the development and the testing of a simulation tool
to be used to predict the behaviour of smart material/structures. Along with the
development of the simulation tool, a new form of the model describing the
behaviour of shape-memory alloy was developed and implemented. The
proposed model was developed based on the existing cosine model,
conventionally used in literature, but it uses hyperbolic tangent functions. The
hyperbolic tangent function was chosen so as to allow the simulation of any
range of temperatures. Experiments were performed to obtain the parameters to
be used in the simulation and to validate the numerical results. Two different
simulations were performed: a one dimensional FEA analysis with a two
dimensional orientation (NiTi SMA wire simulation) and a three dimensional FEA
analysis (NiTi SMA plate) [Msomi and Oliver, 2015]. Alongside the FEA analysis,
two experiments were performed with the purpose of obtaining the material
parameters to be used in FEA analysis and to compare the FEA results to the
experimental results.
A steel beam SMA experiment and a smart aileron deflection experiment were
performed. The one dimensional FEA analysis was performed using a C++
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program implementing combined beam and bar elements. The displacement was
calculated using a prescribed thermal history causing a phase change in the
SMA material which produces equivalent nodal forces. The solution variable for
this particular analysis is only displacement with an associated solution of the
phase kinetic equations and the temperature field is input from experimental
data, not solved for.

The smart aileron deflection FEA analysis was performed on the ABAQUS
simulation package using C3D8T elements, and the developed material
algorithm was incorporated into ABAQUS using the available FORTRAN user
written material subroutine (UMAT). The user material subroutine was for a
coupled thermo-mechanical solution with associated phase kinetic equations and
was solved as a coupled temperature-displacement problem in ABAQUS. For the
implementation into ABAQUS, the algorithmic tangent moduli for the non-linear
solution needed to be prescribed in the user material subroutine along with the
determination of the state of stress for a total strain and temperature state. The
temperature state is also dependent on the phase kinetics through the latent heat
effect. There is no dissipation of elastic strain energy considered in the material
implementation, in keeping with the research goals.
The experimental and numerical results are compared in the text and the FEA
results show good correlation with the experimental results in both types of
analysis following the material parameter estimation within the one dimensional
finite element solution.
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TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................X
LIST OF FIGURES ........................................................................................................ XI
CHAPTER 1 ...................................................................................................................... 1
INTRODUCTION .............................................................................................................. 1
CHAPTER 2 .................................................................................................................... 20
2.0 MODELS FOR SHAPE-MEMORY ALLOYS. .............................................. 20
2.1 SHAPE-MEMORY ALLOY MODEL ............................................................... 22
2.1.1 PROPOSED SHAPE-MEMORY ALLOY MODEL............................. 22
CHAPTER 3 .................................................................................................................... 30
3.1 EXPERIMENTAL PROCEDURES .................................................................. 30
3.2 Beam deflection test experiment (1-D analysis) ...................................... 30
3.3 Deflection Transducer’s Calibration ........................................................... 32
3.4 Deflection Transducer Calibration results ................................................ 34
3.5 Deflection Test Results .................................................................................. 35
3.6 Characterization of the Shape-memory Alloy plate ................................ 39
3.7 Smart aileron experiment (3-D analysis) ................................................... 41
3.7.1 NICKEL TITANIUM SHAPE-MEMORY PLATES.............................. 41
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3.7.2 SHORT BRUSH ALUMINIUM PLATES ............................................. 42
3.7.3 SILICONE SELF-ADHESIVE HEATER MAT KIT ............................. 42
3.8 EXPERIMENTAL RESULTS for THE SMART AILERON ........................ 43
3.9 Data acquisition setup .................................................................................... 46
3.10 Smart Aileron Deflection Results ................................................................ 48
CHAPTER 4 .................................................................................................................... 56
4.1 SOLUTION ALGORITHMS FOR THE IMPLEMENTATION OF SMA
MATERIAL INTO FE PROGRAMS ............................................................................ 56
4.1.1 SMA MATERIAL MODEL DESCRIPTION ......................................... 56
4.2 Finite element analysis on 2-D beam setup .............................................. 64
4.3 Implementation of SMA material model in a 1-D Beam-Bar finite
element with a two dimensional orientation ......................................................... 65
4.4 Beam Bar SMA FEA Results ......................................................................... 70
4.5 THREE DIMENSIONAL IMPLEMENTATION INTO A COMMERCIAL
FINITE ELEMENT PROGRAM (ABAQUS)............................................................... 75
4.5.1 NUMERICAL IMPLEMENTATION OF THE SMA CONSTITUTIVE
MODEL ................................................................................................................ 76
4.5.2 FINITE ELEMENT ANALYSIS FOR NON-LINEAR MATERIALS .. 76
4.5.3 COMPACT SOLUTION ALGORITHM IMPLEMENTATION ........... 79
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4.5.4 THREE DIMENSIONAL FINITE ELEMENT ANALYSIS RESULTS
80
COMPARISON OF RESULTS..................................................................................... 98
CHAPTER 5 .................................................................................................................. 101
REFERENCES.............................................................................................................. 104
APPENDICES............................................................................................................... 117

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LIST OF TABLES

Table Page
TABLE 3.1: HEATER MAT KIT SPECIFICATIONS ......................................................................................................... 42
TABLE 4.1: MATERIAL PARAMETERS FOR 0.5 MM DIAMETER NITI SMA WIRE USED DURING SIMULATION .... 70
TABLE 4.2: SOLUTION ALGORITHM FOR MODELING PHASE TRANSFORMATION PHENOMENON IN SMAS ......... 79
TABLE 4.3: MATERIAL PROPERTIES FOR NITI SMA PLATE USED DURING SIMULATION...................................... 98

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