Embed Size (px)
Citation preview
Design of DC-Link Capacitor of High Power
Switch Module of an Aircraft Power & Thermal
Management Controller
by
Mohammad Anisur Rahman
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto, 2015
© Copyright by Mohammad Anisur Rahman 2015
ii
Design of DC-Link Capacitor of High Power
Switch Module of an Aircraft Power & Thermal
Management Controller
Mohammad Anisur Rahman
Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto, 2015
Abstract
DC –Link Capacitor used in power converters as an energy buffer is one of the key components
of aircraft Power and Thermal Management Controller (PTMC). Several factors in order to
reduce the cost of the PTMC have been identified including the integration of the DC-link
capacitors, DC bus bars and Snubber caps. Redesign of DC-link capacitor integrated with DC
bus bars and Snubber caps not only diminishes the cost but also reduces the weight of PTMC. In
this thesis, Pro/Engineer, commercial Computer Aided Design (CAD) software, is utilized to
develop the CAD model of redesigned DC-link capacitor integrated with DC bus bars and
Snubber caps. The key factor of this redesigned DC-link capacitor is to justify its structural
functionality subjected to random vibration and temperature loadings. Finite Element Method
(FEM) using ANSYS is used to predict the life cycle of the structure (redesign DC link capacitor
integrated with DC bus bar and Snubber caps) subjected to random loading. The impact of
temperature loading and the resulting deflection and stresses induced in various parts of the
structure are also investigated. Finally the new design is verified by fatigue life and thermal
stress analyses and the reduction of cost is evaluated in terms of the weight and cost saving
factors.
iii
Acknowledgements
Completing this work would not have been possible without the help and support of several
wonderful people. First and foremost, I would like to present my deep gratitude to my supervisor
Dr. Kamran Behdinan for providing me with the opportunity to work on this project and to learn
from him. His guidance, patience, and encouragement through the duration of my Master’s
program are most appreciated. Apart from the academic side, I always see him as an inspiring
person in my personal life.
My sincere appreciation goes to my industry advisors Mark Phillips and Vahe Gharakhanian for
their continuous support during my research work. I am grateful and an indebted to Honeywell
Aerospace, Canada for providing the access of using various commercial software and valuable
suggestions during this research work.
I should also express my appreciation for the members of the Advanced Research Laboratory for
Multifunctional Lightweight Structures at the Department of Mechanical and Industrial
Engineering. Being among these bright and warm people has made my experience more
enjoyable. I have had the pleasure of friendship of many beautiful people at the University of
Toronto. I wish to thank them for their kindliness and I consider our companionship an
inordinate gift I received during the time span of this program.
Last but definitely not last, I owe the completion of this work to my family. My spouse, my
father, my mother, my brothers and my sisters have been the greatest sources of motivation for
me. Their deep love, understanding and continuous support has certainly made me to be better in
what I am doing. It is to them that this thesis is dedicated.
iv
Contents
Abstract ii
Acknowledgement iii
List of Tables vii
List of Figures
viii
List of Appendices
x
Nomenclature
xi
CHAPTER 1: INTORDUCTION
1
1.1 Motivation 1
1.2 Objectives 4
1.3 Project Overview 5
1.4 Thesis Overview 7
CHAPTER 2:LITERATURE REVIEW
8
2.1 Background 8
2.2 Historical Overview of Fatigue 9
2.3 Related Work 10
2.4 Overview 14
CHAPTER 3: FATIGUE AND THERMAL ANALYSIS THEORY
15
3.1 Fatigue Analysis
15
3.1.1 Modal Analysis 15
3.1.2 Stress Life Approach 17
3.1.3 Frequency Domain Approach 22
3.2 Palmgren-Miner Rule 28
3.3 Fatigue Analysis Methodology 31
3.4 Thermal Stress Analysis due to Temperature Loading 33
v
3.5 Thermal Stress Analysis Methodology
34
CHAPTER 4: CAD AND FE MODEL OF HPSM
37
4.1 PTMC and HPSM
37
4.2 CAD Model of HPSM
37
4.3 Finite Element Model (FEM) of HPSM 39
4.3.1 Materials of the Model 40
4.3.2 Connections of the Model 42
4.3.3 Boundary Condition of the Model 42
4.3.4 Mesh of the Model 43
CHAPTER 5: FINITE ELEMENT ANALYSIS OF HPSM
45
5.1 Fatigue Analysis
45
5.1.1 Modal Analysis 46
5.1.2 Random Vibration Analysis
48
5.2 Stress due to Temperature Loading 55
5.2.1 Materials 55
5.2.2 Temperature Distribution 56
5.2.3 Structural Analysis 57
5.3 Results and Discussion 59
5.3.1 Vibration Performance of the Redesign DC-Link Capacitor 59
5.3.2 Structural Functionality of the Redesign DC-Link Capacitor
due to Temperature Loading
59
5.3.3 Weight Reduction and Cost Saving of the Redesign DC-
Link Capacitor
60
5.3.3.1 Weight Reduction 60
5.3.3.1 Estimated Cost Reduction 60
vi
CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS 62
6.1 Concluding Remarks 62
6.2 Future Directions 63
REFERENCES 64
vii
List of Tables
4-1 Mechanical Properties of the materials for the various components of HPSM
40
4-2 Number of elements of the model and corresponding natural frequencies for
various modes
43
5-1 First six natural frequencies of the HPSM assembly model
47
5-3 Number of Service Cycle (n) at Various Levels
50
5-4 Cumulative Damage Index (0.01) at X direction
52
5-5 Cumulative Damage Index (0.01) at Y direction
53
5-6 Cumulative Damage Index (0.01) at Z direction
54
5-7 Thermal Properties for Various Component of HPSM
55
5-8 Thermal Analysis Results from Pervious Thermal Analysis Report
56
5-9 Thermal Stress at Various Components of DC-Link Capacitor and HPSM
58
viii
List of Figures
1-1 Housing of Power and Thermal Management Controller
2
1-2 High Power Switch Module (HPSM)
2
1-3 Existing model of DC-Link Capacitor, Snubber, mounting bracket and DC
Bus bar
3
3-1 A vibrating spring-mass system [27]
15
3-2 S-N diagram for UNS G41300 steel [29]
17
3-3 S-N diagram for steel and aluminum [31]
18
3-4 Sinusoidal fluctuating stresses (a) with zero mean and (b) with nonzero mean
18
3-5 Example of S-N curve with non zero means stress [36]
21
3-6 Schematic presentation of analysis process used in the thesis work
22
3-7 Random processes [37]
23
3-8 Using an FFT to characterize a time signal [37]
24
3-9 Definition of PSD [37]
25
3-10 Gaussian distribution curve. The probability of a range of X is given by the
area under the curve in that range [27 ]
26
3-11 Another method for showing the Gaussian distribution [27 ]
26
3-12 Spectrums of amplitudes of stress cycles [10]
29
3-13 Constant amplitude S-N curve [10]
30
4-1 CAD model of the DC-link capacitor integrated with DC bus bars and
Snubber caps
38
4-2 Assembly CAD Model of HPSM
38
ix
4-3 S-N curve for Al 5052
41
4-4 Figure 4-4 S-N curve for Al 6061
41
4-5 Beam Connections among various components of the assembly model
42
4-6 Boundary Conditions (fixed support) at the bottom of the assembly model
42
4-7 Natural frequency Vs Number of Element curve
43
4-8 Mesh Model of the HPSM Assembly
44
5-1 First Mode Shape of the HPSM Assembly Model
47
5-3 Max. Von-Mises stress (3992.2 psi) on assembly model at X direction
51
5-4 Max. Von-Mises stress (3992.2 psi) on weakest component at X direction
51
5-5 Response PSD at Critical Location
51
5-6 Temperature Distribution at the model
56
5-7
Equivalent Stress (Max: 28263 psi) at Component P of DC-Link Capacitor
57
x
List of Appendices
Appendix A :
Weight Analysis 68
Appendix B : Material Properties for Al 5052-H32
69
Appendix C : Mode Shapes of HPSM Assembly Model
70
Appendix D : Von-Mises Stresses at weakest Component along Y and Z Direction
71
Appendix E : Thermal Stresses of all key Components of HPSM
73
xi
Nomenclature
PTMC Power and Thermal Management Controller
HPSM High Power Switch Module
VMS Vehicle Management System
APU Auxiliary Power Unit
DC Direct Current
AC Alternating Current
CCA Circuit Card Assembly
IGBT Isolated Gate Bipolar Transistor
ESL Equivalent Series Inductance
PSD Power Spectral Density
CAM Computer Aided Manufacturing
CAD Computer Aided Design
FEA Finite Element Analysis
FEM Finite Element Method
CDI Cumulative Damage Index
PCB Printed Circuit Board
BGA Ball Grid Array
DOF Degree of Freedom
PDE Partial Differential Equation
FFT Fast Fourier Transform
xii
RMS Root Mean Square
S-N Stress to Number of Cycles
NTE Negative Thermal Expansion
CTE Coefficient of Thermal Expansion
ICC Electrical Power Controller
IPPC Integrated Power Package Controller
DFMA Design for Manufacturing and Assembly
s , σ Stress
Y Young Modulus
υ Poisson’s Ratio
n Number of Service Cycle
N Number of Cycle which could cause Failure
SEQVf Equivalent von-Mises Stress for Fatigue
k The Spring Rate
m Mass of the body
SEQVf Equivalent von-Mises Stress for Fatigue
1
CHAPTER-1: INTRODUCTION
1.1 Motivation
Aircraft Power and Thermal Management Controller (PTMC) is an integrated system, and in
combination with the aircraft vehicle management system (VMS), performs aircraft functions
traditionally reserved for the auxiliary power unit (APU), the environmental control system
(ECS) and the backup power system.
Power and Thermal Management Controller (PTMC) has two main electrical power management
functions. One is to start the turbomachine by inverting the DC voltage into AC voltage to drive
the power management and generation and another one is to supply power onto the aircraft
electrical distribution bus, by converting AC voltage from the rotating power management and
generation into regulated DC voltage. In addition, PTMC controls of various valves in order to
control the turbomachine speed, to regulate the temperature and pressures in the closed loop.
Honeywell Aerospace Canada, one of the leading companies in the Canadian aerospace industry,
designs and manufactures a high power electronic Power and Thermal Management Controller
(PTMC) for an aircraft and is working to support its customers cost reduction goals in advance of
production ramp-up. In order for the Canadian aerospace industry to maintain its contribution to
the country’s economy, companies such as Honeywell must remain competitive in the global
aerospace market and constantly maintain their high quality, reliable and first to market products.
Currently, Honeywell produces Power and Thermal Management Controller (PTMC). They are
aiming to increase their production volume in 2016. In order to make cost saving during the mass
production it is important to focus on creating cheaper design alternatives.
The PTMC consists of three major components, the chassis or housing, the High Power Switch
Module (HPSM) and the control electronics which consist of multiple circuit card assemblies
(CCA’s). The HPSM is bolted into place inside the chassis and consists of a liquid cooled heat
2
exchanger with various components mounted on it such as Isolated-Gate Bipolar Transistors
(IGBTs), gate driver CCAs, Bus bars, Snubber caps and DC link capacitors.
Figure 1-1 Housing of Power and Thermal Management Controller
Figure 1-2 High Power Switch Module (HPSM)
DC link capacitors are commonly used in power converters as an energy buffer since they have a
high energy-storage capability for their size. When the redesigned DC link Capacitor structure is
integrated with Snubbers (by-pass capacitor) and DC bus bars for connection into the IGBT
module, a significant reduction in equivalent series inductance (ESL) can be achieved as
compared to traditional designs.
3
Figure 1-3 Existing model of DC-Link Capacitor, Snubber, mounting bracket and DC Bus bar
Among the three major components of PTMC, HPSM is the most costly component and the most
challenging component due to its volume and weight to assemble into the housing of PTMC.
Honeywell is aiming to reduce the cost of PTMC and reduce volume and weight of HPSM.
With an aim addressing these issues, this research focuses on redesigning the current HPSM in
order to reduce the total cost of the PTMC unit. This research places emphasis on redesign the
component of the controller, High Power Switch Module (HPSM), in order to reduce the cost of
raw materials and manufacturing processes required to fabricate the HPSM.
More specifically, this research work focuses on reducing the cost of the DC-link capacitors, bus
bars and Snubber caps. Several opportunities for cost takeout have been identified including the
integration of some of the aforementioned subassemblies. The secondary objective of the project
is to reduce the volume of the HPSM. This will make it easier to assemble in the chassis and
reduce end unit labor cost. The re-designed HPSM must also weigh the same as or less than the
current HPSM to meet customer requirements.
In order to accomplish the cost reduction and decreasing the space consumption of the HPSM in
its housing chassis, several possible opportunities have been assessed such as:
Redesigning the DC bus bar to reduce the weight of the HPSM
Redesigning the DC-link capacitor so that the DC bus bars are integrated within them (DC
bus bars and Snubber caps will be integrated within the DC-link capacitor)
4
Relocating the DC bus bars from the bottom to the top of the HPSM to reduce the required
length of the bus bars, hence reducing the power dissipation and improving the cooling
effectiveness in the entire chassis
HPSM and its components are frequently subjected to the oscillating loads which are random in
nature. Random vibration theory has been introduced for more than three decades to deal with all
kinds of random vibration behavior. Since fatigue is one of the primary causes of component
failure, fatigue life prediction has become a most important issue in almost any random vibration
problem. Traditionally fatigue damage is associated with time dependent loading, often in the
form of stress or strain. Alternatively, a frequency based fatigue calculation can be utilized where
the loading and response are categorized using Power Spectral Density (PSD) functions.
During redesigning of HPSM, fatigue is not only the issue but also thermal stress due to
temperature loading. Thermal stress effects are simulated by coupling a heat transfer analysis
(steady-state or transient) and a structural analysis (static stress with linear or nonlinear material
models or Mechanical Event Simulation).
1.2 Objectives of the Thesis
The main objectives of the thesis are:
a) redesigning the DC bus bar , DC-ling capacitor and Snubber caps to reduce the weight of
HPSM
b) developing CAD models of the specified components
c) performing FEA simulation of the assembly CAD model to predict life cycle of the weakest
structure of the HPSM
d) performing thermal stress analysis to investigate the impact of temperature loading and the
resulting deflection & stresses induced in various parts of the DC-link capacitor
5
1.3 Project Overview
The goal of my thesis was to justify structural functionality of redesign DC link capacitor
integrated with DC bus bar and Snubber caps subjected to random vibration loading and
temperature loading. In this thesis, numerical method was used not only to predict the life cycle
of the structure (redesign DC link capacitor integrated with DC bus bar and Snubber caps) due to
random loading but also to calculate thermal stresses to investigate the impact of temperature
loading and the resulting deflection & stresses induced in various parts of the structure.
The first step of my project was to make part models of various components of proposed DC link
capacitor, DC bus bar and Snubber caps. After developing all part models, an assembly model of
High Power Switch Module (HPSM), which consists of two modified DC link capacitors, four
modified DC bus bars, six modified Snubber caps, one existing Heat Exchanger and six existing
Integrated Bipolar Gate Drivers, was developed. There are various commercial Computer Aided
Design (CAD) software packages available including AutoCAD, SolidWorks, UniGraphics,
CATIA, and Pro/Engineer. Pro/Engineer was selected because it has powerful surface generating
functions and it is easier to change parameters directly in this software.
The second step of this research was to generate mesh (a discretized geometry which is used for
calculation) of the assembly model of HPSM which was used for the numerical simulation. The
Finite Element Method (FEM), which is a numerical technique particularly good at solving
complex structural problems, was used. The idea was to discretize the assembly model (HPSM)
into regions, each of which has many smaller elements called nodes (intersections of mesh
elements). Properties of material of each component of the assembly model were defined in
terms of elasticity and density and then the theoretical vibrational behavior of the assembly
model was solved through matrix manipulations. This allowed the primary Eigen frequencies of
a structure to be determined, as well as the visualization of the mode shapes. After modal
analysis, the input Power Spectral Density (PSD) and Damping ratio were specified to calculate
the von-Mises stresses at critical region of every component of redesigned DC link capacitor
integrated with DC bus bar and Snubber caps. The commercial software package ANSYS was
used for mesh generation, obtaining natural frequencies and stresses (von-Misses). In this thesis,
weakest component was identified on the basis of computed von-Mises stresses and Cumulative
6
Damage Index (CDI) of that component was also calculated. On the basis of calculated CDI, life
cycle of redesign DC link capacitor integrated with DC bus bar and Snubber caps was predicted
which met the Honeywell’s customer requirement.
The third step of this research was to calculate thermal stresses of every component of redesign
DC link capacitor integrated with DC bus bar and Snubber caps due to temperature loading.
Thermal stress effects were simulated by coupling a heat transfer analysis (steady-state or
transient) and a structural analysis (static stress with linear or nonlinear material models or
Mechanical Event Simulation). The process consists of two basic steps:
A heat transfer analysis which was performed previously to determine the temperature
distribution; and
The temperature results are directly input as loads in a structural analysis to determine the
stress and displacement caused by the temperature loads.
After finding thermal stresses, weakest component was identified and recommendation has given
to make the component strong either by changing cross-sectional area or assigning different
material whose yield strength is greater than the computed von-Mises stress of that component.
7
1.4 Thesis Overview
The main body of the thesis consists of six chapters. These chapters present the thesis material in
an organized way as the following paragraphs briefly explain.
Chapter 2 covers literature review on random vibration analysis based on time domain as well as
frequency domain.
Chapter 3 presents the theoretical foundation required for understanding the methodology of the
fatigue analysis due to random vibration loading and thermal stress analysis due to temperature
loading.
Chapter 4 provides an introduction of PTMC and HPSM. It discusses about the CAD model and
Finite element modeling of the HPSM.
Chapter 5 is the core chapter of the thesis focusing on the modal analysis of the model and
determination of the fatigue life of the model. In this chapter, thermal stress effects are
simulated by coupling a heat transfer analysis and a structural analysis. This chapter also
presents the results. The outcome of each discipline is presented and discussed.
Chapter 6 summarizes the contribution of the thesis and proposes directions for further research
on the project.
8
CHAPTER 2: LITERATURE REVIEW
2.1 Background
Electronic equipment can be subjected to many different forms of vibration over wide frequency
ranges and acceleration levels. Mechanical vibrations can have many different sources. In
airplanes, missiles, and rockets the vibration is due to jet and rocket engines and to aerodynamic
buffeting.
From various researches, it is understood that vibration and shock cause 20 percent of the
mechanical failures in airborne electronics. Proper design procedures for ensuring equipment
survival in a shock and vibration environment are therefore essential.
Interestingly, the remaining 80 percent of mechanical failures relate to thermal stresses induced
by high thermal gradients, high thermal coefficients of expansion and a high modulus of
elasticity.
In both cases, failures occur primarily from broken component lead wires, cracked solder joints,
cracking of the component body, plated hole cracking, broken circuit traces and electrical
shorting.
In this thesis, the structural integrity of the model is estimated when subjected to random
vibration and thermal loadings.
Most structural analyses are conducted using static equivalent load. This is due to the fact that it
is difficult to define and analyze dynamic environments. Some fatigue analysis attempts have
been made assuming damage due to block loadings or time history loading inputs. Block
loadings are independent of frequency, so the dynamic response of the structure is omitted from
the calculations. The time history method is a refinement of this and is usually based upon stress
calculations for the loadings at different points in time without using the displacement, velocity,
and acceleration values at each node as an input for the next iterative step. Thus inaccuracies are
9
incurred if the frequency range of the dynamic environment includes any resonant frequencies of
the structure. Furthermore, the input files defining the load time histories can be very large,
requiring calculations for thousands of time steps.
2.2 Historical Overview of Fatigue
The term “fatigue” is introduced to explain failures happening due to alternating stresses in the
1840s and 1850s. The first usage of the word “fatigue” in print comes into view by Braithwaite,
although Braithwaiten states in his paper that it is coined by Mr. Field [1]. Then, a general
opinion starts to develop in such a way that the material gets tired of bearing the load or
repeating application of a load exhausts the capability of the material to carry load which
survives to this day [2].
August Wöhler, a German railway engineer, sets and performs the first systematic fatigue
examination from 1852 to 1870. He carries out experiments on full‐scale railway axles and also
on small scale torsion, bending, and axial cyclic loading test specimens for different materials.
Wöhler’s data for Krupp axle steel are plotted as nominal stress amplitude versus cycles to
failure. This presentation of fatigue life leads in the S‐N diagram. Furthermore, Wöhler indicates
that the range of stress is more important than the maximum stress for fatigue failure [3]. Gerber,
Goodman and some other researchers examine the influence of mean stress in loading
throughout 1870s and 1890s.
Bauschinger [4] points out that the yield strength in compression or tension decreases after
applying a load of the opposite sign that results in inelastic deformation. It is the first indication
that a single exchange of inelastic strain could alter the stress‐strain behavior of metals. Ewing
and Humfrey [5] study on fatigue mechanisms in microscopic scale observing micro cracks in
the early 1900s. Basquin [6] represents alternating stress versus number of cycles to failure (S‐N)
in the finite life region as a log‐log linear correlation in 1910.
10
Grififth [7], an important contributor to fracture mechanics, presents theoretical calculations and
experiments on brittle fracture by means of glass in the 1920s. He states that the relation Sa =
constant, where S is the nominal stress at fracture and a is the crack size at fracture.
Palmgren [8] introduces a linear cumulative damage model for loading with varying amplitude in
1924. Neuber [9] demonstrates stress gradient effects at notches in the 1930s. Miner [10]
formulates linear cumulative fatigue damage criterion proposed by Palmgren in 1945 which is
now known as Palmgren‐Miner linear damage rule.
2.3 Related Work
Modern electronic equipment used in aircraft applications must be able to survive vibration
environment. The reliability of such equipment is defined by the ability of internal electronic
components to survive vibration without developing mechanical fatigue. Therefore, scientists
have been interested in developing methods of examining the mechanical fatigue of various
equipments. Below some of these studies are summarized.
Barry Controls and Hopkinton [11] presented an article where they explained about some
fundamental concepts of random vibration which should be understood when designing a
structure or an isolation system.
In their article, they mentioned that random vibration is becoming increasingly recognized as the
most realistic method of simulating the dynamic environment of aircraft applications. Whereas
the use of random vibration specifications was previously limited to particular missile
applications, its use has been extended to areas in which sinusoidal vibration has historically
predominated, including propeller driven aircraft and even moderate shipboard environments.
These changes have evolved from the growing awareness that random motion is the rule, rather
than the exception, and from advances in electronics which improve our ability to measure and
duplicate complex dynamic environments.
11
Arshad Khan et. al [12] used finite element modeling to predict the fatigue life cycle of a chassis
mounted component, an Auxiliary Heater Bracket concept which was, in actual scenario,
subjected to random vibration excitations from the road. The weld fatigue life was also
calculated in this exercise. It was estimate that the bracket concept was not able to sustain
infinite life in the 1σ level of confidence. A redesign of the Auxiliary Heater Bracket was
suggested to achieve infinite fatigue life. There is a requirement about the bracket that it must
endure infinite life in 1σ and 2σ level of confidence. Infinite life cycle in the FEA simulation was
achieved for the modified bracket. Random Vibration Analysis was performed on the bracket
model in Abacus and response was calculated up to 130 Hz. RMS stresses were used for the
fatigue life cycle calculations and the fatigue life cycle was determined from the Basquin's
relation.
Da Ya et al. [13] developed an assessment methodology based on vibration tests and finite
element analysis (FEA) to predict the fatigue life of electronic components under random
vibration loading. A specially designed PCB with ball grid array (BGA) packages attached was
mounted to the electro-dynamic shaker and was subjected to different vibration excitations at the
supports. An event detector monitored the resistance of the daisy chained circuits and recorded
the failure time of the electronic components. In addition accelerometers and dynamic signal
analyzer were utilized to record the time-history data of both the shaker input and the PCB’s
response. The finite element based fatigue life prediction approach consists of two steps: The
first step aims at characterizing fatigue properties of the Pb-free solder joint (SAC305/SAC405)
by generating the S–N (stress-life) curve. A sinusoidal vibration over a limited frequency band
centered at the test vehicle’s 1st natural frequency was applied and the time to failure was
recorded. The resulting stress was obtained from the FE model through harmonic analysis in
ANSYS. Spectrum analysis specified for random vibration, as the second step, was performed
numerically in ANSYS to obtain the response power spectral density (PSD) of the critical solder
joint. The volume averaged Von Misses stress PSD was calculated from the FEA results and then
was transformed into time-history data through inverse Fourier transform. The rain flow cycle
counting was used to estimate cumulative damages of the critical solder joint. The calculated
fatigue life based on the rain flow cycle counting results, the S–N curve, and the modified
Miner’s rule agreed with actual testing results.
12
M.I.Sakri et al. [14] estimated of fatigue-life of electronic packages subjected to random
vibration load. Bo Yuan et al. [15] used used the FEA method to estimate the nature frequency
and mode shape of Electronic Apparatus Rack. Roberts and Stillo [16] used finite element
modeling to analyze the vibration fatigue of ceramic capacitors leads under random vibration.
Barker et al. [17], XZ. Liguore et al. [18] and Fields et al. [19] studied vibration fatigue problems
in leadless chip carrier. Ham and Lee [20] developed a fatigue-testing system to study the
integrity of electronic packaging subjected to vibration. Jih and Jung [21] used finite element
modeling to study the crack propagation in surface mount solder joints under vibration. Wong et
al. [22] developed a model to estimate the vibration fatigue life of BGA solder joints.
G. W. Brown and R. Ikegami [23] described an experimental investigation which was carried out
to determine the fatigue life of two aluminum alloys (2024-T3 and 6061-T6). They were
subjected to both constant-strain-amplitude sinusoidal and narrow-band random-strain-amplitude
fatigue loadings. The fatigue-life values obtained from the narrow-band random testing were
compared with theoretical predictions based on Miner's linear accurnu1ation of damage hypo
thesis.
Cantilever-beam-test specimens fabricated from the aluminum alloys were subjected to either a
constant-strain-amplitude sinusoidal or a narrow-band random base excitation by means of an
electromagnetic vibrations exciter. It was found that the S-N curves for both alloys could be
approximated by three straight-line segments in the low-, intermediate- and high-cycle fatigue-
life ranges. Miner's hypothesis was used to predict the narrow-band random fatigue lives of
materials with this type of S-N behavior. These fatigue-life predictions were found to
consistently overestimate the actual fatigue lives by a factor of 2 or 3. However, the shape of the
predicted fatigue-life curves and the high-cycle fatigue behavior of both materials were found to
be in good agreement with the experimental results.
Francis G. Pascual and William Q. Mekker [24] used a random fatigue-limit model to describe
(a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the
unit-to-unit variation in the fatigue limit. They fit the model to actual fatigue date sets by
maximum likelihood methods and study the fits under different distributional assumptions. Small
quantiles of the life distribution are often of interest to designer. Lower confidence bounds based
13
on likelihood ratio methods are obtained for such quantiles. To assess the fits of the model, we
construct diagnostic plots and perform goodness-of-fit tests and residual analyses.
Bishop [25] has been involved in developing new fatigue analysis theories and structural analysis
techniques in the frequency domain. He performed some design applications in finite element
environment by using time domain and frequency domain fatigue methods. It is pointed out that,
time domain approach lacked the dynamics of the structure if the analysis is performed by
assuming that the loading is statically applied. Furthermore in order to include the dynamics of
the structure in the time domain, a transient dynamic analysis has to be performed which is very
time consuming and sometimes practically impossible. Instead of the time domain methods, a
more computationally efficient spectral method using the random vibration theory can be used.
The benchmarks represented showed that spectral methods and transient dynamics method
results were consistent and accurate enough for numerical analysis.
H.Y. Liou et al. [26] studied damage accumulation rules and fatigue life estimation methods for
components subjected to random vibration loading. In this study, random vibration theory was
used to estimate the fatigue life and fatigue damage with Morrow’s plastic work interaction
damage rule. Experimental work was carried out to verify the derived formulas. From fatigue
tests the damage results were compared with the traditional cycle by cycle counting method. The
results showed that the prediction of Morrow’s plastic work interaction damage is even more
accurate as compared with cycle-by-cycle calculation. The degree of accuracy of Morrow’s
method depends strongly on the selection of an appropriate plastic work interaction exponent.
But the iterative process required to find out the plastic work exponent which accounts for the
material’s sensitivity to the variable amplitude loading is one of the reasons why Palmgren-
Miner’s damage rule is more preferred.
14
2.4 Overview
In this research, finite element modeling is used to predict the fatigue life cycle due to random
loading and to estimate the thermal stress due to temperature loading to justify the structural
functionality of the model. Structural Static Analysis is used to find out thermal stress of every
components of the model due to temperature loading. During random load analysis, frequency
domain approach is used because this approach is computationally more efficient and requires
less time than the traditional time domain approach. Finally, Palmgren-Miner’s damage rule is
used to calculate the Cumulative Damage Index (CDI).
15
CHAPTER 3: FATIGUE AND THERMAL
ANALYSIS THEORY
3.1 Fatigue Analysis
Fatigue damage is a process which causes premature failure of a component subjected to
repeated loading. It is a complicated process which is difficult to accurately describe and model.
Despite these complexities, fatigue damage assessment for design of structures must be made.
Therefore fatigue analysis methods have been developed.
Analysis for random load is a two step process. In the first step, a modal (Eigenvalue) analysis is
performed to obtain natural frequencies and modes of the structure. In the second step, the input
PSD (power spectrum density) spectra and damping ratio are specified and a spectrum analysis is
performed. In this chapter, modal analysis, stress life approach and the Spectrum (Non
deterministic random vibration e.g. frequency domain approach) analysis will be explained
successively.
3.1.1 Modal Analysis
A body vibrating in the absence of external force and due to an initial excitation is doing free
vibration. The frequencies under which the body in free vibration moves are designed as natural
frequencies. The number of natural frequencies an object possessed depends on the number of
Degree of Freedom (DOFs) it has. Figure 3-1 illustrates a vibrating spring-mass system with no
damping.
Figure 3-1 A vibrating spring-mass system [27]
16
This system has only one DOF and its natural frequency can be found using 𝑓 = 1
2𝜋√
𝐾
𝑚
relationship in which k is the spring rate and m is the mass of the body into the system. The
natural frequency of a spring-mass system is independent of mass of the spring.
Most of the real world systems are continues ones rather than discrete assemblies of lumped
masses. However, it is possible to model them as Multi-DOF discrete systems which are
governed by ordinary differential equations. Continues systems are more challenging to model
without making simplifying assumptions. The resultant model will be governed by partial
differential equations (PDEs) [28]. The analytical solution of PDEs if possible, is not always
straightforward; hence the PDEs are usually solved using numerical techniques, e.g. Finite
Element (FE) method.
The technique of finding the natural frequencies and mode shapes of a body is known as
Eigenvalue analysis or Modal analysis. The governing equation of a vibrating multi-DOF system
neglecting all the damping effects as bellow [28]:
[𝑚]�⃗��̈�(𝑡) + [𝐾]�⃗�𝑇(𝑡) = 0⃗⃗ (3.1)
Where �⃗� is a constant and T is a function of time. The vector �⃗� is describing the mode shapes of
the system while function T governs the behavior of the system in time. [m] and [K] are system
mass and stiffness matrices which depend on the inherent characteristic equation for finding the
natural frequencies:
[[𝐾] − 𝜔2[𝑚]]�⃗� = 0 (3.2)
Different values of 𝜔 are distinct natural frequencies of the system. Each of the natural
frequencies (also known as Eigen value) corresponding to a mode shape (also known as the
Eigen Vector). Considering continues system such as the HPSM assembly, FE technique can be
utilized to discretize the system to small elements that can be treated as single or multi-DOF
objects.
Fatigue can be approached in several ways and in particular by three main methods: These are
stress- life approach, strain-life approach and the fracture mechanics (study of the crack
propagation rate) approach. One of the design constraints of the redesign DC-link capacitor
integrated with DC bus bar and Snubber caps (structure) is to survive higher number of cycles.
17
Moreover, previous analysis for the existing model shows that the components of the structure
remain mostly in the elastic region. For the above mentioned reasons, stress-life method has used
in this research. In this chapter, the application of the stress-life method used in the thesis will be
explained.
3.1.2 Stress Life Approach
The S-N approach is still the most widely used in design applications where the applied stress is
primarily within the elastic range of the material and the resultant lives (number of cycles to
failure) are long. The basis of the stress-life method is the Wöhler or S-N diagram, which is a
plot of alternating stress, S, versus cycles to failure N. The most common procedure for
generating the S-N data is the rotating-bending test. Tests are also frequently conducted using
alternating uni-axial tension- compression stress cycles. A large number of tests are run at each
stress level of interest, and the results are statistically massaged to determine the expected
number of cycles to failure at that stress level. Taking into account the great variations of N with
S; data are plotted as stress S versus the logarithm of the number N of cycles to failure. The
values of S are taken as alternating stress amplitudes; Sa sometimes max S values can also be
used. Curves can be derived for smooth specimens, individual components, sub-assemblies or
complete structures. Figure 3-2 is an example of a typical fatigue life curve.
Figure 3-2 S-N diagram for UNS G41300 steel [29]
18
For some ferrous (iron base) alloys, the S-N curve becomes horizontal at higher N values; or,
there is a limiting stress level, called the fatigue limit (also called endurance limit), below which
there is never failure by fatigue whatever the number of cycles is applied. Below this stress level
material has an “infinite” life. For engineering purposes, this infinite life is usually considered to
be 1 million cycles. Furthermore, for many steels, fatigue limits range between 35-60% of the
tensile strength. In the case of nonferrous alloys (aluminum, copper, magnesium, etc.) however
the true endurance limit is not clearly defined and the S-N curve has a continuous slope. Thus
fatigue will certainly occur regardless of the magnitude of the stress. In such cases it is common
practice to define a” pseudo-endurance limit” for these materials which is taken as the stress
value corresponding to life of 5×108 cycles for aluminum alloys [30](Figure 3-3).
Figure 3-3 S-N diagram for steel and aluminum [31]
In actual operation the shape of the stress-time pattern takes many forms. Perhaps the simplest
fatigue stress spectrum to which a structure may be subjected is a zero means sinusoidal stress-
time pattern of constant amplitude and fixed frequency, applied for a specific number of cycles,
often referred to as a completely reversed cyclic stress, illustrated in Figure 3-4a. A second type
of stress-time pattern often encountered is the nonzero mean spectrum shown in Figure 3-4b.
Figure 3-4 Sinusoidal fluctuating stresses (a) with zero mean and (b) with nonzero mean
19
The following relationships and definitions are defined when discussing cyclic loading:
Sa : Alternating stress amplitude
Sr : Stress range
Sm : Mean stress
Smax: Maximum stress amplitude
Smin : Minimum stress amplitude
R : Stress ratio, Smin / Smax (3.1)
A : Amplitude ratio, Sa/Sm (3.2)
Although stress components have been defined by using a sinusoidal stress, the exact shape of
the stress versus time curve does not appear to be of particular significance. Most of the time,
random type loading is present in mechanical systems.
In place of the graphical approach a power relationship can be used to estimate the S-N curves.
The relation suggested by Basquin in 1910 is in the form
N.Sb = C (3.3)
Where;
N : The number of cycles to failure at stress level, S
S : Stress amplitude
b : Stress (Basquin) exponent
C : Constant
In the above expression the stress tends towards zero when N tends towards the infinite. This
relation is thus representative of the S-N curve only in intermediate zone (high cycle region)
between infinite life and low cycle.
The range of variation of b is between 3 and 25 for the metals. However, the most common
values are between 3 and 10 [30]. M.Gertel and C.E.Crede, E.J.Lunney proposed a value of 9 to
be representative of the most materials. This led to the choice of 9 by such standards as MIL-
STD-810, etc. This value is satisfactory for copper and most light alloys but it may be unsuitable
for other materials. For example, for steels, the value of b varies between 10 and 14 depending
20
on the alloy. Therefore it is necessary to be very careful in choosing the value of this parameter
(average value) especially when reducing test times for constant fatigue damage testing
(qualification tests) [30] [32].
The relation between the stress exponent b is related to the slope of the S-N curve by
b =1/ log10 (slope) (3.4)
Due to the exponential nature of the S-N relationship, slight change in stress can cause
considerable change in fatigue life. For example if b is taken as 10, which is an approximate
value for the soft solder (63-37 Tin-Lead), then if the stress level is increased by a factor of 2,
fatigue life will be reduced by a factor of 103.
Fatigue life depends primarily on the amplitude of stress or strain but this is modified by the
mean value of stress existing in the component. Many components carry some form of “dead
load” before the working stresses are applied, and some way of allowing for this is then needed.
The magnitude of the mean stress has an important influence on the fatigue behavior of the
specimen particularly when the mean stress is relatively large compared to alternating stress. The
influence of mean stress on fatigue failure is different for compressive mean stress values than
for tensile mean stress values.
In the tensile mean stress region, the allowable amplitude of alternating fatigue stress gets
smaller as the mean stress becomes more tensile whereas in the compressive mean stress region,
failure is rather insensitive to the magnitude of the mean stress and fatigue life increases to a
lesser extent.
Moreover the influence of mean stress in the compressive region is greater for shorter lives than
for longer lives [33] such that if the stresses are enough large to produce significant repeated
plastic strains as in the low cycle fatigue, the mean stress is quickly released and its effect can be
weak [34][35].
21
S-N curves of material when there is nonzero mean stress can be represented by plotting Sa
versus N for various values of Sm . Empirical relations are then derived in accordance with Sm
for the constants “C” and “b” of the Basquin’s relation N.Sb = C . Tensile mean stress existing in
the structure reduces the endurance limit of the system as shown in Figure 3-5.
Figure 3-5 Example of S-N curve with non zero means stress [36]
The application of static stress led to a reduction in Sa as stated above. It is thus interesting to
know the variations of Sawith Sm.Several empirical relationships that relate failure at a given life
under nonzero mean conditions to failure at the same life under zero mean cyclic stresses have
been developed. These methods use various curves to connect the fatigue limit on the alternating
stress axis to either the yield strength, ultimate strength, or the true fracture stress on the mean
stress axis. By using these methods, for finite-life calculations, the endurance limit can be
replaced with purely alternating stress (zero mean stress) level corresponding to the same life as
that obtained with the stress condition Sa and Sm .The value for this fully reversed alternating
stress can then be entered on the S-N diagram to obtain the life of the component.
In this research, random vibration load is defined, which is given by the customer, in terms of its
magnitude at different frequencies in the form of Power spectral Density (PSD) plot. Therefore
frequency domain method will be used instead of time domain approach to analyze the DC-Link
Capacitor fatigue failures.
22
3.1.3 Frequency Domain Approach
In this research, Commercial software is used for frequency domain vibration fatigue analysis of
the DC-Link Capacitor. The details of the vibration fatigue life prediction approach are outlined
in Figure 3-6 below:
Figure 3-6 Schematic presentation of analysis process used in the thesis work
23
Finite Element based tools for fatigue life prediction are now widely available. It is necessary to
define vibration induced fatigue as the estimation of fatigue life when the stress histories
obtained from the structure or components are random in nature.
There are several alternative ways of specifying the same random process. Fourier analysis
allows any random loading history of finite length to be represented using a set of sine wave
functions, each having a unique set of values for amplitude, frequency and phase. It is still time
based and therefore specified in the time domain. As an extension of Fourier analysis, Fourier
transforms allow any process to be represented using a spectral formulation such as a Power
Spectral Density (PSD) functions. It is described as a function of frequency and is therefore said
to be in the frequency domain (Figure 3-7). It is still a random specification of the function. In a
frequency domain representation, it is possible to see trends that would be impossible to identify
in the time domain. For example natural frequencies of vibration are easily detected.
Figure 3-7 Random processes [37]
Random vibrations are generally represented by power spectral density functions in frequency
domain. In Many design standards give data on random processes in the form of power spectral
24
density functions (PSD). In this research, data on random loading in the form of PSD is obtained
from the client of PTMC.
In order to obtain the PSD of the input loading, first of all it is necessary to transform the loading
input in the time domain in to the frequency domain. This is achieved by Fourier series
representation. In practice however, time histories will be recorded digitally by a computer in a
discrete format .Therefore what is really needed is a discrete version of the Fourier transform
pair which can be applied to real, digitally recorded data.
The discrete transform pair does the same job as the Fourier transform pair but operates on
digitally recorded data. A very rapid discrete Fourier transform algorithm was developed in
1965, by Cooley and Tukey, known as the ‘Fast Fourier Transform’ (or FFT) [37] (Figure 3-8).
Figure 3-8 using an FFT to characterize a time signal [37]
PSDs are obtained by taking the modulus squared of the Fast Fourier Transform (FFT). The PSD
is a statistical way of representing the amplitude content of a signal. The FFT outputs a complex
number given with respect to frequency but in a PSD only the amplitude of each sine wave is
retained (Figure 3.8). In the definition of the PSD given in Figure 3-9 stands for the sample
period which can also be defined as 1 𝑓𝑠 ⁄ , 𝑓𝑠 being the sampling frequency of the recorded signal.
All phase information is discarded. In most engineering situations, it is only the amplitude of the
25
various sine waves that is of interest. In fact, in many cases it is found that the initial phase angle
is totally random, and so it is unnecessary to show it.
For this reason the PSD function alone is usually used. In ANSYS, the input loading can be
defined in the form of PSD. The user can enter random loading as a plot. One very useful
characteristic can be calculated directly from the PSD is the so-called root mean square (RMS)
value of the input loading. It is defined as the square root of the area under the PSD curve.
Figure 3-9 Definition of PSD [37]
In order to predict the probable stress (or acceleration levels) levels the electronic equipment will
see in a random vibration environment, it is necessary to understand probability distribution
functions. The distribution most often encountered, and the one that lends itself most readily to
analysis, is the Gaussian (or normal) distribution, which is defined by
𝑌 = 𝑒
−𝑋2
2𝜎2
𝜎√2𝜋 (3.5)
The right side of the above equation represents the probability density function, or the
probability, per unit of X, for the ratio of the instantaneous acceleration (X) to the RMS
acceleration (σ).
The Gaussian distribution curve, shown in figure 3-10, represents the probability for the value of
the instantaneous acceleration levels at any time. The abscissa is the ratio of the instantaneous
26
acceleration to the RMS acceleration, and the ordinate is the probability density, sometimes
called the probability of occurrences.
Figure 3-10 Gaussian distribution curve. The probability of a range of X is given by the area
under the curve in that range [27].
The total area under the curve is unity. The area under the curve between any two points then
directly represents the probability that the accelerations will be between these two points. For
example, the shaded area under the curve in Figure 3-10 shows that the instantaneous
accelerations will be between + l σ and - l σ about 68.3% of the time.
Figure 3-10 can be presented in another way, as shown in Figure 3-11. This plot shows the
probability that a given acceleration level will be exceeded.
Figure 3-11 another method for showing the Gaussian distribution [27].
27
Figures 3-10 and 3-11 show how the Gaussian distribution relates to the magnitude of the
acceleration levels expected for random vibration. The instantaneous acceleration will be
between the + 1σ and the - 1σ values 68.3% of the time. It will be between the +2σ and the - 2σ
values 95.4% of the time. It will be between the + 3σ and the -3σ values 99.73% of the time.
Another way of expressing the Gaussian distribution is shown in Figure 3-11 as follows. The
instantaneous acceleration will exceed the la value, which is the RMS value, 31.7% of the time.
It will exceed the 2σ value, which is two times the RMS value, 4.6% of the time. It will exceed
the 3σ value, which is three times the RMS value, 0.27% of the time.
It is important to remember that in a random vibration environment, all of the frequencies in the
bandwidth are present instantaneously and simultaneously.
Likewise, the lσ (or RMS), the 2σ, and the 3σ acceleration levels are all present at the same time
in the proportions shown above. Remember also that the square root of the area under the PSD-
versus-frequency curve represents the RMS accelerations in gravity units (G). The square root of
the area under the input PSD curve represents the input RMS acceleration level, and the square
root of the area under the response (or output) PSD curve represents the response RMS
acceleration level.
The maximum acceleration levels considered for random vibrations are the 3σ levels, because
the instantaneous accelerations are between the + 3σ and the -3σ levels 99.73% of the time,
which is very close to 100% of the time. Higher acceleration levels of 4σ and 5σ can occur in the
real world, but they are usually ignored because virtually all of the test equipment for random
vibration has 3σ clippers built into the electronic control systems. These clippers limit the input
acceleration levels to values that are 3 times greater than the RMS input levels.
Displacements, forces, and stresses will occur in exactly the same proportions as the
accelerations described above, for linear systems. In other words, the maximum displacements,
forces, and stresses expected in a random vibration environment will be 3 times greater than the
RMS displacements, forces, and stresses.
28
Every structural member has a useful fatigue life and that every stress cycle uses up a part of this
life. When enough stress cycles have been accumulated, the effective life is used up and the
component will fail. Component damage calculation, in this thesis, will be performed by using
Palmgren-Miner's rule.
3.2 Palmgren-Miner Rule
Almost all available fatigue data for design purposes is based on constant amplitude tests.
However, in practice, the alternating stress amplitude may be expected to vary or change in some
way during the service life when the fatigue failure is considered. The variations and changes in
load amplitude often referred to as spectrum loading, make the direct use of S-N curves
inapplicable because these curves are developed and presented for constant stress amplitude
operation.
The key issue is how to use the mountains of available constant amplitude data to predict fatigue
in a component. In this case, to have an available theory or hypothesis becomes important which
is verified by experimental observations. It also permits design estimates to be made for
operation under conditions of variable load amplitude using the standard constant amplitude S-N
curves that are more readily available.
Many different cumulative damage theories have been proposed for the purposes of assessing
fatigue damage caused by operation at any given stress level and the addition of damage
increments to properly predict failure under conditions of spectrum loading. Collins, in 1981,
provides a comprehensive review of the models that have been proposed to predict fatigue life in
components subject to variable amplitude stress using constant amplitude data to define fatigue
strength.
The original model, a linear damage rule, originally suggested by Palmgren (1924) and later
developed by Miner (1945) [10]. This linear theory, which is still widely used, is referred to as
the Palmgren-Miner rule or the linear damage rule.
29
Life estimates may be made by employing Palmgren-Miner rule along with a cycle counting
procedure. Target is to estimate how many of the blocks can be applied before failure occurs.
This theory may be described using the S-N plot.
In this rule, the assumptions can be summarized as follows:
i) The stress process can be described by stress cycles and that a spectrum of amplitudes of
stress cycles can be defined. Such a spectrum will lose any information on the applied
sequence of stress cycles that may be important in some cases.
ii) A constant amplitude S-N curve is available, and this curve is compatible with the
definition of stress; that is, at this point there is no explicit consideration of the possibility
of mean stress.
Figure 3-12 Spectrums of amplitudes of stress cycles [10]
In Figure 3-12, a spectrum of amplitudes of stress cycles is described as a sequence of constant
amplitude blocks, each block having stress amplitude Si and the total number of applied cycles
ni. The constant amplitude S-N curve is also shown in Figure 3-13.
By using the S-N data, number of cycles of S1 is found as N1 which would cause failure if no
other stresses were present. Operation at stress amplitude S1 for a number of cycles n1 smaller
than N1 produces a smaller fraction of damage which can be termed as D1 and called as the
damage fraction.
30
Figure 3-13 Constant amplitude S-N curve [10]
Operation over a spectrum of different stress levels results in a damage fraction Di for each of the
different stress levels Si in the spectrum. It is clear that, failure occurs if the fraction exceeds
unity:
𝐷1 + 𝐷2 + … … . . +𝐷𝑖−1 + 𝐷𝑖 ≥ 1.0 (3.6)
According to the Palmgren-Miner rule, the damage fraction at any stress level Si is linearly
proportional to the ratio of number of cycles of operation to the total number of cycles that
produces failure at that stress level, that is
𝐷𝑖 = 𝑛𝑖
𝑁𝑖 (3.7)
Then, a total damage can be defined as the sum of all the fractional damages over a total of k
blocks,
𝐷 = ∑𝑛𝑖
𝑁𝑖
𝑘𝑖=1 (3.8)
and the event of failure can be defined as D ≥1.0 (3.8)
31
The limitations of the Palmgren-Miner rule can be summarized as the following:
i) Linear: It assumes that all cycles of a given magnitude do the same amount of damage,
whether they occur early or late in the life.
ii) Non-interactive (sequence effects): It assumes that the presence of S2 etc. does not affect
the damage caused by S1.
iii) Stress independent: It assumes that the rule governing the damage caused by S1 is the
same as that governing the damage caused by S2.
The assumptions are known to be faulty; however, Palmgren-Miner rule is still used widely in
the applications of the fatigue life estimates.
3.3 Fatigue Analysis Methodology
Analysis for random load is a two-step process. In the first step, a modal (Eigenvalue) analysis is
performed to obtain natural frequencies and modes of the structure. In the second step, the input
PSD (power spectrum density) spectra and damping ratio are specified and a spectrum analysis is
performed. The spectrum solution is obtained by the ANSYS’ mode superposition method.
Since random vibration analysis is probabilistic in nature, the ANSYS results are associated with
a probability distribution. ANSYS results are calculated for 1 standard deviation (1σ), meaning
that the resultant value (force, stress, displacement, etc) will be equal to or less than the stated
value 68.3% of the time (assuming a Gaussian distribution). For the purposes of analysis, the
maximum result parameters are evaluated up to the 3σ level. The probability of the result
parameter lying in the range defined by -3σ and +3σ is 99.73%. The probability that the result
parameter will exceed a 3σ value is 0.27%. As such, using values up to the 3σ level provides a
description of the maximum response of the structure 99.73% of the time. This is the accepted
practice for engineering calculation purposes.
For analyses requiring fatigue calculations, a cumulative fatigue damage index (CDI) parameter
is calculated. The CDI is determined using Miner's rule, which states that fatigue damage is
accumulated linearly based on the number of cycles at each discrete stress level and a constant
amplitude S-N (Stress to number of cycles) curve. The fraction of life consumed at each stress
32
level is the number of cycles sustained, nl , at the particular stress level, divided by the number of
cycles to failure at that stress level, Nl ,as defined by the S-N curve. Theoretical failure is
predicted to occur when the sum of all fractions at each stress level equals 1. Therefore for
failure:
∑ni
Ni
ki=1 ≥ 1 (3.9)
Where
k = number of stress levels
The stress levels chosen for evaluating the Fatigue Damage Index are the 1σ, 2σ and 3σ levels,
such as ANSYS stress value x (1, 2 or 3 respectively). The stress value may be multiplied by an
applicable stress concentration factor. Alternately, an S-N curve for a known stress concentration
could be used to evaluate Ni. To calculate the number of cycles sustained by the unit at the 1σ,
2σ and 3σ stress levels, the dominant natural frequency must be determined. This frequency is
taken from the modal analysis results at the frequency (ies) with the highest effective mass. This
frequency is then used to calculate the total number of cycles using the following formula:
M = f × t × C (3.10)
Where
f = frequency (Hz , cycles per second)
t = test duration (hours)
C = conversion factor (3600 seconds/hour)
To obtain the number of cycles at the 1σ, 2σ and 3σ stress levels, the probability associated with
each level is multiplied by the total number of cycles (M).
Number of service cycle at 1σ level , n1 = M × 0.683 (3.11)
Number of service cycle at 2σ level, n2 = M × 0.271 (3.12)
Number of service cycle at 3σ level, n3 = M × 0.0433 (3.13)
In summary, the part or structure is considered acceptable if:
n1
N1+
n2
N2+
n3
N3<
1
FS (3.14)
Where, FS= Factor of safety on life
33
3.4 Thermal Stress Analysis due to Temperature Loading
The heat transfer analysis was previously performed to determine temperatures of the
components of DC-Link Capacitor as well as HPSM. This analysis helps to ensure materials and
components do not exceed their allowable temperature limit and provides the temperature
regarding for stress analysis
The results are used to determine the survivability of the components and materials in the DC-
Link Capacitor. The results are also used for thermal stress calculations of the different parts of
the DC-Link Capacitor.
The temperature distribution in a part causes thermal stress effects (stresses caused by thermal
expansion or contraction of the material). Examples of this phenomena include interference fit
processes (also called shrink or press fit, where parts are mated by heating one part and keeping
the other part cool for easy assembly) and creep (permanent deformation resulting from
prolonged application of a stress below the elastic limit, such as the behavior of metals exposed
to elevated temperatures over time).
Thermal expansion is the tendency for a material's volume to change in response to a change in
temperature. Most materials undergo an increase in volume when subjected to a positive change
in temperature, hence the name thermal expansion. However, some materials will exhibit thermal
contraction, or negative thermal expansion (NTE), and decrease in volume when subjected to a
positive temperature change. The materials that exhibit this behavior typically only do so over a
small temperature range, rendering them difficult to use in real-world situations.
Thermal stresses occur when there is differential expansion in a structure
Two materials connected, uniform temperature change (different thermal expansion
coefficients lead to differential expansion)
Temperature gradient in single material (differential expansion is from temperature variation)
34
The degree of linear or volume expansion of a material with increasing temperature is an
important thermo-mechanical parameter in predicting and assessing stresses.
The coefficient of thermal expansion (CTE) may be based on either linear or volume expansion.
Unless otherwise stated, CTE for this discussion is based on linear expansion and is the ratio of
the change in length per °C to the length at 0°C, as follows:
lT = l0 (1 + αT) (3.15)
Or
α = (lT − l0)/l0T (3.16)
where lT is the length at temperature T, l0 is the length at 0°C, and α is the CTE. Coefficients of
thermal expansion are reported as in/in/0°C or, more generally, as unit/unit/0°C or ppm/0°C.
CTEs vary with temperature and are usually reported for a temperature range. The coefficients of
volume expansion are generally three times those for linear expansion.
A temperature change of ∆T with respect to a base or reference level produces a thermal strain
εt = α∆T (3.17)
Thermal stress is the product of thermal strain and modulus of elasticity (E) of the material that
is
σt = Eεt (3.18)
3.5 Thermal Stress Analysis Methodology
Thermal stress effects can be simulated by coupling a heat transfer analysis (steady-state or
transient) and a structural analysis (static stress with linear or nonlinear material models or
Mechanical Event Simulation). The process consists of two basic steps:
A heat transfer analysis is performed (previously) to determine the temperature distribution;
and
35
The temperature results are directly input as loads in a structural analysis to determine the
stress and displacement caused by the temperature loads.
In this study, the structural analysis is done by using one of the numerical analyzing methods
called “Finite Elements”.
Finite Elements Method (FEM) is a numerical technique for finding approximate solutions of
partial differential equations as well as of integral equations. The basic idea of FEM is to divide
the body into finite elements, often just called elements, connected by nodes and obtain an
approximate solution. The stages of finding approximate solution with FEM method is as
follows:
Step (i): Discretization of the structure
The first step in the Finite Elements Method is to divide the structure or solution region into
subdivisions or elements. Hence, the structure is to be modeled with suitable finite elements. The
number, type, size, and arrangement of the elements are to be decided.
Step (ii): Selection of a proper interpolation or displacement model
Since the displacement solution of a complex structure under any specified load conditions
cannot be predicted exactly, we assume some suitable solution within an element to reach the
unknown solution. The assumed solution must be simple from a computational standpoint, but it
should satisfy certain convergence requirements. In general, the solution or the interpolation
model is taken in the form of a polynomial.
Step (iii): Derivation of element stiffness matrices and load vectors
From the assumed displacement model, the stiffness matrix [K(e)] and the load vector P⃗⃗⃗(e)of
element “e” are to be derived by using either equilibrium conditions or a suitable variational
principle.
36
Step (iv): Assemblage of element equations to obtain the overall equilibrium equations
Since the structure is composed of several finite elements, the individual element stiffness
matrices and load vectors are to be assembled in a suitable manner and the overall equilibrium
equations have to be formulated as
[K] ∅̅ = P̅ (3.19)
Where [K] ] is the assembled stiffness matrix, ∅̅ is the vector of nodal displacements, and P̅ is
the vector of nodal forces for the complete structure.
Step (v): Solution for the unknown nodal displacements
The overall equilibrium equations have to be modified to account for the boundary conditions of
the problem. After the incorporation of the boundary conditions, the equilibrium equations can
be expressed as
[K] ∅̅ = P̅ (3.20)
For linear problems, the vector ∅̅ can be solved very easily. However, for nonlinear problems,
the solution has to be obtained in a sequence of steps, with each step involving the modification
of the stiffness matrix [K] and/or the load vector P̅
Step (vi): Computation of element strains and stresses
From the known nodal displacements ∅̅ , if required, the element strains and stresses can be
computed by using the necessary equations of solid or structural mechanics.
In this study, software called ANSYS is used in order to analyze the heat transfer. All Finite
Elements Methods’ stages which are explained above have been developed by ANSYS.
37
CHAPTER 4: CAD AND FE MODEL OF HPSM
4.1 PTMC and HPSM
The Power and Thermal Management Controller (PTMC) provides control to aircraft auxiliary
power, cabin cooling and pressurization, avionics cooling, and mechanical equipment thermal
management. This controller consists of two sub-controllers: the Integrated Power Package
Controller (IPPC) and the Electrical Power Controller (ICC). The IPP interfaces with Vehicle
Management System (VMS) to provide power to start the main engine and to control the cooling
load accommodation in the aircraft.
The PTMC is cooled by a liquid coolant flowing through ducts in the outer walls of the chassis.
In order to maximize cooling, the liquid coolant ductwork is routed to run adjacent to the top and
bottom CCA edge interfaces. The liquid coolant ductwork also runs in the wall directly
underneath the interface to the Electromagnetic Interference (EMI) Filter module. Finally the
liquid coolant is ducted into the HPSM where it removes heat from this module via a heat sink.
High Power Switch Module (HPSM) (Figure 4-2) consists of the following main subassemblies:
Gate Driver Circuit Card Assembly (CCA) , two DC-link Capacitors integrated with DC bus bar
and Snubber caps, and six IGBT Modules (Integrated Gate Bipolar Transistors) mounted on
HPSM Heat Exchanger (Hx) cooled by the liquid coolant and CCA.
4.2 CAD Model of HPSM
In this research, Design for Manufacturing and Assembly (DFMA) process, which considers
piece count reduction, was used to redesign the DC-link capacitor integrated with DC bus bars
and Snubber caps. After redesigning of the above mentioned subassembly, CAD model of the
every component of the subassembly was developed by using Pro/Engineer, a CAD/CAM,
38
feature based solid modeling program. There are various commercial Computer Aided Design
(CAD) software packages available including AutoCAD, SolidWorks, UniGraphics, CATIA,
and Pro/Engineer. Pro/Engineer was selected because it has powerful surface generating
functions and it is easier to change parameters directly in this software.
The DC-link capacitor integrated with DC bus bars and Snubber caps is shown below:
Figure 4-1 CAD model of the DC-link capacitor integrated with DC bus bars and Snubber caps
The above mentioned subassembly was assembled into the High Power Switch Module. The
assembly CAD model of HPSM, which is integrated with DC-link capacitor, DC bus bars,
Snubber caps, Insulated-gate bipolar transistor (IGBT), Heat Sink and IGBT Gate Driver CCA,
was also developed by using Pro/Engineer. The HPSM assembly and the assembly CAD model
are shown below:
Figure 4-2 Assembly CAD Model of HPSM
39
4.3 Finite Element Model (FEM) of HPSM
The analysis was performed using the Finite Element (FE) Method. The FE program, ANSYS,
Rev. 15.0, was used to solve and post-process the analysis. The FE model was generated using
the ANSYS Workbench module by importing solid model from Pro/Engineer, a CAD/CAM,
feature based solid modeling program. The CAD model was simplified for the purpose of
analysis. Following were the assumptions for the HPSM assembly model:
a. The DC-Link Capacitor integrated with DC bus bars and Snubber caps, peripheral heat sinks
and other components, where applicable, were modeled with solid elements. The CCAs were
modeled with shell elements representing the printed wiring board (PWB) with their nominal
thickness.
b. For dynamic analysis, modal damping ratio of 5% was used for all components of the model.
The damping ratio was specified as a material parameter in the ANSYS software.
c. A web (or spoke) made of beam elements were connected to the fastener holes. The centre of
the web in the corresponding fastener holes was connected by a beam element representing the
fastener. In the FE model, the fastener is considered for the purpose of load transfer between
components and therefore is characterized to be rigid and of negligible mass.
d. In general, where necessary, the structural component densities are adjusted to reflect the
measured or estimated design weight. The total DC-Link Capacitor integrated with DC bus bars
and Snubber caps mass calculated by using the ANSYS FE model. The weight breakdown of the
DC-Link Capacitor integrated with DC bus bars and Snubber caps is showed in Appendix-A.
40
4.3.1 Materials of the Model
The HPSM assembly consists of several parts. For each single part a single property card was
defined which includes information on the material and section specification of the
corresponding part. For solid part, the property card specifies only the material specification, i.e.
Young Modulus (Y) and Poisson’s Ratio (υ). A thin-shell property card includes material
specification plus the thickness of the shell. In this research, various types of materials such as
Aluminum, Copper, FR4 (Glass Fabric Reinforcement), and Dually Phthalate were selected for
various components of the model. FR4 was selected because it has extremely high mechanical
strength at moderate temperature and very good stability of electrical properties under high
humidity. Al 5052-H32, this alloy has good workability, very good corrosion resistance, high
fatigue strength, and moderate strength. Other materials those were selected have specific
characteristics which are suitable for the assigned components of the model.
Table 4-1 shows lists of mechanical properties of the materials for the key components of the
HPSM used in the FE model.
Material / Properties
Temp Density Elasticity Modulus Poisson Ratio
T 𝜌 Y υ
Units deg F lb/in^3 psi
Material A 70 0.0968 1.01E+07 0.33
Material B 70 0.0975 1.0E+07 0.33
Material C 70 0.06 3.0E+06 0.112
Material D 70 0.0314 55 0.3
Material E 70 0.323 1.7E+07 0.3
Material F 70 0.0676 1.7E+05 0.3
Table4-1 Mechanical Properties of the materials for the various components of HPSM
41
Following S-N curves were utilized for computing the Cumulative Damage Index (CDI) during
spectrum analysis:
Figure 4-3 S-N curve for Al 5052 (Material A)
Figure 4-4 S-N curve for Al 6061
42
4.3.2 Connections of the Model
During analysis, automatic bonding and beam connections were considered to make joint among
various parts of the model. Beam connections were considered to make join between IGBT &
Heat Sink; IGBT & DC-Link Capacitor; Gate Driver & PCB mounting bracket; Mounting
Bracket & IGBT; and Gate Driver & Heat Sink. Figure4-5 shows the beam connections among
various components of the HPSM.
Figure 4-5 Beam Connections among various components of the assembly model
4.3.3 Boundary Condition of the Model
Bottom of the HPSM assembly model will be attached with the one of the panels of the chassis.
In physically, HPSM, which has ten holes at the bottom, is connected on the panel by ten screw-
nuts. In this research, inside regions of these ten holes at the bottom of the HPSM were
considered as fixed regions.
Figure 4-6 Boundary Conditions (fixed support) at the bottom of the assembly model
43
4.3.4 Mesh of the Model
The mesh quality and size were chosen to be uniform throughout the model with Tet10
(Tetrahedral), Hex20 (Hexahedral) and Wed15 elements. In this research, natural frequencies
for the first, second and third modes of the model were computed by varying the element
numbers of the model which sown in the table 4-2.
Element Number Natural Frequency for
the First Mode
Natural Frequency for
the Second Mode
Natural Frequency for
the Third Mode
123686 177.99 216.43 233.96
127027 180.22 213.44 232.23
140332 179.47 209.96 228.66
147223 178.47 209.76 220.42
Table4-2 No. of elements of the model and corresponding natural frequencies for various modes
Figure 4-7 Natural frequency Vs Number of Element Curve
The figure 4-7 shows that natural frequency for the first mode is not too much sensitive with the
number of element of the model. In this research, a fairly large FE model having 138315 element
and 282080 nodes was used which necessitated using a powerful computing machine to obtain
0
50
100
150
200
250
120000 130000 140000 150000
Nat
ura
l Fre
qu
en
cy i
n H
z
Number of Element
Frequency Vs Number of Element
Natural Frequencyfor the 1st Mode
Natural Frequencyfor the 2nd Mode
Natural Frequencyfor the 3rd Mode
44
the desired solution in a reasonable amount of time. Figure 4-8 represents the mesh model of the
HPSM assembly.
Figure 4-8 Mesh Model of the HPSM Assembly
45
CHAPTER 5: FINITE ELEMENT ANALYSIS OF
HPSM AND RESULTS AND DISCUSSION
5.1 Fatigue Analysis
Finite Element based tools for fatigue life prediction are now widely available. The basic aim of
such tools is to enable fatigue life calculations to be done at the design stage of a development
process. Nearly all structures or components have traditionally been designed using time based
structural and fatigue analysis methods. However, by developing a frequency based fatigue
analysis approach, the true composition of the random stress or strain responses can be retained
within a much optimized fatigue design process.
In this research, frequency based fatigue technique was used because this can yield many
advantages, the most important being, (i) an improved understanding of system behavior, (ii) the
capability to fully include the true structural behavior rather than a potentially inadequate
simplified version and (iii) a more computationally efficient fatigue analysis procedure.
Analysis for random load is a two-step process. In the first step, a modal (Eigenvalue) analysis
was performed to obtain natural frequencies and modes of the structure. In the second step, the
input PSD (power spectrum density) spectra and damping ratio were specified and a spectrum
analysis was performed.
The above mentioned two steps for random load analysis which were performed in this research
have been explained step by step in this chapter.
46
5.1.1 Modal Analysis
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and
frequencies of the model during free vibration. It is commons to use into the finite element
method (FEM) to perform this analysis because, like other calculations using the FEM, the object
being analyzed can have arbitrary shape and the results of the calculations are acceptable. The
types of equations which arise from modal analysis are those seen in Eigen systems. The
physical interpretation of the Eigen values and Eigenvectors which come from solving the
system are that they represent the frequencies and corresponding mode shapes. Sometime, the
only desired modes are the lowest frequencies because they can be the most prominent modes at
which at the object will vibrate, dominating all the higher frequency modes.
A normal mode of an oscillating system is a pattern of motion in which all part of the system
move simultaneously with the same frequency and in phase. The frequencies of the normal
modes of a system are known as its natural frequencies or resonant frequencies. A physical
object, such as DC-link capacitor, has a set of normal modes that depend on its structure,
materials and boundary conditions. A mode of vibration is characterized by a modal frequency
and a mode shape, and is numbered according to the number of half waves in the vibration. For
example, if a vibrating beam with both ends pinned displayed a mode shape of half of a sine
wave (one peak on the vibrating beam) it would be vibrating in mode 1. If it had a full sine wave
(one peak and one valley) it would be vibrating in mode 2.
Each mode is entirely independent of all other modes. Thus all modes have different frequencies
(with lower modes having lower frequencies) and different mode shapes.
In this thesis, Modal analysis was carried out to determine the natural frequencies and mode
shapes up to 2000 Hz which were taken into consideration in calculations. During the model
analysis, damping and any applied loads were ignored.
In many engineering applications damping effects are neglected and the system matrices are
symmetric. For those problems ANSYS provides various Eigen solvers such as Block Lanczos
method, Subspace method, Reduced method and Power dynamics method. In this research, the
Block Lanczos method was used because it is a very efficient algorithm to perform a modal
analysis for large models. Moreover, HPSM assembly model was combination of solids and
47
shells and this solver performs well when the model consists of shells or a combination of shells
and solids. The first mode shape of the HPSM assembly model is showed in Figure 5-1.
Figure 5-1 First Mode Shape of the HPSM Assembly Model
The first mode is a sideways motion with 178.79 Hz. Viewed from the left side (not shown) the
motion occurs at about 30° to the tangential. Second and third mode shapes are shown at
appendix C.
Modal analysis, which precedes the random vibration analysis, was performed to obtain the
natural frequencies of the structure (Assembly model). Table 5-1 presents the first six natural
frequencies of the structure.
Mode Frequency (Hz)
1 178.79
2 214.77
3 232.76
4 257.18
5 275.18
6 277.16
Table 5-1 First six natural frequencies of the HPSM assembly model
48
The natural frequencies and mode shapes are important parameters in the design of a structure
for dynamic loading conditions. Mode shape pictures are helpful in understanding how a part or
an assembly vibrates, but do not represent actual displacements. This modal analysis has served
as a starting point for more detailed dynamic analysis.
5.1.2 Random Vibration Analysis
In this research, the severity of damage for random vibration was specified in terms of its power
spectral density (PSD), a measure of vibration signal’s power intensity in the frequency domain.
Looking at the time–history plot in Figure 3-7, it is not obvious how to evaluate the constantly
changing acceleration amplitude. The way to evaluate is to determine the average value of all the
amplitudes within a given frequency range. Although acceleration amplitude at a given
frequency constantly changes, its average value tends to remain relatively constant. This
powerful characteristic of the random process provides a tool to easily reproduce random signals
using a vibration test system.
In this research, random vibration analysis was performed over a large range of frequencies. This
research did not focused on a specific frequency or amplitude at a specific moment in time but
rather statistically looked at a structure’s response to a given random vibration environment.
Certainly, this research tried to find out if there was any frequency that causes a large random
response at any natural frequency, but mostly, wanted to find out the overall response of the
structure. The square root of the area under the PSD curve gives the root mean square (RMS)
value of the acceleration, or Grms, which is a qualitative measure of intensity of vibration.
49
In this research, customer given random vibration profile was used to performed spectrum
analysis. Figure 5-2 presents the customer given random vibration profile.
Figure 5-2 PSD Loading Curve
Table 5-2 lists the power spectral density (PSD) levels. Forcing frequency range is from 15 Hz to
2000 Hz.
Frequency
[Hz]
PSD [G2/Hz]
15 0.031
47 0.031
200 0.136
900 0.136
2000 0.028
Table 5-2 Random Vibration PSD
0
0.05
0.1
0.15
0 500 1000 1500 2000 2500
PSD
[G
2 /H
z]
Frequency [Hz]
Random Vibration Profile
50
In this research, customer given random vibration profile and power spectral density (PSD)
levels over a specified forcing frequency range were used to performed spectrum analysis.
In this analysis, the duration for the random vibration test representing one life of the controller
was 8 hours along each axis. Analysis was performed in each orthogonal direction. Numbers of
service cycles at various levels were calculated by using equations 3.11, 3.12 and 3.13.
To obtain the number of cycles at the 1σ, 2σ and 3σ stress levels, the probability associated with
each level was multiplied by the total number of cycles (M).
The No. of cycles at 1σ stress level, n1 = M × 0.683 = f × t × C × 0.683 = 3516871
The No. of cycles at 2σ stress level, n2 = M × 0.271 = f × t × C × 0.271 = 1395420
The No. of cycles at 3σ stress level, n3 = M × 0.0433 = f × t × C × 0.0433 = 222958
Table 5-3 represents the number of service cycle (n) at various stress levels for the natural
frequency of the first mode.
Stress level: σ1 Stress level : σ2 Stress level : σ3
Probability 0.683 0.271 0.0433
Duration(hrs), t 8 8 8
Factor (sec/hr), C 3600 3600 3600
Natural Frequency (Hz), f 178.79 178.79 178.79
No. of Service Cycle (n) 3516871 1395420 222958
Table 5-3 No. of Service Cycle (n) at Various Levels
51
Computed von- Mises stresses in X direction are showed in figure 5-3 & 5-4 respectively for
HPSM assembly model and the weakest component of the model and response PSD at critical
location is presented in figure 5-5.
Figure 5-3 Max. Von-Mises stress (3992.2 psi) on assembly model at X direction
Figure 5-4 Max. Von-Mises stress (3992.2 psi) on weakest component at X direction
Figure 5-5 Response PSD at Critical Location
All other figures, which show the von-Mises stresses at weakest component along the Y and Z
directions, are shown into appendix D.
Frequency
Res
po
nse
PSD
[in
2 /Hz]
52
In this research, equivalent von-Mises stresses for fatigue were calculated after getting maximum
von-Mises stress (3992.2 psi) for the weakest component. These were done by simply multiplying
the maximum von-Mises stresses with corresponding casting factor, fitting factor and stress level
factor. By using S-N data for Al 5052 (Figure 4-3), numbers of cycles, which could cause failure,
were obtained corresponding equivalent von-Mises stresses for fatigue at various stress levels.
In this analysis, damage fraction was calculated by using equation 3.7 and finally Cumulative
Damage Index (CDI) was obtained from equation 3.8. Cumulative Damage Index in X direction is
showed in Table 5-4.
Stress level: σ1 Stress level : σ2 Stress level : σ3
maxSEQV (psi) 3992.2 3992.2 3992.2
Factor 1 2 3
Casting Factor 1 1 1
Fitting Factor 1.15 1.15 1.15
Equivalent von Mises Stress
for Fatigue (SEQVf) (psi)
4591.03 9182.06 13773.09
Number of cycles which could
cause failure, N (from S-N
curve based on SEQVf) 5.00E+08 5.00E+08 5.00E+08
Number of Service cycles, n 3516871 1395420 222958
Damage Index (DI) = n/N 0.0070 0.0028 0.0004
Cumulative Damage Index
(CDI), 𝐷 = ∑𝑛𝑖
𝑁𝑖
3𝑖=1 0.01
Table 5-4 Cumulative Damage Index (0.01) at X direction
Since the calculated Cumulative Damage Index along X-direction is less than one, the weakest
component will survive at least 2 lives per customer requirement.
53
In this research, Cumulative Damage Indices of the weakest component along other orthogonal
directions were also calculated as same way as X direction.
Damage Index along Y-direction was calculated by dividing the number of cycles found in the
frequency domain for each stress along Y- direction to the number of cycles found from the S-N
curve for Al 5052 (Figure 4-3). Cumulative Damage Index (CDI) along Y-direction was obtained
from equation 3.8.
Table 5-5 presents the numbers of service cycles, numbers of cycles which could cause failure,
damage fraction and Cumulative Damage Index at Y-direction.
Stress level: σ1 Stress level : σ2 Stress level : σ3
maxSEQV (psi) 4577.9 4577.9 4577.9
Factor 1 2 3
Casting Factor 1 1 1
Fitting Factor 1.15 1.15 1.15
Equivalent von Mises Stress
for Fatigue (SEQVf) (psi)
5264.585 10529.17 15793.755
Number of cycles which could
cause failure, N (from S-N
curve based on SEQVf) 5.00E+08 5.00E+08 2.00E+08
Number of Service cycles, n 3516871 1395420 222958
Damage Index (DI) = n/N 0.0070 0.0028 0.0011
Cumulative Damage Index
(CDI), 𝐷 = ∑𝑛𝑖
𝑁𝑖
3𝑖=1 0.01
Table 5-5 Cumulative Damage Index (0.01) at Y direction
Since the calculated Cumulative Damage Index along Y-direction is less than one, the weakest
component will also survive at least 2 lives per customer requirement.
54
Damage Index along Z-direction was calculated by dividing the number of cycles found in the
frequency domain for each stress along Z- direction to the number of cycles found from the S-N
curve for Al 5052 (Figure 4-3). Cumulative Damage Index (CDI) along Z-direction was also
obtained from equation 3.8.
Table 5-6 presents the numbers of service cycles, numbers of cycles which could cause failure,
damage fraction and Cumulative Damage Index respectively Y direction.
Stress level: σ1 Stress level : σ2 Stress level : σ3
maxSEQV (psi) 4983.64 4983.64 4983.64
Factor 1 2 3
Casting Factor 1 1 1
Fitting Factor 1.15 1.15 1.15
Equivalent von Mises Stress
for Fatigue (SEQVf) (psi)
5731.186 11462.372 17193.558
Number of cycles which could
cause failure, N (from S-N
curve based on SEQVf) 5.00E+08 5.00E+08 1.00E+08
Number of Service cycles, n 3516871 1395420 222958
Damage Index (DI) = n/N 0.0070 0.0028 0.0022
Cumulative Damage Index
(CDI), 𝐷 = ∑𝑛𝑖
𝑁𝑖
3𝑖=1 0.01
Table 5-6 Cumulative Damage Index (0.01) at Z direction
Since the calculated Cumulative Damage Index along Z-direction is less than one, the weakest
component will also survive at least 2 lives per customer requirement.
55
5.2 Stress due to Temperature Loading
One of the objectives of this thesis is to carry out structural analysis to select appropriate material
for each components of DC-link Capacitor integrated with DC bus bar and Snubber caps. In
particular, it is intended that this analysis is employed to make a realistic assessment of the types
and values of materials properties that will provide “optimum” resistance to the thermal
(temperature) load experienced by the structure. Because of the complex nature of the problem
the finite element method is selected as an appropriate and versatile.
5.2.1 Materials
Table 5-7 lists mechanical (thermal) properties for the key components of the HPSM utilized in
the FE model.
Material / Properties
Name of the components
Reference Temp Linear Thermal
Expansion
T α
Units deg F in/in/℉
Material A
Component of M and P of
DC-Link Capacitor ,
Component A of CCA
70 1.23E-05
Material B IGBT, Heat Exchanger 70 1.31E-05
Material C Component B of CCA
70 1.60E-05
Material D Component E of DC-Link
Capacitor 70 9.8E-12
Material E
Component C and D of DC-
Link Capacitor, Component
A and B of DC Bus Bar
70 9.8E-06
Material F Component A and B of DC-
Link Capacitor 70 1.06E-05
Table 5-7 Thermal Properties for Various Component of HPSM
56
5.2.2 Temperature Distribution
Temperatures from previous thermal analysis were input as loads in the structural analysis to
determine the stress and displacement of all components of HPSM. Collected data are shown in
table 5-8.
Name of the components
Maximum Steady State Temperature (℉)
Component A of HPSM 201.2
DC-link Capacitor (Component E of HPSM) 183.2
Component B of HPSM 224.6
Component C of HPSM 240.8
Component D of HPSM 98.6
Table 5-8 Thermal Analysis Results from Pervious Thermal Analysis Report
The above maximum steady state temperatures were assigned to the corresponding component of
HPSM to carry out the structural analysis. The figure 5-6 shows the temperature distribution at
HPSM.
Figure 5-6 Temperature Distribution at the model
57
5.2.3 Structural Analysis
Structural analysis was carried out to determine the stress and displacement caused by the
temperature loads at various components of HPSM. In this analysis, same boundary condition
was considered as in fatigue analysis. Only temperature was considered as load in this analysis.
In this research, thermal stresses of all the components of DC-link capacitor integrated with DC
bus bar and Snubber caps were obtained from the analysis and compared with their materials
yield strength.
Thermal stress of the Component P of DC-Link Capacitor shown in figure 5-7 is more than its
material yield strength.
Figure 5-7 Equivalent Stress (Max: 28263 psi) at Component of P of DC-Link Capacitor
Figures which show the thermal stresses of other components of the HPSM are shown in
appendix E
58
Thermal stress at various components of HPSM and DC-Link Capacitor are shown in table 5-9.
Name of the components
Maximum Equivalent
Stress (von-Mises) (psi)
Allowable Stress
Component A of HPSM 31021 -
Component C of HPSM 13351 -
Component A of DC-Link Capacitor 336.21 -
Component B of DC-Link Capacitor 656.59 -
Component C of DC-Link Capacitor 1238.8 -
Component D of DC-Link Capacitor 6744.9 -
Component E of DC-Link Capacitor 0.13207 -
Component F of DC-Link Capacitor 2.6973 -
Component A of DC Bus Bar 5832.2 -
Component B of DC Bus Bar 3066.8 -
Component M of DC-Link Capacitor 15684 23000
Component P of DC-Link Capacitor 28263 23000
Component I of DC-Link Capacitor 671.45 -
Table 5-9 Thermal Stress at Various Components of DC-Link Capacitor and HPSM
Since the thermal stress of component P of DC- link capacitor, is greater than its material yield
strength, either x-sectional area of the component have to be increased or assigned different
material whose yield strength is greater than its calculated thermal stress due to temperature
loading.
59
5.3 Results and Discussion
5.3.1 Vibration Performance of the Redesign DC-Link Capacitor
In this research, random fatigue analysis is carried out to justify the structural functionality of the
redesigned DC-link Capacitor as well as modified HPSM. In this analysis, the duration for the
random vibration test representing one life of the controller is assumed as X hours along each
axis. Analysis is performed in each orthogonal direction. The number of service cycle (n), shown
in Table 5-3, at various stress levels are calculated and von- Mises stresses in all directions of
every component of new DC-link Capacitor are also calculated. In this analysis, the weakest
component of the modified DC-link Capacitors is identified and Cumulative Damage Index
(CDI) at all orthogonal direction for that component is calculated. Calculated CDI along the X, Y
and Z directions are respectively 0.01, 0.01 and 0.01. On the basis of CDI, it can be concluded
that modified DC-link Capacitor will survive at least X life cycles per customer requirement. So
structural functionally of modified and existing DC-link Capacitors is same.
5.3.2 Structural Functionality of the Redesign DC-Link Capacitor due to
Temperature Loading
In this research, structural analysis due to temperature loading is also performed to determine the
stress and displacement at various components of HPSM. During this analysis, equivalent (von-
Mises) stresses, shown in table 5-9, are calculated and weakest component is identified.
Component P of DC-Link Capacitor has the maximum stress which is equal to 28,263 psi. Yield
strength of the material (Al 5052-H32) of Component P of DC-Link Capacitor is 23,000 psi
which is less than the computed von-Mises stress due to thermal load. From this analysis, it is
understood that assigned material for Component P of DC-Link Capacitor is not appropriate.
Yield strength of the material for Component P of DC-Link Capacitor should be greater than
29,263 psi such as steel. In this research, calculated von-Mises stresses of the other components
of HPSM are also compared with their respective materials’ yield strength and concluded that
they are within the limits.
60
5.3.3Weight Reduction and Cost Saving of the Redesign DC-Link Capacitor
In this research, one of the objectives is to reduce the weight of the DC-link Capacitor. The
amount of weight and consequently the reduction of the cost are explored in this section.
5.3.3.1 Weight Reduction
The weight analysis of the new DC-link Capacitor, shown in Appendix A, is performed and
weight comparison between existing and new DC-link Capacitors is also performed in this study.
From this weight analysis, it can be concluded that weight of the new DC-link Capacitor is
approximately 0.356 lb less than the existing one. Since HPSM has two sets of DC-link
Capacitors, weight of the modified HPSM is (0.356*2 lb) 0.712 lb less than the existing HPSM.
This is more than 7.4% of material saving per DC-link Capacitor integrated with DC-bus bar and
Snubber Caps.
4.806−4.449
4.806× 100 = 7.4% (6.1)
The result offers significant reduction in the weight which is due to all structural modification of
DC- link capacitor, DC bus bar and Snubber caps.
5.3.3.2 Estimated Cost Reduction
Cost estimation and assessment is not always straightforward. It is commonly completed with
some extent of estimations. Especially in the Aerospace and Defense industry, collaborating
companies need to exchange the cost of the services they offer to each other. Since each
company has some competitors in the market, they are not willing to release the exact pricing
data of the services and usually propose a final number as their bid for the service.
The DC-link capacitor integrated with DC-bus bar and Snubber caps are manufactured by a third
party company who also manufactures the existing model. The third party company put the price
61
quotations for existing and proposed models. From these price quotations, it is clear that
proposed model is cheaper than existing model.
Redesigned DC-link capacitor reduces the number of operations by integrated DC-bus bar and
Snubber caps with it. This redesigned DC-link capacitor makes easier to assemble HPSM into
housing of the PTMC which reduce the end unit labor cost.
The effect of weight reduction is interpreted as cost reduction using as approximate rule
commonly used within the company. In Aerospace industry, 1 gram weight reduction means a
huge saving. The redesigned DC-link capacitor reduces weight of HPSM which is equal to 0.7 lb
(318 gram).
In the existing HPSM, two DC-link capacitors are used and they have different part numbers
due to their structural variation. But in proposed design, both of the DC-link capacitors have
same part number which makes a significant cost saving.
The economic influence of the new technologies constantly introduced to the industry sectors
cannot be neglected. The redesigned DC-link capacitor illustrates this influence excellently as
discussed in various parts of the current work.
62
CHAPTER 6: CONCLUSIONS AND
RECOMMENDATIONS
6.1 Concluding Remarks
The structural functionality of the redesigned DC-link capacitor integrated with DC bus bar and
Snubber caps is presented in this thesis. A CAD model of the redesigned DC-link capacitor has
been developed by using Pro-E. Finite Element Method is employed to predict the life cycle of
the model and to assess the impact of temperature loading at various components of the model.
The outcome of the research project can be summarized as:
An significant weight reduction has been achieved in the redesigned DC-link capacitor
integrated with DC bus bar and Snubber caps.
The redesigned DC-link capacitors are properly assembled to the HPSM. This reduces the
volume of the HPSM and makes it easy to install into the housing and also reduces end unit
labor cost as well.
According to Design for Manufacturing and Assembly (DFMA) principles, the redesigned
DC-link capacitor integrated with DC bus bar and Snubber caps is less expensive because it
reduces part count and makes it easier to assemble into the HPSM.
Cumulative Damage Indices of the weakest component of the model along with all
orthogonal directions are calculated by using ANSYS dynamic analysis solver in order to
find the fatigue life of the model. Fatigue life estimates are found realistic.
Infinite life cycle in the FEA simulation is achieved for the redesigned DC-link capacitor
integrated with DC bus bar and Snubber Caps.
63
One of the components is identified whose material yield strength is less than the calculated
von Mises stress (stress due to temperature loading). A recommendation is given to assign
different material for that component that the newly assigned material yield strength should
be greater than the calculated von Mises stress of the component.
The structural functionality of the redesigned DC-link capacitor integrated with DC bus bar
and Snubber caps due to random and temperature loading is satisfactory.
6.2 Future Directions
One of the interesting extensions of the current study could be to build a theoretical framework
in the light of the nonlinear random structural response. The theoretical research could be
combined with the obtained experimental data to further the understanding of the physical
problem.
64
REFERENCES
[1] F. Braithwaite, “On the fatigue and consequent fracture of metals”, Institution of Civil
Engineers, Minutes of Proceedings, vol. 13, pp. 463–474, 1854.
[2] N. E. Frost, K. J. Marsh, and L. P. Pook, “Metal Fatigue”, DoverPublications, Mineola, NY,
1999.
[3] “Wöhler’s Experiments on the Strength of Metals”, Engineering, pp. 160, 1867.
[4] J. Bauschinger, “On the Change of the Position of the Elastic Limit of Iron and Steel Under
Cyclic Variations of Stress”, Mitt. Mech.‐Tech. Lab., Munich, vol. 13, no. 1, 1886.
[5] J. A. Ewing, and J. C. W. Humfrey, “The Fracture of Metals under Repeated Alterations of
Stress”, Phil. Trans. Roy. Soc., London, vol. CC, pp. 241, 1903.
[6] O. H. Basquin, “The Experimental Law of Endurance Tests”, Proceedings of the ASTM, vol.
10, part II, pp. 625, 1910.
[7] A. A. Grififth, “The Phenomena of Rupture and Fow in Solids”,Trans. Roy. Soc., London,
vol. A221, pp. 163, 1920.
[8] A. Palmgren, “Die Lebensdauer von Kugellagern”, ZDVDI, vol. 68, no. 14, pp. 339, 1924.
[9] H. Neuber, “Kerbspannungslehre”, Springer‐Verlag, Berlin, 1937.
[10] M. A. Miner, “Cumulative Damage in Fatigue”, Transactions of the ASME, Journal of
Applied Mechanics, vol. 67, pp. A159, 1945.
[11] Barry Controls and Hopkinton, “Random Vibration- an overview”, Abstract, 2013.
65
[12] Arshad Khan, Devashish Sarkar, Reshad Ahmar and Hitenkumar Patel, “Random vibration
analysis and fatigue life evaluation of auxiliary heater bracket”, SIMULIA India Regional Users
Meeting -11, pp. 1 of 12.
[13] Da Yu , Abdullah Al-Yafawi, Tung T. Nguyen , Seungbae Park and Soonwan Chung,
“High-cycle fatigue life prediction for Pb-free BGA under random vibration loading”,
Microelectron Reliab, vol 51, pp. 649–656, 2011
[14] M.I. Sakri, S. Saravanan, P.V. Mohanram, and S. Syath Abuthakeer, “Estimation of
Fatigue-life of Electronic Packages Subjected to Random Vibration Load”, Defense Science
Journal, vol. 59, no. 1, pp. 58-62, 2009.
[15] Bo Yuan, Limei Xu, Jianfeng Ren, Dagui Huang, “Vibration Suppression Optimization of
Electronic Apparatus Rack using Design of Experiment Method” Asia International Symposium
on Mechatronics , pp. 27-31, 2008.
[16] J.C.Roberts, D.M.Stillo,”Random Vibration analysis of a Printed Wiring Board with
electronic components”, Journal of IES, January/February, pp. 25-31, 1991.
[17] Sidharth, and D.B.Barker,”Vibration Induced Fatigue Life Estimation of Corner Leads of
Peripheral Leaded Components,”Journal of Electronic Packaging, vol. 118, pp. 244-249, 1996.
[18] Liguore, and D. Folllowell,”Vibration Fatigue of Surface Mount Technology (SMT) Solder
Joints”, Proceedings of Annual Reliability and Maintainability Symposium, pp. 18-26, 1995.
[19] S.Fields, S.Liguore, D.Followell, R.Perez, R.,”High and Low-Cycle Fatigue Characteristics
of Leadless Chip Carrier Solder Joints”, ASME paper, 92-WA/EEP-26, 1992.
[20] S.J.Ham, S.B.Lee,”Experimental Study for Reliability of Electronic Packaging under
Vibration”, Experimental Mechanics, vol. 36, no. 4, pp. 339-344, 1996.
66
[21] E.Jih, W.Jung,”Vibrational Fatigue of Surface Mount Solder Joints”, Proceedings of
InterSociety Conference on Thermal Phenomena, pp. 246-250, 1998.
[22] T.E.Wong, B.A.Reed, H.M.Cohen, D.W.Chu,”Development of BGA Solder Joint Vibration
Fatigue Life Prediction Model”, Proceedings of 1999 Electronic Components and Technology
Conference, pp. 149-154, 1999.
[23] G.W. Brown and R. Ikegami,”The Fatigue of Aluminum Alloys Subject to Random
Loading”, Experimental Mechanics, pp. 321- 327, 1970.
[24] Francis G.Pascual and William Q. Meeker,” Estimating Fatigue Curves With the Random
Fatigue-Limit Model”, Technometrics, vol. 41, no. 4, pp. 277-290, 1999.
[25] Bishop, NWM, “Vibration Fatigue Analysis in the Finite Element Environment” XVI
Encuentro Del Grupo Español De Fractura, Spain, 1999.
[26] Wu, W. F., Liou, H. Y., Tse, H. C., “Estimation of Fatigue Damage and Fatigue Life of
Components Under Random Loading”, International Journal of Pressure Vessels and Piping, vol.
72, pp. 243-249.
[27] Dave S. Steinberg, “Vibration Analysis Electronic Equipment, third edition”, Johan Wiley
& Sons, Inc. Canada, 2000.
[28] S.S. Rao, “Mechanical Vibration, second edition”, Addison-Wesley, New Jersey, 1990.
[29] Shigley J.E., Mischke, C.R., “Mechanical Engineering Design”,Fifth Edition,McGraw-Hill
International Editions,1989.
[30] Lalanne, C., “Mechanical Vibration & Shock, Fatigue Damage Volume IV“, Hermes Penton
Ltd, 2002.
[31] Candan, B., “Yorulma Teorisine Giriş, Eğitim Notları”, Figes, 2003.
67
[32] Hieber, G., 2005, Use and Abuse of Test Time Exaggeration Factors, ttp:\\www.ttiedu.com,
visited on August 2006.
[33] Collins, J.A.,”Failure of Materials in Mechanical Design”, “Analysis, Prediction,
Prevention”,Second Edition, John Wiley & Sons,1993.
[34] Topper T.H.,Sandor B.I.,Morrow,J.D.,”Cumulative fatigue damage under cylic strain
control”,Journal of Materials,vol. 4, pp. 189-199, 1969.
[35] Yang, J.N.,”Simulation of random envelope processes”, Journal of Sound and Vibrations,
vol. 21, pp. 73-85, 1972.
[36] nCode Training Notes, “Integrated Durability Management”, December 2004.
[37] NWM Bishop, F. Sherratt, “Finite Element Based Fatigue Calculations”, NAFEMS, 2000.
68
Appendix A: Weight Analysis
Item
#
Part Name or
Description of Item
Qt
y
Weight (lbs) of existing
component
Weight (lbs) of modified
component Weight
(lbs)
Reduction Unit
Part
Total
Parts
Total
Subassy
Unit
Part
Total
Parts
Total
Subassy
Part A x.xxx x.xxx 0.636
128
Component A of DC
Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
129
Component B of DC
Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
130
Component C of
DC Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
131
Component D of DC
Bus Bar 5 x.xxx x.xxx x.xxx x.xxx
132
Component E of DC
Bus Bar 5 x.xxx x.xxx x.xxx x.xxx
133
Component F of DC
Bus Bar 2 x.xxx x.xxx x.xxx x.xxx
1
Component G of DC
Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
2 Component H of DC
Bus Bar 2 x.xxx x.xxx x.xxx x.xxx
3 Component I of DC
Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
4
Component J of DC
Bus Bar 1 x.xxx x.xxx x.xxx x.xxx
Part B x.xxx x.xxx -0.280
102
DC-Link Capacitor
& H/W 1 x.xxx x.xxx
121 Capacitor, Snubber 6 x.xxx x.xxx
107
Component G of
DC Link Cap & HW
(Pem Nut)
1 x.xxx x.xxx
1001
Component A of DC-
Link Capacitor 1 x.xxx x.xxx
1002
Component B of DC-
Link Capacitor 1
x.xxx x.xxx
1003
Component H of DC-
link Capacitor 8
x.xxx x.xxx
1004
Component I of DC-
link Capacitor 17
x.xxx x.xxx
1005
Component E and F of
DC-Link Capacitor 2
x.xxx x.xxx
1006
Component C of DC-
Link Capacitor 1
x.xxx x.xxx
1007
Component D of DC-
Link Capacitor 1
x.xxx x.xxx
1008
Component M of DC-
Link Capacitor 1
x.xxx x.xxx
1009 Component P of DC-
Link Capacitor 1
x.xxx x.xxx
1010 Epoxy (61.925 in³) x.xxx x.xxx
Tot.Weight
Red’n (lbs) 0.356
69
Appendix B: Material Properties for Al 5052-H32
Material /
Propertie
s
Tem
p
Coefficient of
Thermal
Expansion (CTE)
Density Elasticity
Modulus
Poissio
n Ratio
Yield
Strength
Ultimate
Strength
Fatigue Strength S-N
Data @ RT (R=-1)
Sourc
e
T XY Z E Sty Stu Se N
Units deg
F in/in/F in/in/F
lb/in^
3 psi psi psi psi cycles
Al 5052-
H32 70
1.26E
-05
1.26E
-05 0.097
1.01E+0
7 0.33
2.30E+0
4
3.10E+0
4
1.60E+0
4
1.00E+0
7
AMS
4016
70
Appendix C: Mode Shapes of HPSM Assembly Model
Second and third mode shapes of HPSM assembly are shown in Figures C-1 and C-2
respectively.
Figure C-1 Second Mode Shape of the Assembly CAD Model
Figure C-2 Third Mode Shape of the Assembly CAD Model
71
Appendix D: Von-Mises Stresses at Weakest Component along Y and Z
Directions
Computed von- Mises stress in Y direction is showed in figure D-1 & D-2 and response PSD at
critical location is presented in figure D-3.
Figure D-1 Max. von-Mises stress (4577.9 psi) at HPSM assembly at Y direction
Figure D-2 Max. von-Mises stress (4577.9 psi) at the weakest component at Y direction
Figure D-3 Response PSD at Critical Location
Frequency
Res
po
nse
PSD
[in
2/H
z]
72
Computed von- Mises stress in Z direction is showed in figure D-4 & D-5 and response PSD at
critical location is presented in figure D-6.
Figure D-4 Max. von-Mises stress (4333.6 psi) at HPSM assembly at Z direction
Figure D-5 Max. von-Mises stress (4333.6 psi) at the weakest component at Z direction
Figure D-6 Response PSD at Critical Location
Frequency
Res
po
nse
PSD
[in
2/H
z]
73
Appendix E: Thermal Stresses of all key Components of HPSM
Thermal stresses at various components of DC-link capacitor and HPSM are shown in figure E-1
to E-14.
Figure E-1 Equivalent (von-Mises) Stress (Max. Stress: 31021 psi) at HPSM
Figure E-2 Equivalent Stress (Max. Stress: 336.21 psi) at Component A of DC-Link Capacitor
74
Figure E-3 Equivalent Stress (Max. Stress: 656.59 psi) at Component B of DC-Link Capacitor
Figure E-4 Equivalent Stress (Max. Stress: 6744.9 psi) at Component D of DC-Link Capacitor
75
Figure E-5 Equivalent Stress (Max. Stress: 1238.8 psi) at Component C of DC-Link Capacitor
Figure E-6 Equivalent Stress (Max: 0.13207 psi) at Component E of DC-Link Capacitor
76
Figure E-7 Equivalent Stress (Max: 2.6973 psi) at Component F of DC-Link Capacitor
Figure E-8 Equivalent Stress (Max: 5832.2 psi) at Component A of DC-Bus Bar
77
Figure E-9 Equivalent Stress (Max: 3066.8 psi) at Component B of DC-Bus Bar
Figure E-10 Equivalent Stress (Max: 15684 psi) at Component M of DC-Link Capacitor
78
Figure E-11 Equivalent Stress (Max: 13351 psi) at Component C of HPSM
Figure E-12 Equivalent Stress (Max: 671.45 psi) at Component I of DC-Link Capacitor
79
Figure E-13 Equivalent Stress (Max: 31021 psi) at Component A of HPSM
