Experimental and Theoretical Analysis of High Power Connectors for Hybrid Vehicles 
 
by 
 
Rujian Fu 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
May 9, 2011 
 
 
 
 
Keywords: high power electric connector, fretting, vibration, finite element modeling  
 
 
Copyright 2010 by Rujian Fu 
 
 
Approved by 
 
Song-yul Choe, Chair, Associate Professor of Mechanical Engineering 
Robert L. Jackson, Associate Professor of Mechanical Engineering 
George T. Flowers, Professor of Mechanical Engineering 
 
ii 
 
 
 
 
 
Abstract 
 
 
Hybrid electric vehicles (HEV) are the next evolutionary step of the automobile which 
substantially increases fuel economy and reduces emissions.  They are comprised of many new 
technologies so there is limited information on their overall life and reliability. The electrical 
connectors used in HEVs conduct much more power and are more susceptible to failure and 
reliability problems under the vibration, thermal cycling and humidity environment in a vehicle. 
This work presents a detailed study on the performance of a round pin, silver-plated high power 
connector used for hybrid vehicles, including experimental testing using a custom-designed test 
stand and theoretical analysis by finite element methods (FEM).  
In order to emulate operational and environmental effects, a test stand is designed for the 
connector that is capable of measuring connector resistance, temperature and motions. When a 
connector is exposed to vibrations, experimental results show that the connector resistance 
increases and oscillates significantly. When the vibrations are stopped, connector resistance 
returns to a value that is close to the original state.  
In order to analyze this phenomenon, a two-dimensional finite element model is 
developed to calculate relative displacement between the male part and female part of the 
connector. After being validated by experiments, the model shows that the simulated relative 
displacement is closely related to the changes of connector resistance under vibration, as 
measured in experiments. The relative displacement is then used as input for a three-dimensional 
finite element model that studies the time response of the contact spring. The simulation has 
iii 
 
shown periodical contact gaps between the spring and other parts of the connector, which cause 
the changes in connector resistance during vibration. 
 
iv 
 
 
 
 
 
Acknowledgments 
 
 
 I would like to express my deep appreciation to my advisor, Dr. Song-yul Choe, for 
giving me the opportunity to get involved in this research project. His wise suggestions and 
generous guidance assisted me to the fulfillment of my study. Without his valuable comments 
and detailed corrections to my papers and thesis, I would hardly finish my research program 
smoothly. I also would like to acknowledge to my committee member, Dr. Robert L. Jackson, for 
his continuous instructions and encouragement, which enabled me to develop a deep 
understanding in the research area. Special thanks would be given to another committee member, 
Dr. George T. Flowers, for his enlightening advice and great contribution of lab resources to the 
project. Finally, I would like to express my gratitude to my parents, Guangda Fu and Xiaoyan Li, 
for their unselfish support of my academic endeavor. 
v 
 
 
 
 
 
 
Table of Contents 
 
 
Abstract ..................................................................................................................................... ii 
Acknowledgments ..................................................................................................................... iv 
List of Tables .......................................................................................................................... viii 
List of Figures ........................................................................................................................... ix 
List of Abbreviations............................................................................................................... xiii 
Chapter 1 Introduction ........................................................................................................1 
Chapter 2 Literature review ................................................................................................5 
2.1 The effect of vibration on fretting corrosion ..................................................................5 
2.2 The effect of vibration on temporary changes of contact resistance ...............................6 
2.3 The effect of ambient temperature and humidity on fretting corrosion ...........................8 
2.4 Measurement techniques and analysis using (FEM) ......................................................8 
Chapter 3 High power connector and experimental setup .................................................. 10 
3.1 Specification for high power connector ....................................................................... 10 
3.2 Experimental Setup ..................................................................................................... 12 
3.2.1 Design of test stand..................................................................................... 12 
3.2.2 Design of electrical and mechanical hardware ............................................. 13 
3.2.3 Instruments ................................................................................................. 16 
3.2.4 Calibrations, uncertainty of measurement and EMI ..................................... 21 
Chapter 4 Accelerated tests under various testing conditions ............................................ 24 
vi 
 
4.1 Methodology of accelerated tests ................................................................................ 24 
4.1.1 Test conditions ........................................................................................... 24 
4.1.2 Definition of coordinates for vibrations....................................................... 25 
4.1.3 Test procedure and test matrix .................................................................... 25 
4.2 Methodology of accelerated tests ................................................................................ 28 
4.2.1 Experimental results of RC .......................................................................... 28 
4.2.2 Experimental results of TC .......................................................................... 33 
4.3 Summary and main findings ........................................................................................ 39 
Chapter 5 Experimental analysis of vibration induced changes in connector resistance . 41 
5.1 Effects of vibration with fixed amplitude and frequency .............................................. 41 
5.2 Effects of vibration with varying amplitudes and fixed frequency ............................... 43 
5.3 Effects of Vibration with Fixed Amplitudes and Varying Frequencies......................... 46 
5.4 Effects of Vibration with Varying Amplitudes and Frequencies .................................. 48 
5.5 The effect of vibration on wear and corrosion (Surface analysis) ................................. 49 
5.6 Summary .................................................................................................................... 51 
Chapter 6 Modeling of the connector system using two-dimensional FEM ....................... 53 
6.1 Experimental results .................................................................................................... 54 
6.2 Modeling of the Connector System by FEM ................................................................ 57 
6.2.1 Set-up ......................................................................................................... 57 
6.2.2 Determination of the equivalent spring constant .......................................... 59 
6.3 Comparison between simulation and experimental results ........................................... 61 
6.4 Modal analysis by simulation ...................................................................................... 65 
Chapter 7 Modeling of the contact spring using three-dimensional FEM ....................... 67 
vii 
 
7.1 Set-up ......................................................................................................................... 67 
7.2 Simulation results........................................................................................................ 68 
7.3 Comparison of 3D simulation results and experimental data ........................................ 72 
Chapter 8 Conclusions and recommendations ................................................................... 76 
8.1 Experimental findings ................................................................................................. 76 
8.2 Theoretical analysis using FEM .................................................................................. 77 
8.3 Recommendations ....................................................................................................... 78 
References ................................................................................................................................ 80 
 
viii 
 
 
 
 
 
List of Tables 
 
 
Table 1: Specification of the connector...................................................................................... 11 
Table 2: Uncertainty of measurement after calibration without considering other disturbances .. 22 
Table 3: Test matrix of accelerated tests .................................................................................... 27 
Table 4: Vibration amplitudes (peak-to-peak) for each test run .................................................. 27 
Table 5: Test conditions for fixed amplitude and frequency ....................................................... 41 
Table 6: Test conditions for varying amplitude and fixed frequency .......................................... 43 
Table 7: Test conditions for fixed amplitude and varying frequency .......................................... 46 
Table 8: Test conditions for varying amplitude and varying frequency ...................................... 48 
Table 9: Test conditions ............................................................................................................ 54 
Table 10: Material and dimensional properties of the male part and cable.................................. 58 
 
ix 
 
 
 
 
 
List of Figures 
 
 
Figure 1: Electric systems for hybrid propulsion systems (from Dr. Song-yul Choe, 
unpublished) ...............................................................................................................1 
 
Figure 2: Trend of HEV propulsion system development (from Dr. Song-yul Choe, 
unpublished) ...............................................................................................................2 
 
Figure 3: Geometrical structures of the connector ...................................................................... 11 
Figure 4: Schematic diagram of test stand ................................................................................. 12 
Figure 5: Testing System Rack with Parallel Power Supplies (above the PC) ............................ 13 
Figure 6: Vibration Shaker and Environmental Chamber ........................................................... 14 
Figure 7: Fixture of connectors on the shaker, enclosed by chamber .......................................... 15 
Figure 8: Data acquisition board with AI modules ..................................................................... 16 
Figure 9: Locations of measurements of voltage drop (VC) and connector temperature (TC) ...... 17 
Figure 10: Metal eyelet for measuring voltage and temperature ................................................. 17 
Figure 11: LEM IT 40-S Current Transmitter ............................................................................ 18 
Figure 12: Non-contacting laser vibrometer system with sensor head  and controller ................. 19 
Figure 13: Setup of non-contacting laser vibrometers ................................................................ 19 
Figure 14: Surface profilometer ................................................................................................. 20 
Figure 15: Agilent 34411A multimeter for calibration ............................................................... 21 
Figure 16: Calibration data of analog input modules and precision multimeter .......................... 21 
Figure 17: Ice point reference used to calibrate thermocouple ................................................... 22 
Figure 18: Comparison of connector resistance and cable resistance under a vibration pretest ... 23 
x 
 
Figure 19: Operating conditions and assessments of connector for accelerated tests .................. 24 
Figure 20: Definition of coordinates for vibrations .................................................................... 25 
Figure 21: Test procedure for accelerated tests .......................................................................... 26 
Figure 22: Averaged RC under different ambient temperatures without vibration ....................... 28 
Figure 23: Definition of ?RC ..................................................................................................... 29 
Figure 24: ?RC under different vibration directions (Test 1 and 2) ............................................. 30 
Figure 25: ?RC under different vibration frequencies (Test 1, 4, 5 and 6) ................................... 31 
Figure 26: ?RC under different ambient temperatures (Test 1, 7 and 8) ...................................... 32 
Figure 27: ?RC under different vibration frequencies and ambient temperatures (Test 11, 12, 
13 and 14) ................................................................................................................. 33 
 
Figure 28: TC under different ambient temperatures without vibration ....................................... 34 
Figure 29: Definition of ?TC...................................................................................................... 35 
Figure 30: ?TC under different vibration directions (Test 1 and 2) ............................................. 36 
Figure 31: ?TC under different vibration frequencies (Test 1, 4, 5 and 6) .................................. 37 
Figure 32: ?TC under different ambient temperatures (Test 1, 7 and 8) ...................................... 38 
Figure 33: ?TC under different vibration frequencies and ambient temperatures (Test 11, 12, 
13 and 14) ................................................................................................................. 39 
 
Figure 34: Vibration-induced changes in RC .............................................................................. 42 
Figure 35: RC at increasing vibration amplitudes and fixed frequency ........................................ 44 
Figure 36: Measurement locations of motions ........................................................................... 45 
Figure 37: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration amplitude ........................... 46 
Figure 38: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration frequency .......................... 47 
Figure 39: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration frequency ........................... 49 
xi 
 
Figure 40: SEM on worn contact surface (Position 1 is wear pit and position 2 is non-
contacting area) ........................................................................................................ 50 
 
Figure 41: (a) AES for surface material analysis of non-worn position. (b)  AES for surface 
material analysis of worn position. ........................................................................... 51 
 
Figure 42: The locations of motions to be studied ...................................................................... 53 
Figure 43: Experimental results of the magnitude ratios of motions ........................................... 56 
Figure 44: Changes of connector resistance, ?RC, versus vibration frequencies. ........................ 57 
Figure 45: Finite element model for the connector system with boundary conditions. ................ 58 
Figure 46: Simplification of the ring shape spring ..................................................................... 59 
Figure 47: Schematic diagrams for calculation of an equivalent spring constant. ....................... 60 
 
Figure 48: The locations of motions to be studied in simulation ................................................ 62 
Figure 49: Comparison between simulated and experimental results.......................................... 63 
Figure 50: Simulation result: The magnitude of the male part (near the contact) (M4) versus 
the excitation (M0) ................................................................................................... 64 
 
Figure 51: Comparison between relative displacement and changes of connector resistance ...... 65 
 
Figure 52: Simulated mode shapes at the first two natural frequencies ....................................... 66 
Figure 53: Finite element model of one repeatable section of contact spring. ............................. 67 
Figure 54: Points for displacement used for simulations ............................................................ 69 
Figure 55: Time response of the displacements versus time when excitation frequency 
equals to 240Hz ........................................................................................................ 69 
 
Figure 56: The deformed shapes at different instants, corresponding to Figure 55. .................... 71 
Figure 57: Time response of the displacements versus time at excitation frequency of 160Hz 
and 60Hz. ................................................................................................................. 72 
 
Figure 58: The comparison of spectrums of connector resistance and contact gaps under 
vibrations (excitation amplitude=0.18mm. excitation frequency=100Hz) ................. 74 
 
xii 
 
Figure 59: Comparison between contact gaps (simulation) and changes of connector 
resistance (experiment) in all frequency domains ..................................................... 75 
 
 
xiii 
 
 
 
 
 
 
List of Abbreviations 
 
 
d The relative displacement between male part and female part at the contact surfaces, 
equaling to |U4- U1| (unit: mm) 
Fr,i The contact force for the ith repeatable section of contact spring in radial direction, 
having two components in x direction (Fx,i) and y direction (Fy,i) (unit: N) 
IC Current going through connector (A) 
ke The equivalent spring constant of the simplified contact spring in two-dimensional 
finite element model (unit: N/mm) 
Mi The magnitude of the motion at certain position of the connector system (unit: mm) 
R Radius of male part of connector (unit: mm) 
RC Connector resistance (unit: m?)    
ri The radial displacement of the ith repeatable section of contact spring from steady 
state position (unit: mm) 
TC Connector temperature (unit: ?C) 
U0 The motion at the fixture, equal to M0? ?0 
U1 The motion at female part, equal to M1? ?1 
U2 The motion at the right end of male part, equal to M2? ?2 
U3 The motion at the midpoint of cable, equal to M3? ?3 
U4 The motion at the male part, equal to M4? ?4 
xiv 
 
|U2 ?U1| The relative displacement between the right end of male part and female part  
|U4 ?U1| The relative displacement between the male part and the female part at contact 
surfaces 
VC Voltage drop of connector (unit: mV) 
?i The angle from the direction of vibration to the radial direction of the ith repeatable 
section of contact spring (unit: degree?) 
?RC The temporary changes in connector resistance under vibration (unit: m?) 
?TC The overall changes in connector temperature under vibration (unit: ?C) 
?i The phase shift of the motion at certain position of the connector system (unit: 
degree?) 
 
 
 
 
 
1 
 
CHAPTER 1 INTRODUCTION 
 
Hybrid electric vehicles (HEV) are the next evolutionary step of the automobile which 
substantially increases fuel economy and reduces emissions. However, the electrical systems 
which propel HEVs are fundamentally different from conventional technologies. There are 
technical barriers that prevent the success of hybrid electric propulsion systems. One of the 
crucial issues for hybrid systems is the reliability of electrical components, which should be 
guaranteed for the same period as the mechanical components.  
High electrical power is required for new vehicles which use electrical propulsion. 
Typical hybrid systems use one or two electric motors that are mechanically connected to shafts 
and electrically to batteries via DC/AC inverters and DC/DC converter, as shown in Figure 1. 
Detachable power connectors are desired for durable and easily removed electrical connections.  
This is especially important for the easy replacement and repair of electrical components.  
 
 
Figure 1: Electric systems for hybrid propulsion systems (from Dr. Song-yul Choe, unpublished) 
 
2 
 
HEV electrical connectors conduct much more power and are more susceptible to failure 
and reliability problems than the connectors in conventional vehicles.  As shown in Figure 2, the 
power and voltage requirements for vehicles are steadily increasing as a vehicle transitions from 
a conventional vehicle to a mild hybrid all the way to a plug-in HEV. Therefore the connectors in 
these vehicles must be able to handle these higher powers.   
 
Figure 2: Trend of HEV propulsion system development (from Dr. Song-yul Choe, unpublished) 
 
Other than high electrical power, mechanical vibrations, thermal cycling and humidity 
that a car undergoes can also cause degradation and failure of the connectors.  If the connector 
contacts degrade, the contact resistance can increase and cause other problems with the power 
electronics and controls of the electrical power drive system.  Eventually, connectors could 
catastrophically fail and become either permanently welded together or effectively non-
conductive. 
3 
 
The main motivation of the current study is to research the performance of connectors for 
HEV vehicles under these realistic operating conditions experimentally and theoretically. To 
emulate these conditions, a test stand for the 300A-rated connector was designed which 
facilitates the supply of high current, generation of vibration and control of environmental 
temperature with the measurement of connector resistance (RC), connector temperature (TC) and 
connector motions.  
Based on the results of the experimental study, increase of connector resistance is most 
likely to occur from vibration in the direction perpendicular to cable axis. In addition, more 
change in connector resistance occurs at higher vibration amplitudes, frequencies and lower 
ambient temperatures. A micro-roughness surface analysis of the silver coating connectors shows 
that the defect area on the surface is best referred to as a worn pit rather than corrosion because 
the main finding is indentation and removal of the coating material.  
According to the experiments, vibration is the most significant cause the increase of 
connector resistance, compared to current rate and ambient temperature. The experimental 
results show that the increase of connector resistance under vibration is primarily due to the 
relative displacement between male and female parts of the connector, rather than fretting 
corrosions. Finite element models are used to analyze this phenomenon and compare with 
experimental results.  A two dimensional finite element model is developed to describe the 
overall connector system with a capability of calculating relative displacements between the 
female part and male part at the contact surfaces. Contact spring present between the female and 
male parts of the connector is modeled in three dimensions and used to analyze time responses of 
the spring.   
4 
 
The two dimensional finite element models show that the relative displacement between 
the female part and male part at the contact surfaces is closely related to the changes of 
connector resistance under vibration. A prominent finding is made from the three dimensional 
model, which shows that contact surfaces of each contact pair do not have the identical motion 
under vibration, and the gaps between the contacts are found.  It is assumed that these contact 
gaps causes connector resistance to increase and oscillates during vibration because they may 
induce capacitance or electric arcing between the contacts. With the validation of experimental 
results, it is proved that the models are powerful to aid in fundamental characterization, 
prototype evaluation and design of high power connectors.  
 
5 
 
CHAPTER 2 LITERATURE REVIEW 
 
Automotive connectors experience a harsh environment comprised of vibrations induced 
by the engine, thermal cycling as the vehicle starts up and shuts down, and a corrosive 
environment which can cause the formation of undesired oxides [1]-[2]. These conditions are 
very demanding on the reliability of connectors and often lead to degradation and failure. A 
vehicle may have more than 400 connectors with 3000 individual terminals but field data has 
shown that connector degradations and failures contribute to 30?60% of the electrical problems 
[3]-[4].  This requires investigations on connector behavior under vehicle conditions and studies 
on its degradation mechanisms so that connectors perform on an acceptable level. 
2.1 The effect of vibration on fretting corrosion 
For connectors subject to vibration, a main degradation mechanism is fretting, which is a 
relative cyclic motion with small amplitude that occurs between two oscillating surfaces, defined 
by Waterhouse [5]. Varenberg et al. also characterized fretting in terms of the local relative 
motion [6]. Fretting is generally found to cause intermittent electrical contact, wear and 
corrosion on contact materials and in turn results in variations of electrical contact resistance 
such as an increase, fluctuation or intermittence.  
Fretting corrosion has been extensively investigated by many researchers. During fretting 
corrosion, fretting wear repeatedly exposes fresh metal to the atmosphere which causes oxidation 
and the accumulation of debris on the contact interface.  This continuously reduces the electrical 
conducting area and conductivity [7]-[9]. Consequently, when vibration is applied, the contact 
resistance will continue to increase gradually with time [7], [9]-[15].  Many works report that the 
6 
 
degradation of the contact interface will cause the contact resistance to increase greatly with 
sudden failure after a certain number of vibration cycles [7], [11]-[12], [14]. These phenomena 
are mostly observed on electrical contacts with conventional coatings, such as tin [7], [9]-[15]. 
2.2 The effect of vibration on temporary changes of contact resistance 
However, superimposed on the gradual increase of contact resistance, various studies also 
show that the contact resistance may increase temporarily and significantly, and then oscillate 
synchronizing with the vibration [14], [16]-[25]. This phenomenon is extremely obvious in our 
vibration tests where silver-plated connectors are used. When vibrations start, the connector 
resistance significantly increases and oscillates. When the vibrations are stopped, the resistance 
is set back to a value that is similar to the original state. It is the relatively stable property of 
silver that makes fretting corrosion less significant so that the temporary changes of contact 
resistance dominates the experimental results. 
The temporary changes of the contact resistance are dependent upon operating 
conditions.  One of the reasons is the wear debris and particles formed at the contact surface [14], 
[16]-[17]. Hubner-Obenland and Minuth found the periodical alternations of contact resistance 
for various contact materials subject to vibration [14], which is caused by debris of a degraded 
contact which behaves like a potentiometer with the least resistance at the rest position of the 
contact. Carvou and Jemaa also found out that when the contact surface moves along the track 
formed by oxide particles, contact resistance varies periodically under vibration [16]. Skinner 
concluded that particles in order of 25?m between the contact terminals lead to changes in 
contact resistance and even disturbance of intermittence [17].  
7 
 
On the other hand, periodic separations of contact surface, or contact gaps, also cause 
temporary increase and oscillation of contact resistance [18]-[21]. This phenomenon is 
commonly found on electrical connectors, relays and switches which may cause electrical arcing.  
Mcbride used a mathematically modeled contact bounce to show that the contact separations are 
small such that the minimum arc voltage is maintained [18]. Ben Jemaa et al. found that the 
electrical arcing causes contact resistance enhanced progressively and started to demonstrate 
high fluctuations under vibrations [19]-[20]. The arcing voltage is due to bounce phenomena 
between the contacts under vibrations [19]. In addition, periodic separation of contact surface 
may vary capacitance between the two contact surfaces, which was measured by Kopanski for 
for a lithographic overlay subject to vibration [21].   
When the changes of contact resistance are associated with short duration discontinuities, 
it is defined as intermittence [22]-[25]. According to a study on intermittence detection by 
Murrell and McCarthy, the contact resistance remains high throughout most of the cycling but 
fluctuates by several orders of magnitude after 10,000 cycles with the presence of significant 
intermittences [22].  The reasons of intermittence are not limited to wear debris buildup [23]-
[25]. Maul, McBride and Swingler provided explanations that the contact area should be small at 
the time when intermittence (or discontinuity) occurs, and the current density in the contact 
region is very high [23]. This mechanism of intermittence is explained using a model by Malucci, 
where cold welded asperities are stretched or sheared during relative motion of the contact 
terminals [24]. Other author like Maul and McBride interpreted the intermittence as the 
temporary disruption of metallic conduction in a closed electrical contact [25]. 
8 
 
2.3 The effect of ambient temperature and humidity on fretting corrosion 
The effect of temperature on fretting is another important consideration for connector 
failures. Y. W. Park et al. found that temperature has a great influence on the fretting corrosion 
of the tin-plated contacts [9]. Relatively higher temperatures tend to soften the contacting 
asperities of tin resulting in less fretting wear. However, high temperatures will also increase the 
rate of oxidation and then accelerate fretting corrosion. In addition, sliding friction in a connector 
leads to a temperature rise and it may be a major source of electrical contact deterioration. In 
2009, Chen et al. created a model that is able to capture the inception of material melting 
temperature rise caused by sliding friction [26].   
The corrosion of automotive connectors can be exacerbated by humidity in vehicles [27] 
and the influence of humidity varies greatly for different coating materials [11], [28], where the 
experimental results show that silver coatings have much longer life times with humidity 
conditions than any other coating materials. Therefore, the power connectors with silver-coatings 
appear to be a good candidate for automotive applications. Bruel [28] found that the contact 
resistance of silver was much more stable than copper, brass and nickel, under the humidity 
environment with applied sliding. Rudolphi and Klafke [12] also found that silver and gold are 
the excellent candidates since they have the lowest resistance increase under sliding and 
humidity conditions.  
2.4 Measurement techniques and analysis using (FEM) 
Since the investigations of the connector performance are mostly realized by accelerated 
tests, a precise measurement can help to better characterize connector fretting and degradation 
mechanisms. It is recommended to use high sampling rate of measuring contact resistance under 
9 
 
vibration to characterize a complete waveform of the contact resistance [19], [23], [27]-[28]. 
Proper instruments are also inevitable for obtaining fretting mechanisms in experimental tests. In 
2003, Flowers et al. used non-contacting laser vibrometer to measure relative displacement of 
contact interface to predict the fretting corrosion of tin-plated connectors [29]. They found that 
the relative motion of contact interface is proportional to the increase rate of contact resistance.  
 Some authors used finite element methods (FEM) to analyze electrical contacts [30]- 
[32].  For example, Xie [30] and Chen [31] used it for analysis of dynamics and fretting of 
connector subjected to vibration and Zhai et al. used it for anlaysis of dynamic characteristics of 
pick-up and drop-out process of contact of electromagnetic relay [32]. However, computational 
time increases drastically to calculate dynamic characteristics of connectors using a three-
dimensional model [31]. Thus, to minimize the computational cost, we developed a two-
dimensional model for the connector system that embeds a detailed three-dimensional model for 
the contact spring.  The model is used to analyze effects of vibrations on the contact surfaces. 
Experiments are conducted to verify the numerical analysis.  
 
 
10 
 
CHAPTER 3 HIGH POWER CONNECTOR AND EXPERIMENTAL SETUP 
 
3.1 Specification for high power connector 
Connectors used for experiments are made of male and female parts contacted by a spring 
that allows for absorbing mechanical vibrations while maintaining a high conductivity, which is 
manufactured by LS CableTM  and shown in Figure 3 (a). The connector has a cylindrical form. 
The male part has a pin with a round shape (Figure 3 (d)), while the female part has a tube form 
(Figure 3 (b)) where a ring-shape spring punched from sheet metal is mounted inside the female 
connector (Figure 3 (c)). The spring serves to produce contact pressure perpendicular to the 
surface of the male and female parts by contact tabs. These contact pressures compress each of 
tabs in the radial direction and provide electrical connections between the female and male parts 
of the connector. The specification and material properties of the connector for 300A current 
rating is listed in Table 1. The connector surface is plated with silver, while the bulk connector 
material is made of copper alloy. The connector system in testing also includes housing and 
supplied cable, which will be shown in a later section. 
11 
 
 
(a) Connector mate 
 
   (b) Female part with cont          (c) Contact spring                 (d) Male part  
Figure 3: Geometrical structures of the connector 
 
Table 1: Specification of the connector 
Components  
  
Material properties  
Bulk material Copper alloy 
Young?s modulus (GPa) 117 
Poisson?s ratio 0.34 
Mass density (kg/m3) 8930 
Surface plating Silver 
Friction coefficient 0.34 
  
Dimensions  
Overall length (mm) 105.3 
Outer diameter (mm) 20.1 
  
Current rating (A) 300 
 
12 
 
3.2 Experimental Setup 
3.2.1 Design of test stand 
In order to investigate connector performance and reliability, a connector test stand 
design is developed to represent real operating condition and provide a controlled testing 
environment. A high DC current is supplied for the connector under a controlled environment 
with desired vibration, temperature and humidity conditions. The test stand facilitates the 
measurement of connector resistance, RC, and connector temperature. TC, during the tests and the 
measured data are processed and displayed in real time. A schematic diagram of the designed test 
stand is depicted in Figure 4. 
 
 
Figure 4: Schematic diagram of test stand 
 
13 
 
3.2.2 Design of electrical and mechanical hardware 
To provide a power source for the connectors, three Sorensen DCS-125E power supplies 
are selected. The maximum current output of each power supply is 125 A. Multiple power 
supplies can be wired in parallel resulting in a maximum current of 375A, as shown in Figure 5. 
The power supply is able to be remotely controlled by PC to output the desired current value and 
complex profile as needed. 
 
 
Figure 5: Testing System Rack with Parallel Power Supplies (above the PC) 
 
Vibration tests are performed using an amplitude-and-frequency-controlled electro-
magnetic shaker and environmental chamber, which enclosed the connector to be tested, as 
shown in Figure 6. The LDS V850 Shaker is able to output any vibration amplitude and 
frequency combination with a maximum G-value of 30g. A CSZ environmental chamber is used 
14 
 
to control the ambient temperature and humidity of the enclosed connector. The temperature 
range can be set from -20 to 400?C, with 0-100% relative humidity. The chamber is placed above 
the shaker so that the connector can be enclosed as shown in Figure 6 (b). 
 
 
(a) LDS V850 Shaker 
 
(b) CSZ environmental chamber 
Figure 6: Vibration Shaker and Environmental Chamber  
 
15 
 
The connector to be tested is placed in the chamber. Fixtures are especially designed to 
secure the connector on the shaker through the cloth that is used to insulate the inner temperature 
and humidity from room environment, as shown in Figure 7. The power supply cable goes 
through the hole on top of the chamber and then connects to the power source. The measuring 
wires of voltage and thermocouple also go through the same hole and then connected to data 
acquisition board. 
 
 
Figure 7: Fixture of connectors on the shaker, enclosed by chamber 
 
The test fixture secures the connector housing so that the connector vibrates in the same 
way with the shaker. The clamp is designed to fix the supplied cable to the shaker. The base of 
the fixture is designed with multiple sets of holes so that the position of the clamp can be 
adjusted for different lengths of the cable. In this way the natural frequency of the connector 
system can be adjusted if needed. Having longer cables involved in vibrating system results in 
lower natural frequency.  
 
16 
 
3.2.3 Instruments  
Within a controlled environment at a specified vibration direction, amplitude, frequency 
and ambient temperature, connector performance and degradation characteristics can be obtained 
by measuring RC, TC, and motions. The analog signals of voltage drop and transmitted current are 
collected by National InstrumentTM analog input modules, shown in Figure 8. The temperature 
readings are collected by thermocouple input modules. The modules are installed in a data 
acquisition board placed in the system rack, as shown in Figure 5. All the signal measuring wires 
are shielded to minimize electrical magnetic interference (EMI). The measuring wires also go 
through magnetic ferrites to further remove EMI, and all power cables are grounded. 
 
 
Figure 8: Data acquisition board with AI modules 
 
3.2.3.1 Measurement of RC and TC 
RC is indirectly estimated by measuring the voltage drop of the connector and DC current 
in the power loop and then by applying ohm?s law: RC=VC/IC. The locations of measuring 
17 
 
voltage drop of connector, VC, are shown in Figure 9. One voltage measuring wire is soldered on 
a metal eyelet that is firmly fixed on the connector terminal by bolt, as shown in Figure 10. The 
other voltage measuring wire is firmly stuck between the right end of male part and cable. This is 
the best way to ensure measurement precision and repeatability.  
 
 
Figure 9: Locations of measurements of voltage drop (VC) and connector temperature (TC)  
 
 
Figure 10: Metal eyelet for measuring voltage and temperature 
 
The current going through the connector, IC, is measured by a LEM IT 400-S current 
transmitter, as shown in Figure 11. This device converts the current into analog signals that can 
be logged by analog input modules. The connector temperature, TC, is measured by K-type 
18 
 
thermocouple. The probe of thermocouple is also soldered on metal eyelets and fixed on the 
connector terminal, as shown in Figure 10. 
 
 
Figure 11: LEM IT 40-S Current Transmitter 
 
3.2.3.2 Measurement of motions 
The measurement of the motions of the connector is carried out using Polytec non-contact 
laser vibrometer system. The system contains two vibrometers and each one has an OFV 353 
sensor heads (laser) and a OFV 2610 controller, as shown in Figure 12. The sensor heads are 
supported by tripods, as shown in Figure 13, and point to a location of interested on the 
connector during vibration. The analog signal can be obtained at the vibrometer system?s output 
that is proportional to the vibration amplitude of the measured location.   
19 
 
 
Figure 12: Non-contacting laser vibrometer system with sensor head  and controller  
 
 
(a) Photograph of the setup of vibrometers 
 
(b) Schematic diagram of the setup of vibrometers 
Figure 13: Setup of non-contacting laser vibrometers 
 
20 
 
Each vibrometer can be used to measure the magnitude of motion at one location of the 
connector system.  When one vibrometer is considered as the reference, the other one can also 
measure the phase shift of the motion. Each motion is given as a polar form in following 
equation: 
 iiiii MtMU ??? ???? )s i n (  (1) 
where Mi is the magnitude and ?i is the phase shift of the motion Ui. i is a value from 0 to 4, 
which corresponds to 5 different locations of the connector system, which be shown in Chapter 5 
and 6. 
3.2.3.3 Measurement of surface profile 
The surface of the tested connector can be measured for the investigation of wear and 
degradation. An optical stylus profilometer is available to measure the surface profile and 
roughness for both 40A and 300A connectors, as shown in Figure 14. 
 
 
Figure 14:  Surface profilometer 
 
21 
 
3.2.4 Calibrations, uncertainty of measurement and EMI 
Calibrations are implemented to improve measurement accuracy. An Agilent 34411A 
high precision multimeter, as shown in Figure 15, is applied to calibrate all analog input modules. 
The calibration data is shown in Figure 16, which includes the readings of analog input module 
and the multimeter over the measurement range.  
 
 
Figure 15: Agilent 34411A multimeter for calibration 
 
 
Figure 16: Calibration data of analog input modules and precision multimeter 
 
22 
 
An ice point reference, shown in Figure 17, is used to calibrate the thermocouples. The 
ice point reference is able to maintain 0 ?0.1 ?C in the wells where probes can be inserted in. By 
noting the temperature difference between the thermocouple reading and the freezing point, the 
thermocouple is calibrated and its accuracy can be improved.  
 
 
Figure 17: Ice point reference used to calibrate thermocouple 
 
After the instruments are calibrated, the uncertainty of measurements are calculated and 
listed in Table 2, using the equation of error propagation.  
 
Table 2: Uncertainty of measurement after calibration without considering other disturbances 
 Voltage drop Current Connector resistance Connector temperature 
Accuracy 0.0037mV (0.08%) 0.047A (0.02%) 0.018?? (0.09%) 0.1% 
 
The calculation of measurement uncertainty shown in Table 2 has not considered the 
effect of EMI, which is probably caused by the electro-magnetic shaker. In order to estimate the 
disturbance of EMI on the measurement data in vibration tests, a vibration pretest is conducted 
23 
 
and the resistances of connector and cable are both measured. As shown in Figure 18, the data 
measured at the connector varies during the vibration, and the data measured at the cable is 
constant during the vibration. Since both connector and cable are exposed to vibration, the 
constant data shown in Figure 18(b) demonstrates that the disturbance of EMI from the shaker is 
negligible, and the variation of data shown in Figure 18(a) is caused by the actual changes in 
connector resistance.  
 
 
(a) Connector resistance                                        (b) Cable resistance 
Figure 18: Comparison of connector resistance and cable resistance under a vibration pretest 
(Vibration amplitude: 0.18mm, frequency: 240Hz, duration: 20s) 
 
 
24 
 
CHAPTER 4 ACCELERATED TESTS UNDER VARIOUS TESTING 
CONDITIONS 
 
4.1 Methodology of accelerated tests 
4.1.1 Test conditions 
This chapter studies the effect of various operating conditions on connector performance, 
which is summarized in Figure 19. Vibrations will be applied to the connectors with different 
direction, amplitude and frequency. At the same time, ambient temperature can be also 
controlled. The connector performance, fretting and failure mechanism are primarily estimated 
by connector resistance, RC. Connector temperature, TC, will be also studied as an auxiliary 
assessment.  
 
 
Figure 19: Operating conditions and assessments of connector for accelerated tests 
 
25 
 
4.1.2 Definition of coordinates for vibrations 
The definition of coordinate is shown in Figure 20. Z direction follows the direction of 
cable. The X and Y direction are perpendicular to the Z direction via the right hand rule. For the 
symmetric nature of connector, vibrations in X and Y directions are identical so that the vibration 
in Y direction is neglected for the connector. 
 
 
Figure 20: Definition of coordinates for vibrations 
 
4.1.3 Test procedure and test matrix 
The test procedure for each test run is defined in Figure 21. Before vibration starts, the 
connector should be fully heated by the constant applied current of 220A with controlled ambient 
temperature environment.  
 
26 
 
 
Figure 21: Test procedure for accelerated tests 
 
Detailed test conditions for each test run are listed in the test matrix, as shown in Table 3. 
A new connector will be used for each test run. Three repeating iterations for each test run are 
required to study the repeatability of data.  
Test 1 is the benchmark test and all other test runs make changes of certain operating 
condition based on Test1. Test 2 and 3 change the direction of vibration. Since the connector is 
symmetric in X and Y direction, test 3 is neglected. Test 4, 5 and 6 change the vibration 
frequency. Test 7 and 8 change the ambient temperature. Test 9 and 10 are supposed to change 
the humidity. However, the effects of humidity on silver-plated connectors can be neglected 
because silver is much more stable than other conventional materials under the humidity 
environment [12], [28]. Therefore, Test 9 and 10 are neglected. Test 11-14 change vibration 
frequency and ambient temperature simultaneously.   
 
27 
 
 
Table 3: Test matrix of accelerated tests 
Test Run Frequency  (Hz) Temperature (0C) Vibration Directions Comments 
1 100 80 Z Benchmark Test 
2 100 80 X Vary direction of vibration 
3 Y direction vibration test is neglected because of symmetry with X 
4 50 
80 Z Vary vibration frequency 5 150 
6 200 
7 100 25 Z Vary temperature 
8 120 
9 Tests of humidity effect are neglected for 300A connectors (silver coating) 
10 
11 50 25 
Z Vary frequency and temperature 12 200 25 13 50 120 
14 200 120 
 
For each test run, the vibration amplitude is increased step by step, as shown in Table 4. 
Vibration is applied for 3 minutes at each amplitude, and held for 1 minute before starting the 
next one. For the tests with vibration frequency higher than 100Hz, the maximum vibration 
amplitude cannot reach 0.8mm because it is limited by the shaker capability. 
 
Table 4: Vibration amplitudes (peak-to-peak) for each test run  
Vibration Amplitudes (mm). 3 minutes for each amplitude with 1 minute break in between 
0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 
 
28 
 
4.2 Methodology of accelerated tests 
4.2.1 Experimental results of RC  
4.2.1.1 Baseline data of RC without applying vibration 
The baseline data of RC are collected before vibration starts in each test run. Without 
vibration, RC is only dependent on ambient temperature under constant current. These baseline 
data are averaged in all tests and plotted versus ambient temperature, as in Figure 22, where the 
error bars show the standard deviations. It is shown that the RC increases slightly with the 
increase of ambient temperature, which is mostly caused by the bulk resistance of the male and 
female parts. 
 
Figure 22: Averaged RC under different ambient temperatures without vibration 
 
29 
 
4.2.1.2 ?RC with all operation conditions 
The change of connector resistance, ?RC, is defined as the average value of connector 
resistance under vibration subtracted by the value before vibration starts. The RC under each 
vibration amplitude can be simplified to one value of ?RC, so that one test run has a series of 
?RC. For example, the data of RC in the 1st test run of 3rd iteration is shown in Figure 23, where 
?RC are marked when vibration amplitudes are 0.3mm, 0.5mm and 0.8mm. 
 
Figure 23: Definition of ?RC 
 
Since each test run (shown in Table 3) is conducted three times repeatedly, the ?RC are 
averaged among the repeating tests and plotted from Figure 24 to Figure 27. In addition, the 
standard deviations of ?RC among the repeating tests are calculated and will be presented as error 
bars. 
The ?RC for test 1 and 2 are plotted in Figure 24 to study the effect of direction of 
vibration. The data shows that ?RC has an increasing trend with the increase of vibration 
amplitudes. The vibration in X direction causes more of an increase in connector resistance 
compared to vibration in Z direction. 
30 
 
 
 
Figure 24: ?RC under different vibration directions (Test 1 and 2) 
 
The ?RC for test 1, 4, 5 and 6 are plotted in Figure 25 to study the effect of vibration 
frequency. The data shows that higher frequency vibrations cause more of an increase in 
connector resistance compared to vibrations at lower frequencies. Due to the limitation of shaker 
capability, the vibration amplitudes at 150Hz and 200Hz cannot reach 0.8mm. 
 
31 
 
 
Figure 25: ?RC under different vibration frequencies (Test 1, 4, 5 and 6) 
 
The ?RC for tests 1, 7 and 8 are plotted in Figure 26 to study the effect of ambient 
temperatures. The data shows that the vibrations at lower ambient temperatures cause more of an 
increase in connector resistance compared to the vibrations at higher ambient temperature. 
 
32 
 
 
Figure 26: ?RC under different ambient temperatures (Test 1, 7 and 8) 
 
The measured ?RC values for test 11, 12, 13 and 14 are plotted in Figure 27 to study the 
effect of vibration frequency and ambient temperatures. Again, the data shows that vibrations in 
higher frequency and lower ambient temperatures cause more of an increase in connector 
resistance. 
 
33 
 
 
Figure 27: ?RC under different vibration frequencies and ambient temperatures (Test 11, 12, 13 
and 14) 
 
4.2.2 Experimental results of TC  
4.2.2.1 Baseline data of TC without applying vibration 
Similarly, the baseline data of TC are collected before vibration starts in each test run. 
Without vibration, TC is only dependent on ambient temperature under constant current. These 
baseline data are averaged in all tests and plotted versus ambient temperature in Figure 28, where 
the error bars show the standard deviations. It is shown that the TC is always approximately 20?C 
higher than the ambient temperature. This must be caused by Joule heating when the current goes 
through the connector and cable. 
 
34 
 
 
Figure 28: TC under different ambient temperatures without vibration 
 
4.2.2.2 ?TC with all operating conditions 
The change of connector temperature under vibration, ?TC, is defined as the overall 
increase of connector temperature over the entire test run. Since TC is an auxiliary factor to assess 
connector performance, each test run has only one ?TC to represent the changes in connector 
temperature. For example, the data of TC in the 1st test run of 3rd iteration is shown in Figure 29, 
where ?TC is marked as the overall increase of connector temperature during the entire vibration. 
 
35 
 
 
Figure 29: Definition of ?TC 
 
Since each test run is conducted three times among repeatedly, the ?TC are averaged 
among the repeating tests and plotted from Figure 30 to Figure 33. In addition, the standard 
deviations of ?TC among the repeating tests are calculated and will be presented as error bars.  
The ?TC for tests 1 and 2 are plotted in Figure 30 to study the effect of direction of 
vibration. The data shows that the ?TC in the Z direction is slightly larger than the X direction. 
However, the standard deviation of ?TC is large, which means that the temperatures in different 
vibration directions may not be statistically significant. 
 
36 
 
 
Figure 30: ?TC under different vibration directions (Test 1 and 2) 
 
The ?TC for tests 1, 4, 5 and 6 are plotted in Figure 31 to study the effect of vibration 
frequency. The data shows that higher frequency vibrations cause more of an increase in 
connector temperature in general, although the ?TC in 150Hz is slightly larger than that in 
200Hz. Since the maximum vibration amplitude for T5 and T6 is 0.25mm, the ?TC for T1 and T4 
is also calculated at 0.25mm in this figure. 
 
37 
 
 
Figure 31: ?TC under different vibration frequencies (Test 1, 4, 5 and 6) 
 
The ?TC for tests 1, 7 and 8 are plotted in Figure 32 to study the effect of ambient 
temperatures. The data shows that ?TC is largest in test 1 and smallest in test 7 and that the 
repeatability of data is not good. It means that the connector temperatures under vibration at 
different ambient temperatures may not be statistically significant. 
 
38 
 
 
Figure 32: ?TC under different ambient temperatures (Test 1, 7 and 8) 
 
The ?TC for tests 11, 12, 13 and 14 are plotted in Figure 33 to study the effect of 
vibration frequency and ambient temperatures. It is shown that higher frequency vibrations cause 
much more of an increase in connector temperature but also that the effect of ambient 
temperature does not have a statistically noticeable effect on ?TC. Since the maximum vibration 
amplitude for T12 and T14 is 0.25mm, the ?TC for T11 and T13 is also calculated at 0.25mm in 
this figure. 
 
39 
 
 
Figure 33: ?TC under different vibration frequencies and ambient temperatures (Test 11, 12, 13 
and 14) 
 
4.3 Summary and main findings 
The accelerated tests have been conducted with various operating conditions including 
vibration direction, amplitude, frequency and ambient temperature with the measurement RC and 
TC. The measurement data are averaged among three repeating tests.  
Generally, the connector degradation and failure are barely observed since there is no 
significant and gradual increase of RC during the vibrations. Instead, experiments have shown the 
temporary increases of RC during the vibration: When a connector is exposed to vibrations, the 
RC significantly increases and oscillates. When the vibrations are stopped, RC is set back to a 
value that is close to the original state. The RC under vibration can increase to a value as large as 
twice of its original state. This will be analyzed experimentally and theoretically in the following 
40 
 
chapters. The overall increase of connector temperature, ?TC, is less significant. It ranges from 0 
to 12 degree Celsius based on the operating conditions. 
Other findings concerning the effects of different operating conditions include: 
? Vibrations at higher amplitudes induce more increase in RC.  
? Vibrations in the X direction (perpendicular to the cable) induce more temporary increase in 
RC compared to the Z direction.  This can be explained by the analysis in Chapter 6, which 
shows the vibration in X direction would induce the deformation of the contact spring more 
directly.   
? Vibrations at higher frequency induce more increase in both RC and TC. The increase of RC 
can be explained by the analysis in Chapter 6, which shows that the relative displacement 
between the female and male parts tends to follow the increase of vibration frequency. The 
increase of TC is likely to be caused by Joule heating with increased RC. The friction between 
contact surfaces may be another heat source. 
? Vibration at lower ambient temperatures induces more increase in RC. It is assumed that 
higher ambient temperatures tend to soften and relax contact material and result in a larger 
asperity contact area. Therefore, the RC is smaller at elevated ambient temperatures. 
41 
 
CHAPTER 5 EXPERIMENTAL ANALYSIS OF VIBRATION INDUCED 
CHANGES IN CONNECTOR RESISTANCE 
 
In the previous chapter, it is found that the connector resistance, RC, temporarily 
increased and oscillated during vibration. Experimental works with analysis are conducted in this 
chapter to explain this experimental finding in this chapter. The analysis will only consider the 
vibration in the X direction since it induces more increase and oscillation of connector resistance 
(see Figure 24). The vibrometers are used to measure the motions of connector and the surface 
profilometer is used to measure the surface profile and roughness for tested connectors. 
5.1 Effects of vibration with fixed amplitude and frequency 
A vibration test is conducted with a constant amplitude of 0.64mm (peak-to-peak) and a 
constant frequency of 100Hz. The duration is approximately 37s with 3700 vibration cycles. The 
ambient temperature is controlled at 25?C and the supplied current is 220A.  The test conditions 
are summarized in Table 5. 
 
Table 5: Test conditions for fixed amplitude and frequency 
Amplitude Frequency Duration Current Ambient Temperature 
0.64mm (peak to peak) 100Hz Approximately 37s 220A DC 25?C 
 
The RC during the test is shown in Figure 34(a). Again, the temporary increase of RC is 
found. When vibration starts, RC significantly increases and oscillates. When the vibration stops, 
the RC decreases to a value that is slightly larger than the original value and remains. 
42 
 
 
(a) Increase and oscillation of the RC under 3700 vibration cycles   
 
(b) Increase and oscillation of the RC under 5 vibration cycles   
 (c) Spectrum of R
C by discrete Fourier transforms 
Figure 34:  Vibration-induced changes in RC 
 
43 
 
  Since the data is logged at a high sampling rate, the plot is magnified for a short 
duration of 50ms, as shown in Figure 34 (b). It is shown that RC increases and varies 
periodically, but is distorted from a harmonic signal. The period of the variation has a component 
at a period of 10ms which is the same as that of the excitation. The spectrum of RC is analyzed 
using discrete Fourier transform in Figure 34 (c). It is important to recognize that the spectrum of 
RC has the highest magnitude at 200Hz, which is twice as the excitation frequency.  
5.2 Effects of vibration with varying amplitudes and fixed frequency 
In this test, the vibration frequency is fixed at 100Hz and the ambient temperature is 
controlled at 25?C.  The vibration amplitude is increased from 0.04mm to 0.64mm with an 
incremental step of 0.04mm at every 30s and then held for 30s without vibration. The measured 
RC is shown in Figure 35. It is observed that the RC tends to follow the increase of the vibration 
amplitude.   
Table 6: Test conditions for varying amplitude and fixed frequency 
Amplitude Frequency Duration Current Ambient Temperature 
0.04mm, 0.08mm, 
? ,0.60mm,0.64mm(peak to peak) 100Hz 
30s for each 
amplitude 
220A 
DC 25?C 
 
44 
 
 
Figure 35 RC at increasing vibration amplitudes and fixed frequency 
 
The measurement of motions is then applied to this vibration test. In this chapter, the 
motions at two locations are measured, as shown in Figure 36. U1 is at the female part of 
connector and U2 is at the right end of male part. Two holes are drilled on the female housing 
and male housing so that the laser beams can measure the two motions. The relative 
displacement between the right end of male part and the female part is estimated by  
 2
1212
2
12121112212 )s i n ()c o s (1 ???????? ?????????? ???????? ?????? MMMMMMMUU  
(2) 
where M1, M2 and ?2 are measured from vibrometers. ?1 equals to zero since U1 is considered as 
reference.  
Actually, |U2-U1| is an only rough approximation of the relative displacement between 
male and female parts at the contact surfaces because U2 is away from the contact surface of 
male part. The motion at the contact surface of male part, U4, is not accessible by experiment 
45 
 
because the female part blocks the laser to access it. U4 can only be calculated by the FEM 
model, which will be shown in the following chapter. 
 
 
Figure 36: Measurement locations of motions 
 
In order to simplify the presentation of RC shown in Figure 35, ?RC is introduced again as 
an average value of change of the RC during vibration. Both |U2-U1| and ?RC are plotted as a 
function of the vibration amplitudes, shown in Figure 37. When the vibration amplitude 
increases, the relative displacement, |U2-U1|, increases. Accordingly, the ?RC tends to follow it. 
This relationship can be approximated by 
 || 121 UUkR C ???  (3) 
where k1 is a constant that can be determined based on the experimental data.  
 
46 
 
 
Figure 37: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration amplitude  
(under increasing vibration amplitudes and fixed frequency) 
 
5.3 Effects of Vibration with Fixed Amplitudes and Varying Frequencies 
In this test, the vibration amplitude is constant at 0.15 mm and the vibration frequency is 
varied from 40Hz to 260Hz with an incremental step of 20Hz every 30s.  Other test conditions 
are unchanged, as shown in Table 7. 
 
Table 7: Test conditions for fixed amplitude and varying frequency 
Amplitude Frequency Duration Current Ambient Temperature 
0.15mm (peak 
to peak) 
40Hz, 60Hz, 
80Hz, ? ,240Hz, 260Hz 30s for each amplitude 
220A 
DC 25?C 
 
The relative displacement, |U2-U1|, is obtained in the same manner as the previous 
sections.  ?RC and |U2-U1| are also plotted as a function of vibration frequency in Figure 38. For 
47 
 
the frequency range that is less than 180Hz, the ?RC follows the amplitude of the relative 
displacement |U2-U1|, but it starts to deviate significantly when the frequency is larger than 
180Hz.  As a result, equation (3) does not represent the ?RC over all ranges of the frequency. The 
?RC should be dependent upon not only the relative displacement |U2-U1|, but also the vibration 
frequency. This relationship can be approximated by  
 2122 || fUUkR C ???  (4) 
as depicted in Figure 38, where k2 is a constant obtained from experiment data. It shows that the 
variation of ?RC tends to follow the product of relative displacement and the square of 
frequency, |U2-U1|f2. In the previous section, since the vibration frequency is a constant, equation 
(4) is also valid and the trend of |U2-U1| and |U2-U1|f2 overlap to each other, shown in Figure 37. 
 
 
Figure 38: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration frequency  
(under increasing vibration frequency and fixed amplitude) 
 
48 
 
5.4 Effects of Vibration with Varying Amplitudes and Frequencies 
Like the previous experiments, the ambient temperature is set at 25?C. The vibration 
frequency is varied from 30Hz to 600Hz with an incremental step of 30Hz, and the 
corresponding vibration amplitude decreases accordingly under a fixed g-value of 10. Other test 
conditions are unchanged, as shown in Table 8. 
 
Table 8: Test conditions for varying amplitude and varying frequency 
Amplitude Frequency Duration Current Ambient Temperature 
Decreases accordingly 
under a fixed g-value of 10 
30Hz, 60Hz, 
90Hz, ? 570Hz, 600Hz 
30s for each 
amplitude 
220A 
DC 25?C 
 
Based on equation (4), ?RC and k2|U2-U1|f2 are plotted in Figure 39, where k2 is an 
experimentally obtained constant.  It should be noted that the overall trends of ?RC and |U2-U1|f2 
are similar. Their peak values are located around the frequency of 150Hz and 450Hz. In addition, 
k1|U2-U1| is also plotted in Figure 39 comparison. However, the prediction of equation (3) 
deviates from the variation of ?RC. 
 
49 
 
 
Figure 39: ?RC, k1|U2-U1| and k1|U2-U1|f2 as a function of vibration frequency 
(under fixed g-value with increasing frequency and decreasing amplitude) 
 
The results obtained from three experimental cases have shown that the variation of RC 
under vibration is affected by both relative displacement between the right end of male part and 
female part |U2-U1|, as well as the vibration frequency. Equation (4) is derived to describe this 
relationship, where the ?RC is based on a product of the relative displacement |U2-U1| and the 
square of frequency, f2.  
5.5 The effect of vibration on wear and corrosion (Surface analysis) 
When vibrations are applied to the connectors, connector resistance changes and wear or 
corrosion may also occur at the contact surfaces.  In order to study the effects of vibration on the 
surface of the connectors, a vibration with 1mm amplitude and 100Hz frequency is applied to a 
connector for half an hour, where the ambient temperature during the vibration is set at 80?C. 
After vibration, the worn connector surfaces are examined and a failure analysis is performed. A 
50 
 
snapshot of a worn surface on the male part of a connector taken from a scanning electron 
microscopy (SEM) is shown in Figure 40.  
 
 
Figure 40: SEM on worn contact surface (Position 1 is wear pit and position 2 is non-contacting 
area) (From Dr. Michael J. Bozack) 
 
The SEM is operated in backscattered electron mode in order to highlight the different 
surface morphologies observed on the connectors. Position 1 is the wear pit caused by friction 
during vibrations. Position 2 refers to the non-contacting area. By observation, the pit in position 
1 is just a hole or valley with a lower altitude compared to position 2. Very little material build-
up is found. 
 The results of auger electron spectroscopy (AES) for position 2 and position 1 are shown 
in Figure 41. AES is a true surface technique, allowing for the detection of all elements of the 
periodic table (except H) located within the first 50? of the surface to a sensitivity of ~ 0.01 
atom %.  In Figure 41 (a), silver is the only element detected in non-worn position. As for Figure 
51 
 
41 (b), copper and its oxide are detected in the worn position where the silver appears to be 
almost worn out. 
 
(a)                                                           (b) 
Figure 41: (a) AES for surface material analysis of non-worn position. (b)  AES for surface 
material analysis of worn position. (From Dr. Michael J. Bozack) 
 
The results show that the defect area on the surface is best referred to as a worn pit rather 
than corrosion because the main finding is indentation and removal of the coating material. If 
fretting corrosion occurs, there would be material accumulation and a more random appearance 
in the SEM image. For example, metallic fretting debris [33] and thick oxide films [14] can be 
found after tin-plated fretting corrosion.  
5.6 Summary 
The investigations of RC and surface analysis have shown that the variation of RC under 
vibration is mainly affected by relative displacement and vibration frequency instead of fretting 
corrosion. It is the relatively stable property of the silver coating that makes fretting corrosion 
less significant so that the temporary changes of contact resistance dominates the experimental 
52 
 
results. The test results from Hubner-Obenland and J. Minuth also supported the benefits of 
silver contacts [14]. Their work showed that the silver-to-silver contact has the lowest contact 
resistance increase after 31 hours of vibration, compared to other combinations of contact 
materials, including tin, silver, and gold. 
 
53 
 
CHAPTER 6 MODELING OF THE CONNECTOR SYSTEM USING TWO-
DIMENSIONAL FEM  
 
The experimental results obtained in the previous paper showed that the ?RC is mainly 
affected by the relative displacement between the right end of the male part and the female part, 
|U2-U1|. In fact, |U2-U1| is different from the relative displacement between the male (U4) and 
the female part (U1) at the contact surface and the previous analysis was not accurate. In this 
chapter, we developed a vibration model using FEM to predict U4, as shown in Figure 42, since 
U4 is not accessible for the measurement. As a result, the model allows for accurate analysis on 
effects of the relative displacement |U4-U1| on the ?RC.  
As shown in Figure 42, the housing for the male part was removed in this chapter in order 
to simplify the connector system and make it easier to model. Removing the housing for the male 
part also helps to study the effects of high natural frequencies that the shaker can excite.  
 
 
Figure 42: The locations of motions to be studied 
 
54 
 
6.1 Experimental results 
Before showing the FEM vibration model, experiments are conducted to collect the 
results for validating the model. The test conditions are shown in Table 9.  The amplitude of 
vibrations is set to be with a constant value of 0.18mm, while the frequency is changed from 
20Hz to 240Hz with an incremental step of 20Hz. Every vibration lasts 2 minutes at each 
frequency with a pause of 1 minute. The tests were conducted under flow of constant DC current 
of 80A and room temperature.  
 
Table 9: Test conditions 
Amplitude Frequency Duration Current Temperature 
0.18mm 20Hz, 40Hz, ?220Hz, 240Hz 2min for each frequency 80A DC Room Temperature 
 
The amplitude of the motions, U0 through U3, and the connector resistance, RC, are 
measured in real time under vibration. Since the connector is fixed with the shaker, it is assumed 
that U0 is the same as to the vibration of the shaker.  The magnitude ratios of the motions (M1/M0, 
M2/M0, and M3/M0) are plotted in Figure 43. 
55 
 
 
(a) The magnitude of the female part (M1) versus the excitation (M0) 
 
(b) The magnitude of the right end of male part (M2) versus the excitation (M0) 
56 
 
 
(c) The magnitude of the midpoint of cable (M3) versus the excitation (M0) 
Figure 43: Experimental results of the magnitude ratios of motions 
 
The frequency response of M1/M0 is shown in Figure 43(a), where M1 is measured at the 
female part. When the frequency increases, the magnitude increases slightly as well. Figure 43 
(b) shows the magnitude of motion at the right end of male part. The magnitude increases 
significantly at 60Hz and 220Hz, which indicate resonances taking place at the two frequencies. 
The frequency response of M3/M0 is shown in Figure 43 (c), where M3 is measured at the middle 
point of power cable. The magnitude increases significantly at 60Hz, which indicates a 
resonance taking place at the frequency. 
Measured ?RC as a function of frequencies is shown in Figure 44 . Generally, the 
connector resistance increases as the frequency increases. The peak values were reached at two 
resonant frequencies, which will be theoretically verified using the model developed.   
57 
 
 
Figure 44: Changes of connector resistance, ?RC, versus vibration frequencies. 
 
6.2 Modeling of the Connector System by FEM 
6.2.1 Set-up 
Set-up for the model is shown in Figure 45(a), where the connector system shown in 
Figure 42 is simplified to four different components: a female part with housing, a male part, a 
supplied cable and a contact spring. The female part with housing is regarded as a mass with a 
shape that encloses the male part and contact spring. The male part and the cable are 
approximated with two beams that attach to each other, whose material properties and 
dimensions are shown in Table 10.  Since the cable contains copper strands and metal shielding 
with unknown material properties, the equivalent values are experimentally obtained applying a 
simple beam theory, where the Young?s modules and the density of cable are derived. The 
contact spring is simplified as two linear springs located between and male and female parts in 
the direction of vibration.  
58 
 
 
(a) The set-up and boundary conditions in the direction of vibration 
 
 (b) The boundary conditions perpendicular to the direction of vibration. 
Figure 45: Finite element model for the connector system with boundary conditions. 
 
Table 10: Material and dimensional properties of the male part and cable. 
 
Connector 
(copper 
alloy) 
Cable (composite 
material of strands 
and shielding) 
Young?s Modulus (GPa) 117 3.3 
Mass Density (kg/m3) 8930 2506 
  Length (mm) 60 270 
Cross-section area (mm2) 150 200 
 
Using the commercial finite element software, ANSYSTM, the four simplified 
components aforementioned are modeled with a two-dimensional structure using one-
dimensional elements. All the material properties and the real constants are used for input 
variables for the element of the Beam3. The contact spring is modeled using the spring-damper 
element, the Combin14, where a spring constant and a damping ratio are needed. The details of 
how to determine the spring constant is explained in the following section.  
Once the element types with material properties had decided, boundary conditions for the 
nodes of elements are needed to start simulation. The nodes on the locations of fixture clamps 
are marked with small triangles and assumed to have the motion same as excitation, as shown in 
Figure 45(a). Also it is assumed that the displacements of all nodes are in the same direction to 
59 
 
that of the excitation, so no other nodes are vibrating in other directions and corresponding 
boundary conditions can be set to be zero, as shown in Figure 45(b).   
6.2.2 Determination of the equivalent spring constant 
The ring shaped spring is approximated with two simple equivalent springs, whose 
simplification steps are depicted in Figure 46 . The spring has 22 repeatable sections that are 
uniformly distributed in the circumference and in contact with the female part on one side and 
male part on the other side. Each section of spring consists of tabs connected over a bridge and is 
compressed in radial direction by the male part.  The 22 repeatable sections are regarded as 22 
linear springs that can be reduced to two springs under an assumption that the displacement of 
the male part is only in the direction of vibration.  
 
Figure 46:  Simplification of the ring shape spring 
 
The spring constant, ke, is derived from a relationship between force and displacement. 
The relationship for a single section of the spring is attained from a three-dimensional static 
simulation and analysis, which will be shown in the next chapter. When the position of male part 
in the radial direction is artificially and incrementally moved, the corresponding contact force is 
produced at different positions. As a result, at the ith repeatable section of the contact spring, a 
60 
 
relationship between the radial displacement from a steady state position, ri (mm), and the radial 
contact force, Fr,i (N), is  obtained: 
 824, ?? iir rF  (5) 
The linear equation above includes an unknown variable, ri. When the male part moves in 
the vibration direction by d, which is known as the relative displacement between male and 
female part, ri changes accordingly. As shown in Figure 47 (a), ri can be expressed as a function 
of d from the triangle QOP, as shown in equation (6): 
 )1( c o sc o s 222 ????? iii dRRdr ??  (6) 
where R is the radius of male part and ?i is the angle from the x direction to the radial direction 
of the ith spring.  
 
 
(a)                                                                       (b) 
Figure 47: Schematic diagrams for calculation of an equivalent spring constant. (a) Calculation 
of the radial displacement for the ith spring. (b) Calculation of the resultant force in X direction 
(direction of vibration) 
 
61 
 
Hence, the contact force in radial direction for the ith spring is obtained from equation (5) 
and (6). The force, Fr,i, can be decomposed into two components, Fx,i and Fy,i, as shown in Figure 
47 (b), where the x represents the direction of the vibration. The sum of all forces exerted to y 
direction is zero because of the cylindrical shape, when the male part is vibrated in x direction.  
As a result, the resultant contact force, Fx, can be expressed as follows: 
 
ii iri ixx FFF ?c o s
22
1 ,
22
1 , ?? ??
??  (7) 
Consequently, the equivalent spring constant ke for the two simplified linear springs can 
be calculated, as shown in equation (8).In this way, the spring constant for the spring element, 
Combin14, is determined. 
                   
 ? ?? ? mmNd dRRddFk ii iixe /2572 c o s8)1( c o sc o s242
22
1
222
???????? ?? ??? (8) 
6.3 Comparison between simulation and experimental results  
The vibration model developed above is compared with experimental results obtained 
using laser vibrometers. The frequency and amplitude of the exciting vibration used for the 
simulation are same as the experiments, as shown in Table 9, where the marked small triangle in 
Figure 48 indicates the excited two points in female parts and one point at the end of cable. Like 
the experimental set-up, U0, presents a reference point. U1, U2, U3 and U4 are the points that are 
calculated in the simulation.  
62 
 
 
Figure 48: The locations of motions to be studied in simulation 
 
Comparison between simulations and experiments are shown in Figure 49(a), (b) and (c) 
at different locations, where the magnitude ratios of M1/M0~M3/M0 are plotted. The results show 
a fair match to each other in M1 and M2, but a deviation around a resonance is observed at M3.   
Because U4 is inaccessible for a probe, only simulations are carried out and their results 
are plotted in Figure 50, where the ratio of the magnitude increases at two resonance frequencies 
of around 60Hz and 190Hz.  
63 
 
 
(a) The magnitude of the female part (M1) versus the excitation (M0) 
 
(b) The magnitude of the right end of male part (M2) versus the excitation (M0); 
 
(c) The magnitude of the midpoint of cable (M3) versus the excitation (M0) 
Figure 49: Comparison between simulated and experimental results 
64 
 
 
 
Figure 50: Simulation result: The magnitude of the male part (near the contact) (M4) versus the 
excitation (M0) 
 
Based on the previous results, the relative displacement between the male and female part 
at the contact surface is studied. The relative displacement, d, is defined as an absolute value of 
the difference between U4 and U1, as follows in equation (9): 
                   
 2
1414
2
1414114 )s i n ()c o s (1 ???
???
?
? ????
?
???
?
? ?????? ????
MMMMMUUd  
(9) 
where U4 and U1  are calculated using the model .  
Simulated relative displacement, d, and change of connector resistance experimentally 
measured, ?RC, at different excitation frequencies are plotted in Figure 51.  The plot shows a 
relative good correlation in magnitudes at the two resonant frequencies that are located at the 
80Hz and 220 Hz, which implies that the change of connector resistance are affected by the 
relative displacement at the contact surface.    
65 
 
 
Figure 51: Comparison between relative displacement (simulation) and changes of n connector 
resistance (experiment) 
 
6.4 Modal analysis by simulation  
A modal analysis for the connector system is conducted by simulation. Figure 52 shows 
the mode shapes of the connector system at the first two natural frequencies. As shown in Figure 
52(a), the male part of connector undergoes a rocking motion at the first natural frequency. At 
the second natural frequency, as shown in Figure 52(b), the male part of connector is more likely 
to undergo a translational motion in the direction of excitation. These results are similar to the 
finding from Xie et al. [30], who have investigated the motions of a blade/receptacle connector 
under vibrations.  
66 
 
 
(a) The mode shape at 60Hz, around the first natural frequency 
 
(b) The mode shape at 220Hz, around the second natural frequency 
Figure 52: Simulated mode shapes at the first two natural frequencies 
 
The change of mode shape shows that |U2-U1| cannot estimate the relative displacement 
between male and female parts at the contact surface over all frequency range. As was shown in 
Figure 38, a deviation is observed between k1|U2-U1| and ?RC at high frequency range because 
the connector system changed the mode shape when frequency increases beyond a certain value. 
Equation (4) used the square of excitation frequency, f2, to compensate this error. However, 
Figure 51 shows |U4-U1| follows the change of ?RC very well over all frequency range, which 
demonstrates that |U4-U1| is a more straightforward and accurate estimation of the changes of 
connector resistance compared to |U2-U1|. 
 
 
67 
 
CHAPTER 7 MODELING OF THE CONTACT SPRING USING THREE-
DIMENSIONAL FEM  
In order to explain the correlation between |U4-U1| and ?RC more clearly, a three-
dimensional model for the contact spring is developed using ANSYS? and used to analyze the 
time responses of vibrations on displacement of contact surfaces.   
7.1 Set-up 
Set-up for the model is shown in Figure 53.  Since the connector is cylindrical, only a 
part of the connector along with one section of spring is considered for the modeling.  The 
connector includes one contact surface area of the female and one contact surface area of the 
male part. According to the actual geometry, the repeatable section of spring has three contact 
tabs over a bridge, two upper tabs and one lower tab.  
 
Figure 53: Finite element model of one repeatable section of contact spring. 
 
In order to perform structural analysis of bulk materials, the element of Solid187 is used, 
which is a high order three-dimensional element with 10 nodes, while Targe170 elements and 
Conta174 elements are needed for analysis of three contact pairs.  The three contact pairs present 
68 
 
two upper tabs and one lower tab.  The material properties of the bulk material and the contact 
pairs are given in Table 1.  
Boundary conditions for the spring model are obtained from the simulation results of 
relative displacements, as shown in Figure 51.  When the connector is vibrated, the female and 
male part oscillates.  For simple calculations, the female part is regarded as fixed while the male 
part oscillates with amplitude of relative displacement, so the boundary conditions for the female 
and male part are determined. For the spring, symmetric boundary conditions can be applied 
because of symmetric geometry of only a repeatable section of contact spring modeled. In 
addition, it is assumed that the displacements of the sides of the spring are only allowed in the 
direction of vibration. 
7.2 Simulation results  
The model developed above is used to study time responses of displacements of the 
spring at four locations: the lower tabs of spring, the upper tab of spring, the contact surface of 
female part and the contact surface of male part, as shown in Figure 54. Simulations can be run 
for different cases, so that a case is selected from the data shown in Figure 51, where the relative 
displacement is 0.153mm at the excitation frequency of 240Hz. The eight periods of the 
vibration is applied, as shown in Figure 55.  
69 
 
 
Figure 54: Points for displacement used for simulations  
 
 
(a) Time response of lower tab of spring 
 
(b) Time response of upper tab of spring 
Figure 55: Time response of the displacements versus time when excitation frequency equals to 
240Hz 
 
70 
 
The displacements of lower tab of the spring and the male part are shown in Figure 55 
(a), where the displacement of lower tab irregularly varies when vibration is applied and goes 
into steady state after the second cycle of vibration. In the steady state, overlapped two lines 
indicate that the lower tab of spring and the male part of connector are in contact. However, 
contact gaps are formed periodically before the male part reaches maximum and minimum 
values. 
The two upper tabs of the spring are symmetrical from the top view and have the same 
responses. Therefore, only the responses of one upper tab and the female part are shown in 
Figure 55(b), where the displacement of the upper tab irregularly varies at the beginning and 
goes into steady state after the second cycle of vibration.  In the steady state, a gap between the 
upper tabs of the spring and the contact surface of female part is periodically produced, so a 
contact with the female part is not continuous.   
The contact gaps explained above are presented in three-dimensional forms.  Three 
deformed shape of the spring at different instants are shown in Figure 56. When the second cycle 
starts at t=0.0043s, the shape around the equilibrium position is very little deformed and no 
contact gap is observed, as shown in Figure 56(a).  At t=0.0050s, the male part compresses the 
spring, so that the low tap loses the contact with the male part, as shown Figure 56(b). At 
t=0.0070s, the male part releases the spring and the spring loses contact with the female part as 
well as with male part, as shown in Figure 56(c). The color bar in the Figure 56(d) indicates the 
displacement of each node in the next contour plots. 
71 
 
 
(a) Deformed shape @ t=0.0043s, around equilibrium position 
 
(b) Deformed shape @ t=0.0050s, male part moving up 
 
(c) Deformed shape @ t=0.0070s, male part moving down 
 
(d) Color bar showing the nodal displacement (mm) 
Figure 56: The deformed shapes at different instants, corresponding to Figure 55. 
 
Similarly, studies are performed for two more cases when the excitation frequency is 
160Hz and 60Hz and corresponding magnitudes of relative displacements are 0.069mm and 
0.022mm respectively, according to the data in Figure 51. Displacements between two contacts 
are shown in Figure 57, where the second cycle is illustrated. At frequency equaling to160Hz, 
the gab produced is relatively small, but is negligible at the frequency of 60Hz. The analysis 
72 
 
shows that the gaps between contact surfaces vary when connector is subjected to vibrations. The 
higher the relative displacement is, the larger the contact gaps are produced, which seemingly 
cause the changes of connector resistance.  
 
 
         (a)Frequency=160Hz                                                              (b) Frequency=60Hz 
Figure 57: Time response of the displacements versus time at excitation frequency of 160Hz and 
60Hz. 
 
7.3 Comparison of 3D simulation results and experimental data 
In order to further study the relation between the changes in connector resistance and the 
contact gaps under vibration, their spectrums are compared and analyzed using discrete Fourier 
transform when vibration frequency equals to 100Hz with 0.18mm amplitude. The spectrum of 
connector resistance measured in experiments is plotted in Figure 58 (a), while the spectrum of 
73 
 
the time response of contact gaps calculated from the three dimensional model is plotted in 
Figure 58 (b). Figure 58 (a) shows that the spectrum of connector resistance has the magnitude at 
the excitation frequency (100Hz) as well as its harmonics. The highest magnitude is at 200Hz, 
which is twice as the excitation frequency.  In Figure 58 (b), it is shown that the spectrum of 
contact gaps has the similar trend as that of the connector resistance. However, the highest 
frequency locates at 700Hz. This might be caused by the numerical error when the FEM model is 
converging with oscillations at a frequency around 700Hz.  
Finally, the simulations of three dimensional model are conducted at all excitation 
frequencies in order to compare the changes in connector resistance measured in experiments. As 
shown in Figure 59, the simulated contact gaps and measured change of connector resistance at 
different excitation frequencies are plotted in Figure 59.  The plot shows that both connector 
resistance and contact gaps increase when excitation frequency increases. However, the 
threshold of the increase of connector resistance locates around 80Hz but the threshold of the 
increase of contact gaps locates around 140Hz. This deviation suggests that the prediction of 
three dimensional model is not accurate in all frequency domain. This might be caused by 
neglecting the material yielding and rough surface contact in the three dimensional FEM model. 
 
 
74 
 
 
(a) The spectrum of connector resistance (experimental) 
 
(b) The spectrum of contact gaps (simulation by 3 dimensional model) 
Figure 58: The comparison of spectrums of connector resistance and contact gaps under 
vibrations (excitation amplitude=0.18mm. excitation frequency=100Hz) 
 
 
75 
 
 
Figure 59: Comparison between contact gaps (simulation) and changes of connector resistance 
(experiment) in all frequency domains 
 
 
76 
 
CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 
 
The work presents an experimental and theoretical study on the round pin, silver-plated 
high power connector used for hybrid vehicles. The temporary change in connector resistance 
under vibration is found when the tests are conducted under different operational conditions. 
Theoretical analysis is conducted based on a two-dimensional finite element model for the 
connector system and a three-dimensional finite element model for the contact spring. The work 
consists of two parts. 
8.1 Experimental findings 
A test stand is designed for the connector which facilitates a controlled environment of 
current supply, vibration and ambient temperature with the measurement of connector resistance, 
RC, connector temperature, TC and motions. In order to study the effects of different operational 
conditions on the connector, the accelerated tests have been conducted with different vibration 
directions, amplitudes, frequencies and ambient temperatures. Based on the averaged data among 
three repeating test iterations, it is found that the temporary increase of connector resistance 
under vibration, ?RC, is more significant under higher vibration amplitude, frequency and lower 
ambient temperature. Also, vibrations in the X direction (perpendicular to the cable) induce more 
?RC compared to the Z direction (parallel to the cable).   
The temporary increase in RC under vibration is the most common and significant finding 
among all test runs: When a connector is exposed to vibrations, the RC significantly increases and 
oscillates. When the vibrations are stopped, RC is set back to a value that is close to the original 
state. In order to analyze this phenomenon, laser vibrometers are used to measure the motions of 
77 
 
the connector. It is found that the temporary increase in RC under vibration is affected by the 
relative displacement between the right end of male part and female part, |U2-U1|, as well as the 
square of vibration frequency.  
On the other hand, fretting corrosion of the connector is negligible because RC does not 
increase gradually over time under the vibration and has little permanent changes after vibration. 
Also, according to the surface analysis by SEM and AES on the worn connector, only 
indentation and removal of the coating material is observed and no accumulation of debris and 
few oxides are found. It is the relatively stable property of silver that makes fretting corrosion 
less significant so that the temporary increase of RC dominates the experimental results. 
8.2 Theoretical analysis using FEM 
Since the mechanism of the changes in connector resistance under vibration is not clear, a 
two-dimensional finite element model for the connector system is developed in AnsysTM for 
analyzing the motions of connector under vibration. The connector system is modeled as 
simplified components and the contact spring is modeled as linear springs with the equivalent 
spring constant. The model is simulated and validated by experiments when studying the motions 
at three locations of the connector system. The model is also able to predict the relative 
displacement between the male part and female part at the contact surfaces, |U4-U1|, which is not 
accessible for measurement. It is shown that the simulated |U4-U1| tends to follow the measured 
?RC very well when the excitation frequency is increased. Therefore, the relative displacement at 
the contact surfaces directly affects changes of connector resistance under vibration.  Also, |U4-
U1| is a more accurate estimation of ?RC than |U2-U1|. 
78 
 
However, the spring used for this high power connector has a very complex shape, whose 
behavior to vibration is unknown. Thus, a three-dimensional model for one repeatable section of 
the contact spring is developed in AnsysTM to calculate time responses of the spring subject to 
vibrations.  According to the simulation results, the oscillating relative displacement between 
male and female parts causes the periodic contact gaps between the spring and other connector 
parts, which changes the connector resistance.  According to the time responses, the gaps in 
steady state are dependent upon the magnitude of relative displacement between the male and 
female parts.   
To sum up, the results gathered in this work have thoroughly explained the mechanism of 
the vibration-induced changes in connector resistance for the silver-plated, round pin high power 
connector. When the connector is exposed to vibrations, relative displacement between the male 
and female parts at the contact surfaces is induced, which in turn causes the periodical contact 
gaps between contact spring and other parts of the connector. Thus, connector resistance 
increases and oscillates under vibration. 
8.3 Recommendations 
The increase of connector resistance during vibration is a potential threat to the reliability 
of high power connector since it significantly raises the connector temperature due to the high 
current flow, which is not the case in the low current connector.  One suggestion of future work 
is to investigate the effect of temporary changes in connector resistance on the reliability of 
connector for high power applications. 
In addition, the two finite element models developed in this work are valuable for 
industry applications to aid in connector design. By investigating the effects of material 
79 
 
properties and geometries, the relative displacement and contact gaps can be reduced and in turn 
the connector resistance under vibration can be minimized. Therefore, the connector 
performance and reliability can be improved. 
 
80 
 
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