An Experimental Investigation and a Multiscale Electro-thermo-mechanical Model of a Flat Pin High Power Electrical Connector by Santosh V. Angadi A dissertation submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Auburn, Alabama December 12, 2011 Keywords: Electrical connector, multi-physics, finite element model/experiment Copyright 2011 by Santosh V. Angadi Approved by Robert Jackson, Chair, Associate Professor of Mechanical Engineering Song-Yul Choe, Associate Professor of Mechanical Engineering Jeffrey Suhling, Professor of Mechanical Engineering George Flowers, Professor of Mechanical Engineering ii Abstract Hybrid and electrical vehicles (HEV) are the next evolutionary step in automobile technology. However, the electrical systems which propel HEVs are fundamentally different from conventional technologies. Therefore, a few limiting technologies will delay widespread HEV success such as the battery, power electronics and connectors. The high temperatures, vibrations, humidity, and contamination in a vehicle can reduce the reliability of these technologies. HEV electrical connectors conduct much more power and are more susceptible to failure and reliability problems than the connectors in conventional vehicles. Thus, in this work, a 40A high power electrical connector, used in HEVs, has been studied extensively by both modeling and experimental approaches. In this work, a multi-physics (involving structural, electric and thermal coupled fields) finite element model considering multi-scale rough surface contact of the 40A high power connector is created. This cutting-edge model includes the coupled effects of nano to macro- scale surface roughness, contact pressures, electrical and thermal contact resistances, stresses, displacements, applied currents, electric potential (voltage drop), current density, temperature, Joule heating and thermal expansion. It is a powerful tool that can be used for fundamental connector characterization, prototype evaluation and design. A few prominent findings were made from the results of the 40A connector model. It appears that the current flows mostly through very small regions that are usually near the iii contacting surfaces in the connector, thereby suggesting that the available conducting material can be more efficiently used by developing optimized connector designs. Interestingly, from the 40A connector model, it was found that the temperature rise (?T or change in temperature) in the bulk material is not very high, although ?T values measured experimentally indicate otherwise. Through analytical calculations and experimental measurements of ?T for the cable and the connector, it is believed that a large portion of the temperature rise in actual 40A connectors is due to the Joule heating in the supply cables. However, the local asperity temperature is also theoretically calculated and should be very high at the contact, which could cause an increased oxidation rate and surface melting. Coming to the experimental investigation in this work, 40A connectors were tested under both stationary as well as vibrating situations. For stationary tests, an increase in connector resistance and connector temperatures with an increase in applied currents is noticed. Also, more importantly, the same increasing trend of connector resistance with respect to applied currents is observed in both the 40A connector model and the stationary connector tests. An environmentally controlled and accelerated 40A connector test methodology was designed and created to characterize connector degradation and fretting under vibrating conditions. This includes the necessary hardware to control connector conditions and to monitor current, voltage drop, connector resistance (R) and connector temperature (T) in real time. A series of parametric tests were completed where the effects of vibration direction, amplitude, frequency, temperature and humidity on R and T were studied. Based on the accelerated test results, larger increases in the values of average and maximum R occur from vibrations in the Y direction (perpendicular to cable axis (Z)). Significant change in R and T (either, average or maximum) occurs at the highest vibration iv frequency of 200 Hz and in the Y direction. Increase in R could be due to an increase in T, fretting corrosion and wear. Also, frictional heating and increased Joule heating lead to an increase in T. v Acknowledgements I wish to acknowledge my sincere gratitude to my advisor, Dr. Robert L. Jackson, for his great motivation, continuous support and encouragement during the course of this study. I would like to thank my committee members, Dr. Song-Yul Choe, Dr. Jeffrey C. Suhling, Dr. George T. Flowers and University Reader, Dr. Robert Dean at Auburn University for their continuous support in this study. I deeply acknowledge and extend gratitude for financial support from the NSF Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3) at Auburn University. I would like to express deep gratitude and gratefulness to my parents, grandparents, sister, brother-in-law, relatives for their enduring love, immense moral support and encouragement towards accomplishing this goal in my life. I also wish to thank all my colleagues at Auburn and friends for their friendship and help. vi Table of Contents Abstract ........................................................................................................................................... ii Acknowledgements ..........................................................................................................................v List of Tables ............................................................................................................................... viii List of Figures ................................................................................................................................ ix List of Abbreviations .....................................................................................................................xv Chapter 1: Background ....................................................................................................................1 1.1 Hybrid Electric Vehicles (HEVs) ............................................................................1 1.2 Motivation ................................................................................................................3 1.3 Literature Review.....................................................................................................4 Chapter 2: Multi-scale Rough Surface Contact Model ..................................................................16 2.1 Introduction ............................................................................................................16 2.2 Model .....................................................................................................................17 2.2.1 Multi-scale Perfectly Elastic Contact ............................................................17 2.2.2 Multi-scale Elastic-plastic Contact ...............................................................19 2.2.3 Electrical Contact Resistance Model ............................................................21 2.2.4 Asperity Temperature Rise model ................................................................23 2.3 Model Predictions ..................................................................................................25 Chapter 3: Multi-physics Finite Element Model including Multi-scale Rough Surface Contact .............................................................................29 vii 3.1 40A Connector Model............................................................................................32 3.1.1 Elements used in 40A Connector Model ......................................................34 3.1.2 Methodology for 40A Connector Model ......................................................34 3.2 General Results of 40A Connector Model .............................................................41 3.3 Predictions for Connector Degradation by Increasing ECR and TCR: 40A Connector .............................................................................................49 Chapter 4: Experimental Testing (without Vibration): 40A Connector .........................................52 Chapter 5: Comparison of Experiment and Simulation Results (without Vibration): 40A Connector ............................................................................57 5.1 Analysis of Temperature Rises (?T, Change in Temperature) in the Cable and Connector ....................................................................................58 Chapter 6: Experimental Testing (with Vibration): 40A Connector .............................................63 6.1 Test Methodology of Accelerated Tests ................................................................67 6.1.1 Test Conditions .............................................................................................67 6.1.2 Definition of Coordinates for Vibrations ......................................................67 6.1.3 Test Procedure ..............................................................................................68 6.2 Accelerated Tests for 40A Connectors ..................................................................70 6.2.1 Effect of Vibration Direction on R and T .....................................................76 6.2.2 Effect of Vibration Frequency on R and T ...................................................84 6.2.3 Effect of Ambient Temperature on R and T .................................................92 Chapter 7: Conclusions ................................................................................................................100 References ....................................................................................................................................102 Appendix A ..................................................................................................................................109 Appendix B ..................................................................................................................................110 viii List of Tables Table 3-1: Material properties for spring and pin parts of the 40A connector ..............................35 Table 5-1: Experimental measurements of cable and connector temperatures and ?T at two different applied currents ............................................................................61 Table 6-1: Test matrix of accelerated tests ....................................................................................70 Table 6-2: Vibration amplitudes (peak-to-peak) and durations for each test run ..........................70 ix List of Figures Figure 2-1: Schematic depicting the decomposition of a surface into superimposed sine waves. Each line represents a different scale of roughness ...............................17 Figure 2-2: Surface profilometer ...................................................................................................18 Figure 2-3: Schematic of ?bottlenecked? current flow through asperities ....................................21 Figure 2-4: Damaged electric contact which had apparently melted and violently exploded due to the application of a high current [1] ................................................................24 Figure 2-5: The model predicted surface separation vs. force for the 40A connector surfaces ....................................................................................26 Figure 2-6: The model predicted electrical contact resistance for the 40A connector surfaces ....................................................................................27 Figure 2-7: Variation of local asperity temperature with current density ......................................28 Figure 3-1: Schematic showing the coupled multi-physics field equations ..................................30 Figure 3-2: The ECR values predicted from the multiscale models to be used in the multi-physics connector model ....................................................................................32 Figure 3-3: 40A connector system .................................................................................................33 Figure 3-4: 40A connector model parts (for modeling analysis) ...................................................33 Figure 3-5: Mesh of the 40A connector model ..............................................................................36 Figure 3-6: Boundary conditions for the 40A connector model ....................................................37 Figure 3-7: Thermal deformation (?) .............................................................................................38 Figure 3-8: Flow chart of the 40A connector model ......................................................................40 Figure 3-9: Displacement (mm) in the 40A connector ..................................................................41 x Figure 3-10: von Mises stress distribution (N/mm2) in the 40A connector ...................................42 Figure 3-11: von Mises stress distribution (N/mm2) in critical regions of the 40A connector .................................................................................................43 Figure 3-12: Electric potential distribution (V) in the 40A connector ...........................................44 Figure 3-13: Temperature distribution (?C) in the 40A connector ................................................45 Figure 3-14: Conduction current density distribution (A/mm2) in the 40A connector ..................46 Figure 3-15: Joule heat generation per unit volume (W/mm3) in the 40A connector ....................47 Figure 3-16: Effect of increase in current on the change in temperature in the 40A connector .................................................................................................48 Figure 3-17: The effect of an increase in contact resistance on the maximum conduction current density in the 40A connector ....................................49 Figure 3-18: The effect of an increase in contact resistance on the change in temperature in the 40A connector ............................................................50 Figure 3-19: The effect of an increase in contact resistance on the voltage drop in the 40A connector ............................................................................50 Figure 4-1: The placement of thermocouples and voltage measuring wires .................................53 Figure 4-2: Connector resistance (R) versus constant current in the 40A connector (with error bars for all 4 tests) ....................................................................................54 Figure 4-3: Connector temperatures at base (T1) versus constant current in the 40A connector (with error bars for all 4 tests) .................................................55 Figure 4-4: Connector temperatures at side (T2) versus constant current in the 40A connector (with error bars for all 4 tests) .................................................56 Figure 5-1: Plot of connector resistance versus applied current from 40A connector model .........................................................................................58 Figure 5-2: Schematic diagram of thermocouple placement on cable and connector ...................60 Figure 5-3: Experimental variation of cable temperature and connector temperature with time for a 40A connector at 35A and 40A applied currents ...............................61 Figure 6-1: Overview of test setup .................................................................................................64 xi Figure 6-2: Vibration shaker removed and detached from the environmental chamber ...............65 Figure 6-3: Environmental chamber ..............................................................................................65 Figure 6-4: Fixture for 40A connector on the shaker (Note: Y-axis is parallel to the slip table of the shaker, that is, ground) ....................66 Figure 6-5: Operating conditions and assessments of connector for accelerated tests ..................67 Figure 6-6: Definition of coordinates for vibrations (40A connector) ..........................................68 Figure 6-7: Test procedure for accelerated tests ............................................................................69 Figure 6-8: Plot of connector resistance versus time for test T6 iteration 1 ..................................73 Figure 6-9: Plot of connector temperature versus time for test T6 iteration 1 ...............................74 Figure 6-10: Connector resistance versus vibration amplitude for test T1 ....................................77 Figure 6-11: Connector temperature versus vibration amplitude for test T1 .................................77 Figure 6-12: Connector resistance versus vibration amplitude for test T2 ....................................78 Figure 6-13: Connector temperature versus vibration amplitude for test T2 .................................78 Figure 6-14: Connector resistance versus vibration amplitude for test T3 ....................................79 Figure 6-15: Connector temperature versus vibration amplitude for test T3 .................................79 Figure 6-16: Average connector resistance versus vibration amplitude for different vibration directions ...............................................................................81 Figure 6-17: Maximum connector resistance versus vibration amplitude for different vibration directions ...............................................................................82 Figure 6-18: Average connector temperature versus vibration amplitude for different vibration directions ...............................................................................83 Figure 6-19: Maximum connector temperature versus vibration amplitude for different vibration directions ...............................................................................84 Figure 6-20: Connector resistance versus vibration amplitude for test T4 ....................................85 Figure 6-21: Connector temperature versus vibration amplitude for test T4 .................................85 Figure 6-22: Connector resistance versus vibration amplitude for test T5 ....................................86 xii Figure 6-23: Connector temperature versus vibration amplitude for test T5 .................................86 Figure 6-24: Connector resistance versus vibration amplitude for test T6 ....................................87 Figure 6-25: Connector temperature versus vibration amplitude for test T6 .................................87 Figure 6-26: Average connector resistance versus vibration amplitude for different vibration frequencies ............................................................................89 Figure 6-27: Maximum connector resistance versus vibration amplitude for different vibration frequencies ............................................................................90 Figure 6-28: Average connector temperature versus vibration amplitude for different vibration frequencies ............................................................................91 Figure 6-29: Maximum connector temperature versus vibration amplitude for different vibration frequencies ............................................................................92 Figure 6-30: Connector resistance versus vibration amplitude for test T7 ....................................93 Figure 6-31: Connector temperature versus vibration amplitude for test T7 .................................93 Figure 6-32: Connector resistance versus vibration amplitude for test T8 ....................................94 Figure 6-33: Connector temperature versus vibration amplitude for test T8 .................................94 Figure 6-34: Average connector resistance versus vibration amplitude for different ambient temperatures ............................................................................96 Figure 6-35: Maximum connector resistance versus vibration amplitude for different ambient temperatures ............................................................................97 Figure 6-36: Average connector temperature versus vibration amplitude for different ambient temperatures ............................................................................98 Figure 6-37: Maximum connector temperature versus vibration amplitude for different ambient temperatures ............................................................................99 Figure B-1: Plot of connector resistance versus time for test T1 iteration 1 ...............................110 Figure B-2: Plot of connector temperature versus time for test T1 iteration 1 ............................111 Figure B-3: Plot of connector resistance versus time for test T1 iteration 2 ...............................112 Figure B-4: Plot of connector temperature versus time for test T1 iteration 2 ............................113 xiii Figure B-5: Plot of connector resistance versus time for test T1 iteration 3 ...............................114 Figure B-6: Plot of connector temperature versus time for test T1 iteration 3 ............................115 Figure B-7: Plot of connector resistance versus time for test T2 iteration 1 ...............................116 Figure B-8: Plot of connector temperature versus time for test T2 iteration 1 ............................117 Figure B-9: Plot of connector resistance versus time for test T2 iteration 2 ...............................118 Figure B-10: Plot of connector temperature versus time for test T2 iteration 2 ..........................119 Figure B-11: Plot of connector resistance versus time for test T2 iteration 3 .............................120 Figure B-12: Plot of connector temperature versus time for test T2 iteration 3 ..........................121 Figure B-13: Plot of connector resistance versus time for test T3 iteration 1 .............................122 Figure B-14: Plot of connector temperature versus time for test T3 iteration 1 ..........................123 Figure B-15: Plot of connector resistance versus time for test T3 iteration 2 .............................124 Figure B-16: Plot of connector temperature versus time for test T3 iteration 2 ..........................125 Figure B-17: Plot of connector resistance versus time for test T3 iteration 3 .............................126 Figure B-18: Plot of connector temperature versus time for test T3 iteration 3 ..........................127 Figure B-19: Plot of connector resistance versus time for test T4 iteration 1 .............................128 Figure B-20: Plot of connector temperature versus time for test T4 iteration 1 ..........................129 Figure B-21: Plot of connector resistance versus time for test T4 iteration 2 .............................130 Figure B-22: Plot of connector temperature versus time for test T4 iteration 2 ..........................131 Figure B-23: Plot of connector resistance versus time for test T4 iteration 3 .............................132 Figure B-24: Plot of connector temperature versus time for test T4 iteration 3 ..........................133 Figure B-25: Plot of connector resistance versus time for test T5 iteration 1 .............................134 Figure B-26: Plot of connector temperature versus time for test T5 iteration 1 ..........................135 Figure B-27: Plot of connector resistance versus time for test T5 iteration 2 .............................136 xiv Figure B-28: Plot of connector temperature versus time for test T5 iteration 2 ..........................137 Figure B-29: Plot of connector resistance versus time for test T5 iteration 3 .............................138 Figure B-30: Plot of connector temperature versus time for test T5 iteration 3 ..........................139 Figure B-31: Plot of connector resistance versus time for test T6 iteration 1 .............................140 Figure B-32: Plot of connector temperature versus time for test T6 iteration 1 ..........................141 Figure B-33: Plot of connector resistance versus time for test T6 iteration 2 .............................142 Figure B-34: Plot of connector temperature versus time for test T6 iteration 2 ..........................143 Figure B-35: Plot of connector resistance versus time for test T6 iteration 3 .............................144 Figure B-36: Plot of connector temperature versus time for test T6 iteration 3 ..........................145 Figure B-37: Plot of connector resistance versus time for test T7 iteration 1 .............................146 Figure B-38: Plot of connector temperature versus time for test T7 iteration 1 ..........................147 Figure B-39: Plot of connector resistance versus time for test T7 iteration 2 .............................148 Figure B-40: Plot of connector temperature versus time for test T7 iteration 2 ..........................149 Figure B-41: Plot of connector resistance versus time for test T7 iteration 3 .............................150 Figure B-42: Plot of connector temperature versus time for test T7 iteration 3 ..........................151 Figure B-43: Plot of connector resistance versus time for test T8 iteration 1 .............................152 Figure B-44: Plot of connector temperature versus time for test T8 iteration 1 ..........................153 Figure B-45: Plot of connector resistance versus time for test T8 iteration 2 .............................154 Figure B-46: Plot of connector temperature versus time for test T8 iteration 2 ..........................155 Figure B-47: Plot of connector resistance versus time for test T8 iteration 3 .............................156 Figure B-48: Plot of connector temperature versus time for test T8 iteration 3 ..........................157 xv List of Abbreviations A area of contact A individual asperity area of contact nA nominal contact area a radius of the area of contact C critical yield stress coefficient d separation of mean asperity height E elastic modulus E? )1/( 2vE ? f spatial frequency (reciprocal of wavelength) k thermal conductivity P contact force P individual asperity contact force p mean pressure ?p average pressure for complete contact yS yield strength Eri electrical contact resistance per scale or frequency level ECR electrical contact resistance TCR thermal contact resistance xvi Greek Symbols ? area density of asperities ? asperity wavelength L? electrical resistivity of surface material ? asperity amplitude v Poisson?s ratio Subscripts E elastic regime P plastic regime c critical value at onset of plastic deformation i scale or frequency level JGH from Johnson, Greenwood, and Higginson [2] asp asperity L electrical 1 CHAPTER 1 Background 1.1 Hybrid Electric Vehicles (HEVs) With the appearance of electric and hybrid electric vehicles, designers are faced with new challenges. The goal of basic vehicle design is to generate high power while minimizing weight and drag forces to maximize fuel economy. With that in mind, the major car companies are continuously juggling with the decisions of electric motor and internal combustion engine (ICE) sizes and power, battery size and capacity, and most importantly how to maximize the potential of each constituent through precise controls. For instance, when implementing the electric motor and advanced battery chemistries, there is obviously additional power available to the vehicle, but there is also the additional weight for the motors to overcome. Through the design process, slight variations are made to accepted configurations, but for the most part there are a few basic blueprints for the design of all hybrid electric and electric vehicles. There are two major designs of electric vehicles that currently capture the majority of the market. First, hybrid electric vehicles (HEV) incorporate an electric motor along with the standard ICE to provide additional power to decrease fuel consumption while recharging the battery at specified portions of the driving cycle. In addition, there are plug-in hybrid electric vehicles (PHEV), which rely on the traditional ICE and the energy supplied by an externally charged battery to power an electric motor. 2 Hybrid configurations appear in a variety of arrangements with the major classifications being the ?parallel? and ?series? configurations. In a series hybrid, the system consists of an ICE and an electric motor connected in series, although the vehicle only experiences a driving force from the electric motor. As a result, all the electrical energy must pass through both the motors and the generator raising the cost substantially. The parallel hybrid configuration also incorporates an ICE and electric motor and can be engaged separately or simultaneously to achieve maximum fuel economy. Parallel hybrid allows for a wide range of uses while series hybrids are reserved for specific applications. Typically, parallel hybrids employ only the electric motor for city travel and utilize the ICE engine for highway travel. Ideally the electric motor, ICE, and battery would be used in unison to obtain greater performance. As a result of the complex multiple motor systems, advanced transmissions such as continuously variable transmissions (CVT) are incorporated. A popular design receives around 50% peak power from the ICE while relying on the electric motor and battery for the additional boost. When the battery is not needed, the generator proceeds to charge the battery during highway travel or through regenerative braking. 3 1.2 Motivation Connectors are an important and critical component of any vehicle containing electrical components. Detachable connectors are desired for durable and easily removed connections. This is especially important for the easy replacement and repair of electrical components. Connectors in HEVs are known to carry very high currents (high power) [3] and due to this there can be a tremendous increase in temperature in these parts during service. High power and the automotive environment (high temperature, vibrations, humidity, etc.) can 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. High electrical power is required for new vehicles which use electrical propulsion (Hybrids, Plug-in, Fuel Cell, etc.). Therefore, the electrical components (connectors, batteries, power electronics, wiring harnesses, etc.) in these vehicles must be able to handle these higher powers. Hence, the main motivation of the current work is to study the reliability and performance of 40A (high power) connectors used in HEV vehicles through modeling and experiment. More specifically, a joint effort of multiscale rough surface contact/multi-physics finite element modeling and experimental testing of these connectors under both vibrating (that is, accelerated test conditions) and stationary conditions has been carried out. 4 1.3 Literature review The fretting behavior occurring in various contact regions of electrical connectors has been an important area of research for three decades. Fretting wear and corrosion are the two major degradation mechanisms, which have been the focus of most research studies. Contact degradation, caused by fretting, occurs as a result of relative motion between two surfaces and this degradation decreases the performance of the contact. This section reviews existing literature on the performance and fretting of electrical connectors in chronological order. This includes both experimental and theoretical work. There are very few papers on fretting in high power connectors and so the focus is mainly on conventional low power connectors. Switchgear connectors show limitations for applications with high currents [4]. Additionally, due to their size, high resistance and high rack-on forces, several problems arise. Allen [4] suggests that usage of large quantities of independent and well defined contact spots is a solution for many of their problems. Current sustainability and resistance were analyzed and comparison is made with the experiment. In the work by Olsson and Oberg [5], by taking into consideration structural design variables, data related to testing of current cycle for electrical contact resistance and service of longer duration were analyzed. For the condition of the surface force that is held constant, a study was done on the significance of the contact pressure distribution. Using the finite elements method, stresses are calculated at the contact surface. Contact resistance is reduced and good stability at longer durations is observed for high contact pressures. The connectors? aging properties are also affected largely by the contact pressure distribution at the surface. From the study, the methods of surface preparation are shown to greatly affect the aging phenomena. 5 Intermetallic phases generation and fretting are the two aging phenomena that are documented at the contact surfaces. A model has been developed by Bryant [6] to determine the electrical contact usable lifetime and contact resistance at any fretting cycle. Several key variables such as frequency and fretting amplitude, contact coating thickness, applied current, normal load, etc. are included into this model [6]. A few important observations can be made from this work. With time, the contact resistance increases in a monotonic fashion. However, large increases in contact resistance can be seen after the initial period. The time to failure of contacts found in field measurements compares well with that predicted by the model. On subjecting a contact to a high number of cycles or as a result of long term usage, the contacts may be thermo-mechanically damaged. In addition, the contacts may get oxidized or contaminated. Under these situations, the contacts are prone to failure due to the added resistance of the less conductive layers. Thus, this paper by Minowa and Nakamura [7] studies the contact surface state along with the electric conductivity through the finite element method approach. Within a contact spot, the distribution of current density was also determined. The study by Ando and Imori [8] investigates the properties of contact resistance on the connector contacts that are plastically deformed. Experiments involving needle type contacts that are inserted inside a plane plate contact were carried out. The experimental results correlated well with those obtained from a tunnel resistivity based theory on contact resistance. The material at the contact is the base metal, which necessitates a key issue of the surface film structural disruption at the contact to be addressed. 6 Rudolphi and Jacobson [9] studied two types of silver plated copper electrical contacts by subjecting them to rolling effects testing in a crossed cylinder contact configuration. One of the two types of silver plated copper contacts contained a middle layer of nickel. Gross plastic fretting is a type of degradation mechanism that involves plastic deformation of electrical contacts [9]. Both vibrations and large contact forces lead to gross plastic fretting in electrical contacts. In both near elastic and plastic conditions, three regimes of fretting are defined. These three plastic deformation regimes, namely, gross weld, temporary weld and gross slip, have specific influence or impact on friction, adhesion and surface damage. In a normal crossed cylinders test, the cylinders are held in a fixed position. However, the paper by Rudolphi and Jacobson [9] reported that when only a single of the two cylinders in this crossed cylinders test is allowed to rotate angularly rather than holding it fixed, the damage imparted to the surface is immensely lowered, frictional stresses are greatly lowered and this may facilitate the electrical contact life under vibration conditions to be prolonged. More friction is seen in the case of sliding than on rolling. This is a well established fact. Also, under vibration situations of electrical contacts, the damage to the contact area can be minimized if the slip is reduced. Fretting corrosion does not occur if the coating of silver does not show wear and thus allows the contact resistance to be low and stable. The study on angular rolling contact of the silver coated copper contact shows that the contact resistance is increased due to an intermediate layer of nickel in copper contacts with a silver coating compared to those contacts without the nickel layer [9]. Copper alloy based electrical contacts are largely plated with tin, which is a low cost material. Tristani, et al. [10] developed a mechanical model based on the very nature or appearance (with respect to shape) of the tangential force-displacement curves obtained by 7 conducting tests on fretting corrosion for connector terminals. This model deals with the wear track profile, stiffness as well as the dynamic friction coefficient. Following the study of the plots [10], two key observations are that over the complete fretting cycle, sliding is not seen in connector terminals. Also, the stiffness, normal force and wear region profiles affect fretting duration differently for each particular type of electrical contact. The work by Antler [11] deals with the fretting degradation mechanism, studying the contact materials behaviour and the factors influencing the contact resistance. In addition, the recommendations to control the fretting process in the case of electronic connectors are presented [11]. The fretting process may result in unstable contact resistance in a vibrating connector. During fretting, there will be build up of an insulating layer of oxide on the electrical contact surface. Naturally occurring vibrations and thermal fluctuations (cycling) cause the movement of electrical contacts leading to their fretting. If the frequency of vibration is low, then the number of cycles to cause failure of the contact is also few, but this finding seems questionable. The contact connection is stabilized either by lowering the fretting vibration amplitude or increasing the normal load at the contact. Fretting failure is common when tin is used as a plating material in most of its alloys. A better contact is a contact that is made up of only tin compared to the one containing a combination of tin and gold. The failure of the contacts due to fretting can be prevented generally through the use of lubrication at the contact. Lubricating the contacts may allow for longer lives and extend the use of contacts that have already failed in the non-lubricated condition. According to Swingler [12], fretting corrosion is among the primary failure mechanisms occurring at the electrical contact interface in automotive connectors. This type of corrosion causes contact resistance to increase irradically. Fretting corrosion is induced at electrical 8 contacts or at contacting regions in components of connector samples by employing a fretting apparatus or test set up subjected to low frequencies. The influence of the varying thermal expansion coefficients of the materials for the components of a connector is simulated or modeled by using low frequency. The initial occurrence of the contact resistance of high values at the contacting regions is delayed by powering the connector at low frequencies. Oxidation of the contact surface is predicted to be hastened due to the temperature rise from Joule heating. However, considering the fretting conditions used in this work, there was dominance of films? electrical breakdown. Two other observations from this work are: (a) less conductive debris is seen at the ends of the wear region of the fretting subjected contact surface or interface, and (b) due to fretting under low frequencies, there is a marginal effect from frictional heating. In the work by Swingler and McBride [13], studies related to the fundamental aspects and that are performed on terminals of the connectors, available on a commercial basis, are combined through the development of the reliability model on multicontacts. Two key issues are taken into account. At first, for a contact interface with a single contact, the contact resistance could regain its lower value once a high contact resistance value is reached. Then, for terminals with many contact interfaces, the simultaneous occurrences of the individual interface failures will lead to the failure of whole connector. A paper by Malucci [14] deals with the studies on fretting corrosion of tin plated electrical contacts. Laboratory tests involve vibrations and thermal cycling in accelerated conditions. These tests aroused the development of an empirical model. As fretting advanced, several observations such as electrical stability and formation of an oxide film on the contact surface were made [14]. A fretting amplitude parameter helped to determine the threshold 9 behaviour at which fretting corrosion begins or initiates. Fretting motion is caused either by thermal cycling or natural vibration in real or actual connectors. In another paper, fretting corrosion is induced in contacts present in connectors through vibration tests and each connector is subjected to only one vibration frequency [15]. The contacts are plated with tin alloy. Several frequencies and vibration levels are applied during the experimental tests. Contact resistance is chosen as the parameter to characterize the performance of the connectors. For each of the vibration frequency, fretting degradation is initiated once a threshold state is demonstrated by the connectors. The high temperature coefficient difference between the constriction resistance and the film resistance is used to distinguish these two resistances by Takano [16]. The contact resistance was measured by employing a ?low DC voltage method?. A very thin insulating gap between the contacts causes the generation of film or tunnel resistance along with the constriction resistance seen in the electrodes or contacts. The work theorizes that tunneling (film) resistance together with constriction resistance leads to total contact resistance. Due to film resistance instability, the film resistance?s content is also an important variable for electrical contact reliability studies. Micro-scale wear tracks are observed by He and Xu [17] on failed electrical contacts. Due to contacting materials, a debris of wear is created when micro motion occurs. Additionally, by micro motion, oxidation of contacting materials and contact resistance (varying and high) are seen. Shocks as well as vibration lead to micro motion and are analyzed. Random profiles of vibration are employed to test the connectors by Flowers, et al. [18]. The authors created a model wherein the rate of fretting corrosion in the early stage is related to the threshold levels of vibration, the profile of vibration and the dynamic features of the test configuration. The model correlates very well with the experimental results. During the 10 vibration tests, a specific threshold is seen no matter what the vibration profile that is implemented to excite the entire system. Vibration tests were carried out by Ben Jemaa and Carvou [19] for an automotive connector terminal to study the amount of wear and its electrical behavior. The authors demonstrated that as the amount of wear increases, the constriction or contact voltage also increases on the order of millivolts and as the amount of degradation (that is, fretting) further increases, the arcing voltage (nearly 12 V) is observed. In addition, when the contact voltage is increased to melting and then arcing voltage, it causes thermal effects and this increases the amount of degradation. This mechanism relates to the case of a high power connector. The surface of the connector terminal in this work is also tin coated (similar to the 40A connector considered in the current work that has tin as the surface finish). The true area of contact at the contacting locations is the primary parameter that influences both contact resistance and friction. The key parameters are both contact resistance as well as friction in switches and connectors in which sliding contact occurs. Higher contact force leads to lower contact resistance values. However, there is a rise in the friction force. The present work by Tamai [20] developed an equation that relates the friction and contact resistance. Additionally, experimental studies were conducted on the friction and contact resistance relationship for different contact surfaces subjected to various operating conditions. Park, et al. [21] studied the behavior of fretting related wear for copper alloy electrical contacts containing tin plating and the contact resistance dependency on fretting wear. Contact resistance was noticed to be stable and low during the initial cycles. In order to explain this observation, the authors developed a model on the basis of contact zone variation and depth of wear versus fretting cycles. Scanning electron microscope (SEM), X-ray mapping, energy 11 dispersive X-ray scanning and EDX spot analysis were used to examine the changes that occur in the contact area zone and to estimate the amount of tin coating wear and wear debris buildup with respect to fretting cycles. As the tin coating is removed continuously, the area of the fretted zone linearly increased until approximately 8000 cycles are reached. This expansion of the fretted zone becomes saturated once the maximum limit of the fretting length is reached. The electrically conduction path established due to consistent constant contact area leads to the observance of stable and low contact resistance until 8000 cycles are reached. Key regimes of fretting corrosion as well as fretting wear are demonstrated on the basis of contact resistance variation with respect to fretting cycles. Fretting corrosion phenomenon, occurring in electrical contacts with tin plating, becomes more complicated due to the mutual dependence of the amount of oxidation and wear [21]. A small power connector is analyzed for its thermal behavior by Wang and Xu [22]. It was noticed that Joule heating caused an increase in the contact resistance. The paper discusses the connector failure mechanism which can be used to improve the connector design or structure. Finite element analysis is employed to analyze the connector temperature distribution. The experimental and finite element analysis results show a better correlation. Ossart, et al. [23] analyzed multilayer electrical contacts for their electromechanical behavior through numerical simulation. A thin surface layer of tin protects a ball-plane contact that is made of a CuZn alloy material. Contact resistance of the entire component is calculated through a finite element coupled field (mechanical and electrical) analysis. Experimental results are compared to the simulation results. When considering low tin layer resistivity values, a decent agreement is noticed between the model calculations and the experimental measurements for tin layer thicknesses in the range of 1 ? 10 ?m. 12 Through the fretting corrosion process, the degradation of the electrical contacts is primarily caused by the vibration and relative motion of contact surfaces. In the work by Carvou and Jemaa [24], the contact interface?s electrical response was examined by subjecting it to vibration and its variations were characterized while fretting is in progress. Vibrations in large numbers were imposed on an individual point contact under conditions of 50 ?m amplitude and 100 Hz. A circuit (10A and 14V) of resistive type constituted the contact. Electrical phenomena cause fluctuations/variations to appear, which is dependent on the stage of degradation. The faster fluctuations correspond to perturbation of electrical conduction. The fluctuations that are slow correlate better to the period of vibration. Also, the work examines the occurrence of self heating due to contact voltage being high owing to current levels being of high values. Park, et al. [25] studied various factors that affect fretting corrosion of tin plated electrical contacts. These factors include normal load, applied current, frequency, fretting amplitude, temperature and humidity. In the conducted fretting corrosion tests, the gross slip fretting of the electrical contacts is considered. Contact resistance versus fretting cycles curves are generated from the tests and the information on the duration required to attain a contact resistance threshold point of 100m? can also be obtained from the experimental tests on fretting corrosion. The fretting corrosion mechanism in the case of tin-plated electrical contacts is explained on the basis of studies done on surface profile variations and contact zone changes through laser scanning microscope (LSM) and other techniques. According to Park, et al. [25], the lifetime or longevity of electrical contacts bearing tin plating on their surfaces is enhanced considerably by lubricating the contacts. The tin plating wear rate is also enhanced when higher frequencies are used. However, higher oxidation rates are noticed when lower frequencies are employed during tests on fretting corrosion. The higher the 13 fretting amplitude, the higher is the amount of oxidation that is observed. In reality, humidity (that is, moisture or water vapour in condensed form) functions like a lubricant and this lubricant reduces the tin plating wear rate. Also, when normal loads are higher, the tin plating wear rate is also higher. However, at smaller normal loads, there is a higher oxidation rate. The oxide film is broken leading to a firm electrical contact when the applied current load is higher [25]. In the work by Abdi and Benjemaa [26], a laser probe is used to determine the contact force through the spring deflection measurement. Contact resistance, insertion force and contact force obtained from contact deflection are measured during insertion. A larger contact region is created depending upon the width of the spring. The effect of the connector geometry variables on the insertion force, the contact force and the contact resistance has been demonstrated. For various contact geometries and contact loads, the changes in contact resistance were determined in a study by Abdi, et al. [27]. New high copper alloy samples were tested by insertion and indentation methods. Contact models, with and without roughness, were generated in ANSYSTM and a profilometer was used to measure the actual roughness. For indentation tests with lower forces, a close agreement was seen between experimental results and the results of the numerical model that considers roughness. The work also establishes the contact force and contact resistance relation. The work by McBride [28] investigated the intermittency events taking place at high frequencies during the process of fretting in in-vivo electrical contact surfaces. The fretting process study related the surface wear to the contact resistance, for various applied forces. The intermittency events while fretting and the performance of the contact surface were largely affected by the fretting cycle amplitude. 14 A contacting pair of a blade and receptacle was studied initially by means of a finite element based model in a simplistic 2D way and the model was correlated to experiments [29]. The work by Chen, et al. [30] is an extension to this initial primary study in that for the above connector set up or configuration, an extensive 3D model was developed and the effects of several parameters were evaluated such as normal force, friction coefficient at the interface, wire mass, etc. through analysis. The model was tested and validated through several experiments. This study shows that the effect of connector design changes on the fretting phenomenon can be evaluated by using finite element based analysis and simulation. In the work by Chudnovsky, et al. [31], experimental direct measurements of the temperature of powered contact surfaces in a low voltage circuit breaker were analyzed statistically. The contact interfaces of 3200A low voltage circuit breakers were studied for their thermal behavior under both ?aged? (in an artificial way) and new conditions. A circuit breaker with three phases is considered and data for each phase having four points of contact is gathered or obtained experimentally. A reliable mathematical model stating the relation among the rise in temperature in electrical contact interfaces and large variations in current was found. At different applied currents, brass electrical contacts that have a tin coating were studied by Park, et al. [32] for fretting corrosion. The variation of contact resistance with respect to fretting cycles is addressed in detail. Scanning electron microscope (SEM), laser SEM, and the X ray based dispersive analysis technique are employed to study the surface profile, surface morphology and contact area chemical element distribution. Also, these tools are used to estimate the oxidation amount and the extent of damage caused by fretting of the surface [32]. Due to the application of currents, either higher or lower values, the contacts naturally get degraded and this is explained by the electrical as well as thermal behavior or effects of the 15 interface where electrical contact occurs. Smaller values of current tend to enhance the longevity of electrical contacts and delay the failure of the contact. When applied current values are higher, wear debris, comprising of oxide, in increasing amounts is formed in the contact area. This accelerates the tin coated electrical contacts degradation. Good agreement between the fretted tin surface profile together with surface morphology and experimental results is established from this work. Based on the literature review, it is evident that a multi-physics finite element model, considering surface characteristics, of a high power connector is unavailable to date. Secondly, experimental studies on vibration based fretting degradation in case of high power connectors used particularly in HEVs is completely missing in the literature. Once the oil reserves become exhausted or as a result of shortage of oil across the globe, it is well known that HEVs will be highly popular and will dominate the automobile industry and transportation sector. Hence, the current research focuses on the behavior of high power connectors (and more specifically a flat pin 40A connector) employed in HEVs through both multi-physics (mechanical, electrical and thermal coupled fields) finite element simulation including multiscale rough surface contact and experimental approaches. Experimental testing of 40A connectors involves stationary as well as accelerated vibration test conditions. The fretting effects in these connectors due to vibration are studied in detail in this work. 16 CHAPTER 2 Multi-scale Rough Surface Contact Model 2.1 Introduction At higher magnifications, it is evident that an electrical contact or any engineering surface possesses roughness although it appears smooth on a macroscopic scale. In reality, when two surfaces come in contact with each other, they are in contact through the asperities or peaks on their surfaces [33]. This implies that there is a reduced real area of contact between two contacting surfaces. The load is carried by the asperities on the contacting surfaces. Due to the relatively high load being carried by the isolated asperities, they usually deform in an elasto- plastic manner. A smaller real area of contact causes constriction for the flow of electric current and conduction of heat between the surfaces. This constriction phenomena together with poorly conducting impurities present on the surfaces (for example, oxides) leads to electrical contact resistance (ECR) and thermal contact resistance (TCR). However, in the case of TCR, due to gaps between the contacting surfaces, the heat transfer may also occur through convection. There are many different methods to model the contact of rough surfaces including statistical [34-38], fractal [39-43], and multiscale models [44-46]. The fractal mathematics based methods were derived to account for different scales of surface features not accounted for by the statistical models. The multiscale models were developed to alleviate the assumptions imposed by fractal mathematics and to also improve how the material deformation mechanics are considered. This work uses a fast Fourier transform to convert the data into a series of stacked 17 sinusoids (see Figure 2-1). Also, the surface characteristics necessary to obtain convergence of the iterative multiscale scheme are examined. Figure 2-1: Schematic depicting the decomposition of a surface into superimposed sine waves. Each line represents a different scale of roughness 2.2 Model 2.2.1 Multi-scale perfectly elastic contact The multi-scale model derived by Jackson and Streator [46] uses the same direction of thought as Archard [47], but provides a method that can be easily applied to real surfaces. First, a stylus profilometer was used to measure the surface data for 40A connectors, as shown in Figure 2-2. Second, a fast Fourier transform is performed on the surface profile data. Then, the resulting data is a summation of a series of sine and cosine waves. The complex forms of the sine and cosine terms at each scale are combined using a complex conjugate to provide the amplitude of the waveform at each scale for further calculations. 18 Figure 2-2: Surface profilometer Each frequency is considered a scale or layer of asperities which are stacked iteratively upon each other. In equation form these relationships are given by: n i i ii AAA ??? ? ??? ?= ? = max 1 ? (2-1) 1?= iii APP ? (2-2) where A is the real area of contact, ? is the areal asperity density, P is the contact load, An is the nominal contact area, and the subscript i denotes a scale or frequency level, with imax denoting the highest scale considered. Note that ?i=2(fi)2 because there are actually two sinusoidal asperity peaks for each square area of 1/f x 1/f. Each scale is modeled using a sinusoidal contact 19 model. Equations previously derived by Jackson and Streator [46] by fitting to the data given by Johnson, Greenwood, and Higginson [2] are used: ( ) ? ? ? ?? ?= *8 3 21 p p fAJGH pi pi (2-3) (2-4) For ( )2JGHi AA = (2-5) For ( ) ( ) 04.1 2 51.1 1 **1 ??? ? ??? ?+ ? ? ? ? ? ? ? ? ?? ? ?? ??= p pA p pAA JGHJGHi (2-6) where p* is the average pressure to cause complete contact between the surfaces of a single scale and is given by [2] as: ii fEp ??=? pi2 (2-7) 2.2.2 Multi-scale elastic-plastic contact However, many of the asperities at the different scales undergo plastic deformation. Therefore, an elastic-plastic sinusoidal contact model is needed to consider this effect. The equations used in the current work to calculate the elastic-plastic contact are derived from FEM results by Krithivasan and Jackson [48]. The methodology is very similar to that of the perfectly elastic case with the exception that a different set of formulas is used once a calculated critical pressure is reached. The critical load and area are given by: ( ) ?? ? ? ??? ? ?? ? ?? ? ??= *12 311 22 p p fAJGH pi 8.0*