Experimental Investigation and Numerical Simulation on the Role of
IEICE TRANS. ELECTRON., VOL.E97–C, NO.9 SEPTEMBER 2014
873
PAPER
Special Section on Recent Development of Electro-Mechanical Devices (IS-EMD2013)
Experimental Investigation and Numerical Simulation on the Role of Sphere Indenter in Measuring Contact Resistance of Flat Rivets Wanbin REN†a) , Member, Yu CHEN† , Shengjun XUE† , Guenther HORN†† , Nonmembers, and Guofu ZHAI† , Member
SUMMARY There has been increasing demand to research the measuring method to characterize the batch consistency of contact rivets. An automated test equipment has been described that makes it possible to measure the electrical contact resistance with high efficiency. The relationship between contact force and contact resistance during the loading and unloading process was measured explicitly using AgPd alloy, stainless steel and sapphire substrate material with Au coatings as sphere indenters separately. To explain the phenomena of contact resistance decreasing more slowly than the traditional theoretical results during loading, the indenter with coating and rivet are modeled by using the commercial FEM software COMSOL Multiphysics. Besides the constriction resistance, the transition region Au coating resistance and the bulk resistance of the substrate are deduced from the simulated current lines profiles and iso-potentials. The difference of electrical conductivity between indenter material and gold coating is the reason for the occurrence of the transition region. key words: sphere indenter, constriction resistance, contact resistance, flat rivet, FEM
1. Introduction Rivet-type contacts are widespread used in all kinds of electrical switches for switching and/or conducting current. The value of the rivets’ contact resistance correlates with the working status and potential failure of the electromechanical devices closely. Also, it could be taken as one of the key characterization parameters for material composition and surface roughness as well as cleanliness. As the miniaturization and high reliability of electromechanical devices increases, rivets with excellent electrical connectivity performance are required urgently. Interest in influencing factors on contact resistance and suppression method in engineering is increasing since Ragnar Holm’s academic monograph in the 1940s. The theory of contact resistance has long remained an academic hot issue [1]–[7]. It was shown that the direct measurement for contact resistance is of great importance for theoretical model and simulation analysis. Meanwhile, a precise specialized measurement method is required for the development of advanced contact materials and particular industrial applications. Measured contact resistance values will include the constriction resistance and bulk resistance of the indenter Manuscript received January 7, 2014. Manuscript revised April 1, 2014. † The authors are with the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China. †† The author is with the ElConMat Consulting Associates, VA, USA. a) E-mail: [email protected] DOI: 10.1587/transele.E97.C.873
and the film resistance between interfaces etc., besides the constriction resistance of the rivet sample. Therefore, the material selection and preparation of an indenter for contacting with rivets during measurement cause both problems and opportunities. Precious metals, such as gold, are always designated to be the choice for indenter tips. Pinnel and Bradford [8] evaluated the effect of variations in the geometry and preparation of gold probe tips for contact resistance measurements. Yunus [9] measured the contact resistance of Au coated carbon nanotube surfaces using a stainless steel hemisphere with 2 mm diameter, sputter coated with 500 nm Au. Tamai [10] utilized a platinum sphere shaped indenter with 1mm diameter to investigate the property and crystal morphology of tin oxide films formed on tin-plated contacts. Jang [11] also researched the failure mechanism of pogo pin-type probe contacts, which use Fe as a base metal and a noble metal such as Au or PdCo as a coating metal. Recently, the nano-scale electrical contact resistance tool (nanoECR, HYSITRON, USA) [12], provides a powerful solution for simultaneous, in-situ electrical and mechanical measurements with the electrically conductive indenter using a diamond tip doped with Boron. In a previous paper by the present authors, the relationship between contact load and contact resistance during loading and unloading is investigated explicitly with different current using a stainless steel hemisphere with gold coating as standard indenter [13]. It is well known that the hardness, electrical conductivity and the surface coating of the indenter will affect the contact area and contact resistance between the indenter and the rivet sample directly. In order to find the preferable indenter metal material for measuring the contact, in the present paper, we shall test the relationship between the mechanical load and contact resistance for silver-palladium alloy, stainless steel and a sapphire ball as three different spherical indenters. We shall then build up the finite element contact model using COMSOL Multiphysics commercial software for interpreting the current line profiles and iso-potentials. In particular, we shall investigate the effect of the additional resistance resulting from the indenter on the contact resistance measurement of rivet sample. 2.
Experimental Details
The test apparatus used in these experiments is described in
c 2014 The Institute of Electronics, Information and Communication Engineers Copyright ⃝
IEICE TRANS. ELECTRON., VOL.E97–C, NO.9 SEPTEMBER 2014
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detail in [13]. A schematic diagram of the test apparatus used in the contact resistance measurement experiments is shown in Fig. 1. The normal contact force was supplied by the bow type spring component and controlled by the Z-axis electric actuator. The contact force maximum value could be set up to 300 g with a resolution of 0.05 g. The flat contact rivet samples with a head diameter of 3 mm are made from pure silver. The probe holder is specially designed for clamping different kinds of indenters. Table 1 provides detail information about the indenters we used in this paper. The indenters and flat specimens were degreased using acetone, methyl alcohol and distilled water in an ultrasonic cleaner in order, dried and carefully mounted in the test rig. The indenter and flat contacts are mated in such a way to create a point contact in “sphere- to-plane” geometry. Twenty rivets could be clamped and measured simultaneously in a multiple rivet contacts sample holder. The measuring instrument is configured for the fourwire technique, which eliminates the lead resistance including the resistance of soldered joints. It has a built-in current source capable of providing a constant current, which could be set from 1 to 1000 mA in steps of 1 mA. The optional open circuit voltage can be varied from 5 to 200 mV in 1 mV steps. The accuracy of the measured resistance between contacts is within ±1% after calibration. The instru-
ment is interfaced to a personal computer using a USB cable. The data acquisition and logging process are controlled through a PC with the help of LabVIEW software specifically programmed for this purpose. The whole load-contact resistance experiment can be described as loading stage and unloading stage. The indenter and rivet sample are brought into contact from 0.5 g to 20 g at a controlled loading rate. After loading force is reached the set value and keeps invariable, the pre-set current passed through the contact pair. The steady value of contact voltage drop could be recorded and saved. The indenter is unloaded at the same rate from 20 g until they are separated. The force step is set 0.5 g. The current is set 10 mA. 3.
Results and discussion
Figure 2 shows the characteristic of the resistance measurement results during loading and unloading by using an Aucoated indenter with different substrate material. There are distinct differences in measured resistance value at the same load force. The variation in contact resistance vs. load depicted in Fig. 2 stems from a combination of several factors: Ref. [13] stated an increase in number of contacting surface asperities as the nominal surfaces are brought closer together under the influence of an increasing load; permanent flattening of the contacting asperities, which reduces the constriction resistance associated with each a-spot and thus reduces the overall contact resistance; work-hardening of the deformed contact asperities, which reduced the rate of asperity flattening etc. Classical mathematical models that attempt to explain the observations of Fig. 2 in terms of details of asperity deformation behaviour during compression predict a relationship between contact resistance and mechanical load. For lower contact load in which the elastic deformation dominates, constriction resistance is expressed as a function of contact load as in Eq. (1) [14]. Rc = [K]F −n
Fig. 1 ing).
(1)
Mechanical part of the automated test equipment (without hous-
Indenters used in this paper.
Table 1 Substrate AgPd alloy Stainless steel 1Cr18Ni9Ti Sapphire
Curvature radius (mm) 1.5
Au coating thickness (µm) 2
0.5
2
Electroplating
1
0.4
Sputtering
Coating method Electroplating Fig. 2 Relationship between resistance and contact force during loading and unloading process with different indenters (every plot data was the average value of 4 rivet samples).
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Here, [K] is a constant. The [K] contains electrical resistivity of metals, its Poisson’s ratios, Young’s modulus and radius of curvature of the probe. And the constriction resistance is proportional to F 1/3 . With the loading experimental data fitting, the index parameter “n” is 0.26, 0.23 and 0.06 for the indenter materials AgPd alloy, stainless steel and sapphire respectively. 4. FEM Modeling for Electric Field Analysis of Sphere Indenter and Flat Rivet The aim of FEM modelling is to demonstrate what the measured contact resistance value makes up. The commercial program COMSOL Multiphysics 4.2b version was used to perform simulations by solving contact mechanical equations and electric field equations through finite element method (FEM). The schematic plot of the simulation model is shown in Fig. 3. The partial sphere indenter with Au coating and the flat rivet (between line “a” and line “b” in Fig. 3) are modelled and meshed with traditional triangular elements. The line “a” and line “b” in Fig. 3 correspond to the two voltage
probes in the experiment. The mesh, presented in Fig. 4, was graded radially outward from the initial point of contact, with the densest mesh in the contact region. The minimal size of the mesh is 0.2 µm and the contact surfaces are assumed smooth. The partial contacting surfaces of the hemisphere and flat surface are defined as contact pair. In addition, the thin contamination film on the contact surfaces is not considered. It is inevitable that these assumptions result in the simulation results of contact resistance being smaller than those obtained in experiments. However, the nature of the difference of conductivity between indenter substrate and surface coating are not changed. Load boundary conditions of the model consisted of a prescribed uniform vertical force on the upper-most surface with the bottom-most surface vertically fixed. The load force is set as 0.5 g, 1 g, 5 g, 10 g and 20 g separately. Axisymmetry was applied to the left-most boundary, resulting in zero horizontal displacement. All of the remaining surfaces were unconstrained in the vertical and horizontal directions. Electrically, a pre-
Fig. 3 Schematic plot of the simulation model and boundary conditions setting.
Fig. 5 (a) Electric current lines profile and isopotential map of AgPd alloy with 2 µm gold coating. (b) A zoomed-in view of results in the contact region. (c) A zoomed-in view of the result in the transition zone. Table 2 Material properties for FEM. All values are from Ref. [15], except for Sapphire from Ref. [16].
Fig. 4 (a) Axisymmetric FEM with Comsol Multiphysics. zoomed-in view of the mesh in the contact region.
(b) A
AgPd alloy Stainless steel Sapphire Gold Silver
Young’s modulus (GPa)
Poisson ratio
Electrical conductivity (S/m)
Density (kg/m3 )
200
0.29
0.24×107
11.4×103
202
0.29
0.137×107
7.9×103
7900 76 81.1
0.28 0.44 0.37
1 4.52×107 6.28×107
4.0×103 19.3×103 10.5×103
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Fig. 6 (a) Electric current lines profile and isopotential contour of stainless steel with 2µm gold coating. (b) A zoomed-in view of results in the contact region. (c) A zoomed-in view of the result in the transition zone.
Fig. 7 (a) Electric current lines profile and voltage potential contour of sapphire with 0.4 µm gold coating. (b) A zoomed-in view of results in the contact zone.
scribed constant current density was applied to the uppermost surface, and the bottom-most surface was electrically grounded. The constant current intensity is 10 mA. Axisymmetry on the left-most boundary results in electrical insulation. The later surfaces of both bodies were also considered electrically insulated. The details of the geometric model and material properties (shown in Table 2) are the same as those used in the experiment. To load the system, the defined vertical load force was stepped downward. Each incremental change in vertical force constitutes a load step. During the whole simulation
Fig. 8
Definition of the transition zone of sphere indenter.
process, the contact radius is calculated under every corresponding load force condition within the mechanical module firstly, and then the distribution of electric current lines and electric potentials are directly dependent on the contact radius. Further, each electrical resistance data point in Fig. 11 represents a single load step at which static equilibrium was achieved. The simulation results of electrical current lines profile and iso-potential maps between silver-palladium, stainless steel, sapphire with gold coating indenter and silver rivet for contact force of 20 g at 10 mA current load are shown in Fig. 5–Fig. 7. The differences of the indenter curvature result in the contact radius to be 20 µm, 6.8 µm and 12.7 µm, respectively. As seen in Fig. 5–Fig. 6, the current lines, which are orthogonal to the potential lines, shrink uniformly radially towards the contact region. Considering the electrical insulation properties of the sapphire indenter, the current passes through the sphere indenter’s coating mostly. The observed contours correlate well with the principles of a steady constant current field [17]. It should be noted that the current lines that existed in the gold coating are getting denser than those in the substrate material, owing to the fact that the conductivity of the gold coating is higher than that of the three substrate materials. The substrate cross section is so limited in the vicinity of contact region that gold coating resistance is smaller than that the parallel substrate resistance. We define the region where the coating resistance is lower than the substrate resistance as the transition zone. The start of the transition zone is marked by “c” in Fig. 8, which shows that the constricting current lines change from vertical to horizontal. And the marker “c” means the border between the
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Fig. 9 Schematic diagram of the sphere indenter resistance components including restriction zone resistance, transition zone resistance and bulk zone resistance.
Fig. 10
The relationship between dRc /dR s and the horizontal distance.
traditional current constriction zone and the transition zone. The resistance within the constriction zone is attributed to the current constriction characteristics of Au–Ag interface with the change of contact radius. But for the transition zone, surface coating resistance is the main content. The resistance within the transition zone is not proportional to the contact radius at the constriction zone. Also, the substrate resistance element dR s and coating resistance element dRc , shown in Fig. 9, are subdivided by taking the obtained simulation equipotential lines as reference. The relationship between the ratio of dRc /dR s and the axial distance of silverpalladium and stainless steel indenter material is shown in Fig. 10. As shown in this figure, the length of the transition zone is 29 µm for silver palladium alloy indenter and 72.2 µm for the stainless steel indenter. So the equipotential marker “d” in Fig. 8, which is corresponding to the ratio of dRc /dR s equal to 1, is the boundary of transition zone and substrate bulk zone. It indicated that the current flow into the substrate and the Au coating have the same value. Beyond marker “d”, the current mainly passes through the substrate zone. Both of
Fig. 11 Relationship between electrical resistance components and contact force (current 10 mA).
two beyond the line, the substrate bulk resistance is the main component of the total contact resistance. So according to the density and shape of current lines, the contact resistance between marker “a” and marker “b” shown in Fig. 3 is divided into the rivet bulk restriction resistance (marker “c” to
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marker “b”), the transition resistance (marker “c” to marker “d”) and the bulk resistance of the indenter (marker “a” to marker “d”). The difference of electrical conductivity between indenter material and gold coating is the true reason for the occurrence of the transition region. So the resistance component that does not meet Hertz theory can be extracted clearly by defining the transition zone, which is important for understanding the changing rules near the contact area. The relationship between load force and electrical resistance between equipotential lines “a” and “b” and relevant components are simulated in detail for different substrate materials with gold coatings. The relationship between constriction resistance, transition resistance, total contact resistance and load force could be expressed by exponential function. As shown in Fig. 11, for AgPd alloy, stainless steel and the sapphire indenter with Au coating, the values of rivet constriction resistance “n” are 0.35, 0.34 and 0.33 individually, which correlates with the classical Holm theory. Except that the sapphire indenter has no transition region, the values for “n” of the other two indenter resistances in the transition region are 0.28 and 0.11, and in the bulk region both are zero. The contact radius increases incrementally with the contact force, which correlates with the reduction in constriction resistance and transition resistance. Furthermore, the bulk resistance of the substrate, corresponding to the region between “a” and “d”, keeps stable with the increment of the contact force. This explains why the values “n” of total contact resistance between “a” and “b” is not equal to 1/3. The total contact resistance between the indenters and the rivet is the sum of above region resistances. It should be noted that the contact resistance decreases more slowly than traditional constriction resistance by introducing transition resistance and bulk resistance of the indenter. Therefore, the indices “n” of contact resistance between marker “a” and marker “b” of AgPd alloy and stainless steel are 0.18 and 0.14. That would be the reason for resistance measurement results during the loading process being lower than that traditional expected values. The difference between measurement results and simulation results of the contact resistance are caused by the coarse morphology of the surface and film resistance which existed in the real indenters and rivets. In addition, as shown in Fig. 11(c), the surface gold coating resistance is the main component for the sapphire indenter. The sapphire ball with gold coating fabricated by sputtering is not suitable as an indenter, although the hardness of substrate is excellent. Because of the higher electrical conductivity of silver palladium alloy, the constriction resistance, transition resistance and subsequent total contact resistance are all lower than those obtained by using the stainless steel indenter. If the substrate material is changed to gold, the same as the coating material, then the transition region resistance will disappear. Therefore, the substrate material electrical conductivity affects the contact resistance measurement results greatly. Gold coating on the surface is necessary for preventing the indenter oxidation or contamination. An indenter material that has similar electrical conductivity
characteristics to gold produces more accurate contact resistance results. 5.
Conclusion
This investigation mainly aims to determine the effect of a sphere indenter on measuring contact resistance of rivets and the corresponding conduction mechanism accurately. A new automatic test equipment for measuring electrical contact resistance of multiple real size rivets simultaneously has been presented. The mechanical load vs. contact resistance hysteresis characteristics of flat Ag rivets were measured and numerically simulated by using silver-palladium alloy, stainless steel and sapphire indenters with gold coating. The experimental results and simulation results both show that the contact resistance of flat rivets follows in an exponential function form from 0.5 to 20 g. During simulation, a turning point of current lines between the sphere indenter with Au coating and flat rivet surface is observed. Therefore, the induced transition zone resistance and bulk substrate resistance cause the contact resistance to decrease slowly during the loading process. Higher electrical conductivity of the indenter material causes an additional resistance decrease, followed by a more accurate rivet contact resistance value. Therefore the indenter of AgPd alloy with gold coating should be designated as the preferable choice for having high electrical conductivity and contributing minimal additional resistance compared to the other two stainless steel and sapphire substrate materials. Acknowledgments The authors express their gratitude for the kind support provided by The National Natural Science Foundation of China (Contract Number 51007010 and 51377029). References [1] R. S. Timsit, “On the evaluation of contact temperature from potential drop measurements,” Proc. Holm Conf. on Electrical Contacts, pp.147–154, 1982. [2] R. S. Timsit, “The ‘melting’ voltage in electrical contacts,” IEEE Trans. Comp. Hybrids, Manufact. Technol., vol.14, no.2, pp.285– 292, June 1991. [3] P. Zhang, Y. Y. Lau, and R. S. Timsit, “On the spreading resistance of thin-film contacts,” IEEE Trans. Electron. Dev., vol.59, no.7, pp.1936–1940, July 2012. [4] R. S. Timsit, “Constriction resistance of thin-film contacts,” IEEE Trans. Compon. Packag. Technol., vol.33, no.3, pp.636–642, Sept. 2010. [5] Y. Sano and T. Kaneko, “Applicability and correction of temperature—voltage relation in the case of point contact,” IEEE Trans. Compon. Packag. Manufact. Technol.–Part A, vol.21, no.2, pp.345–351, June 1998. [6] S. Sawada, K. Shimizu, Y. Hattori, T. Tamai, and K. Iida, “Analysis of contact resistance behavior for electric contacts with plating layer,” Proc. 56th IEEE Holm Conf. on Electrical Contacts, USA, pp.65–72, 2010. [7] G. Norberg, S. Dejanovic, and H. Hesselbom, “Contact resistance of thin metal film contacts,” IEEE Trans. Compon. Packag. Technol., vol.29, no.2, pp.371–378, June 2006.
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[8] M. R. Pinnel and K. F. Bradford, “Influence of geometric factors on contact resistance probe measurements,” IEEE Trans. Comp. Hybrids Manufact. Technol., vol.3, no.1, pp.159–165, Mar. 1980. [9] E. M. Yunus, J. W. McBride, and S. M. Spearing, “The relationship between contact resistance and contact force on Au coated carbon nanotube surfaces,” Proc. 53rd IEEE Holm Conf. on Electrical Contacts, pp.167–174, 2007. [10] T. Tamai, S. Sawada, and Y. Hattori, “Deformation of crystal morphology in tin plated contact layer caused by loading,” IEICE Trans. Electron., vol.E95-C, no.9, pp.1473–1480, Sept. 2012. [11] C. Jang, S. Park, B. Infantolino, L. Lehman, R. Morgan, and D. Sengupta, “Failure analysis of contact probe pins for SnPb and Sn applications,” Microelectron. Reliab., vol.48, no.6, pp.942–947, June 2008. [12] http://www.hysitron.com/products/options-upgrades/nanoecr [13] W. Ren, Y. Chen, S. Cao, L. Cui, and H. Liang, “A new automated test equipment for measuring electrical contact resistance of real sizes rivets,” Proc. 59th IEEE Holm Conf. on Electrical Contacts, USA, pp.295–301, 2013. [14] R. Holm, Electric Contacts, Theory and Applications, 4th ed., Springer-Verlag, 2000. [15] A. Keil, W. A. Merl, and E. Vinaricky, Elektrische Kontakte und ihre Werkstoffe, Springer-Verlag, 1984. [16] http://www.swissjewel.com/1/sapphire/ [17] J. A. Sttraton, Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941.
Wanbin Ren was born in 1977. He received the M.S. degree and Ph.D. degree from Harbin Institute of Technology, China, in 2003 and 2006 respectively. He is currently an associated professor of school of Electrical Engineering and automation at Harbin Institute of Technology. His main research interests include the electrical contact theory and measurement techniques for electrical contact materials. Dr. Ren is a member of IEICE and a member of IEEE.
Yu Chen was born in 1991. He received the B.S. from Department of Electrical Engineering of Harbin Institute of Technology, Harbin, China, in 2013, and now he is pursuing his M.S. degree in Harbin Institute of Technology. His study interests include theory and techniques of contact resistance measurement of rivet contacts.
Shengjun Xue was born in 1988. He received the B.S. degree in July 2012 from Harbin Institute of Technology, Harbin, China. Now he is a graduate student of School of E.E. and Automation, Harbin Institute of Technology. His research direction is interface characteristics measurment in micro and nano scale.
Guenther Horn received his Masters Degree in Applied Physics from the University of Giessen Germany in 19669. After managing the Contact Laboratories of DODUCO GmbH in Pforzheim, Germany, he transferred in 1977 to the USA as the Technical Director and VP of Marketing at DODUCO’s plant in NJ. while at the same time continuing research and development work on switching electrical contacts. From 1989 to 2008 he was the VP of Technology for AMI DODUCO, Inc., responsible for R&D as well as Application Engineering and for technical support in the company’s growth through global acquisitions. In this role he spent six years in Tianjin, China, for the start-up of the company’s Asian contact manufacturing operations. With his retirement in 2008 he started the ElConMat Consulting business concentrating on electrical contacts technology and technical publishing. He published over 30 technical papers and co-authored text books about electrical contact materials and their application. He continues to serve in various positions of the IEEE Holm Conference organization and is the 1994 recipient of the Armington Recognition Award.
Guofu Zhai was born in 1964. He received his Ph.D. from Harbin Institute of Technology, Harbin, China, in 1998. He is currently a professor of the Department of Electrical Engineering at Harbin Institute of Technology. His main research interests include electrical contacts and the reliability and testing techniques of electrical apparatus.
873
PAPER
Special Section on Recent Development of Electro-Mechanical Devices (IS-EMD2013)
Experimental Investigation and Numerical Simulation on the Role of Sphere Indenter in Measuring Contact Resistance of Flat Rivets Wanbin REN†a) , Member, Yu CHEN† , Shengjun XUE† , Guenther HORN†† , Nonmembers, and Guofu ZHAI† , Member
SUMMARY There has been increasing demand to research the measuring method to characterize the batch consistency of contact rivets. An automated test equipment has been described that makes it possible to measure the electrical contact resistance with high efficiency. The relationship between contact force and contact resistance during the loading and unloading process was measured explicitly using AgPd alloy, stainless steel and sapphire substrate material with Au coatings as sphere indenters separately. To explain the phenomena of contact resistance decreasing more slowly than the traditional theoretical results during loading, the indenter with coating and rivet are modeled by using the commercial FEM software COMSOL Multiphysics. Besides the constriction resistance, the transition region Au coating resistance and the bulk resistance of the substrate are deduced from the simulated current lines profiles and iso-potentials. The difference of electrical conductivity between indenter material and gold coating is the reason for the occurrence of the transition region. key words: sphere indenter, constriction resistance, contact resistance, flat rivet, FEM
1. Introduction Rivet-type contacts are widespread used in all kinds of electrical switches for switching and/or conducting current. The value of the rivets’ contact resistance correlates with the working status and potential failure of the electromechanical devices closely. Also, it could be taken as one of the key characterization parameters for material composition and surface roughness as well as cleanliness. As the miniaturization and high reliability of electromechanical devices increases, rivets with excellent electrical connectivity performance are required urgently. Interest in influencing factors on contact resistance and suppression method in engineering is increasing since Ragnar Holm’s academic monograph in the 1940s. The theory of contact resistance has long remained an academic hot issue [1]–[7]. It was shown that the direct measurement for contact resistance is of great importance for theoretical model and simulation analysis. Meanwhile, a precise specialized measurement method is required for the development of advanced contact materials and particular industrial applications. Measured contact resistance values will include the constriction resistance and bulk resistance of the indenter Manuscript received January 7, 2014. Manuscript revised April 1, 2014. † The authors are with the School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China. †† The author is with the ElConMat Consulting Associates, VA, USA. a) E-mail: [email protected] DOI: 10.1587/transele.E97.C.873
and the film resistance between interfaces etc., besides the constriction resistance of the rivet sample. Therefore, the material selection and preparation of an indenter for contacting with rivets during measurement cause both problems and opportunities. Precious metals, such as gold, are always designated to be the choice for indenter tips. Pinnel and Bradford [8] evaluated the effect of variations in the geometry and preparation of gold probe tips for contact resistance measurements. Yunus [9] measured the contact resistance of Au coated carbon nanotube surfaces using a stainless steel hemisphere with 2 mm diameter, sputter coated with 500 nm Au. Tamai [10] utilized a platinum sphere shaped indenter with 1mm diameter to investigate the property and crystal morphology of tin oxide films formed on tin-plated contacts. Jang [11] also researched the failure mechanism of pogo pin-type probe contacts, which use Fe as a base metal and a noble metal such as Au or PdCo as a coating metal. Recently, the nano-scale electrical contact resistance tool (nanoECR, HYSITRON, USA) [12], provides a powerful solution for simultaneous, in-situ electrical and mechanical measurements with the electrically conductive indenter using a diamond tip doped with Boron. In a previous paper by the present authors, the relationship between contact load and contact resistance during loading and unloading is investigated explicitly with different current using a stainless steel hemisphere with gold coating as standard indenter [13]. It is well known that the hardness, electrical conductivity and the surface coating of the indenter will affect the contact area and contact resistance between the indenter and the rivet sample directly. In order to find the preferable indenter metal material for measuring the contact, in the present paper, we shall test the relationship between the mechanical load and contact resistance for silver-palladium alloy, stainless steel and a sapphire ball as three different spherical indenters. We shall then build up the finite element contact model using COMSOL Multiphysics commercial software for interpreting the current line profiles and iso-potentials. In particular, we shall investigate the effect of the additional resistance resulting from the indenter on the contact resistance measurement of rivet sample. 2.
Experimental Details
The test apparatus used in these experiments is described in
c 2014 The Institute of Electronics, Information and Communication Engineers Copyright ⃝
IEICE TRANS. ELECTRON., VOL.E97–C, NO.9 SEPTEMBER 2014
874
detail in [13]. A schematic diagram of the test apparatus used in the contact resistance measurement experiments is shown in Fig. 1. The normal contact force was supplied by the bow type spring component and controlled by the Z-axis electric actuator. The contact force maximum value could be set up to 300 g with a resolution of 0.05 g. The flat contact rivet samples with a head diameter of 3 mm are made from pure silver. The probe holder is specially designed for clamping different kinds of indenters. Table 1 provides detail information about the indenters we used in this paper. The indenters and flat specimens were degreased using acetone, methyl alcohol and distilled water in an ultrasonic cleaner in order, dried and carefully mounted in the test rig. The indenter and flat contacts are mated in such a way to create a point contact in “sphere- to-plane” geometry. Twenty rivets could be clamped and measured simultaneously in a multiple rivet contacts sample holder. The measuring instrument is configured for the fourwire technique, which eliminates the lead resistance including the resistance of soldered joints. It has a built-in current source capable of providing a constant current, which could be set from 1 to 1000 mA in steps of 1 mA. The optional open circuit voltage can be varied from 5 to 200 mV in 1 mV steps. The accuracy of the measured resistance between contacts is within ±1% after calibration. The instru-
ment is interfaced to a personal computer using a USB cable. The data acquisition and logging process are controlled through a PC with the help of LabVIEW software specifically programmed for this purpose. The whole load-contact resistance experiment can be described as loading stage and unloading stage. The indenter and rivet sample are brought into contact from 0.5 g to 20 g at a controlled loading rate. After loading force is reached the set value and keeps invariable, the pre-set current passed through the contact pair. The steady value of contact voltage drop could be recorded and saved. The indenter is unloaded at the same rate from 20 g until they are separated. The force step is set 0.5 g. The current is set 10 mA. 3.
Results and discussion
Figure 2 shows the characteristic of the resistance measurement results during loading and unloading by using an Aucoated indenter with different substrate material. There are distinct differences in measured resistance value at the same load force. The variation in contact resistance vs. load depicted in Fig. 2 stems from a combination of several factors: Ref. [13] stated an increase in number of contacting surface asperities as the nominal surfaces are brought closer together under the influence of an increasing load; permanent flattening of the contacting asperities, which reduces the constriction resistance associated with each a-spot and thus reduces the overall contact resistance; work-hardening of the deformed contact asperities, which reduced the rate of asperity flattening etc. Classical mathematical models that attempt to explain the observations of Fig. 2 in terms of details of asperity deformation behaviour during compression predict a relationship between contact resistance and mechanical load. For lower contact load in which the elastic deformation dominates, constriction resistance is expressed as a function of contact load as in Eq. (1) [14]. Rc = [K]F −n
Fig. 1 ing).
(1)
Mechanical part of the automated test equipment (without hous-
Indenters used in this paper.
Table 1 Substrate AgPd alloy Stainless steel 1Cr18Ni9Ti Sapphire
Curvature radius (mm) 1.5
Au coating thickness (µm) 2
0.5
2
Electroplating
1
0.4
Sputtering
Coating method Electroplating Fig. 2 Relationship between resistance and contact force during loading and unloading process with different indenters (every plot data was the average value of 4 rivet samples).
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Here, [K] is a constant. The [K] contains electrical resistivity of metals, its Poisson’s ratios, Young’s modulus and radius of curvature of the probe. And the constriction resistance is proportional to F 1/3 . With the loading experimental data fitting, the index parameter “n” is 0.26, 0.23 and 0.06 for the indenter materials AgPd alloy, stainless steel and sapphire respectively. 4. FEM Modeling for Electric Field Analysis of Sphere Indenter and Flat Rivet The aim of FEM modelling is to demonstrate what the measured contact resistance value makes up. The commercial program COMSOL Multiphysics 4.2b version was used to perform simulations by solving contact mechanical equations and electric field equations through finite element method (FEM). The schematic plot of the simulation model is shown in Fig. 3. The partial sphere indenter with Au coating and the flat rivet (between line “a” and line “b” in Fig. 3) are modelled and meshed with traditional triangular elements. The line “a” and line “b” in Fig. 3 correspond to the two voltage
probes in the experiment. The mesh, presented in Fig. 4, was graded radially outward from the initial point of contact, with the densest mesh in the contact region. The minimal size of the mesh is 0.2 µm and the contact surfaces are assumed smooth. The partial contacting surfaces of the hemisphere and flat surface are defined as contact pair. In addition, the thin contamination film on the contact surfaces is not considered. It is inevitable that these assumptions result in the simulation results of contact resistance being smaller than those obtained in experiments. However, the nature of the difference of conductivity between indenter substrate and surface coating are not changed. Load boundary conditions of the model consisted of a prescribed uniform vertical force on the upper-most surface with the bottom-most surface vertically fixed. The load force is set as 0.5 g, 1 g, 5 g, 10 g and 20 g separately. Axisymmetry was applied to the left-most boundary, resulting in zero horizontal displacement. All of the remaining surfaces were unconstrained in the vertical and horizontal directions. Electrically, a pre-
Fig. 3 Schematic plot of the simulation model and boundary conditions setting.
Fig. 5 (a) Electric current lines profile and isopotential map of AgPd alloy with 2 µm gold coating. (b) A zoomed-in view of results in the contact region. (c) A zoomed-in view of the result in the transition zone. Table 2 Material properties for FEM. All values are from Ref. [15], except for Sapphire from Ref. [16].
Fig. 4 (a) Axisymmetric FEM with Comsol Multiphysics. zoomed-in view of the mesh in the contact region.
(b) A
AgPd alloy Stainless steel Sapphire Gold Silver
Young’s modulus (GPa)
Poisson ratio
Electrical conductivity (S/m)
Density (kg/m3 )
200
0.29
0.24×107
11.4×103
202
0.29
0.137×107
7.9×103
7900 76 81.1
0.28 0.44 0.37
1 4.52×107 6.28×107
4.0×103 19.3×103 10.5×103
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Fig. 6 (a) Electric current lines profile and isopotential contour of stainless steel with 2µm gold coating. (b) A zoomed-in view of results in the contact region. (c) A zoomed-in view of the result in the transition zone.
Fig. 7 (a) Electric current lines profile and voltage potential contour of sapphire with 0.4 µm gold coating. (b) A zoomed-in view of results in the contact zone.
scribed constant current density was applied to the uppermost surface, and the bottom-most surface was electrically grounded. The constant current intensity is 10 mA. Axisymmetry on the left-most boundary results in electrical insulation. The later surfaces of both bodies were also considered electrically insulated. The details of the geometric model and material properties (shown in Table 2) are the same as those used in the experiment. To load the system, the defined vertical load force was stepped downward. Each incremental change in vertical force constitutes a load step. During the whole simulation
Fig. 8
Definition of the transition zone of sphere indenter.
process, the contact radius is calculated under every corresponding load force condition within the mechanical module firstly, and then the distribution of electric current lines and electric potentials are directly dependent on the contact radius. Further, each electrical resistance data point in Fig. 11 represents a single load step at which static equilibrium was achieved. The simulation results of electrical current lines profile and iso-potential maps between silver-palladium, stainless steel, sapphire with gold coating indenter and silver rivet for contact force of 20 g at 10 mA current load are shown in Fig. 5–Fig. 7. The differences of the indenter curvature result in the contact radius to be 20 µm, 6.8 µm and 12.7 µm, respectively. As seen in Fig. 5–Fig. 6, the current lines, which are orthogonal to the potential lines, shrink uniformly radially towards the contact region. Considering the electrical insulation properties of the sapphire indenter, the current passes through the sphere indenter’s coating mostly. The observed contours correlate well with the principles of a steady constant current field [17]. It should be noted that the current lines that existed in the gold coating are getting denser than those in the substrate material, owing to the fact that the conductivity of the gold coating is higher than that of the three substrate materials. The substrate cross section is so limited in the vicinity of contact region that gold coating resistance is smaller than that the parallel substrate resistance. We define the region where the coating resistance is lower than the substrate resistance as the transition zone. The start of the transition zone is marked by “c” in Fig. 8, which shows that the constricting current lines change from vertical to horizontal. And the marker “c” means the border between the
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Fig. 9 Schematic diagram of the sphere indenter resistance components including restriction zone resistance, transition zone resistance and bulk zone resistance.
Fig. 10
The relationship between dRc /dR s and the horizontal distance.
traditional current constriction zone and the transition zone. The resistance within the constriction zone is attributed to the current constriction characteristics of Au–Ag interface with the change of contact radius. But for the transition zone, surface coating resistance is the main content. The resistance within the transition zone is not proportional to the contact radius at the constriction zone. Also, the substrate resistance element dR s and coating resistance element dRc , shown in Fig. 9, are subdivided by taking the obtained simulation equipotential lines as reference. The relationship between the ratio of dRc /dR s and the axial distance of silverpalladium and stainless steel indenter material is shown in Fig. 10. As shown in this figure, the length of the transition zone is 29 µm for silver palladium alloy indenter and 72.2 µm for the stainless steel indenter. So the equipotential marker “d” in Fig. 8, which is corresponding to the ratio of dRc /dR s equal to 1, is the boundary of transition zone and substrate bulk zone. It indicated that the current flow into the substrate and the Au coating have the same value. Beyond marker “d”, the current mainly passes through the substrate zone. Both of
Fig. 11 Relationship between electrical resistance components and contact force (current 10 mA).
two beyond the line, the substrate bulk resistance is the main component of the total contact resistance. So according to the density and shape of current lines, the contact resistance between marker “a” and marker “b” shown in Fig. 3 is divided into the rivet bulk restriction resistance (marker “c” to
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marker “b”), the transition resistance (marker “c” to marker “d”) and the bulk resistance of the indenter (marker “a” to marker “d”). The difference of electrical conductivity between indenter material and gold coating is the true reason for the occurrence of the transition region. So the resistance component that does not meet Hertz theory can be extracted clearly by defining the transition zone, which is important for understanding the changing rules near the contact area. The relationship between load force and electrical resistance between equipotential lines “a” and “b” and relevant components are simulated in detail for different substrate materials with gold coatings. The relationship between constriction resistance, transition resistance, total contact resistance and load force could be expressed by exponential function. As shown in Fig. 11, for AgPd alloy, stainless steel and the sapphire indenter with Au coating, the values of rivet constriction resistance “n” are 0.35, 0.34 and 0.33 individually, which correlates with the classical Holm theory. Except that the sapphire indenter has no transition region, the values for “n” of the other two indenter resistances in the transition region are 0.28 and 0.11, and in the bulk region both are zero. The contact radius increases incrementally with the contact force, which correlates with the reduction in constriction resistance and transition resistance. Furthermore, the bulk resistance of the substrate, corresponding to the region between “a” and “d”, keeps stable with the increment of the contact force. This explains why the values “n” of total contact resistance between “a” and “b” is not equal to 1/3. The total contact resistance between the indenters and the rivet is the sum of above region resistances. It should be noted that the contact resistance decreases more slowly than traditional constriction resistance by introducing transition resistance and bulk resistance of the indenter. Therefore, the indices “n” of contact resistance between marker “a” and marker “b” of AgPd alloy and stainless steel are 0.18 and 0.14. That would be the reason for resistance measurement results during the loading process being lower than that traditional expected values. The difference between measurement results and simulation results of the contact resistance are caused by the coarse morphology of the surface and film resistance which existed in the real indenters and rivets. In addition, as shown in Fig. 11(c), the surface gold coating resistance is the main component for the sapphire indenter. The sapphire ball with gold coating fabricated by sputtering is not suitable as an indenter, although the hardness of substrate is excellent. Because of the higher electrical conductivity of silver palladium alloy, the constriction resistance, transition resistance and subsequent total contact resistance are all lower than those obtained by using the stainless steel indenter. If the substrate material is changed to gold, the same as the coating material, then the transition region resistance will disappear. Therefore, the substrate material electrical conductivity affects the contact resistance measurement results greatly. Gold coating on the surface is necessary for preventing the indenter oxidation or contamination. An indenter material that has similar electrical conductivity
characteristics to gold produces more accurate contact resistance results. 5.
Conclusion
This investigation mainly aims to determine the effect of a sphere indenter on measuring contact resistance of rivets and the corresponding conduction mechanism accurately. A new automatic test equipment for measuring electrical contact resistance of multiple real size rivets simultaneously has been presented. The mechanical load vs. contact resistance hysteresis characteristics of flat Ag rivets were measured and numerically simulated by using silver-palladium alloy, stainless steel and sapphire indenters with gold coating. The experimental results and simulation results both show that the contact resistance of flat rivets follows in an exponential function form from 0.5 to 20 g. During simulation, a turning point of current lines between the sphere indenter with Au coating and flat rivet surface is observed. Therefore, the induced transition zone resistance and bulk substrate resistance cause the contact resistance to decrease slowly during the loading process. Higher electrical conductivity of the indenter material causes an additional resistance decrease, followed by a more accurate rivet contact resistance value. Therefore the indenter of AgPd alloy with gold coating should be designated as the preferable choice for having high electrical conductivity and contributing minimal additional resistance compared to the other two stainless steel and sapphire substrate materials. Acknowledgments The authors express their gratitude for the kind support provided by The National Natural Science Foundation of China (Contract Number 51007010 and 51377029). References [1] R. S. Timsit, “On the evaluation of contact temperature from potential drop measurements,” Proc. Holm Conf. on Electrical Contacts, pp.147–154, 1982. [2] R. S. Timsit, “The ‘melting’ voltage in electrical contacts,” IEEE Trans. Comp. Hybrids, Manufact. Technol., vol.14, no.2, pp.285– 292, June 1991. [3] P. Zhang, Y. Y. Lau, and R. S. Timsit, “On the spreading resistance of thin-film contacts,” IEEE Trans. Electron. Dev., vol.59, no.7, pp.1936–1940, July 2012. [4] R. S. Timsit, “Constriction resistance of thin-film contacts,” IEEE Trans. Compon. Packag. Technol., vol.33, no.3, pp.636–642, Sept. 2010. [5] Y. Sano and T. Kaneko, “Applicability and correction of temperature—voltage relation in the case of point contact,” IEEE Trans. Compon. Packag. Manufact. Technol.–Part A, vol.21, no.2, pp.345–351, June 1998. [6] S. Sawada, K. Shimizu, Y. Hattori, T. Tamai, and K. Iida, “Analysis of contact resistance behavior for electric contacts with plating layer,” Proc. 56th IEEE Holm Conf. on Electrical Contacts, USA, pp.65–72, 2010. [7] G. Norberg, S. Dejanovic, and H. Hesselbom, “Contact resistance of thin metal film contacts,” IEEE Trans. Compon. Packag. Technol., vol.29, no.2, pp.371–378, June 2006.
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[8] M. R. Pinnel and K. F. Bradford, “Influence of geometric factors on contact resistance probe measurements,” IEEE Trans. Comp. Hybrids Manufact. Technol., vol.3, no.1, pp.159–165, Mar. 1980. [9] E. M. Yunus, J. W. McBride, and S. M. Spearing, “The relationship between contact resistance and contact force on Au coated carbon nanotube surfaces,” Proc. 53rd IEEE Holm Conf. on Electrical Contacts, pp.167–174, 2007. [10] T. Tamai, S. Sawada, and Y. Hattori, “Deformation of crystal morphology in tin plated contact layer caused by loading,” IEICE Trans. Electron., vol.E95-C, no.9, pp.1473–1480, Sept. 2012. [11] C. Jang, S. Park, B. Infantolino, L. Lehman, R. Morgan, and D. Sengupta, “Failure analysis of contact probe pins for SnPb and Sn applications,” Microelectron. Reliab., vol.48, no.6, pp.942–947, June 2008. [12] http://www.hysitron.com/products/options-upgrades/nanoecr [13] W. Ren, Y. Chen, S. Cao, L. Cui, and H. Liang, “A new automated test equipment for measuring electrical contact resistance of real sizes rivets,” Proc. 59th IEEE Holm Conf. on Electrical Contacts, USA, pp.295–301, 2013. [14] R. Holm, Electric Contacts, Theory and Applications, 4th ed., Springer-Verlag, 2000. [15] A. Keil, W. A. Merl, and E. Vinaricky, Elektrische Kontakte und ihre Werkstoffe, Springer-Verlag, 1984. [16] http://www.swissjewel.com/1/sapphire/ [17] J. A. Sttraton, Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941.
Wanbin Ren was born in 1977. He received the M.S. degree and Ph.D. degree from Harbin Institute of Technology, China, in 2003 and 2006 respectively. He is currently an associated professor of school of Electrical Engineering and automation at Harbin Institute of Technology. His main research interests include the electrical contact theory and measurement techniques for electrical contact materials. Dr. Ren is a member of IEICE and a member of IEEE.
Yu Chen was born in 1991. He received the B.S. from Department of Electrical Engineering of Harbin Institute of Technology, Harbin, China, in 2013, and now he is pursuing his M.S. degree in Harbin Institute of Technology. His study interests include theory and techniques of contact resistance measurement of rivet contacts.
Shengjun Xue was born in 1988. He received the B.S. degree in July 2012 from Harbin Institute of Technology, Harbin, China. Now he is a graduate student of School of E.E. and Automation, Harbin Institute of Technology. His research direction is interface characteristics measurment in micro and nano scale.
Guenther Horn received his Masters Degree in Applied Physics from the University of Giessen Germany in 19669. After managing the Contact Laboratories of DODUCO GmbH in Pforzheim, Germany, he transferred in 1977 to the USA as the Technical Director and VP of Marketing at DODUCO’s plant in NJ. while at the same time continuing research and development work on switching electrical contacts. From 1989 to 2008 he was the VP of Technology for AMI DODUCO, Inc., responsible for R&D as well as Application Engineering and for technical support in the company’s growth through global acquisitions. In this role he spent six years in Tianjin, China, for the start-up of the company’s Asian contact manufacturing operations. With his retirement in 2008 he started the ElConMat Consulting business concentrating on electrical contacts technology and technical publishing. He published over 30 technical papers and co-authored text books about electrical contact materials and their application. He continues to serve in various positions of the IEEE Holm Conference organization and is the 1994 recipient of the Armington Recognition Award.
Guofu Zhai was born in 1964. He received his Ph.D. from Harbin Institute of Technology, Harbin, China, in 1998. He is currently a professor of the Department of Electrical Engineering at Harbin Institute of Technology. His main research interests include electrical contacts and the reliability and testing techniques of electrical apparatus.
