Wear, 162-164 (1993) 913-918
A general model for sliding wear in electrical contacts R. G. Bayer 4609 iUanhal1 Drive West, Vestal, NY 13850 (USA)
Abstract A variety of models, generally either based on abrasive, adhesive or surface fatigue wear concepts, have been used with some success in describing the sliding wear of electrical contacts. There are also empirical observations which support the individual or simultaneous occurrence of these various mechanisms in wear of such contacts. In addition to these mechanisms, which may be referred to as surface wear mechanisms, a subsurface mechanism has also been identified in recent studies of the wear of a card-edge connector system. This mechanism is associated with the plastic deformation of the substrate and can coexist with all, or any, of the surface mechanisms. In this paper, a model is developed for this subsurface mechanism and combined with models for the surface mechanisms to provide a general model for the sliding wear of contact systems. The relationships, which result from these models, are shown to agree with observed behavior in the case of a card-edge contact system. It is suggested that the method of combining the effects of several simultaneous wear mechanisms may be applicable to more general wear situations.
1. Introduction Several types of wear mechanisms have been associated with the wear of electrical contacts. These included the common ones of adhesive, abrasive, and surface fatigue wear mechanisms, which are primarily associated with surface or near surface behavior [l-4]. More recently, a fourth mechanism has also been identified . This fourth mechanism is related to subsurface behavior and involves progressive plastic deformation of the substrates of plated contact surfaces. There is evidence, both in terms of wear scar morphology and the success of models based on these mechanisms, which suggests that all of these mechanisms can and do occur [l-5]. While the physical evidence frequently points to the co-existence of several mechanisms, models have usually been based on individual mechanisms. Because of this, these models tend to have limited ranges of applicability in terms of materials, loading conditions, and environment. In this paper, a more general model, which allows for the simultaneous occurrence of several mechanisms, is proposed. This model is then applied to a contact wear situation in which there are surface and subsurface wear mechanisms present. In addition, a relationship for the subsurface mechanism is developed and related to observed behavior. In this paper, the general model is presented first. Following this, individual wear relationships for adhesive, abrasive, and surface fatigue wear modes, which
are used by the general model, are developed. A model is then proposed for the subsurface mechanism and used to develop a wear relationship for this mode, which is also required for the general model. These individual relationships, as well as the composite relationship provided by the general model, are then compared with empirical relationships obtained for a card-edge contact system.
2. General model The basic hypothesis of the model is that the wear depth is the weighted sum of the wear depths associated with the individual mechanisms, assuming they were the sole mechanism. Mathematically, h = &hi
where hi is the depth for the ith mechanisms and (Y~ is the weighting factor. ai represents the relative contribution or signticance of the ith mechanism in a sliding motion and Cc$=l
Approximating the wear relationships for each of the individual mechanisms by a power relationship, hi = C,Ly
ffi = ci/cci
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R. G. Bayer / Sliding wear in electrical contacts
where L is the number of sliding actions experienced by the contact. Ci is a function of the various parameters that affect wear, such as load, materials, geometry, etc. The explicit forms of these dependencies vary with the mechanisms, as can be seen by comparing eqns. (7)-(9) and (29). Upon substitution,
The basic equation used for both abrasive and adhesive wear is
a progressively deeper wear groove in the surface and the formation of buckles in the surface layers. Above these buckles localized surface wear occurs. With repeated cycling, localized exposure of sublayer material eventually occurs at these sites, with or without a general thinning of the surface layers . The appearance is one suggestive of local upsurgence of the sublayers, through the surface, as shown in Fig. 1. It was reported that this mechanism was affected by load, number of cycles, and the thickness and stiffness of the surface layers. Increasing the load resulted in a reduction in the number of cycles for exposure of sublayer material. It was also found that with sufficiently thick and stiff layers the mechanism could be eliminated. The presence of this mechanism was found to affect the load dependency of the empirical wear relationships. When this mechanism was present in the card-edge contact system described in Table 1, it was found that for the flat surface
h = (X,2L;)/Xi
While in the present case only four mechanisms are considered, i.e. i G 4, it can be extended to any number of mechanisms. With this formulation, Ci for a particular mechanism is zero, if the mechanism is not present or contributing to the wear.
3. Models for surface wear mechanisms
where V is the volume of wear; P is the normal load; and S is the amount of sliding . K, the wear coefficient, is different for adhesive and abrasive wear and is a function of the materials and environment. For most geometries, eqn. (6) can be reduced to the form given by eqn. (3). For a situation in which a spherical surface wears a groove into a flat surface, which is the condition for the card-edge contact referred to later in this paper, it can be shown that eqn. (6) reduces to the following hi = Ka3p2’3([email protected]
where R is the radius of the spherical surface and L is the number of cycles of reciprocating sliding. For surface fatigue wear, the zero and measurable models can be used to provide the appropriate expressions for hi 17, 81. With these models, two modes of wear are possible, a constant energy mode and variable energy mode. In the variable energy mode, wear rate decreases as stress level decreases; in the constant energy mode, it stays constant as wear progresses. Using these models, it can be shown that the following relationships result for a sphere wearing into a flat surface
PI hi =K.R - 1~6Po~8Lo~27variable energy
h, = KR -4P2La3
where Kz is a wear coefficient dependent and environment.
When it was not,
h is the depth of the wear scar. For this system negligible
wear occurred on the counter face. It should be noted that the exponents of P are based on a larger database than those given in ref. 5. Those given in ref. 5, 2 and 0.5 respectively, are within the standard deviation of the larger database. Also observed in this system was an inverse correlation with this mechanism and the coefficient of friction. As the thickness of the surface layers was increased, it was found that the coefficient of friction tended to increase, reaching its maximum value for those conditions in which buckling or “upsurgence” did not occur. In that system, the coefficient of friction can be correlated to the plate stiffness, @, of the surface layers, e.g. the Au and Ni layers . This is shown in Fig. 2 for the data given in ref. 5. The wear situation for which the subsurface mechanism was observed can be represented by an unwearing
4. Model for the subsurface wear mechanism With this wear mechanism, progressive plastic deformation occurs in the substrate. This flow results in
Fig. 1. Illustration of a typical cross-section on a card tab, showing thinning of the deformation, buckling, and penetration the substrate, i.e. upsurgence.
of a wear scar produced surface layer, substrate of the surface layer by
R. G. Bayer / Sliding wear in electrical contacts TABLE
Card Edge Geometry Metallurgy Thicknesses
of the card-edge
2.5-10 pm hard and soft Au surface 2.5-10 pm Ni-sublayer 50-100 pm Cu-substrate Hardnesses Soft Au hard Au Ni cu Spring Geometry Metallurgy: Thicknesses
90 200 230 125
kg kg kg kg
mm-* mm-’ mm-’ mm-*
Fig. 3. Illustration for the subsurface the development of the model.
0.6 mm radius
0.25-l pm 2.5-4 pm 1-3 pm > 100 pm
soft Au surface Pd-Ni-sublayer Ni-sublayer Be-Cu-substrate
soft Au Pd-Ni Ni Be-Cu
90 400 230 350
mm-’ mm-* mmm2 mm-’
CIU over Qu over
dWdL = 2wD’(7,,,,/7_)
Using eqn. (17) and the Hertz contact stress equations for parallel cylinders, it can also be shown that
T = (WI)‘~
dh IdJ? = 200( ?,,,/7$
where L is the number of cycles. Once flow occurs and for h -K R, the contact geometry can be approximated by the contact between a cylinder of length, T, and radius, r, against a flat surface. From the geometry, it can be shown that
Letting 2w be the amount of sliding in a cycle, eqns. (12) and (13) can be changed to the following
Fig. 2. Data from ref. 5, showing the correlation between plate stiffness of the combined layers of Au, Ni, and Pd-Ni, and the coefficient of friction. The data is for three different plating systems, as indicated.
reciprocating spheroid of radii R and r wearing a groove in a flat surface. The wear situation proposed for the subsurface wear mechanism in this case is depicted in Fig. 3. The general nature of this mechanism suggests that the rates of deformation should be related to the level of the stress in comparison with the elastic limit of the substrate. Therefore the following relationships are proposed for this mode h =D(&&)
The dot over a quantity denotes the derivative with respect to sliding distance; T,,, is the maximum shear stress; TVis the yield point in shear. Since some of the flow can be accommodated by distortion outside the wear scar and since there can be multiple buckles, it is to be expected that
Hardnesses kg kg kg kg
(19) where b is the width of the contact; I_Lis the coefficient of friction; and r,, is given by r,,=
E and Yare the effective Young’s moduli and Poisson’s ratios for the two surfaces. For the condition when the amplitude of the motion is greater than b, i.e. w equals b, integration of eqns. (15) and (16) results in the following h=
0.59(n+5)0.19T(1+/.&~P’“+‘)~L 7”R(“+‘)/(“+S)r(“-‘)ny,2(n-l)n Y
R. G. Bayer I Sliding
6 = 0.59(n + 5)0.19%( 1+ /.L.)“P’” + 1)‘2L4’(n+5, ,,$?K”‘4R(”+ I)/@++(?I - l)Rr,Z(n- 1)/2
wear in electrical
4/(n + 5) = 0.2
Using this value of n to simplify eqns. (21) and (22), the following wear relationships for the subsurface mechanism are obtained,
(26) The data regarding this mechanism had shown that with increased thicknesses of either Pd-Ni and Ni, or Au and Ni surface layers, this mechanism could be eliminated . As a result, it is hypothesized that the amount of buckling and flow that takes place will be influenced by the stiffnesses and thicknesses of the surface layers. One parameter that combines both these elements is the plate stiffness of the surface layers. Since a correlation with this parameter and friction was also found , the following relationships for K and k are proposed, K=K’([email protected]
where @ is the plate stiffness and G0 is the stiffness which is required to eliminate the occurrence of buckling. K’ and k’ are coefficients related to the substrate material. For the card-edge system referred to earlier, it was found that buckling was eliminated with combined surface layer thicknesses of 15 pm. This implies that for these materials and a Cu substrate, Q0 is approximately 0.02 N mm. By examination of eqn. (25) it can be seen that it can be put into the same form as the expressions for the other wear mechanisms, viz. h, = K,P’.6R -2.2L0.2 where K, is dependent the environment.
with wear data
Because of the large range of cycles used in establishing the empirical wear relationship associated with this mechanism, the observed exponent for the number of cycles is used to estimate n, i.e.
h = 0.0028K”.2(1 + /L)~Z”.~Lo,2 7 3~0.8,.1.44r 1.4
(29) on materials and, through
In Table 2 the exponents for the load, Y, and number of cycles, L, in the wear relationship for each of the mechanisms is summarized. Comparing the exponents for L in Table 2 for adhesive and abrasive wear with the empirical value of eqns. (10) and (11) for the cardedge contact, it can be seen that there is a considerable difference. On this basis, it can be concluded that neither of these mechanisms is significant for this particular card-edge contact system. On a similar basis, it can also be concluded that the constant energy mode for surface fatigue does not apply either. However, this comparison indicates approximate agreement for the exponent of L with both the subsurface mechanism and the variable energy mode for surface fatigue. Therefore, both are potentially significant in the wear. For those situations in which the subsurface mechanism is also eliminated, i.e. those associated with eqn. (ll), all Ci values would be zero except that for the energy mode for surface fatigue. Equation (5) results in the following relationship, /, =m - 1.6f,O.8LO.27 (30) which agrees well with the empirical equation, eqn. (11). For the more general situation of this card-edge contact system, i.e. those conditions described by eqn. (lo), only the subsurface mechanism and the variable energy mode for surface fatigue would have non-zero values for C,, and eqn. (5) can be written as: h = (Ks,,2P2.4 + K~,~ZP0~8L0~07)I(K~~bP0~8 + Kfat)Lo.’
where Ksub and K,, are coefficients associated with those two mechanisms, and which are functions of the materials and geometries involved. Since the exponent of L within the brackets is so small, its effect can be neglected and eqn. (31) can be approximated by h = (Ksu;P2.4 + Kfa,2Po~8)I(Ks,,Po~8+ Kfal)Lo.2
The load dependency predicted by this equation is more complex than the simple exponential relationship TABLE surface
for a sphere
Mechanism Adhesive wear Abrasive wear Surface fatigue wear Constant energy mode Variable energy mode Subsurface deformation h =depth P = load;
of wear; K=wear coefficient L = number of cycles of sliding.
h = Kp0.67L0.67 h =KpO.q,O.67 h = Kp550.67 h ~Kpq,O.*7 h = Kp’ 6LO.2 (material
R. G. Bayer / Sliding wear in electrical contacts
of eqn. (lo), which was found over a limited range of load. However, experiments with the same contact system over a much wider range of loads, i.e. from 50 to 1200 g, indicated a more complex relationship, which was found to be in good agreement with the theoretical one. In these experiments, discussed in ref. 5, wear scar depth was measured after 50 cycles. At the lower loads there was little evidence of the subsurface mechanism; however, at the higher loads, there was significant evidence of both the subsurface mechanism and general thinning of the surface layers. The wear depths measured in these tests are shown as points in Figs. 4 and 5. For a fixed number of cycles, eqn. (32) can be simplified to the following form h = (CV’.” + bzP8)/(cP0.* + b)
where h:& = cP1.6
h;. = bP”.’
h* is wear depth associated with the two mechanisms after 50 cycles. In Figs. 4 and 5 the agreement between 1.6 c = .00021
Fig. 4. Wear depth as a function of load for the card-edge contact under lubricated conditions. Amplitude of sliding was 3 mm at 10 cycles min-‘. The metallurgy on the card was 6 pm Au over 3.5 pm Ni. The lubricant was a thin coating of a polyoester. The legend shows the values used with eqn. (33) to obtain the curve. 1 D ;
Fig. 5. Wear depth as a function of load for the card-edge contact under unlubricated conditions. Amplitude of sliding was 3 mm at 10 cycles min-r. The metallurgy on the card was 6 pm Au over 3.5 pm Ni. The legend shows the values used with eqn. (33) to obtain the curve.
eqn. (33), represented by the curve, and the wear data, represented by the points, is shown for two cases. In Fig. 4 the data is for a lubricated system; Fig. 5, for an unlubricated system. The values for b and c shown in these figures were determined by a numerical iteration technique, fitting eqn. (33) to the data. It can be seen that the values of the coefficients for the lubricated and unlubricated conditions differ by approximately a factor of two. This is in approximate agreement with what the model would predict for a change in the coefficient of friction between these two conditions. The coefficient of friction for the lubricated system was found to be typically in the 0.1 to 0.25 range; unlubricated, 0.4 to 0.5 was typical [5, lo]. For surface fatigue, the model indicates that the wear depth should be proportional to (~/0.31)~.~ for p greater than 0.031 and independent of p for lower values. This predicts an increase of between 1.8 and 3 times for the unlubricated condition. For the subsurface mechanism, the model indicates that the wear depth should be proportional to (1 + p)3 and results in an increase of 1.4 to 2.5 times. These values for c and b can also be used to evaluate the theoretical effect of stiffness given by eqn. (27). The plate stiffness, @, for the metallurgy used in these load tests was 0.008 N mm. While the range of plating thicknesses involved in this study was large, the nominal plating thicknesses were 2.5-3 pm for both the Ni and the Au. The corresponding range of @was from 0.001 to 0.003 N mm. For the lower value of @ and the values for b and c shown in Figs. 4 and 5, eqns. (27) and (33) indicate approximately a 10% increase in wear depth. This agrees well with the data given in ref. 5, which indicate less than a 10% increase in wear depth for nominal thicknesses as compared with that for thicknesses which eliminate the subsurface mechanism.
6. Discussion While not providing direct proof of the validity of the model, practical engineering experience tends to provide support. This model has been used in the evaluation and design of several contact systems. General agreement with the predicted trends for such elements as the amount of usage, lubrication, load, geometry, and substrate properties has been found in those studies. In these applications the considerations were not limited to the subsurface mechanism and the variable energy mode for surface fatigue. All the potential mechanisms needed to be considered, since studies have shown that these other mechanisms or modes can predominate in other systems [l, 21. Because of the general nature of the assumptions involved with this model and the success that has been
R. G. Bayer I Sliding
obtained with it, it is suggested that this general model may be applicable to more general wear situations. It is proposed that eqns. (1) and (5) provide a general way of treating the simultaneous occurrence of more than one mechanism in a wear situation. The concern with wear in electrical contacts stems from the adverse effects of corrosion on contact resistance. Corrosion can occur when base metal sublayers are exposed as a result of wear. For the general model, that is proposed in this paper, this occurs when PO - (h - kudl
(h-h,,,) is the wear depth resulting from all the mechanisms with the exception of the subsurface mechanism, which is hsub. It is effectively the amount of thinning of the surface layer that results from the surface wear mechanism.
7. Summary A model has been proposed for the simultaneous occurrence of multiple wear mechanisms. In addition, a mathematical model has been developed for a subsurface wear mechanism, which can occur with layered
wear in electrical
surfaces. Both of these models were compared with the observed wear behavior of card-edge electrical contact and good agreement was found. It was proposed that, because of the general nature of the model for simultaneous wear, it could be applied to other wear situations involving multiple mechanisms. References M. Antler, Znsulation/Circuits, Jan. (1980) 15-19. M. Braunovic, N. S. McIntyre, W. J. Chauvin and I. Aitcheson, IEEE
R. G. Bayer, W. C. Clinton
and J. Sirico, Wear, 7 (1964)
R. G. Bayer and J. Sirico, IBM J. Rex Dev., 15 (2) (1971) 103-107.
R. G. Bayer, E. Hsue Materials
and J. Turner,
Proc. Znt. Wear of
(1991) 48w96. Friction and Wear of Materials,
E. Rabinowicz, Wiley, New York, 1966, pp. 125-198. R. G. Bayer, Wear, I1 (1968) 319-332. R. G. Bayer and T. C. Ku, Handbook of Analytical Procedures for Wear, Plenum, New York, 1964. P. A. Engel, R. G. Bayer and E. Hsue, Hardness, Friction, and Wear of Electrical Contacts, submitted to 1993 Znt. Wear of Materials Conf 10 E. Hsue and R. Bayer, Proc. 34th IEEE Holm Conf Contacts, 1988.