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Effects of adhesive junctions and metal transfer on the mechanism of fluctuations in contact resistance
Wear, 38 (1976) 87 - 100 @ Elsevier Sequoia &A., Lausanne - Printed in the Netherlands
87
EFFECTS OF ADHESIVE JUNCTIONS AND METAL TRANSFER ON THE MECHANISM OF FLUCTUATIONS IN CONTACT RESISTANCE
T. TAMAI and K. TSUCHIYA Faculty of Science and Technology,
Sophia University, Tokyo (Japan)
(Received April 1, 1975; in final form October 2, 1975)
Summary Fluctuation in contact resistance during sliding contact, an important indication of the contact interface condition, has been analyzed from the viewpoint of adhesive wear. An equation which is able to estimate the fluctuations in contact resistance was deduced, as the adhesive junction is considered to be the main electric current path. It was shown that fluctuations in contact resistance caused by adhesive wear can be estimated in terms of (W/P)-” and the properties of the contaminant films. Moreover, in metal transfer, which is important in dissimilar metal combinations, it was found that the nature of the transfer is determined by W,,/Pand hardness. In the combination of metals with a high value of W,,/Pand a large difference in hardness, a smooth stable sliding condition was obtained by transfer of the soft metal.
1. Introduction Sliding electrical contacts are extensively used in machines and play an important role but the theoretical analysis of their performance has not been satisfactorily carried out. The basic phenomena of the contacts involve the wear of metal surfaces, contact resistance and voltage or current fluctuations due to irregular fluctuations in contact resistance, i.e. electrical noise. Mechanical, physicochemical and electrical phenomena take place concurrently; thus the contact phenomena are complicated and have not been analyzed in detail. The sliding of the metal surfaces shown by Bowden and Tabor [l] and Holm et al. [ 21 to be influenced essentially by adhesion phenomena caused by interatomic forces is now an established theory. A method of estimating the size of the adhesive junction of the contact interface has recently been proposed by Rabinowicz [3,4]. The phenomenon of adhesive wear has been fairly well explained by this quantitative method. Therefore, when considering sliding contacts, adhesion phenomena should be considered first. In the present paper, the performances of sliding contacts in the electric circuit are discussed from the viewpoint of adhesive wear. The fluctuation of
88
contact resistance, the cause of the noise voltage, which is an important aspect of sliding contact was studied. An equation showing the noise voltage due to the fluctuations of contact resistance was deduced from the concept of an adhesive junction, which is considered to be the main electric current path. With this equation, the noise voltage generated in the sliding contacts of similar metal combinations was estimated. Based on this the fluctuation in contact resistance generated by dissimilar metal combinations was developed from the standpoint of a metal transfer phenomenon. A method of reducing the fluctuations in contact resistance is presented. 2. Mechanism
of fluctuation
of contact
resistance
due to adhesive wear
Wear arising from two metal surfaces in sliding contact is mainly adhesive. Therefore, investigations of the mechanism of sliding contacts must be focussed on adhesion. A metal surface may be considered as a boundary compared with the metal inside, as the atoms in the upper space separated by the surface itself have been removed. The field of attraction among the constituent atoms is greater on the surface and the energy state higher than that of the bulk material. This excess energy per unit area is defined as the surface energy. If two clean metal surfaces are made to contact and atoms in these surfaces become close enough to attract one another, the contact interface is unified. This phenomenon is different from welding, for example, because of the diffusion of atoms and is designated adhesion; it is a main cause of friction between sliding metals. The effect of the surface energy in the contact interface may be described according to Rabinowicz’s theory using the model shown in Fig. 1. The adhesion energy El between the contact interface is given by
where a is the diameter of the contact area, which is assumed to be circular, and IV,, is the surface energy in the contact area. If the surface energy exists over the whole contact area, this area becomes an adhesive junction. As the adhering surface must bear the normal load, the deformation energy is stored in the bulk metal below the adhering surface. This energy E2 is given by
where the vertical strain is assumed to be equal to the residual stress in the bulk metal, Y is Young’s modulus and u is the residual stress. This is the situation under static contact conditions deduced by Rabinowicz. However, in the sliding process one surface slides over the other and if the binding strength of the adhesive area is greater than the strength of the bulk metal the bulk metal will be sheared. For El = E2, metal particles will be torn off the bulk metal. Therefore,
89
Fig. 1. Idealized representation
of Rabinowicz’s model for an adhesive junction.
Fig. 2. Schematic illustration of an interface of a sliding contact.
1 u2 77a3 ---= 2 Y 12 Simplification be considered
rra2 2--
(3)
%b
of eqn. (3) gives the diameter of the adhesion to be the adhesive area due to sliding, i.e.
area which can
a = 12 W&Y/o2
(4)
where o/Y = 3 X 10p3. If P represents so that the adhesion area is given by a = 12 x lo3 w&,/P
the hardness,
u = P/3 holds generally, (5,)
The adhesive area can be estimated directly from the surface energy and the hardness. In practice adhesion does not take place as suggested by Rabinowicz (Fig. 1) but as shown in Fig. 2. Adhesive areas are scattered in the true contact area which is determined by Hertzian deformation theory. Although the effect of load must be taken into account in the Hertzian theory, the true contact area is larger than the adhesive area given by eqn. (5) at a load greater than the critical value. If surface conditions such as the shape of the surface, the surface roughness and contaminant films which affect the contact interface are constant, the condition of the true contact area shown in Fig. 2 will be unchanged during sliding, and the number of adhesive areas will be constant. Thus, as the true contact surface moves along in the sliding direction, the process of repeated generation and annihilation of adhesive areas maintains a constant number of adhesive areas. In the sliding process, most of the adhesive areas are main electric current paths. When current flows in the sliding contact, fluctuations of the contact resistance in adhesive areas result in fluctuations in the voltage drop or fluctuations in the current. The contact resistance R is generally given by the sum of the constriction resistance R, and the film resistance RI [2] :
R=R,+Rf=%?++!& 4rn
7rr2
(6)
where p1 and p2 are the specific resistances of the contact metals, pf is the resistivity of the contaminant film, 6 is the film thickness, r the radius of the
90
contact area and n the number of areas. To determine fluctuations resistance, eqn. (6) was differentiated with respect to the diameter
in contact a:
dR/da = C, at2 + fi ae3
(7)
where dR/da is the fluctuation of the contact resistance, C, = -(pl + p2)/n and fr = -8p,6/nn. ‘From this equation, it is found that the constriction resistance is related to fluctuations in contact resistance through the term ae2, and the film resistance is related through the term a- 3. For the process of transforming the adhesive area into the contacting area separated by the film, eqn. (5) can be applied not only to the first term of eqn. (7) but also to the second term. Substituting eqn. (5) into eqn. (7), the following equation is obtained: ;;
-C2
(I$?)
-2+f2
(%) -3
(8)
where C2 = (12 X 103)-2 C, and f2 = (12 X 103)-3 fi. Moreover, for the condition of flow of electric current I, the following equation holds: dV=kIdR
(9)
where dV is the variation of the voltage drop across the contacts, dR is the variation of the contact resistance due to sliding motion, and k is a constant which involves the effect of current. In this study, to avoid the mechanism of noise generation being complicated by electric current flow, the current is assumed to be small enough to have no influence on the properties of the contact interface. Substituting eqn. (8) into eqn. (9), the following noise voltage equation is obtained: -2
.- 3
where dV/da is the fluctuation of the voltage due to the fluctuations of the adhesive area, i.e. the noise voltage. Therefore, for practical applications, once the contact metal is determined, fluctuations of the contact resistance can be estimated for the sliding of clean surfaces, i.e. when the first term on the right-hand side of eqn. (10) is dominant. Thus metals with larger values of W,,/P are expected to have a lower level of noise voltage. Even with a clean surface, the constriction resistance is dependent on the specific resistance p as well as the contact area, as C2 in eqn. (10) is related to the specific resistance p. However, variation of the specific resistance of various metals is much smaller than that of the factor determining the adhesive area, as seen from Table 1. Therefore fluctuations of contact resistance or noise voltage can be estimated from these factors. On the other hand, for the effect of contaminant oxide or sulfide films on fluctuations of the contact resistance, the second term on the righthand side of eqn. (8) should be considered, and pi6 is more effective than the contact area [ 51. The behaviour of films which affects the phenomena during
f.c.c.
8.2
556
0.9
f.c.c.
21
110
4.0
450
Pb
b.c.t.
12
110
5.3
570
Sn
f.c.c. face-centered cubic; b.c.t. body-centered
Crystalline
(X
Resistivity p lO+ cm)
(X
W/P lo-‘cm)
Hardnes_s2P (kg mm )
Surface energy 500 r[19] (erg cme2)
In
h.c.p.
f.c.c.
2.3
19
58
1120
Au
f.c.c.
1.75
14
80
1100
Cu
f.c.c.
1.65
11
80
900
Ag
f.c.c.
11
18
100
1800
Pt
210
100
f.c.c.
10.8
cubic.
f.c.c.
8
8.1
1700
1000
10
Ni
Pd
tetragonal; h.c.p. hexagonal close-packed; b.c.c. body-centered
f.c.c.
6.1
20
33 2.9
38
750
900 27
Zn
AI
Some material properties for applied specimens
TABLE 1
b.c.c.
5.03
9.3
240
2250
MO
b.c.c.
5.5
5.3
435
2300
W
92
1.2 -
i8
1:
(al
. .
0
..dwt
,w
I 10-z
I
conductwe
10-1
soft
metal
_iz; 1
100
Load (g)
IO’
102 (W/P)
x 10-81cm)
Fig. 3. Typical relationships between the coefficient of friction, electrical conductivity load.
and
Fig. 4. Noise voltage due to fluctuations in contact resistance as a function of the W/P ratio.
sliding is influenced by the properties of the bulk metal [6], as shown by three characteristic curves of the variation of the coefficient of friction and the electrical conductivity with load in Fig. 3 [7, 81. For low hardness metals, the film is easily broken by sliding motion and the metals contact each other directly. When the hardness of the bulk metal is high, the film is more likely to lie in the contact interface. With a low hardness metal (Fig. 3(a)) even under a light load the film is broken and torn off by deformation and shearing of the bulk metal. Consequently, metallic contact occurs. Thus conductivity is high but the coefficient of friction is high as adhesion occurs easily [91.Metals of low hardness such as In, Sn, Pb, Al and Zn are examples of this. Figure 3(b) shows characteristics of metals of medium hardness. The film is not broken under a light load and so a high electrical resistance is obtained. However, the coefficient of friction is small since the film acts as a lubricant. Under heavy load, the film is broken [ 10, 111 and characteristics similar to Fig. 3(a) are obtained; Cu, Ag, Pt and Ni are examples. Figure 3(c) is the characteristic curve for high hardness metals which form a tenacious film. For these metals, the film always exists under the load range shown in Fig. 3 and so a high electrical resistance is obtained. The coefficient of friction is small due to the lubricating effect of the film. This is noticeable with Cr, MO and W. From the relationship W/P and the facts presented in Fig. 3, metals with a large W/P are found to be of low hardness (Table 1). A large W/P corresponds to the characteristics shown in Fig. 3(a) where metallic contact is prevalent. In contrast, a small W/P indicates that the effect of the film is considerable (Fig. 3(c)). In this case, firstly the surface energy does not affect the adhesion of metals and decreases with film growth. Secondly, the resistivity of the film, which is determined by pr6, is so effective that the
93
second term on the right-hand side of eqn. (8) is the main factor in the fluctuations in contact resistance. An intermediate characteristic such as that shown in Fig. ‘3(b) also exists. It was earlier established [ 121 that a certain relationship exists between noise voltage due to the fluctuations in contact resistance and W,,/P with similar metal combinations, as shown in Fig. 4. This relationship is explained by the generation mechanism of fluctuations in contact resistance described above. Based on eqn. (lo), the relationship between the adhesive area, i.e. W/P, and the noise voltage V, can be expressed as V, = a aCp Substituting the method
(11)
the measured values shown in Fig. 4 into eqn. (11) and applying of least squares, the coefficients (Yand /I can be determined as
v, = 1.62 X lo-’
(W,,/P)-577
(12)
By applying eqn. (10) to the relationship in Fig. 4, the term ( W/P)-2 is found to be significant for metals with a large W/P and the terms ( W/P)-3 and pf6 for metals with a small W/P. To summarize, it is concluded that the generation mechanism of fluctuations in contact resistance due to adhesive wear, i.e. the noise voltage, can be quantitatively explained in terms of W/P. For metals with a large W/P, the electric current paths are large and the shearing strength of the adhesive area is weak. Thus the metals can slide smoothly over each other, i.e. fluctuations in contact resistance or the noise voltage can be reduced. 3. Effect of metal transfer in the sliding contact of dissimilar metal combinations on fluctuations in contact resistance When similar metals are in sliding contact, the contact area of the rider always takes part in sliding against the slider. Therefore the difference in working, i.e. hardening, appears in the contact surfaces and a prow grows on the rider surface by metal transfer [ 13 - 151. For the combination of dissimilar metals, considerable transfer takes place [ 161 which influences fluctuations in contact resistance. From the standpoint of the contact mechanism considered in the previous section, metal transfer phenomena occur. The transfer is dependent both on the binding strength of the adhesive area and on the shearing strength of the bulk metals. The amount of transferred metal is given by eqn. (5) and the direction of transfer is determined by the shearing strength of both bulk metals. For metals with a large W/P, the volume of transferred metal is larger, and the transfer is from the metal with a low shearing strength to the metal with a high shearing strength. From this fact and eqn. (8), it is clear that, in dissimilar metal combinations the interfaces of which have large values of W,JP and large differences in shearing strength, considerable metal transfer takes place with the initial sliding motion, and the sliding interface becomes that of similar metals with a low shearing strength. Thus, fluctua-
o Sn sltder
Fig. 5. Relationship
between
.
Zn shder
n
NI
slider
WJP and WaJPson.
tions in contact resistance are determined by the W&/Pof the transferred metal. For a combination of similar metals, W,, is given by 27, where y is,the surface energy of one of the surfaces. However, for dissimilar metal combinations W,,is dependent on the properties of both metal surfaces. The surface energy W,, is generally given by [ 17 J w,b
=
Ya
+
?b
-
Tab
(13)
where y. is the surface energy of one of the metals, Tb is the surface energy of the other metal and Tab is the energy which opposes adhesion. For a combination of similar materials Tab = 0; for’a combination of materials whose physical properties are compatible (a 2 6), Yob = (l/4)(% + Yb); and for a combination of incompatible materials (a # b), Yab = (l/2)(7, f 7s). In metals, however, the value of Tab is unclear. From the crystal structure, the metals shown in Table 1 are classified into face-centered cubic, body-centered cubic, hexagonal close-packed and tetragonal structures. In this classification, Ni, Zn and Sn, for example, present different physical properties. &&,,, were examined for combinations of these metals and the others in Table 1. Figure 5 shows the relationship between W&/P and W-/P.This relationship varies with metal combination. The combination of Ni and other metals shows a tendency similar to that of similar metal combinations, i.e. with regard to W&/P r W,,/P. The Zn combinations show higher values of W&/Pdue to the effect of Zn on metals with a low WJP. For the Sn combinations, the properties of Sn dominate, i.e. Sn may be widely transferred to the mating metal. In Sn combinations, therefore, the contact interface becomes Sn on Sn during sliding. Consequently, a low level in fluctuations of contact resistance will be generated. Accordingly, with dissimilar metal combinations of different properties, the type of combination depends to a great extent on the value of w,b/P which affects the level of fluctuations in contact resistance.
95
Rider
5mA Current Slidmg
arm
out
dwection
Fig. 6. (a) Diagram of the circuit for measuring the noise voltage due to fluctuations in contact resistance. (b) Arrangement of test specimens.
3.1. Experimental To examine the characteristics of combinations of dissimilar metals, combinations of Ni, Zn and Sn and other simple metals shown in Table 1 were prepared as specimens. The sliding device described elsewhere [6, 121 was used, in which the slider reciprocates linearly against the rider. The sliding stroke was 50 mm and the sliding velocity changed sinusoidally during one cycle. The contact ’ load was applied by a spring at the opposite end of the arm to which the rider specimen was attached. Fluctuations in contact resistance were obtained directly from noise voltage measurement under constant current conditions. The noise voltage was measured according to MIL specifications [ 181. The experimental set-up is shown schematically in Fig. 6. Ni, Zn and Sn were used as sliders, and the other metals shown in Table 1 were used as riders. They moved relative to one another with their surfaces in contact, as shown in Fig. 6. The rider specimen measured 5 X 5 X 1 mm and the slider specimen measured 10 X 80 X 1 mm. The surface of each specimen was polished and ultrasonically cleaned. The measuring conditions consisted of a load of 20 g, a velocity of 1 Hz and a current of 5 mA. Under these experimental conditions, changes in the noise voltage with sliding time were measured. Metal transfer and wear of the surfaces were also observed by optical methods. 3.2. Results and discussion Some typical examples of changes in noise voltage with sliding time for Ni, Zn and Sn sliders are shown in Fig. 7. Low noise voltage in the steady state, which indicates no influence of the wear particle, is shown plotted against W,,/P in Fig. 8 for each slider, and these relationships are compared with those (eqn. (12)) of similar metal combinations. As seen from Fig. 8(a), characteristics for combinations of a Ni slider and other metal riders are similar to that’of eqn. (12). In comparison, Zn slider combinations (Fig. 8(b)) have a noise level lower by approximately one order of magnitude due to the
96
10
10) t
Rider
.
Aq
o
Pd
I
100
10-l
10“
10' 100 Slldmgtune lmln)
lo2
I
I
102 10’ Slldmgttme (mm)
10'
10)
Fig. 7. Change in noise voltage us. sliding time for dissimilar metal combinations.
transfer of Zn. With a Sn slider, Sn transferred to the rider surface and the characteristics shown in Fig. 8(c) are those of Sn on Sn. Thus, the low noise voltage level of combinations of Sn and other metals are similar to that of Sn on Sn (Fig. 4). Observation of the sliding surface with an optical microscope showed that metal transfer is dependent on the properties of the metal combinations. For the combination of a Ni slider and other metal riders, except for MO and
I
I
I
0 W
la.)
Ni slider
Fig. 8. Noise voltage as a function of W/P ratio.
W, the Ni surface was dotted with islands of transferred metal. Oxidized blackened wear particles were accumulated around the islands. These greatly affected fluctuations in contact resistance. With a Zn slider, transfer to the rider surface extended over a wide area. With a Sn slider, the surface of the Sn was greatly worn and a considerable amount of Sn was transferred to the rider surface. Consequently the sliding interface between a Sn slider and another metal became Sn on Sn. Some typical examples of transferred surface are shown in Fig. 9. Ag on Ni and Au on Ni showed a low noise level initially but as sliding progressed the noise level increased, as shown in Fig. 7(a). This phenomenon’may be explained as follows. During initial sliding, Ag and Au were transferred to the Ni surface as islands. Thus the contact resistance became stable because of similar noble metal contacts. With repeated sliding, however, oxidized wear
98
*
If)“’ Fig. 9. Optical micrographs of sliding surfaces showing the presence of transferred metal on the wear track of a hard metal: (a) Ag on Ni, Ni surface; (b) Au on Ni, Ni surface; (c) Won Zn, W surface; {d) MO on Zn, MO surface; (e) Au on Sn, Au surface; (f) MO on Sn, MO surface.
particles of Ni were accumulated around the islands of the transferred noble metal as shown in Figs. 9(a) and 9(b). With Pb on Ni, a considerable amount of soft Pb was transferred. However, wear particles accumulated around the islands of transferred Pb, thus in~u~ncing fluctuations in contact resistance. On the other hand, for W on Ni the difference in shearing strength, i.e.
99
the hardness of these metals, is opposite
to that of the former combinations. Therefore, Ni was transferred to the W surface. For MO on Ni, characteristic MO wear particles accumulated, which affected the noise voltage. A similar situation was found with the MO on Zn combination. With Zn slider combinations, such as Ag on Zn and Pd on Zn (Fig. 7), the noise level decreased as sliding progressed. On Ag and Pd rider surfaces a considerable amount of transferred Zn was found. This Zn affects the low noise level characteristic. Moreover, for W on Zn and Ni on Zn combinations, a steady noise level of medium value was maintained; Zn was transferred in layers to Ni or W surfaces as shown in Fig. 9(c). For the MO on Zn combination, MO particles similar to those found with the MO on Ni combination were transferred and pressed together as shown in Fig. 9(d), and so a high noise level was generated similar to that with MO on Ni. With a Sn slider, Sn is always transferred to the rider surface of.other metals because of its high value of U&,/l&. This state is clearly shown on the sliding surfaces. For all metal combinations the sliding surface of Sn always wore, and transferred Sn was found on the rider surfaces as shown in Figs. 9(e) and (f), to give Sn sliding on Sn. From the results and observations, metal transfer behaviour correlated with theoretical estimates in terms of W/P. 4. Conclusions Fluctuation phenomena in contact resistance in sliding contact, i.e. noise voltage, were studied in conjunction with adhesive wear. Fluctuations in contact resistance caused by changes in the electric current path, considered to be adhesive junctions, were estimated in terms of surface energy. This method was developed for dissimilar metal combinations. It was established that fluctuation in contact resistance, which is an important external sign of the condition of a contact interface under sliding, can be estimated theoretically by means of W/P. In conclusion, for metals with a high value of W/P fluctuation in contact resistance is dependent on the term ( W/P)-2, resulting in a stable low level. For metals with a low value of W/P,contact resistance is dependent on the term ( WPe3 and the nature of contaminant films. In dissimilar metal combinations, by selection of a metal combination with a large value of W,JP,a smooth sliding condition due to metal transfer is obtained. If surface energy is studied in more detail, properties of more practical sliding contacts such as those of alloys may be evaluated by the method derived in the present paper. This may be a means of improving the performance of sliding contacts. Acknowledgments The authors wish to thank Hattori part of this work.
Hokokai
for a research
grant for
100
References 1 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part I, Clarendon Press, Oxford, 1954. 2 R. Holm, Electric Contacts Handbook, Springer, Berlin, 1958. 3 E. Rabinowicz, Wear, 7 (1964) 9. 4 E. Rabinowicz, J. Appl. Phys., 32 (1961) 1440. 5 T. Tamai and K. Tsuchiya, Trans. Inst. Elec. Eng. Jpn, 93-A (1973) 237. 6 K. Tsuchiya and T. Tamai, Wear, 19 (1972) 245. 7 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 8 R. W. Wilson, Proc. Phys. Sot. (London), Sect. B, 68 (1955) 625. 9 R. T. Spurr, Wear, 7 (1964) 551. 10 W. Hirst and J. K. Lancaster, J. Appl. Phys., 27 (1956) 1057. 11 M. Cocks, Proc. Phys. Sot. (London), Sect. B, 67 (1964) 238. 12 K. Tsuchiya and T. Tamai, Wear, 16 (1970) 337. 13 M. Antler, Wear, 7 (1964) 181. 14 M. Antler, ASLE Trans., 5 (1962) 297. 15 M. Antler, ASLE Trans., 13 (1970) 79. 16 E. Rabinowicz and D. Tabor, Proc. R. Sot. London, Ser. A, 208 (1951) 455. 17 D. McLean, Grain Boundaries in Metals, Clarendon Press, Oxford, 1957. 18 U.S. Military Standard, MIL-R-12934, 1960. 19 E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965.
87
EFFECTS OF ADHESIVE JUNCTIONS AND METAL TRANSFER ON THE MECHANISM OF FLUCTUATIONS IN CONTACT RESISTANCE
T. TAMAI and K. TSUCHIYA Faculty of Science and Technology,
Sophia University, Tokyo (Japan)
(Received April 1, 1975; in final form October 2, 1975)
Summary Fluctuation in contact resistance during sliding contact, an important indication of the contact interface condition, has been analyzed from the viewpoint of adhesive wear. An equation which is able to estimate the fluctuations in contact resistance was deduced, as the adhesive junction is considered to be the main electric current path. It was shown that fluctuations in contact resistance caused by adhesive wear can be estimated in terms of (W/P)-” and the properties of the contaminant films. Moreover, in metal transfer, which is important in dissimilar metal combinations, it was found that the nature of the transfer is determined by W,,/Pand hardness. In the combination of metals with a high value of W,,/Pand a large difference in hardness, a smooth stable sliding condition was obtained by transfer of the soft metal.
1. Introduction Sliding electrical contacts are extensively used in machines and play an important role but the theoretical analysis of their performance has not been satisfactorily carried out. The basic phenomena of the contacts involve the wear of metal surfaces, contact resistance and voltage or current fluctuations due to irregular fluctuations in contact resistance, i.e. electrical noise. Mechanical, physicochemical and electrical phenomena take place concurrently; thus the contact phenomena are complicated and have not been analyzed in detail. The sliding of the metal surfaces shown by Bowden and Tabor [l] and Holm et al. [ 21 to be influenced essentially by adhesion phenomena caused by interatomic forces is now an established theory. A method of estimating the size of the adhesive junction of the contact interface has recently been proposed by Rabinowicz [3,4]. The phenomenon of adhesive wear has been fairly well explained by this quantitative method. Therefore, when considering sliding contacts, adhesion phenomena should be considered first. In the present paper, the performances of sliding contacts in the electric circuit are discussed from the viewpoint of adhesive wear. The fluctuation of
88
contact resistance, the cause of the noise voltage, which is an important aspect of sliding contact was studied. An equation showing the noise voltage due to the fluctuations of contact resistance was deduced from the concept of an adhesive junction, which is considered to be the main electric current path. With this equation, the noise voltage generated in the sliding contacts of similar metal combinations was estimated. Based on this the fluctuation in contact resistance generated by dissimilar metal combinations was developed from the standpoint of a metal transfer phenomenon. A method of reducing the fluctuations in contact resistance is presented. 2. Mechanism
of fluctuation
of contact
resistance
due to adhesive wear
Wear arising from two metal surfaces in sliding contact is mainly adhesive. Therefore, investigations of the mechanism of sliding contacts must be focussed on adhesion. A metal surface may be considered as a boundary compared with the metal inside, as the atoms in the upper space separated by the surface itself have been removed. The field of attraction among the constituent atoms is greater on the surface and the energy state higher than that of the bulk material. This excess energy per unit area is defined as the surface energy. If two clean metal surfaces are made to contact and atoms in these surfaces become close enough to attract one another, the contact interface is unified. This phenomenon is different from welding, for example, because of the diffusion of atoms and is designated adhesion; it is a main cause of friction between sliding metals. The effect of the surface energy in the contact interface may be described according to Rabinowicz’s theory using the model shown in Fig. 1. The adhesion energy El between the contact interface is given by
where a is the diameter of the contact area, which is assumed to be circular, and IV,, is the surface energy in the contact area. If the surface energy exists over the whole contact area, this area becomes an adhesive junction. As the adhering surface must bear the normal load, the deformation energy is stored in the bulk metal below the adhering surface. This energy E2 is given by
where the vertical strain is assumed to be equal to the residual stress in the bulk metal, Y is Young’s modulus and u is the residual stress. This is the situation under static contact conditions deduced by Rabinowicz. However, in the sliding process one surface slides over the other and if the binding strength of the adhesive area is greater than the strength of the bulk metal the bulk metal will be sheared. For El = E2, metal particles will be torn off the bulk metal. Therefore,
89
Fig. 1. Idealized representation
of Rabinowicz’s model for an adhesive junction.
Fig. 2. Schematic illustration of an interface of a sliding contact.
1 u2 77a3 ---= 2 Y 12 Simplification be considered
rra2 2--
(3)
%b
of eqn. (3) gives the diameter of the adhesion to be the adhesive area due to sliding, i.e.
area which can
a = 12 W&Y/o2
(4)
where o/Y = 3 X 10p3. If P represents so that the adhesion area is given by a = 12 x lo3 w&,/P
the hardness,
u = P/3 holds generally, (5,)
The adhesive area can be estimated directly from the surface energy and the hardness. In practice adhesion does not take place as suggested by Rabinowicz (Fig. 1) but as shown in Fig. 2. Adhesive areas are scattered in the true contact area which is determined by Hertzian deformation theory. Although the effect of load must be taken into account in the Hertzian theory, the true contact area is larger than the adhesive area given by eqn. (5) at a load greater than the critical value. If surface conditions such as the shape of the surface, the surface roughness and contaminant films which affect the contact interface are constant, the condition of the true contact area shown in Fig. 2 will be unchanged during sliding, and the number of adhesive areas will be constant. Thus, as the true contact surface moves along in the sliding direction, the process of repeated generation and annihilation of adhesive areas maintains a constant number of adhesive areas. In the sliding process, most of the adhesive areas are main electric current paths. When current flows in the sliding contact, fluctuations of the contact resistance in adhesive areas result in fluctuations in the voltage drop or fluctuations in the current. The contact resistance R is generally given by the sum of the constriction resistance R, and the film resistance RI [2] :
R=R,+Rf=%?++!& 4rn
7rr2
(6)
where p1 and p2 are the specific resistances of the contact metals, pf is the resistivity of the contaminant film, 6 is the film thickness, r the radius of the
90
contact area and n the number of areas. To determine fluctuations resistance, eqn. (6) was differentiated with respect to the diameter
in contact a:
dR/da = C, at2 + fi ae3
(7)
where dR/da is the fluctuation of the contact resistance, C, = -(pl + p2)/n and fr = -8p,6/nn. ‘From this equation, it is found that the constriction resistance is related to fluctuations in contact resistance through the term ae2, and the film resistance is related through the term a- 3. For the process of transforming the adhesive area into the contacting area separated by the film, eqn. (5) can be applied not only to the first term of eqn. (7) but also to the second term. Substituting eqn. (5) into eqn. (7), the following equation is obtained: ;;
-C2
(I$?)
-2+f2
(%) -3
(8)
where C2 = (12 X 103)-2 C, and f2 = (12 X 103)-3 fi. Moreover, for the condition of flow of electric current I, the following equation holds: dV=kIdR
(9)
where dV is the variation of the voltage drop across the contacts, dR is the variation of the contact resistance due to sliding motion, and k is a constant which involves the effect of current. In this study, to avoid the mechanism of noise generation being complicated by electric current flow, the current is assumed to be small enough to have no influence on the properties of the contact interface. Substituting eqn. (8) into eqn. (9), the following noise voltage equation is obtained: -2
.- 3
where dV/da is the fluctuation of the voltage due to the fluctuations of the adhesive area, i.e. the noise voltage. Therefore, for practical applications, once the contact metal is determined, fluctuations of the contact resistance can be estimated for the sliding of clean surfaces, i.e. when the first term on the right-hand side of eqn. (10) is dominant. Thus metals with larger values of W,,/P are expected to have a lower level of noise voltage. Even with a clean surface, the constriction resistance is dependent on the specific resistance p as well as the contact area, as C2 in eqn. (10) is related to the specific resistance p. However, variation of the specific resistance of various metals is much smaller than that of the factor determining the adhesive area, as seen from Table 1. Therefore fluctuations of contact resistance or noise voltage can be estimated from these factors. On the other hand, for the effect of contaminant oxide or sulfide films on fluctuations of the contact resistance, the second term on the righthand side of eqn. (8) should be considered, and pi6 is more effective than the contact area [ 51. The behaviour of films which affects the phenomena during
f.c.c.
8.2
556
0.9
f.c.c.
21
110
4.0
450
Pb
b.c.t.
12
110
5.3
570
Sn
f.c.c. face-centered cubic; b.c.t. body-centered
Crystalline
(X
Resistivity p lO+ cm)
(X
W/P lo-‘cm)
Hardnes_s2P (kg mm )
Surface energy 500 r[19] (erg cme2)
In
h.c.p.
f.c.c.
2.3
19
58
1120
Au
f.c.c.
1.75
14
80
1100
Cu
f.c.c.
1.65
11
80
900
Ag
f.c.c.
11
18
100
1800
Pt
210
100
f.c.c.
10.8
cubic.
f.c.c.
8
8.1
1700
1000
10
Ni
Pd
tetragonal; h.c.p. hexagonal close-packed; b.c.c. body-centered
f.c.c.
6.1
20
33 2.9
38
750
900 27
Zn
AI
Some material properties for applied specimens
TABLE 1
b.c.c.
5.03
9.3
240
2250
MO
b.c.c.
5.5
5.3
435
2300
W
92
1.2 -
i8
1:
(al
. .
0
..dwt
,w
I 10-z
I
conductwe
10-1
soft
metal
_iz; 1
100
Load (g)
IO’
102 (W/P)
x 10-81cm)
Fig. 3. Typical relationships between the coefficient of friction, electrical conductivity load.
and
Fig. 4. Noise voltage due to fluctuations in contact resistance as a function of the W/P ratio.
sliding is influenced by the properties of the bulk metal [6], as shown by three characteristic curves of the variation of the coefficient of friction and the electrical conductivity with load in Fig. 3 [7, 81. For low hardness metals, the film is easily broken by sliding motion and the metals contact each other directly. When the hardness of the bulk metal is high, the film is more likely to lie in the contact interface. With a low hardness metal (Fig. 3(a)) even under a light load the film is broken and torn off by deformation and shearing of the bulk metal. Consequently, metallic contact occurs. Thus conductivity is high but the coefficient of friction is high as adhesion occurs easily [91.Metals of low hardness such as In, Sn, Pb, Al and Zn are examples of this. Figure 3(b) shows characteristics of metals of medium hardness. The film is not broken under a light load and so a high electrical resistance is obtained. However, the coefficient of friction is small since the film acts as a lubricant. Under heavy load, the film is broken [ 10, 111 and characteristics similar to Fig. 3(a) are obtained; Cu, Ag, Pt and Ni are examples. Figure 3(c) is the characteristic curve for high hardness metals which form a tenacious film. For these metals, the film always exists under the load range shown in Fig. 3 and so a high electrical resistance is obtained. The coefficient of friction is small due to the lubricating effect of the film. This is noticeable with Cr, MO and W. From the relationship W/P and the facts presented in Fig. 3, metals with a large W/P are found to be of low hardness (Table 1). A large W/P corresponds to the characteristics shown in Fig. 3(a) where metallic contact is prevalent. In contrast, a small W/P indicates that the effect of the film is considerable (Fig. 3(c)). In this case, firstly the surface energy does not affect the adhesion of metals and decreases with film growth. Secondly, the resistivity of the film, which is determined by pr6, is so effective that the
93
second term on the right-hand side of eqn. (8) is the main factor in the fluctuations in contact resistance. An intermediate characteristic such as that shown in Fig. ‘3(b) also exists. It was earlier established [ 121 that a certain relationship exists between noise voltage due to the fluctuations in contact resistance and W,,/P with similar metal combinations, as shown in Fig. 4. This relationship is explained by the generation mechanism of fluctuations in contact resistance described above. Based on eqn. (lo), the relationship between the adhesive area, i.e. W/P, and the noise voltage V, can be expressed as V, = a aCp Substituting the method
(11)
the measured values shown in Fig. 4 into eqn. (11) and applying of least squares, the coefficients (Yand /I can be determined as
v, = 1.62 X lo-’
(W,,/P)-577
(12)
By applying eqn. (10) to the relationship in Fig. 4, the term ( W/P)-2 is found to be significant for metals with a large W/P and the terms ( W/P)-3 and pf6 for metals with a small W/P. To summarize, it is concluded that the generation mechanism of fluctuations in contact resistance due to adhesive wear, i.e. the noise voltage, can be quantitatively explained in terms of W/P. For metals with a large W/P, the electric current paths are large and the shearing strength of the adhesive area is weak. Thus the metals can slide smoothly over each other, i.e. fluctuations in contact resistance or the noise voltage can be reduced. 3. Effect of metal transfer in the sliding contact of dissimilar metal combinations on fluctuations in contact resistance When similar metals are in sliding contact, the contact area of the rider always takes part in sliding against the slider. Therefore the difference in working, i.e. hardening, appears in the contact surfaces and a prow grows on the rider surface by metal transfer [ 13 - 151. For the combination of dissimilar metals, considerable transfer takes place [ 161 which influences fluctuations in contact resistance. From the standpoint of the contact mechanism considered in the previous section, metal transfer phenomena occur. The transfer is dependent both on the binding strength of the adhesive area and on the shearing strength of the bulk metals. The amount of transferred metal is given by eqn. (5) and the direction of transfer is determined by the shearing strength of both bulk metals. For metals with a large W/P, the volume of transferred metal is larger, and the transfer is from the metal with a low shearing strength to the metal with a high shearing strength. From this fact and eqn. (8), it is clear that, in dissimilar metal combinations the interfaces of which have large values of W,JP and large differences in shearing strength, considerable metal transfer takes place with the initial sliding motion, and the sliding interface becomes that of similar metals with a low shearing strength. Thus, fluctua-
o Sn sltder
Fig. 5. Relationship
between
.
Zn shder
n
NI
slider
WJP and WaJPson.
tions in contact resistance are determined by the W&/Pof the transferred metal. For a combination of similar metals, W,, is given by 27, where y is,the surface energy of one of the surfaces. However, for dissimilar metal combinations W,,is dependent on the properties of both metal surfaces. The surface energy W,, is generally given by [ 17 J w,b
=
Ya
+
?b
-
Tab
(13)
where y. is the surface energy of one of the metals, Tb is the surface energy of the other metal and Tab is the energy which opposes adhesion. For a combination of similar materials Tab = 0; for’a combination of materials whose physical properties are compatible (a 2 6), Yob = (l/4)(% + Yb); and for a combination of incompatible materials (a # b), Yab = (l/2)(7, f 7s). In metals, however, the value of Tab is unclear. From the crystal structure, the metals shown in Table 1 are classified into face-centered cubic, body-centered cubic, hexagonal close-packed and tetragonal structures. In this classification, Ni, Zn and Sn, for example, present different physical properties. &&,,, were examined for combinations of these metals and the others in Table 1. Figure 5 shows the relationship between W&/P and W-/P.This relationship varies with metal combination. The combination of Ni and other metals shows a tendency similar to that of similar metal combinations, i.e. with regard to W&/P r W,,/P. The Zn combinations show higher values of W&/Pdue to the effect of Zn on metals with a low WJP. For the Sn combinations, the properties of Sn dominate, i.e. Sn may be widely transferred to the mating metal. In Sn combinations, therefore, the contact interface becomes Sn on Sn during sliding. Consequently, a low level in fluctuations of contact resistance will be generated. Accordingly, with dissimilar metal combinations of different properties, the type of combination depends to a great extent on the value of w,b/P which affects the level of fluctuations in contact resistance.
95
Rider
5mA Current Slidmg
arm
out
dwection
Fig. 6. (a) Diagram of the circuit for measuring the noise voltage due to fluctuations in contact resistance. (b) Arrangement of test specimens.
3.1. Experimental To examine the characteristics of combinations of dissimilar metals, combinations of Ni, Zn and Sn and other simple metals shown in Table 1 were prepared as specimens. The sliding device described elsewhere [6, 121 was used, in which the slider reciprocates linearly against the rider. The sliding stroke was 50 mm and the sliding velocity changed sinusoidally during one cycle. The contact ’ load was applied by a spring at the opposite end of the arm to which the rider specimen was attached. Fluctuations in contact resistance were obtained directly from noise voltage measurement under constant current conditions. The noise voltage was measured according to MIL specifications [ 181. The experimental set-up is shown schematically in Fig. 6. Ni, Zn and Sn were used as sliders, and the other metals shown in Table 1 were used as riders. They moved relative to one another with their surfaces in contact, as shown in Fig. 6. The rider specimen measured 5 X 5 X 1 mm and the slider specimen measured 10 X 80 X 1 mm. The surface of each specimen was polished and ultrasonically cleaned. The measuring conditions consisted of a load of 20 g, a velocity of 1 Hz and a current of 5 mA. Under these experimental conditions, changes in the noise voltage with sliding time were measured. Metal transfer and wear of the surfaces were also observed by optical methods. 3.2. Results and discussion Some typical examples of changes in noise voltage with sliding time for Ni, Zn and Sn sliders are shown in Fig. 7. Low noise voltage in the steady state, which indicates no influence of the wear particle, is shown plotted against W,,/P in Fig. 8 for each slider, and these relationships are compared with those (eqn. (12)) of similar metal combinations. As seen from Fig. 8(a), characteristics for combinations of a Ni slider and other metal riders are similar to that’of eqn. (12). In comparison, Zn slider combinations (Fig. 8(b)) have a noise level lower by approximately one order of magnitude due to the
96
10
10) t
Rider
.
Aq
o
Pd
I
100
10-l
10“
10' 100 Slldmgtune lmln)
lo2
I
I
102 10’ Slldmgttme (mm)
10'
10)
Fig. 7. Change in noise voltage us. sliding time for dissimilar metal combinations.
transfer of Zn. With a Sn slider, Sn transferred to the rider surface and the characteristics shown in Fig. 8(c) are those of Sn on Sn. Thus, the low noise voltage level of combinations of Sn and other metals are similar to that of Sn on Sn (Fig. 4). Observation of the sliding surface with an optical microscope showed that metal transfer is dependent on the properties of the metal combinations. For the combination of a Ni slider and other metal riders, except for MO and
I
I
I
0 W
la.)
Ni slider
Fig. 8. Noise voltage as a function of W/P ratio.
W, the Ni surface was dotted with islands of transferred metal. Oxidized blackened wear particles were accumulated around the islands. These greatly affected fluctuations in contact resistance. With a Zn slider, transfer to the rider surface extended over a wide area. With a Sn slider, the surface of the Sn was greatly worn and a considerable amount of Sn was transferred to the rider surface. Consequently the sliding interface between a Sn slider and another metal became Sn on Sn. Some typical examples of transferred surface are shown in Fig. 9. Ag on Ni and Au on Ni showed a low noise level initially but as sliding progressed the noise level increased, as shown in Fig. 7(a). This phenomenon’may be explained as follows. During initial sliding, Ag and Au were transferred to the Ni surface as islands. Thus the contact resistance became stable because of similar noble metal contacts. With repeated sliding, however, oxidized wear
98
*
If)“’ Fig. 9. Optical micrographs of sliding surfaces showing the presence of transferred metal on the wear track of a hard metal: (a) Ag on Ni, Ni surface; (b) Au on Ni, Ni surface; (c) Won Zn, W surface; {d) MO on Zn, MO surface; (e) Au on Sn, Au surface; (f) MO on Sn, MO surface.
particles of Ni were accumulated around the islands of the transferred noble metal as shown in Figs. 9(a) and 9(b). With Pb on Ni, a considerable amount of soft Pb was transferred. However, wear particles accumulated around the islands of transferred Pb, thus in~u~ncing fluctuations in contact resistance. On the other hand, for W on Ni the difference in shearing strength, i.e.
99
the hardness of these metals, is opposite
to that of the former combinations. Therefore, Ni was transferred to the W surface. For MO on Ni, characteristic MO wear particles accumulated, which affected the noise voltage. A similar situation was found with the MO on Zn combination. With Zn slider combinations, such as Ag on Zn and Pd on Zn (Fig. 7), the noise level decreased as sliding progressed. On Ag and Pd rider surfaces a considerable amount of transferred Zn was found. This Zn affects the low noise level characteristic. Moreover, for W on Zn and Ni on Zn combinations, a steady noise level of medium value was maintained; Zn was transferred in layers to Ni or W surfaces as shown in Fig. 9(c). For the MO on Zn combination, MO particles similar to those found with the MO on Ni combination were transferred and pressed together as shown in Fig. 9(d), and so a high noise level was generated similar to that with MO on Ni. With a Sn slider, Sn is always transferred to the rider surface of.other metals because of its high value of U&,/l&. This state is clearly shown on the sliding surfaces. For all metal combinations the sliding surface of Sn always wore, and transferred Sn was found on the rider surfaces as shown in Figs. 9(e) and (f), to give Sn sliding on Sn. From the results and observations, metal transfer behaviour correlated with theoretical estimates in terms of W/P. 4. Conclusions Fluctuation phenomena in contact resistance in sliding contact, i.e. noise voltage, were studied in conjunction with adhesive wear. Fluctuations in contact resistance caused by changes in the electric current path, considered to be adhesive junctions, were estimated in terms of surface energy. This method was developed for dissimilar metal combinations. It was established that fluctuation in contact resistance, which is an important external sign of the condition of a contact interface under sliding, can be estimated theoretically by means of W/P. In conclusion, for metals with a high value of W/P fluctuation in contact resistance is dependent on the term ( W/P)-2, resulting in a stable low level. For metals with a low value of W/P,contact resistance is dependent on the term ( WPe3 and the nature of contaminant films. In dissimilar metal combinations, by selection of a metal combination with a large value of W,JP,a smooth sliding condition due to metal transfer is obtained. If surface energy is studied in more detail, properties of more practical sliding contacts such as those of alloys may be evaluated by the method derived in the present paper. This may be a means of improving the performance of sliding contacts. Acknowledgments The authors wish to thank Hattori part of this work.
Hokokai
for a research
grant for
100
References 1 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part I, Clarendon Press, Oxford, 1954. 2 R. Holm, Electric Contacts Handbook, Springer, Berlin, 1958. 3 E. Rabinowicz, Wear, 7 (1964) 9. 4 E. Rabinowicz, J. Appl. Phys., 32 (1961) 1440. 5 T. Tamai and K. Tsuchiya, Trans. Inst. Elec. Eng. Jpn, 93-A (1973) 237. 6 K. Tsuchiya and T. Tamai, Wear, 19 (1972) 245. 7 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Part II, Clarendon Press, Oxford, 1964. 8 R. W. Wilson, Proc. Phys. Sot. (London), Sect. B, 68 (1955) 625. 9 R. T. Spurr, Wear, 7 (1964) 551. 10 W. Hirst and J. K. Lancaster, J. Appl. Phys., 27 (1956) 1057. 11 M. Cocks, Proc. Phys. Sot. (London), Sect. B, 67 (1964) 238. 12 K. Tsuchiya and T. Tamai, Wear, 16 (1970) 337. 13 M. Antler, Wear, 7 (1964) 181. 14 M. Antler, ASLE Trans., 5 (1962) 297. 15 M. Antler, ASLE Trans., 13 (1970) 79. 16 E. Rabinowicz and D. Tabor, Proc. R. Sot. London, Ser. A, 208 (1951) 455. 17 D. McLean, Grain Boundaries in Metals, Clarendon Press, Oxford, 1957. 18 U.S. Military Standard, MIL-R-12934, 1960. 19 E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965.