Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
Wear -
431
WEAR EQUATION FOR POLYMERS SLIDING AGAINST METAL SURFACES
S. K. RHEE The Bendix (Received
Corp., Research Laboratories,
Southfield,
Mich. 48075 (U.S.A.)
August 28, 1970)
SUMMARY
An empirical wear equation is proposed for predicting material losses of asbestos-reinforced polymers caused by sliding against metal surfaces. The equation has been tested with four different kinds of friction pairs and found to correlate extremely well with the experimental results. The wear equation is in the form of AW=KFaVbtc, where AW is the weight lost, K the wear factor, F the load, V the velocity, t the time of sliding, and a, b and c one set of parameters. INTRODUCTION
When a polymer or polymer-bonded friction material slides against a metal surface, the friction material wears out by one or a combination of the following wear mechanismsly2: (I) abrasive wear (2) thermal wear (3) adhesion and tearing (4) macroshear (5) fatigue Each of these mechanisms can reasonably be expected to be dependent on the conditions of sliding, i.e. load, speed, and time. If the system does not reach a steady state, but goes through a transient state such as rising temperature due to friction, the relative contribution to the total wear of the individual wear mechanisms may vary with temperature. Thus, predicting the wear of a friction material under these conditions becomes extremely difficult. As a result, a satisfactory universal wear equation does not presently exist. Holm3 found that the total wear of metal friction materials was qualitatively proportional to the load and sliding distance. Lewis4 directly applied his qualitative correlation to predicting the wear of polymer-matrix friction materials, and obtained the following equation : v=KFVt
(1)
where z,= volume lost, F = load, V = sliding velocity, t = time, and K = wear factor (or wear coefficient). When this equation was used to express the wear of Teflon-matrix bearing materials, the wear coefficient was found to vary by a factor of twos. Also, in our Wca+‘,16 (1970) 431-445
laboratory, the above equation was found to be less tllan ~atislactor>~ for c,orrrlatirl;: the lining wear of automotive brakes wit11 the loads, speeds ancl timch, thts tcnl.perature being a function of these three variables. Since the total wear of a polymer-matrix friction material must be a function of the load, speed and time, the following general wear equation
is proposc‘d herein
h~=h’~;al/bte
:
(2)
where AW = weight loss of a friction material, and a, b, c are parameters. This wear equation is tested under various experimental conditions, different kinds of metal surfaces, polymer-matrix friction materials.
and is found to describe
including
satisfactorily
the wear of
were evaluated
for wear by
IblATERIALS
Polymer-bonded
automotive
friction
materials
sliding against two different kinds of metal surfaces: cast iron and chromium. The specific gravities and compositions of the friction materials are given in Table I. The
TABLE CHEMICAL
I1 COMPOSITIONS
OF DRUM
MATERIALS
(Wt. ",)
Drum materials
Cast iron Cast iron ring in chromium copper drum Chromium copper
typical microstructures of these materials are shown in Figs. I and 2. Cast iron and chromium copper drums were used. The chromium copper drums had a friction surface of cast iron I/S in. thick or electroplated hard chromium 0.050 in. thick. The chemical compositions of the drum materials are given in Table II. The chromium copper-cast iron composite drum was manufactured by casting the copper alloy around the cast iron ring. All of the drums were of the standard configuration of SAE J66Ia (II in. id.) (Fig. 3). The microstructure of the cast iron drum and that of the cast iron insert are shown in Figs. 4 and 5 respectively. Wear, 16 (1970) 431-445
POLYMERS
SLIDIKG
AGAINST
METrZL SURFACES
433
Wear,
I6 (1970)
4.3-445
d
435
POLYMERS SLIDING AGAINST METAL SURFACES
Fig. 5. Microstructure (x 500)
of cast iron ring used as the friction surface in a chromium
copper drum.
EQUIPMENT AND PROCEDURE A drag dynamometer designed and built at Bendix Research Laboratories was used (Fig. 6). This dynamometer, which has been described elsewhere by TEITELBAUM et al.5 and also by SPENCER AND SPURGEON~ was modified from a dead-weight loading system to a pneumatic loading system. It is capable of loading up to 225 lb. and can operate in either a constant input or constant output mode at speeds up to 500 r.p.m. It is instrumented for measurement of both dynamic frictional force and drum temperature during the tests, with a chromel-alumel thermocouple located 0.050 in. below the friction surface. The friction surface of each drum was prepared by grinding and then polishing with successively finer abrasive papers. Final polishing was accomplished with a 320 grit paper. The friction material test samples had a I in. by I in. contact face and were approximately r/4 in. thick. The sample contact face was ground to a radius of curvature equal to that of the drum friction surface. Test data were recorded in the form of coefficient of friction ,u versus time t, ,u
Wear, 16 (Iwo) 431-445
BYXSUStemperature
7‘ and 7‘ UYSUS 2. Wear measurements
were made by weighing thti
test samples before and after each run. All tests were made under constant load co11-ditions, and each test consisted of t\vo break-in runs and two subsequent runs. I;or all tile drums, the break-in to a drum tcmperaturr
runr xvcre performed over the range from room tcmperaturt~ of 550 I’, \r.itlr tllcx trmperaturt~ rise chw 5*k~l\- tcj frictional
liextinp,.
Equation
(2) can bc rewritten
as follows:
log A T-T;= log R + u log I; + h log T’ + c log t
(31
If only one variable (~a>, F) is varied, keeping the other variables (V’ and t) constant, the parameter a can be determined from the slope of the line (log AW TJCYSUS log F), assuming that this equation satisfactorily describes the wear. Finally, the wear factor K can be determined, based on the values of a, b and C. This equation has been applied to four different systems as discussed below. The system cast iron drum and liniq A The test results are summarized in Table III. The load was varied from IOO to 175 p.s.i., the speed from 300 to 450 r.p.m., and the time from 6 to 9 min. The maxi-
POLYMERS TABLE FRICTION
SLIDING AGAINST
437
METAL SURFACES
III AND
WEAR
TEST
RESULTS
FROM
THE
SYSTEM
CAST
IRON
Load (fi.5.i.)
Speed
~._
_____
100
300
125
300
Coeff. friction
Time (min)
(r.P.rn.)
of
DRUM
Maximum
drum
(“F)
6
0.34
230
6
0.36
280
LINING
Wear measured
temperature
(average)
AND
ii
~____-...___.
---~
__ _._
(s
x
103)
._.
.~..___.
Weav ___.
4.01
‘4.9 t9.3 ‘9.3 23.5 24.2
300
6
0.37
330
‘75
300
6
0.36
370
100
350
6
0.36
2 60
12.2
3.94
100
400
6
0.36
300
r5.0 16.8
3.92
IO0
450
0.38
330
18.6 r9.0
3.84
TOO
300
0.38
260
12.7
3.88
300
0.37
280
300
0.37
290
IO0
__~
3.44
9.8 9.8 ‘4.5
150
100
factor
K x 1011
3.94 3.96
13.6
12.7 15.0
3.84
18.3 18.5
3.78
16.2
Avg.
3.90
.-.-_
I
0
’
!
2
Fig. 7. Temperature
’
! 1
TIME
1
i Ii’:’ Tit.3, W,N”TESI
3
10
!
’
12
rise in the drum (cast iron drum and lining A)
: IOOp.s.i.
and 300 rev./min.
wear, 16 (rg70) 431-445
,OO
200 150 LOAD (psi)
300 400 5clO 6 SPEED Crpn)
7 8 9 10 12 i-,HE (einj
15
IO0
150 200 LOAD (psi)
305 400 SPEED (rpm)
6
7 8 9 10 12 TIME (mini
Fig. 9. IDcpenclcnce of v-car on the load, speed, and time (cast iron drum and lining .\\. Fig. 10. ~kpendencc
of wear on the load, spwd, and time (cast iron drum and Iining B).
mum drum temperature was 37o’F. The average coefficient of friction was found to vary from 0.34 to 0.38. The wear measurements were reasonably reproducible, as shown in Table III. Typical examples of temperature rise in the drum and variation of the coefficient of friction with time are shown in Figs. 7 and 8 respectively. The drum temperature measured 0.050 in. below the friction surface increases parabolically, and the coefficient of friction becomes stabilized after about a minute. The wear results are plotted in Fig. 9. As can be seen, eqn. (3) satisfactorily describes the wear under the given conditions. All of the parameters a, b, and c are E’ear, 16 (1970) 431-445
I5
POLYMERS TABLE
SLIDING
AGAINST
SURFACES
FROM
THE SYSTEM
439
IV
FRICTION AND WEAR TEST RESULTS
Load (P&i
METAL
Speed (r.p.m.)
Tim (min)
CAST IRON
DRUM
Coeff. of friction (average)
Maximum drum temperature
AND
B
LINING
Wear measured (s
x
103)
Wear factor K x ION
(“I;)
300
6
0.34
235
6.0 6.1
9.12
125
300
6
0.34
280
8.0
9.25
150
300
6
0.35
320
100
400
6
0.36
100
100
100
450 300
300
8.6
9.06
9.9 IO.9 8.6
9.44
9.9
6 7.5
9
IO.1
8.89
255
10.3 7.1
8.76
‘75
7.5 x.7
9.08
0.35
310
0.34 0.34
9.4
found to be 1.60. For each test condition,
i\vg.
9.09
the wear factor K is given in Table III.
The
wear factor is found to be practically constant in all cases, ranging from 3.78 x 10-11 to 4.02 x 10-11. Probably, the wear factor K is a function of the coefficient of friction, but K does not appear to be very sensitive to the variation of ,u. Thus, the wear of lining A in this system under the given conditions can be described by the equation :
AW=3.go wherehwising,
x Io-~l FI.~oJ,‘I.~o~‘.~o Finp.s.i.,
(4)
Vinr.p.m.andtinmin.
The system cast irolz drum and lining B The test results are summarized
in Table
IV. This lining was subjected
to the
test conditions similar to those of the system cast iron drum and lining A. The average coefficient of friction did not vary much: 0.34-0.36, and the maximum temperature reached was 320°F. The wear of this lining was substantially lower than that of lining A. The wear results are plotted in Fig. IO to determine the parameters a, b and c. The parameters are again found to be constant : a = b = 1.35 and c = 1.0. The calculated values for the wear factor are given in Table IV; it varies from 8.76 x IO-9 to 9.44 x 10-9. The wear of lining B in this system can be best described by the equation : AW=9.09
x 10-9
(FL’)135
t
(5)
The wear factor is substantially larger than the one in eqn. somewhat less sensitive to the variation of the load, velocity lining A. Temperature rise in the drum and variation of the shown for the experimental conditions of IOO lb., 300 r.p.m. 12 respectively. The system cast iron friction surface in a chromium The test results are summarized in Table
(4). Wear of this lining is and time, compared with coefficient of friction are and 9 minin Figs. II and
copper drum and lining A V. Since copper alloy drums were Wear. 16 (1970) 431-445
Cl
I;
2””
‘k”
-+--’ “DS,
Fig.
POLYMERS SLIDING AGAINST METAL SURFACES TABLE FRICTION COPPER
441
V AND DRUM
Load (p.s.i.)
WEAR AND
TEST
RESULTS
Speed (r.p.m.)
FOR
THE
SYSTEM
CAST
IRON
FRICTION
SURFACE
IN CHROMIUM
A
LINING
Time (min)
Coeff. of friction
Maximum
(average)
(“F)
drum
Wear measured
temperature
(g
x
103)
Wear factor K x 108
IO0
485
6.5
0.44
280
20.7 21.3
5.18
‘50
485
6.5
0.43
360
27.9 29.9
5.1*
200
485
6.5
0.43
455
33.3 38.8
5.28
200
400
6.5
0.40
380
28.9 29.6
5.20
200
300
6.5
0.40
305
21.7 21.7
5.14
200
485
9.75
0.42
540
69.0 74.9
5.19
200
485
0.42
590
127.3 128.5
5.57
I3
Avg.
5.24
-I 7
0 0
I 0
200
’
! 2
’
I 1
400 TlME cwxucIS,
’
1
ml
I:’
B TIME WINUTES,
WI
: 8
10
’
]
’
12
Fig. I 3_ Temperature rise in the drum (cast iron friction surface in chromium copper drum and lining A) : 200 p.s.i. and 485 rev. /min. W&a+‘,16 (1970) 431-445
found to run substantially cooler than cast iron drums 7,s, more severe test conditions were adopted for this system. The maximum drum temperature was 59o’E‘ after 1.3 min under the condition of zoo p.s.i. and 485 r.p.m. (Fig. 13), and the coefficient of friction under this condition is given in Fig. 14.The average coefficient of friction was
Fig. 14, Cofficient of friction p.s.i. and 485 rev. /min.
(cast iron friction surface in chromium copper drum and lining A)
: zoo
found to vary from 0.40 to 0.44. The wear results are plottedin Fig. 15.The parameters are found to be a = 314, b = 1.0, and c = 714, The values for the wear factor varied from 5.11 x 10-5 to 5.28x10-5 except in the last test (5.57 x IO-~). This high wear is probably due to the high temperature (600°F). The wear can be described by the equation : Aw=5.24
x 10-s
(Ft) f vi!
(6)
Equation (6) is considerably different from eqn. (4). This difference is probably due to the difference in microstructure of the cast iron (Figs. 4 and 5)) and also the difference in thermal conductivity of the two drums. The system chromium friction
surface in a chromium copper drum and lirting A This investigation was undertaken because information on the frictional behaviors of chromium and polymer friction pairs was not readily available in the Wear, 16 (1970) 431-445
POLYMERS SLIDING AGAINST METAL SURFACES TABLE FRICTION COPPER
VI AND DRUM
WEAR AND
Speed (r.p.m.)
Load (psi)
TEST
RESULTS
FOR
THE
SYSTEM
Time (min)
Coeff. of friction
Maximum
(average)
(OF)
temperature
485
6.5
0.47
3eo
150
485
6.5
0.42
370
200
485
6.5
0.43
450
200
400
6.5
0.41
385
200
300
6.5
0.42
325
200
485
7.5
0.44
480
200
485
9
0.43
52“
120 100
CHROMIUM
FRICTION
SURFACE
IN CHROMIUM
A
LINING
100
150
443
drum
Wear measured (g
x
103)
Wear factor K x 105
26.0 28.5 32.4 32.4 36.1 37.9 31.1 33.9 27.4 28.7
1.27
43.4 43.7 53.8 55.0
1.29
1.27 1.28 1.26 1.29
1.33 Avg.
1.28
E ’ ’ “““““‘A
30. 25.20 100
ca.
3 t 150
b 200
LOAD (psi)
300 SPEED
t
1.0
400 500 (rpn)
6 7 8 9 10 12 15 TIME
(mln)
Fig. 15. Dependence of wear on the load, speed, and time (cast iron friction surface in chromium copper drum and lining A).
literature. The test results are summarized in Table VI. The coefficient of friction was approximately 0.43, very much similar to the cast iron systems; it varied from 0.41 to 0.47, Temperature rise in the drum and variation of the coefficient of friction with time are shown for one test condition in Figs. 16 and 17 respectively. The wear results are plotted in Fig. 18. Here again, the parameters a, b, and c are constant, being 0.43, 0.60, and 1.06 respectively. The wear factor varies from 1.26 x 10-2 to 1.33 x 10-2. The wear can be described by the equation : AW= 1.28 x 10-5
F0.43
vO.60
il.06
(7)
The wear factor is much larger than in eqn. (6), but the parameters a and b are smaller than those in eqn. (6). W-‘, 16 (1970)431-445
0
I’
0
do0 TIME ,SECONDS,
200
I 2
’
! 1
’
I
6 TlME IMINUTES,
Fig. 16. Temperature rise in the drum lining A) : zoo p.s.i. and 485 rev./min.
Fig. 17. Coefficient of friction 2oop.s.i. and 485 rev./min.
’
(chromium
6ca
; 8
(chromium
friction
I
*Do
I
:’
12
10
friction
’
surface
in chromium
surface in chromium
copper
drum and
copper drum and lining A)
:
POLYMERS SLIDING AGAINST METAL SURFACES
I
20
100
,I0
150 200 LOAO (psi)
445
II111111 300 400 500 6 7 6 910 12 TIME (mln) SPEED (rpm)
15
Fig. 18. Dependence of wear on the load, speed, and time (chromium friction surface in chromium copper drum and lining A). CONCLUSIONS
(I) The wear of polymer-bonded friction materials caused by sliding against metal surfaces can be satisfactorily described for the four systems investigated by the equation : AW=K
Fa Vbtc
where AW is the weight lost, K the wear factor, F the load, V the speed, t the time, and a, b, and c are a set of parameters for a given system. (2) The wear factor K is practically constant for a given system. (3) The coefficient of friction for lining A sliding against electroplated hard chromium is found to be approximately 0.4, similar to the system lining A and cast iron. (4) Applicability of the wear equation to other friction pairs such as polymerpolymer, metal-metal and ceramic--metal should be investigated. ADDENDUM
Further test results indicate that there may exist two sets of the parameters a, b, and c for a given system, depending on the severity of the test conditions. ACKNOWLEDGEMENT
The author wishes to thank Mr. H. M. Danbert and Mr. R. D. Stapleton for running the tests, and Mr. R. T. Du Charme for supervising the tests. The encouragement and support of Dr. W. M. Spurgeon are greatly appreciated. REFERENCES I z 3 4 5
W. M. SPURGEON AND A. R. SPENCER, Bendix Tech. J., 2 (3) (1969) 57. R. P. STEIJN, Metals Eng. Quart, 7 (2) (1967) 9. E. RABINOWICZ, Friction and Wear ofMaterials, Wiley, New York, 1965, p. 137. R. B. LEWIS, Mech. Eng., 86 (IO) (1964) 32. B. R. TEITELBAUM, W. C. SUTTLE AND C. B. SUNG, SAE Paper No. 650488, preselzted at the Mid-Year Meeting of the Society of Automotive Engineers, Chicago. Illinois, June rg65. 6 A.R. SPENCERANDW.M.SPURGEON, SAETralzs., 75(1967)773. 7 S. K. RHEE, R. M. RUSNAK AND W. M. SPURGEON. SAE Paper No. 690443, presented at the Mid-Year Meeting of the Society of Automotive Elzgineers, Chicago, Illinois, May 1969. 8 S. K. RHEE, J. L. TURAK AND W. M. SPURGEON, SAE Paper No. 700138, presented at the Engineering Congress of the Society of Automotive Engineers, January 1970. Also SAE J., 78 (6) (1970) 20. Wear, 16 (1970) 431-445