Wear equation for polymers sliding against metal surfaces

Wear equation for polymers sliding against metal surfaces

Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands Wear - 431 WEAR EQUATION FOR POLYMERS SLIDING AGAINST METAL SURFACES S. K. RHEE The B...

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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