Wear, 81 (1982) 347 - 356 347

AN EQUATION FOR THE ABRASIVE WEAR OF ELASTOMERIC O-RING MATERIALS

BRUCE H. BURR

Product Research Group, Hughes Tool Division, Hughes Tool Company, Box 2539, Houston, TX 77001 (U.S.A.)

KURT M. MARSHEK

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712 (U.S.A.)

(Received May 22,1982)

Summary

An empirical equation was obtained via dimensional analysis, which relates the abrasive wear volume to the friction force, specimen load, sliding distance and specimen breaking strength for O-ring materials. Wear experi- ments on O-rings molded from four nitrile compounds and one polyurethane material were conducted on a special pin-disc-type testing machine. Speci- mens cut from a size 330 O-ring were held against a roughened rotating steel wear cylinder with a load which varied from 5 to 15 lbf. Both the specimen and the wear cylinder were immersed in an abrasive mud of the type used for oil well drilling. The sliding velocity was held constant at 11 in s-l. The wear resistance of the polyurethane was two times better than the best nitrile compound.

1. Introduction

The literature reveals many simple expressions for predicting the wear rates of various types of materials. For sliding electrical contacts, Archard and Hirst [l] related the wear volume to the sliding distance, normal load and yield pressure of the softer material. Ratner et al. [ 21 proposed a rela- tionship for plastic materials which showed that the wear volume depended on the breaking elongation, breaking strength, hardness and coefficient of friction. Kar and Bahadur [3] used experimental data and dimensional analysis to develop an equation for the volumetric wear rate of filled and un- filled polyoxymethylene.

The literature suggests that material properties such as yield pressure, hardness, breaking strength, elastic modulus, specific heat and thermal con- ductivity are important in predicting wear volume. The work presented in this paper uses the techniques of dimensional analysis to establish relation-

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348

Fig. 1. Three-element rolling-cutter rock bit.

ships between O-ring material properties, which are important in abrasive wear and are easily measured in a laboratory. Experiments were carried out with different materials, loads and sliding distances to determine the con- stants in the relationship between dimensionless groups.

The O-rings of interest are used as rotary seals in rolling-cutter rock bit bearings (Fig. 1). The O-rings prevent drilling fluid and abrasive rock cuttings from entering the bearings and causing bearing failure. In performing their task, O-rings are often subject to severe abrasive wear depending on the drilling conditions. A knowledge of the material properties which influence abrasive wear resistance would aid in the selection of O-rings for this and similar applications.

This work was specifically aimed at (1) determining the wear character- istics of four nitrile compounds (nit~l~butadien~~bber (NBR)) and one polyurethane material under conditions of varying sliding distances and normal loads and (2) establishing the relative effect of material properties important in the abrasive wear resistance of O-rings.

349

2. Experimental equipment

2. I. O-ring specimens Physical properties of the nitrile compounds and polyurethane are

listed in Table 1. Size 330 O-rings were chosen for the experimental work be- cause they are used to seal standard-size rock bit bearings. This O-ring has a nominal 2$ in inside diameter and r&in diameter cross section.

TABLE 1

Properties of O-ring materials

~u~erial Shore A hardness Breaking strength Specific gravity (lbf iK2)

NBR 1 80 2367 1.28 NBR 2 70 1516 1.28 NBR 3 80 2093 1.17 NBR 4 90 2381 1.34 Urethane 90 4078 1.17

2.2. O-ring wear test machine The wear test machine designed and built for this work is shown sche-

matically in Fig. 2 and has the following capabilities: (1) the wear surface sliding speed can be set at any speed between 11 and 190 in s-l; (2) the specimen load can be set at up to 45 lbf with dead weights; (3) the friction force and specimen temperature can be recorded continuously; (4) two spec- imens can be tested simultaneously; (5) the test specimens can be run in a container of abrasive mud or other fluid. A photograph of the test machine is shown in Fig. 3 and a description of the machine and its instrumentation is given in ref. 4.

,-Loading Arm

Pulley

Abrasive Fluid

Wear Cylinder

Weight

Fig. 2. Diagram of O-ring wear test machine.

Holder

Fig. 3. Loading mechanisms and wear cylinder.

3. Experimental results

A series of wear tests, where the specimen volume loss was measured as a function of time, was run for each O-ring material. The test results were then plotted as the logarithm of volume loss uersus the logarithm of time (Figs. 4 - 8). A series of wear tests, where the specimen volume loss was mea- sured as a function of specimen load, was also run for each material. The results of these tests were then plotted as the logarithm of volume loss uersus the logarithm of load (Figs. 9 - 13). The experimental procedure is described in ref. 4.

1.”

[; 3.0 i

0.4 -

Y 3 2 0.2 -

0.1 1 I III I I I 2 4 6 8 IO 20 40 608OKJo 200 4

TIME, MINUTES

10

Fig. 4. Volume loss vs. time for NBR 1: - - -, analytically predicted; -c-, from ex- periment.

351

0.1 ’ I II, I I III

2 4 6 6 IO 20 40 6060100 200 1

TIME, MINUTES

)O

Fig. 5. Volume loss us. time for NBR 2: - - -, analytically predicted; -c-, from ex- periment.

0.1 1 I I I I II, I

2 4 66D 20 40 6060100 200 4

TIME, MINUTES

IO

Fig. 6. Volume loss us. time for NBR 3: - - -, analytically predicted; -G-, from ex- periment .

The full straight line on each graph is a least-squares fit of the experi- mental data. The broken straight line is the relationship predicted by a wear equation derived using dimensional analysis.

As in all wear testing, there was some scatter in the results. The scatter is caused by small differences in test parameters such as (1) the surface finish on the cylinder and O-ring, (2) sliding surface material properties and (3) abrasive fluid consistency.

The graphs of volume loss uersus time (Figs. 4 - 8) indicate that the initial wear rate during the first 6 min is greater than the subsequent wear rate. This is a result of the sharp asperities on the sand-blasted wear cylinder, which provide a high degree of two-body abrasive wear during the first few

0.1 1 I ,,I 8 I II, ,

2 4 680 20 40 608000 20 4

TIME, MINUTES

10

Fig. 7, Volume loss us. time for NBR 4 : - - -, analytically predicted; -o-, from ex. periment.

“0

m;i!; c 3 /J

9 0.2-

0.12 4 6 I 8 / IO I 20 / 40 608oloO I n I 200 L

TIME, MNUTES

K 0

Fig. 8. Volume loss vs. time for urethane: - - - , analytically predicted; --o--, from ex- periment.

minutes. The peaks of these asperities are quickly worn down by the abrasive particles and the lapping action of the elastomer. The valleys of the sand- blasted wear cylinder surface remain and draw abrasive particles in between the wear surfaces. Three-body abrasion then emerges as the predominant and steady state mode of abrasive wear.

The graphs of volume loss versus load (Figs. 9 - 13) show that wear is a power function of load, and analysis predicts an average load exponent of 1.35. This unusual relationship could be caused by the draping effect of the elastomer surface over asperities. An increased load would cause more drap- ing and thus even deeper penetration of asperities into the elastomer.

4.0

3.0

2.0

-i 2 1.0

lfj 0.8

8 _I 0.6

!I OA

G

0.2

6 8 IO 15 20

LOAD, LB,

1520 1

LOAD, LBF

Fig. 9. Volume loss us. load for NBR 1: - - -, analytically predicted; +, from ex- periment.

Fig. 10. Volume loss us. load for NBR 2: - - -, analytically predicted; -G-, from ex- periment.

4.0

3.0

2.0

“0 x

“7 I..0

”

4

0.8

0.6

g 0.4

3

P

0.2

0. I I I

2 4 6 8 IO 15 20 40

LOAD, LB,

IC 4.0

3.0

20

%

x -is 0.6 1.0

% 9 0.6

!g 0.4

3

9

0.2

0.1 2‘ I I I I , I _ _ _ _ _ _ ̂

d 4 u u IU 19 zo LOAD, LBF

3

Fig. 11. Volume loss us. load for NBR 3: - - -, analytically predicted; u, from ex- periment.

Fig. 12. Volume loss us. load for NBR 4: - - -, analytically predicted; -G-, from ex- periment.

?k - l.O-

3 CJ 0.8-

w 0.6 -

if $ 0.4 -

0.2 i-

0.1 L 01 I1 L I

2 4 6 8 IO 1520 ’

LOAD, LBF

3

Fig. 13. Volume loss us. load for urethane: - - -, analytically predicted; +, from ex- periment.

4. Dimensional analysis

The variables considered in the abrasive wear of the O-ring were as follows: V, specimen volume worn away; f, friction force; W, specimen load; x, sliding distance; S, specimen breaking strength, The basic dimensions for the selected variables are force and length.

The Buckingham pi theorem states that the number of independent dimensionless groups that may be used to describe a phenomenon involving n variables and r basic dimensions is equal to the difference n - r [ 5,6] .

Accordingly, the pi theorem predicts that the problem can be described with three dimensionless groups. The volume worn away may be expressed implicitly as a function h off, W, x and 5’:

v = h(f, w, x, S)

In dimensionless form, eqn. (1) may be written

(1)

V & f sx2 -= i 1 x3 W’W (2)

The dimensionless variables may be assumed to satisfy the following relation:

(3)

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TABLE 2

Experimentally obtained values for m and n

Material m mAVE a STDb n nAVE STD

NBR 1 1.42 0.36 NBR 2 1.14 0.44 NBR 3 1.51 1.35 0.14 0.29 0.35 0.07 NBR 4 1.40 0.38 Urethane 1.29 0.28

aAVE, average. bSTD, standard deviation.

TABLE 3

Wear constant K and related variables

Material V (in3) at 60 min

P W (lbf) x (in) S (lbf inm2) K at 60 min

NBR 1 1.24 x 1O-4 0.366 10 4.17 x 104 2367 0.0041 NBR 2 1.86 x 10-4 0.404 10 4.17 x 104 1516 0.0034 NBR 3 1.33 x 10-4 0.505 10 4.17 x 104 2093 0.0038 NBR 4 1.34 x 10-4 0.492 10 4.17 x 104 2381 0.0045 Urethane 0.65 x 1O-4 0.305 10 4.17 x 104 4078 0.0044

aThe coefficient of friction values are the averages of all the coefficient of friction values for each material at 6 min of testing.

or

V=Kf"WmxnSb (4)

where K is a dimensionless wear constant, m = - a - b and n = 3 + 2b. Val- ues for m and n were obtained from the least-square fits illustrated in Figs. 4 - 13 and are summarized in Table 2.

If the average values for m and n from Table 2 are used and the coef- ficient of friction is defined as 1_1= f/W, eqn. (4) becomes

V=Kp- 0.025w1.325x0.35~1.325 (5)

The wear constant K for each material was calculated using eqn. (5); the data and material properties are given in Table 3. The K values are also listed in Table 3.

The wear constants K and friction coefficients (u were then substi- tuted into eqn. (5) to yield the wear curves predicted by dimensional analysis. These curves are plotted as broken lines alongside the actual experi- mental data points (see Figs. 4 - 13).

Inspection of eqn. (5) shows the importance of specimen load, specimen breaking strength and sliding distance. The friction coefficient has very little effect on wear, and this variable could be eliminated from the equation. The

356

appropriateness of the choice of variables, selected for dimensional analysis, is established by the agreement between the experimental data obtained from the laboratory and the results predicted by the dimensional analysis.

To use eqn. (5), the wear constant K must first be established by run- ning one wear test. This wear constant may then be used in the equation to predict specimen wear for varying conditions of load and sliding distance or time. In dynamic O-ring service, the specimen load is related to the sur- face contact stress resulting from the squeeze imposed on the O-ring by its gland.

5. Conclusions

An equation has been developed which shows that the abrasive wear of an O-ring is related to the material breaking strength, load, sliding dis- tance, coefficient of friction and a material wear constant. If one relatively short wear test is made first to determine the material wear constant, the equation may then be used to make predictions of the wear volume loss for varying conditions of the elastomer surface contact stress and time.

References

1 J. F. Archard and W. Hirst, The wear of metals under unlubricated conditions, hoc. R. Sot. London, Ser. A, 236 (1956) 397 - 410.

2 S. B. Ratner, I. I. Farberova, 0. V. Rayukevich and E. G. Lurie, Connection between wear-resistance of plastics and other mechanical properties, Sou. Plast., 7 (1964) 37.

3 M. K. Kar and S. Bahadur, The wear equation for unfilled and filled polyoxymethylene, Wear, 30 (1974) 337 - 348.

4 B. H. Burr and K. M. Marshek, O-ring abrasive wear test machine, Wear, 68 (1981) 21 - 32.

5 G. Murphy, Similitude in Engineering, Ronald Press, New York, 1950. 6 M. J. Moran and K. M. Marshek, Some matrix aspects of generalized dimensional

analysis, J. Eng. Math., 6 (1972) 291 - 303.