Wear in a conical pivot bearing

Wear -

Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands

WEAR

IN A CONICAL PIVOT BEARING

A. F. RASHED Production

AND

405

A. M. HAMOUDA

Engineeri?zg Department,

Faculty

of Engineering, University of Alexandria. Alexandria

(EuPt) (Received May 28, 1969; in final form October 8, rg6g)

SUMMARY

Conical effect on their pivot bearings poses, has been

pivot bearings, widely used in mechanical comparators, have a great precision. A relationship between wear and rate of wear in conical and their characteristic parameters, which is of value for design purdetermined.

NOMENCLATURE

a

Apex angle, running time, c degree of surface finish, d angle of oscillation, ratio of radial to axial load, e n angle of oscillation (in turns), R, degree of surface finish (pm c.l.a.), Raz optimum degree of surface finish that gives minimum weight of removed metal, t running (working) time (min), W axial load (g), Wt weight of removed metal per unit axial projected area (wear) (mg cm-z), II1’ttrate of wear, (mg cm-2 min-l), ratio of radial to axial loads, r 4 apex angle (radians). Suffixes initial, : final. b

INTRODUCTION

Work was carried out to investigate how the characterizing parameters of a conical pivot bearing affect its wear. Wear was measured by the weight loss per unit axial projected area using a one-pan balance of OS mg sensitivity. The results were analysed and certain relationships, useful for the design of conical pivot bearings in mechanical comparators, obtained. Wear, 14 (1969) 405-413

406

A. I;. RASHED,

A. M. HAMOUDA

The apparatus used, Fig. I, was designed and constructed to avoid the possible sources of error. A thrust bearing, 8, allows the seat holder, 6, to float to avoidec-

SC‘

Fig.

fll”

1.

-f 15mm

1 Cc---_-224mm

Fig.

-1

2.

Wear. ‘4

(19fj9) 405-4’3

WEAR IN A CONICAL PIVOT BEARING

407

centricity between the pivot and the seat center line. A self-ahgning bearingro, allows the seat holder to tilt to ensure perpendicularity to the pivot center line. A connecting rod, 16,hinged at the slide, 15, transmits motion from the spindle which rotates at 60 rev./min. The oscillatory motion of the gear, 12, is controlled by the relative position of the slide attached to the main driving gear, 13. A radial load is applied to the seat holder by a weight attached to a wire and pulley arrangement, 2J.. Conical pivot bearing specimens larger than those in mechanical comparators were used. The specimens were made of brass to allow a reasonable wear rate and quick results to be obtained. The dimensions of a specimen are given in Fig. z ; apex angles of 60”, 90’ and 120’ were used. EXPERIMENTAL

PROCEDURE

The test conditions, chosen to suit practical applications, were as follows. Axial pressure on conical pivot bearing, 700 g/cm2. Ratios of radial to axial load, 0.05, o.ro, 0.20, 0.30 and 0.50. Oscillations, 60 c/min. Running intervals, 15, 15, 30, 60 and 60 min, giving a total running tune of 180 min. EXPERIMENTAL

RESULTS

Relationship between wear aad waning tinze Figures 3, 4 and 5 present graphically the wear-time results obtained from specimens with apex angles 60°, go” and 120’ respectively. Tests were carried out on specimens of 7.5, 5.5,3.0,1.5 ando. pm c.1.a. surface finish r~pective~yunder con-

Apex

angle (60’)

120

180

Time tmin)

Fig. 3. ~~e~~, f4 (rQfJ9) 405-413

408

A.

Apex

angle

F.

RASHED,

A.

M.

HAMOUDA

(90’1

Time (min)

Fig. 4.

Apex

h

angle

120’

6.

; <

+4.

%

Time (min)

Fig. 5.

stant axial pressure of 700 g cm-z, zero radial load and angle of oscillation of 1/4turn. After a total running time of 180 min, the surface finish of each specimen was measured. The initial and final surface finishes (Rai and Raf) are given in Table I. From the results, the final surface finish of a specimen is approximately equal to the initial surface finish of a successive specimen, of different increasing apex angle. Therefore, for each apex angle, the wear of a specimen can be cumulative regarding running time. Figure 6 shows wear measured by the weight loss against running time. The wear rate follows the normal well-known wear characteristic curve’, which shows three stages. (I) Removal of surface peaks to reduce the c.1.a. reading. (2) A uniform rate of wear, as sharp peaks are removed. (3) Smoothing of the surface by the removed particles acting as abrasives. Wear, 14

(1969)405-413

WEAR

IN A CONICAL

PIVOT

409

BEARING

The wear results for specimens of surface finish of 7.5 pm c.1.a. were not plotted in Fig. 6 as the high values obtained would not be acceptable for practical use. From Fig. 6, the following relationships were obtained for the different stage of wear. (I) From t =o to t =7o min Wt =(0.407 4-0.378 ~,Q+o.ogz3 $3) t mg cm-2. (2) From t =70 to t =540 min Wt=[0.0385-0.0267 (#-n/3)]t +70(o.407~-o.378~2+o.ogz3 $3) mgcm-2. (3) From t =540 to t =720 min Wt = [0.0775 -0.~477 (4--n/3)] t +540 jo.0385 -0.0267 ($ -7cd/3)]+70 (0.407 # -0.378 42 +0.0923 #3) mg cm-2. TABLE I

Apex

7.5 5 3 I.5 0.6

Apex angle

angle

Apex angle

60"

9o”

I2O0

4.75 2.65 I.2 6.75 6.45

4.9 3.3 1.6 0.70 0.40

5.2 3.8 I.75 0.70 9.35

40.

p

a

30.

0 Fig.

6 1st stag

180

300 2nd staqe

420

340 660 min I’ 36 stoqe

6.

The second stage of wear is the most desirable in conical pivot bearings since it gives a uniform wear rate. A relationship can be obtained for this wear regime between the weight of metal removed/cm2 of axial projected area and the resulting degree of surface finish which is R,=[5.25-1.43

(#-n/3)]

- [(0.186+0.103

(#-n/3)]

Wt

expressed in pm c.1.a. Wea+‘,14 (1969)495-413

A. 1:. RASHED,

410

A. M. HAMOUDA

Relationshi@ between wear and the optimum surface finish The experimental results can be used to show the relationship between wear and surface finish for different apex angles at different times. Figure 7 shows this for an apex angle of 60”. The curves show an optimum value of surface finish corresponding to minimum wear at different times. A straight line joining the points of minimum wear is drawn and linearly scaled with respect to time which allows the minimum wear rate to be calculated after a known running time, once the surface finish is determined. and I 20”

Similar

l

180

I\

15-

-’

graphs to Fig. 7 can be obtained

Apex

for apex angles of c)Oi

ongle(60°)

min

0 120

fl

d 60

'I

a30

'5

t15

'I

CR,) ~-‘m ~.!.a Fig.

7.

Following a period of running, accumulated debris first fills the valleys between the surface asperities, then acts as an abrasive to increase the wear rate. With a smooth surface, the volume of gaps between asperities is small and is filled in a relatively short time and excessive abrasive wear occurs. With a rough surface, the volume of gaps between asperities is large but the rate of wear by asperity removal is relatively high. For an intermediate surface finish, the volume of removed metal is minimum for the same running period. The latter surface has what may be termed “the optimum degree degree of of surface finish with regard to running time” which is a time-dependent surface finish and increases with the running period. To generalise, the use of line indicating minimum wear and optimum surface finish, Fig. 8 indicates the variation of minimum wear with variation of running time and apex angle. This variation of minimum wear can be represented by the following relationship.

Wt=A

R,‘+Ht+C

WEAR

IN A CONICAL

PIVOT

BEARING

where A =2.63 56+0.567 @--0.325 B=46

4-70

#2+20

C = - 1.48 -3.35

(Rat Fig.

43

$3

($-n/3)

pm c1.a.

8.

Relatiomhip bekveen wear and the angle of pivot oscillation Experiments were carried out on specimens with apex angles of 60°, go” and 120~ for angle of oscillations measured in terms of turns, A complete turn, which is equal to WC,is considered to be a unit measure for an angle of oscillation. The applied axial load was 700 g. After a running period of 2 h each of the specimens had an optimum surface finish of z ,um c.1.a. From the results, a linear relationship exists between the weight of metal removed and the number of turns, up to 1x5 turns, as in mechanical comparators (Fig. 9). This relationship can be expressed by Wt = r34.75 - 16.75 (4 -n/3)1

*

Since the optimum surface finish for the specimens used lies in the second stage of wear, which shows a uniform rate, the value of WU is obtained by merely dividing Wear,

14 (1969)

405-4’3

A.

412

Wt by the running period which is

120

F. RASHED,

A. M. HAMOVDA

min. Therefore,

Relationshifi between wear and the ratio of radial to axial load The experiments reported in the previous section were repeated under the same conditions for axial load, optimum degree of surface finish and an angle of oscillation of one turn, while varying the ratio of radial to axial load, 7, from 0.05 to o.50. The results, as plotted in Fig. IO, show a linear increase in wear up to q=o.15. For

5o.

Fig.

9.

Fig.

IO.

. Apex angle 60’

values of yeabove 0.15, the rate of wear decreases especially for a specimen with an apex angle of 60”. Thus the radial load must be kept as small as possible to minimise wear. Then, up to q =o.I~, the wear can be presented by a straight-line relationship. Wt=mq-K where m is the slope which varies with the apex angle, 4, c is a constant corresponding to an angle of oscillation, n, of one turn, and no radial load and varies with the apex angle. For an angle of oscillation of n turns, the value of c will be given by c = r34.75 - 16.75 t+--3tiI Therefore Wt=(178 TV&w,rq

(1969)

#-I44 405-413

(d”+32.3

n (63) q+[34.75-16.75

($-n/3).1

‘2

WEAR

IN A CONICAL

PlVOT

413

BEARING

The rate of wear can be expressed in terms of the axial load, W, in line with Archard’s theory2, which states that the weight of removed metal is directly proportional to the normal load. Wtt = [(I78 #-I44

#2+32.3

$@) Yl- [34.75-16.75

(F”-;)]

n} & mg cm-2

mm-r

CONCLUSIONS

The results show a relationship between wear and rate of wear in conical pivot bearings, as used in mechanical comparators, and their characteristic parameters. These relationships can be used and are of value in the design of conical pivot bearings. REFERENCES I V. DOBROVOLSKY et al., Machine Elements 1960. 2 J. J. KAUZLARISH et al., Effect of wear on pivot

thrust

bearings,

ASLE

Trans., g (1966) 00.

Weav, 14 (1969) 405-413