W E A R OF M A T E R I A L S U N D E R H Y D R O A B R A S I V E C O N D I T I O N S

A. I . Z o l o t a r ' UDC 667.637.222

It is well known that with increasing velocit ies of collision between abras ive part icles and the su r - face of a part the serv ice life of parts in pumps used for pulps decreases . A relationship has been es tab- lished between the wear ra te and collision velocity in the form of a power function

where ~ is the wear rate; w is the coll ision velocity; a is a constant of the testing conditions, equal to the wear at w = l m / s e c ; b is a dimensionless constant charac ter iz ing the sensi t ivi ty of the mater ia l to the coll ision velocity.

Relationship (1) is used in designing hydromachines to determine the suitability of a par t icular ma - ter ia l or design. The wear res i s tance of mater ia ls under new conditions is predicted by extrapolation of the relat ive wear res i s tance fac tor f rom previous investigations. The formula for extrapolation takes the fo rm

[11

O ~ o 0 ~ b , - - ~ ,

where ~ and ~0 a re the relat ive wear res i s tance fac tors at velocit ies w and w 0 (~0 is known f rom previous studies); v --w/w0; subscr ipts 1 and 2 re fe r to different materials .

Since constants a and b have not been determined for minera l -po lymer coatings, wear res is tant alloys, and rubber, the designs a re based on approximate values, which lessens the effectiveness of the solutions. The relat ionships of phenomena a re usually investigated under steady conditions. In operation, the coll i- sion veloci ty often var ies , and therefore the relationship determined under steady conditions must be r e - calculated for actual conditions.

Here we present values for constants a and b for severa l mater ia ls used in hydromachines and also a method of recalculat ing relat ionship (1) obtained with w = const for conditions charac ter ized by changes in collision velocity.

To determine the values of a and b, labora tory studies were made of the effect of coll ision veloci ty on the wear of metal alloys and minera l -po lymer composites. Cylindrical samples of the mater ia ls were placed in the impel ler of a special apparatus [2] simulating the leading edge of the blade. Two to four s a m - pies of each metal alloy and five samples of each minera l -po lymer coating were subjected to each testing condition. With this number of samples and changes in the coll ision velocity f rom 5.3 to 17 m / s e c , the Coefficient of var ia t ion of the experimental data was less than 5.5%.

In treating the test resu l t s we used the coefficient of the scale effect [3] accounting for the change in the flow conditions on the surface as compared with conditions taken as standard. The wear ra te (mm 3 /min) was determined f rom experimental data on the s teady-s ta te section of the curve for wear versus time. Since relat ionship (1) is a power function, in logari thmic coordinates it is rectified and, consequently, b = d l o g e / d l o g w is the tangent of the slope, The calculated values of a and b a re given in Table 1.

It follows f rom Table 1 that two mater ia ls can be selected so that a i > a 2 and b 1 < b 2. In this case, as can be seen f rom Fig. 1, inversion of the wear res i s tance will occur (the sequence of s imi lar mater ia ls in o rder of wear res is tance will be disrupted). Obviously, with a i > a 2 and b t > b 2 no inversion of the wear res i s tance will be observed.

Translated f rom Khimicheskoe i Neftyanoe Mashinostroenie, No. 1, pp. 36-38, January, 1973.

�9 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street,. New York, N. Y. 10011. All rights reserved. This article cannot be reproduced [or any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

76

T A B L E 1

Alloy

IChKla28 N2 (SB) . . . . . . . . . IChKh16MT . . . . . . : . . . . . IChKhlSM2 . . . . . . . . . . . . IChKh2N4 (Nihard) . . . 35KhNVFL . . . . . . ~ ." . . . . " 40KhGSNL . . . . . . . . . . . Steel 25:

normanzed. . . . . . . . . . . annealed . . . . . . . . . . . . .

I-tardness, HB

650 108 10 - 5 610 180 10 _ 5 512 " 157 10 - 5 540 216 10 - 5 400 357 10 - 5 400 355 10 - 5

16o 1 ~7.1o-5 m

129 11'79"1~

a b

2,79 2,68 2,75 2,73 2,55 2,38

2,39 2 23

Binder of the mineral-polymer coating

Epoxy . . . . . . . . . . . . . . . . . . . . Epoxy- phenol formaldehyde resin. , Methacrylate resin . . . . . . . . . . . . Phenol formaldehyde liquid . . . . . Vulcanite . . . . . . . . . . . . . . . . . Phenol formaldehyde powder . . . . Ceramic . . . . . . . . . . . . . . . . . .

H a r d n e s s ,

HTP. mini 0,30

0,45

0,55

1,80

4,00

2,00

4,50

a b

2886 �9 10 - 5 3,06

2705 �9 10 - 5 3,20

3056 �9 10 - 5 3,13

2626 �9 1 0 - 5 3,30

5917 �9 10 -5 3,02

2946 .10 _ 5 3,40

0 0 3 . 1 0 - 5 4,14

e, mmZ/min

F / I I 1 I

700 I I I I

I I I I IIII

so I #/

10 / X

5 lO

If I/I r I// 4/

r i l l 11111

w, m/sec

F ig . 1. W e a r r a t e ~ of m i n e r a l - p o l y -

m e r c o a t i n g s v e r s u s c o l l i s i o n v e l o c i t y w of a b r a s i v e p a r t i c l e s w i t h t he c o a t -

ing. 1, 2, 3) C o a t i n g s w i t h p o w d e r e d p h e n o l f o r m a l d e h y d e , v u l c a n i t e , and

l i q u i d p h e n o l f o r m a l d e h y d e b i n d e r s ,

r e s p e c t i v e l y .

T h e s p e c i f i c c o n d i t i o n s i n w h i c h i n v e r s i o n of t h e w e a r r e s i s t a n c e o c c u r s a r e of p r a c t i c a l i m p o r t a n c e , m a k i n g i t p o s s i b l e to d e t e r m i n e t h e e x p e d i e n c y of u s i n g one m a t e r i a l o r a n o t h e r . U s i n g r e l a t i o n s h i p (1), i t

i s p o s s i b l e to o b t a i n a c o n d i t i o n in w h i c h m a t e r i a l s h a v e an e q u a l w e a r r e s i s t a n c e . T h i s c o n d i t i o n i s w r i t t e n

lg at - - ig a2 l g w =

b2 - - bt

I n v e r s i o n i n the o r d e r o f w e a r r e s i s t a n c e o c c u r s w i t h

lg at --- Ig a2. (where ~t > 22) lg w > ba - - bt

and

lg at - - lg a2 Ig w < (where 2t <.:5 z2).

b2 - - bt

U n d e r p r o d u c t i o n c o n d i t i o n s t h e p a r a m e t e r s of a p u m p f l u c t u a t e c o n s t a n t l y a r o u n d s o m e a v e r a g e v a l u e .

A l o n g w i t h the v a r i o u s f l u c t u a t i o n s i n p r o c e s s e s due to d y n a m i c c a u s e s , t h e c h a n g e s i n t he o p e r a t i n g c o n - d i t i o n s of a p u m p l e a d to c h a n g e s i n t h e v e l o c i t y of c o l l i s i o n of a b r a s i v e p a r t i c l e s w i t h t he s u r f a c e of t he

m a t e r i a l . W i t h a d i s c r e t e c h a n g e in t he c o l l i s i o n v e l o c i t y w t h e w e a r ~? c a n b e d e s c r i b e d a s t he s u m of w e a r i n c r e m e n t s i n d i f f e r e n t t i m e i n t e r v a l s A t = t / n ( w h e r e t i s w e a r t i m e ; n i s t he n u m b e r of l o a d s ) , i . e . ,

k

~ l = A t ~ , m~ =t~_~ =iPi, i = 1 , 2 . . . . . k, (2) i ~ l t ~ 1

77

TABLE 2

I proportionality fac- tor X at different coefficients of

b [vari_.__ati~_._.._ _

[ 0,10 0,20 0,30

1,00 1,00 1,00 1,00

1,25 l,OO 1,01 1,01

1,50 1,00 1,01 1,03

1,75 1,01 1,03 1,06

2;00 1,01 1,04 1,09

2,25 1,01 1,05 1,12

2,50 1,02 1,07 1,16

2,75 1;02 1,09 1,21

Proportionality fac~ tor X at different coefficients of

b variation

] O~ 0,2"--0 0,30

3,00 1,03 1,12 1,27

3,25 1,04 1,14 1,32

3,50 1,04 1,17 1,39

3,75 1,05 1,20 I 47

4,00 1,00 1,24 1,56

4,25 1,07 1,28 1,65

4,50 1,03 1,32 1,78

4,75 1,09 1,37 1,87

TABLE 3

Coefficient of variation Yw,

0,10

0,20

0,30

Proportionalit factor X

experimental

1 nq+O,lO '~--0,04

1 19+~ '09 ' --0,08

1 31 +0,08 ' --0,06

theoretical

1,01

1,05

1.12

Note. The upper deviation of the experimental factor X refers to m w = 17 m/see and the lower to m w = 5.3 m/see.

w h e r e Pi -- h i / n is the f r e que nc y of the o c c u r r e n c e of a t t acks ; n i is the n u m b e r of changes in the ope ra t i ng condi t ions of the pump a t the s a m e c o l l i s i on ve loc i ty .

Subs t i tu t ing r e l a t i o n s h i p (1) into (2) and taking the c o l l i s i on ve loc i ty as w i = w(1 + VwUi) , i .e , ex - p r e s s i n g i t i n t e r m s of the coef f ic ien t of v a r i a t i o n of the e m p i r i c a l d i s t r i b u t i o n of v w = s / w (where s and

a r e the e m p i r i c a l s t anda rd dev ia t ion and a r i t h m e t i c mean) and the n o r m a l i z e d dev ia t ion ui = {wi - w ) / s , we obta in

k

l=1

To d e t e r m i n e the w e a r with con t inuous changes in the c o l l i s i on v e l o c i t y we i n t r oduc e the va lue of the dev ia t ion of the c u r r e n t c o l l i s i o n ve loc i t y f r o m the a r i t h m e t i c m e a n x, equal to w - w. With dev ia t ions of the ve loc i ty w, the i n c r e m e n t of wea r , with va lues be tween x and x + Ax, takes the f o r m

d ~= t ~r(x)dx, (3)

whe re p(x) is the p robab i l i t y dens i t y func t ion of r a n d o m va lues .

Af te r i n t e g r a t i o n of e x p r e s s i o n (3), tak ing a c c oun t of equal i ty (1) and the n o r m a l i z a t i o n of the de - v i a t i on of r a n d o m va lue s , we ob ta in

anigz "q = am~ t ~ f(Iw, u) p (u) du,

groin

where Tw = ~ w / m w is the t h e o r e t i c a l coef f ic ien t of v a r i a t i o n ; m w and a w a r e the m a t h e m a t i c a l expec ta t ion and s t a n d a r d dev ia t ion of the t h e o r e t i c a l d i s t r i bu t i on ; u = (w - m w ) / ~ w .

If the ve loc i t y w has a s t a n d a r d d i s t r i b u t i o n with p r oba b i l i t y

- ( ~ - m ~ } ~

1 2~2 p ( w ) = ~ e

then the e x p r e s s i o n for c a l cu l a t i ng w e a r has the f o r m

whe re

2 = (1 + 7~ u) b e d u . ( 4 )

--co

The va lues of coef f ic ien t ~ = q(Yw, b) a r e g iven in Tab le 2.

T h e o r e t i c a l r e l a t i o n s h i p (4) was ve r i f i ed in c o n f o r m i t y with [4] by t e s t i ng annea l ed s a m p l e s of s t ee l 25. The v a l u e s of a and b w e r e f i r s t d e t e r m i n e d for the r a n g e of v e l o c i t i e s m w f r o m 5.3 to 17 m / s e e (Table 1). Then t e s t s w e r e made with s t epwise changes in the ro t a t i ona l ve loc i ty of the i m p e l l e r in which each t e s t was c h a r a c t e r i z e d by the va lue of m w and the coef f ic ien t of v a r i a t i o n Yw- The ro t a t i ona l ve loc i ty

78

was calculated f r o m the a v e r a g e speed of the hard par t ic les [3] and the values of the normal dis t r ibut ion of ve loc i t ies w. On the bas i s of the exper imenta l appara tus avai lable , we se lec ted the following values of co l - l i s ion veloci ty and coeff icient of var ia t ion: m w = 5.3, 10.6, and 17 m / s e c ; 7w = 0.1, 0.2, and 0.3. The wea r was de te rmined a f t e r 20 s tepped changes in the ro ta t ional ve loc i ty of the impe l le r . The t ime of r o t a - t ion during each change in veloci ty was 1 rain. The sequence of values of rotat ional ve loci t ies of impe l l e r during s tepwise changes was de te rmined f r o m the table of random numbers .

Compar i son of the values of ~ (Table 3) indicate that the propor t ional i ty fac tor de te rmined exp e r i - menta l ly is higher thantha t calculated by fo rmula (4).

The d ivergence of the theore t ica l and exper imenta l va lues of the propor t ional i ty fac tor can be ex- plained by the fact that a change in col l is ion ve loc i ty leads to an unaccounted for change in the ave r ag e value of the angle of a t t ack and a change in the concentra t ion of ab ra s ive pa r t i c les in the liquid at the s u r - face . However , this d ivergence is admis s ib l e for engineer ing calculat ions, which makes it poss ible to r e c o m m e n d the method for p rac t ica l use.

1o

2. 3.

4.

L I T E R A T U R E C I T E D

I. R. Kleis , in: Proceed ings of Tal l in Polytechnical Insti tute [in Russian] , Ser. A. No. 237, Tall in (1966). A. I. Zo lo ta r ' , Khim. i Neff. Mashinos t r . , No. 3 (1969). N.D. Polotski i and A. I. Zo lo ta r ' , in: Mining Machinery and Automation [in Russian] , No. 5, TsNIEIuglya, Moscow (1970). I. V. Krage l ' sk i i , E. F. Nepomnyashchi i , G. M. Kharach, and M. P. Zyul 'kov, Mashinovedeuie, No. 1 (1968).

79