E X P E R I M E N T A L I N V E S T I G A T I O N O F T H E S T R E S S

IN B E L T C O N V E Y O R D R U M S

I~. S. U m a n s k i i a n d G. L . K a l i k h m a n

C O N D I T I O N

UDC 539.3

The drum in a belt conveyor is a c r i t i c a l and loaded unit. There a r e five to eight d r u m s weighing up to 4-6 tons each in modern, l a r g e - c a p a c i t y conveyors . The weight of d r u m s in ex t ra l a r g e - c a p a c i t y a s - s e m b l i e s i s even g r e a t e r . The load on the d r u m s is tens of tons, and in some ca se s , 100 tons and m o r e . In recen t y e a r s , breakdowns of d r u m s became m o r e frequent as a r e su l t of the i n c r e a s e in the output c a p a - c i ty of conveyors . This led to, long s t ands t i l l s of highly eff icient a s s e m b l i e s . The re fo re , the p r o b l e m s of planning, designing, and expe r imen ta l inves t iga t ion of d r u m s is of g rea t i n t e r e s t . In the p re sen t paper , the appa ra tu s is d e s c r i b e d and r e s u l t s a r e given of t e n s i o m e t e r t e s t s c a r r i e d out on conveyor d r u m s in the l abo ra to ry of the Depar tment of Strength of M a t e r i a l s at the Kiev Poly technic Inst i tute.

The object of the t e s t s was the de t e rmina t ion of s t r e s s e s in a number of points of s t a t i ca l ly loaded idle d r u m s with f iat d isks , the a n a l y s i s of r e s u l t s obtained f rom exper imen ta l inves t iga t ions , the c o m p a r i - son with des igned data, and the check of a l lowances accepted in the ca lcu la t ions .

Desc r ip t i on of the Device . The device which was used for t e s t ing d r u m s i s shown in Fig . 1. Supports 2 of the d rum and legs 3 of the tension mechan i sm a r e mounted on bedpla te 1.

Nuts with s c r e w s 4 pass ing through the nuts and turned by means of handle 5 a r e p r e s s f i t ted into the base of the legs . Sliding blocks 7 fixed to sc rew 4 by a nut and a lock-nut move along guides 6 to the legs . A th rus t bear ing is mounted between the nut and the s l id ing block to reduce the f r i c t ion of the r o t a t - ing s c r ews . The inves t iga ted d rum 9, the bas ic p a r a m e t e r s of which a r e shown in Fig . 2, is mounted on the p r i s m s 8 of the suppor ts 2. The load on the d rum is t r a n s m i t t e d f rom the conveyor belt 10 which is connected with one end through a r m 11 and hinges 12 to the s l id ing block 7, and with the o ther end through a r m 13, d y n a m o m e t e r s 14, and bolts 15, to the bedplate 1. The angle of contact between the d rum and the bel t 2 fl0 = 180~ The fo rce ac t ing on the d rum was d e t e r m i n e d by means of r ing d y n a m o m e t e r s 14. St ra in gages were s tuck onto the d y n a m o m e t e r s and dia l i nd ica to r s were mounted. The force was addi t ional ly con t ro l led by means of pickups 48, 49 (see Fig . 2) stuck onto the shaft of the d rum. The l eads f rom a l l

F ig . 1. Ex te rna l view of the s tand for s ta t ic t e s t of d rums .

Kiev Polytechnic Inst i tute . T r a n s l a t e d f rom P r o b l e m y Prochnos t i , No. 7, pp. 64-67, July, 1970. Or ig ina l a r t i c l e submit ted A p r i l 5, 1970.

�9 1971 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 for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher [or $t5.00.

670

, 15o ~ : 5 5go v i e w G - - J w _ 5~o - . ~ ! E

I~ ---------.E ' ' -- ------__--__ 7Z :---__I--- -

v ,~c_.~- - _Tq ~ _ - - _ . - ~ - - - _ - ~ - ~ ~ ZB-k-; : : r - - -

View F

~ B e l t ~

F i g . 2. D i a g r a m of d r u m with a t t a c h e d p i c k u p s .

p i c k u p s w e r e w e l d e d to the c o r r e s p o n d i n g t e r m i n a l s on the p a n e l of p l u g - a n d - s o c k e t s 16 which, in tu rn , w e r e c o n n e c t e d to m u l t i p o s i t i o n s w i t c h e s 17 c o n n e c t e d to the m e a s u r i n g i n s t r u m e n t . An "Or ion" E M G - 2353 t ype e l e c t r o n i c b a l a n c i n g b r i d g e was u s e d a s a m e a s u r i n g i n s t r u m e n t f o r s t a t i c m e a s u r e m e n t of s t r a i n s . The e x a m i n e d p ickup was c o n n e c t e d to one of the a r m s of the b r i dge , and a c o m p e n s a t i n g p ickup s t u c k to a s t e e l p l a t e was c o n n e c t e d to the o t h e r a r m .

T h e s t r e s s cond i t i on of the d r u m was i n v e s t i g a t e d by m e a n s of 47 t e n s i o m e t e r s , the m e t h o d of a t - t a c h m e n t of which i s shown in F i g . 2. The p i c k u p s w e r e g r o u p e d in the fo l lowing s e c t i o n s : in the m i d d l e o f the s h e l l ( A - A ) , on the c o n t o u r of the j o in t be tw e e n the s h e l l and the d i s k ( B - B a n d B' - B ' ) , on the e x - t e r f i a l ( C - C) and on the i n t e r n a l ( D - D and D' - D') c o n t o u r s of the d i s k , and a l s o on the p r o t r u d i n g p a r t of t he s h e l l ( E - E ) .

M o s t of the p i c k u p s w e r e a t t a c h e d to the e x t e r n a l s u r f a c e s of the s h e l l and d i s k s , in o r d e r to m e a - s u r e the s t r e s s e s in the p o i n t s of the u p p e r p a r t of s e c t i o n A - A ( - 9 0 ~ < fl < 90~ the p ickups w e r e s tuck to the i n t e r n a l s u r f a c e of the she l l to p r o t e c t t h e s e f r o m d i r e c t c on t a c t wi th the be l t . T o m a k e a c c e s s to t h e s e p i c k u p s p o s s i b l e , t e c h n o l o g i c a l c u t s w e r e m a d e in one of the d i s k s ( see F ig . 1). T h i s m a d e i t p o s - s i b l e to m e a s u r e the s t r e s s e s in the zone of the cu t s by m e a n s of the p i c k u p s No. 1, 2. In the s h e l l s e c - t i on A - A , w h e r e the d i r e c t i o n s of the p r i n c i p a l s t r e s s e s a r e known, the s t r a i n g a g e s w e r e s tuck in the m e r i d i o n a l and c i r c u m f e r e n t i a l d i r e c t i o n s ; in the B - B , B ' - B ' , and E - E s h e l l s e c t i o n s , the s t r a i n g a g e s w e r e s t u c k in a " r o s e t t e " a r r a n g e m e n t in the c i r c u m f e r e n t i a l and m e r i d i o n a l d i r e c t i o n s us ing the p ickuSs No. 1, 2. In the s h e l l s e c t i o n s C - C , D - D , and D ' - D ' , the p i c k u p s w e r e s tuck in the r a d i a l and c i r c u m - f e r e n t i a l d i r e c t i o n s .

T h e c o o r d i n a t e s of the p i c k u p s in the c i r c u m f e r e n t i a l d i r e c t i o n s a r e g iven below:

P i c k u p No. fl, deg P i c k u p No. fl, deg P i c k u p No. fl, deg P i c k u p No. /3, deg

1 28 13 90 25 21 37 90 2 60 14 26 38 3 90 15 27 39

100 64 180 4 16 28 40

0 5 17 29 41

140 6 ] 18 30 42

7 I 180 19 180 31 90 43 0 8 20 32 44 9 21 33 45

0 180 10 22 34 46 180

0 11 23 35 21 47 12 12 24 36 48 34

T h e s y m m e t r y p l a n e of the d r u m in which the r e s u l t a n t of the s t r e s s e s in the r u n n i n g - o n and r u n n i n g - o f f b r a n c h e s of the be l t l i e s i s u s e d f o r beg inn ing the c a l c u l a t i o n .

671

o, kgf/cm 2 .

'~176 " l \ ,~176 "), / '" . , I i ~/ \150 B, deg

[ - " t / / A ~ ' ~ " 1

'\ / / k v " I I- ",, ' , / . / \ / / I

- aO0~ Xv"" ~ 6P / a

o, ,kgf/cm 2

lOg

0 -I00

30 50 9~f 120 lSOJ~ deg

F i g . 3. G r a p h s f o r s t r e s s e s in the d e - s i gn s e c t i o n s of the d r u m . a) In the m i d d l e of the she l l (A-A); b) e x t r e m e s e c t i o n of the she l l (B-B); c) e x t e r n a l c o n t o u r qf the d i s k (C-C); d) i n t e r - na l con tou r of the d i s k (D-D)

o, kgf/cm ~

100

O_ 30 ~ o -IO0 ~o(

-200 b

7o 12,o

-300 . -'.

100

_L .L ~90 i 0 30 60 \ lZg IJOfl, deg

-I00 ~. 5.

-201 ~ c ~ o "306

In the m e a s u r e m e n t s , the d r u m was r o t a t e d t h r o u g h 30 ~ Th i s m a d e i t p o s s i b l e to m e a s u r e the s t r e s s e s in a l a r g e n u m b e r of po in t s .

The r e s u l t s of the m e a s u r e m e n t s a r e c o m p a r e d with t h e o r e t i c a l d a t a in F i g . 3. The con t inuous l i n e s show the s t r e s s e s o b t a i n e d by c a l c u l a t i o n . The c a l c u l a t i o n was m a d e by m e a n s of an e l e c t r o n i c c o m p u t e r and by t ak ing into a c - count the r e l a t i v e r i g i d i t y of the she l l , d i s k s , and sha f t . T h e t e n s i o n of the be l t was T = 4000 kgf. T h e s y m b o l s V, O, and [] c o r r e s p o n d to the e x p e r i m e n t a l r e s u l t s o b t a i n e d f o r crfl, a r , and r . A s c a n be s e e n f r o m the f i g u r e , a t a s u f f i c i e n t l y h igh l e v e l of s t r e s s e s (~ > 150 kgf /cm2) , the a g r e e m e n t be tw e e n the c a l c u l a t e d and e x p e r i m e n t a l da t a i s s a t i s f a c t o r y . When the s t r e s s l e v e l i s low, s c a t t e r in t he r e s u l t s o c c u r s s i n c e the m a g n i t u d e s of the s t r e s s e s a r e wi th in the a c c u r a c y l i m i t s of t he m e t h o d (p ickups No. 9, 13, 14, 15, 20, 22, 25, 28, 30, and 32)* A c o m p a r a t i v e - ly l a r g e d i s c r e p a n c y be tw e e n the t h e o r e t i c a l and e x p e r i - m e n t a l da t a i s a l s o noted fo r the p o i n t s wi th a h igh s t r e s s g r a d i e n t (p ickups No. 13, 15, 27-32) . T h i s i s due to the

fac t tha t an a v e r a g i n g of s t r a i n s and s t r e s s e s o c c u r s o v e r the l eng th of the p ickup a = 10 r am. The a n g l e

a.360 10.360 _ 2.1% h ~ - - 2R - - 2 ~ . 2 7 o

w h e r e R i s the e x t e r n a l r a d i u s of the d r u m , R = 270 m m , r e f e r s to t h i s l eng th when the p i ckup i s s t u c k in the c i r c u m f e r e n t i a l d i r e c t i o n . In a r a n g e fl = 80 -100 ~ the s t r e s s e s on the a r c 2 ~ v a r y by 15-30%.

The p i ckups No. 35-40 s tuck onto the s h e l l beyond the l i m i t s of the s u p p o r t i n g d i s k s r e c o r d v e r y i n s i g n i f i c a n t s t r e s s e s . S t r e s s e s in t h i s s e c t i o n w e r e not d e t e r m i n e d t h e o r e t i c a l l y , s i n c e i t was a s s u m e d tha t the p r o t r u d i n g p a r t s of the she l l c an be i g n o r e d .

It should a l s o be noted tha t the e f fec t of the cu t s in one d i s k on the s t r e s s cond i t i on of the s h e l l was i n s i g n i f i c a n t , s i n c e the s t r e s s e s in the s e c t i o n s B - B and B' - B ' w e r e found to be a l m o s t i d e n t i c a l . In the d i s k i t s e l f , t he s t r e s s e s a t the e d g e s of the c u t s e x c e e d f ive to t e n t i m e s the s t r e s s e s in the s a m e p o i n t s

* T h e s e p o i n t s a r e not shown in F ig . 3.

672

of the disk which is not weakened by the cuts, although the absolute values of these s t r e s s e s are not high.

C ONC L U S I O N S

1. The tens iometr ic method of investigation shows that the agreement between theoret ical and experi- mental data is sa t is factory. Consequently, the assumptions which have been made on designing idle drums with a flat disk * can be accepted: a) the drum is rigidly mou~ted on the shaft; b) the width of the belt is equal to the distance between the supporting disks; c) the par t of the shell protruding beyond the limits of the supporting disks can be ignored. As a result , the interaction between the d i sk and the shell can be r e - presented by the contour forces .

The latter assumption is confirmed by an additional investigation of the s t r e ss condition of the p ro - t ruding shell par ts .

2. The discrepancy, noted for a number of points, between theoret ical and experimental data is due to the e r r o r obtained by using this method if the level of s t r e s ses is not high and by averaging the s t rains over the length of a pickup. This is par t icular ly noticeable for points with a high s t r e s s gradient.

3. The a symmet r i c and nonuniform application of load over the length of the drum on the side of the belt hardly d is tor ts the picture of its s t r e s s condition.

*l~. S. Umanskii and G. L. Kalikhman, "On the design of idle drums in belt conveyors" , in: Strength of Mater ia ls and Theory of Construct ion [in Russian], 10th issue, Budivel 'nik, Kiev (1970).

673