DYNAMOMETER

WITH

A

PHOTOELASTIG

MEASURING

ELEMENT

G. A. Katkov

UDC 531.78 : 622.284

In e x p e r i m e n t a l investigations of rock pressure, the loads on the supports of d e v e l o p m e n t and m i n i n g - o u t workings are measured using a very wide range o f methods and instruments. The most popular methods a r e those based on d k e c t measurement o f loads by means o f individual devices l o c a t e d between the support e l e m e n t s or at its p e r i m eter, or involving the use of special dynamometer platforms and supports. In most cases the measuring instruments are dynamometers (mechanical, hyckaulic, or electrical). In these instruments the deformations of the measuring elements induced by the application of an e x t e r n a l load are measured by indicators, gages, e l e c t r i c strain gages, and inductive and m a g n e t o e l a s t i e transducers [1]. In recent years attempts have been m a d e to use photoelastic transducers as the measuring e l e m e n t s of force m e a s u r e m e n t instruments [2, 3]. The A. A. Skochinskii Mining Institute has developed a d y n a m o m e t e r with photoelastic measuring elements to measure concentrated and distributed loads on the supports of m i n e workings. A m e m b r a n e dynamometer with a photoelasdc strain gage has been proposed for the m e a s u r e m e n t of loads on m e t a l supports of special profile. The dynamometer (Fig. 1) consists of a casing 1, a m e m b r a n e 2, resting freely on the periphery or fixed r i g i d ly to it, a uniaxial photoelastic strain gage 3, glued at both ends in the center of the inner side of the membrane, bolts 4 to fix the m e m b r a n e to the casing, a tube 5 for the strain gage readings, a nut 6, and a cover 7. When a distributed or concentrated load acts on the dynamometer, the m e m b r a n e is depressed and tensile stresses (deformations), recorded by the photoelastic straIn gage, are induced on its inner side. The mean relative deformation at the base o f the strain gage is r e l a t e d to the a p p l i e d load. When the m e m b r a n e is fixed rigidly to the periphery, the absolute deformation at the point of a t t a c h m e n t of the photoelasfic strain gage will be t/2{

3_q..q l (l -- ]x') [ R ' -

A l = 2 1 edl = L/

45 z

l~ ]

2E

(1) '

0 and the average r e l a t i v e deformation will be

e'av--

AI q q ( t - ~x~)[R ~ _~] l -862E -9

(2)

When the membrane is not fixed to the periphery, the average r e l a t i v e deformation will be e av--

3q[

8~

R2 (3 --

2~x - - [.t 2) - - ~

(1 -~- ~t2)

]

(3)

9

A. A. Skochinskii Mining Institute. Translated from F i z i k o - T e k h n i c h e s k i e Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 105-107, May-June, 1973. Original article submitted January 24, 1972.

9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

323

:r *v

. ~ ,

r

2

S

! 150 ~ "'7, PO

.

4

t

~ " ~?z4_--,z----~

P,; t o n s

:

\ \

2

El ---s

,

0

0

400

~

6'00

~200

;600

2000

'400

4 m~ Fig. 2, Relative path difference of polarized beams in a strain gage vs load on the d y n a mometer.

Fig. 1, Diagram of dynamometer with photoelastic m e a ~ r i n g element.

When a concentrated load P acts on the membrane a t the center, the r e l a t i v e deformations at the base of the strain gage are as follows: for a rigidly attached m e m b r a n e

ear=

0.436P

(4) ERa6 "

for a freely resting membrane

I

]

R2 ( 3 - 2 ~ t - ~ t 2 ) - - - ~ ( 1 +Ix ~)

eav-: 0,068P where AI is the absolute deformation in centimeters, e av is the average r e l a t i v e m e m b r a n e thickness in centimeters, R is of the membrane m a t e r i a l in k g / c m z, g load in kilograms.

E R z 5 ' (1 -- e) (5 + V)

(5)

the membrane secwr in centimeters, I is the length of the strain gage in deformation in the sector, q is the distributed load in k g / c m z, 6 is the the radius of the m e m b r a n e in centimeters, E is the modulus of e l a s t i c i t y is Poisson's ratio for the m e m b r a n e m a t e r i a l , and P is the concentrated

The deformation o f the strain gage is determined by measuring the r e l a t i v e path d i f f e r e n c e o f polarized beams by a unidirectional polar[scope or from band d i s p l a c e m e n t (when a photoelastic strain gage with a "frozen" band p a t terns is used). From the measured path difference, the value of q or P can be determined by m e a n s o f the following equations: for a rigidly attached m e m b r a n e q = 1.33 ~

F;

(6)

P = 1.03 k R 2 F ; for a freely resting membrane q---~ 1.33 k~F; P=7.35

324

klR2F.

(7)

Here k=

E62

E6~ /~1 ---

12

C~t [ R' (3-- 2p,-- p,')-- Ti'-(1-Jr- ~t')]

;

C ~s the optical constant of the strain-gage material with respect to deformation, and t is the thickness of the strain gage in centimeters. The value of the load c a n aim be determined from a calibration curve when membranes of various different thicknesses are used in the dynamometer. Figure 2 shows such a curve for determining a concentrated load P from the measured relative path difference of polarized beams, F, for membranes 0.3-1.0 cm thick. This curve can be used to determine the required m e m b r a n e thickness for a given sensitivity and a given load measurement range. A dynamometer with a photoelastic e l e m e n t has a number of advantages over m e c h a n i c a l dynamometers. Its use excludes the effect of the measuring instrument on the rigidity of the support and therefore on the conditions of its interaction with the rock, owing m the slight thickness of the part of the easing located on the outer side of the support e l e m e n t ; it thus eliminates the effect of the a m b i e n t medium (moisture, temperature variations) on the operative stability of the strain gage, and also simplifies the device itself and the readings, owing to the absence of leads to the strain gage. The dynamometer can be used not only as an individual measuring instrument, but also as the measuring e l e m e n t of stressmeter platforms and supports. LITERATURE 1,

2. 3.

CITED

G. A. Katkov, Measurement of Loads on the Supports of Mine Workings [in Russian], Nedra, Moscow (1969). A. Roberts and J. Hawkes, "A laboratory study of the phomelastic stressmeter,' Inrernat. J. Rock. Mech. and Min. Sci., No. 3 (1964). A. Roberts, J. Hawkes, a n d F. Williams, "Some fields of application of the photoelastic stressmeter," Internat. J. Rock. Mech. and Min. Sci., No. i (1965).

325