ME CHANICAL ME A S U R E M E N T S STRAIN-GAUGE DYNAMOMETER

UDC 531.781.2

Yu. A. Shevtsov

A strain-gauge dynamometer system in the form of a body of rotation is simple to make and convenient to use; some such gauges are available as circular plates for clamping on the outside diameter, with the load applied to a rigid center [I]. The wire device is mounted near the rim. Such a device can be used only in axially symmetrical loading. If the load is not axially symmetrical, three components have to be defined: two projections and the moment in the plane of action of the force, and therefore the strain-gauge system must have a three-channel output. Here we consider a design method for this case. The device consists of a circular elastic plate I with the rigid center 2 and outer ring 4, which is used in mounting the device (Fig. I). The gauges proper 5 are cemented to the elastic plate i. The force is applied to the pin 3 mounted in the rigid center 2. The thickness of the elastic plate and the relationship between the load and the output signal may be derived from the superposition principle applied to the components Fs, Fn, and M A. It is assumed that the strain is small by comparison with the thickness h, and h itself is small by comparison with the radius R. Expressions are available [1-3] for the radial stresses % and the circumferential stresses % , and these indicate that the stresses due to F s are less by two orders of magnitude than those due to F n and MA, while the largest stresses arise at a point O --r and We neglect the stresses due to F s and specify R and r from design considerations, whereupon h can be found from the energy theory of strength [4]: f

r2

1 Fn

r

(1 ~ r~

where n is the safety, factor, ~ is Poisson's ratio, Oy is the yield point of the straingauge material, and a is the distance from point A in the pin to the center 0 of the strain gauge. When the dimensions of the gauge have been defined, one has to determine the maximum deflection ~ of the center and the angle 0 of rotation from the following expressions [2, 3]:

k

R/ F2

O=

3(MA--aFs) ~Eh3

(1--~2)

In

(3) r2

~+-~

'

where E is Young's modulus for the material. The maximum output signal is provided by making the device of spring steel having a high o , while the strain gauges are placed close to the outer ring and to the center (Fig. i). T~e gauges Rzs, Rx~, R~s and Rs~ are cemented to a separate compensating plate (not shown in Fig. i). Figure 2 shows the mode of connection.

Translated from Izmeritel'naya Tekhnika, No. 6, pp. 33-34, June, 1979.

684

0543-1972/79/2206-0684507.50

9 1979 Plenum Publishing Corporation

$

/-

RE

,,,,,,,.

,:.,, , .,, , :]

[1chart. 12chan;I Ychan Fig. 2

Fig. 1

The expressions for o O and o~ give the load in relation to the readout hi: Fn = rnlhl; M 0 ----tn,zh~ @ kxFn; Fs = t't~h3 + k~.F. + k3Mo; MA = 34O -{- aFs,

where m i is the scale factor, M 0 is the moment applied at point 0, and k i is a coefficient of proportionality (i =i, 2, 3), where the coefficients m i and k i are to be determined by calibration. The calibration is performed in the following sequence. With a load F s applied to the rigid center in the plane of the elastic plate, we have

Fs m,-

h~ '

(4)

where hl =h2 =0. When F s is applied to point A parallel to the plane of the plate, we have ~ _------;

h~ ks=--

Fs

-

m~h~ aFs

(5)

-

When F n is applied to point A perpendicular to the plane of the plate, we have Fn

mI ~

hl

k, = __

m~h____~ ; Fn

k, = .

m03 Fn

(6)

This method was tested by making a device of 60S2A steel having Oy =1500 N/mm 2, E = 2.09"105 N/mm 2, and ~ =0.3, with the dimensions as follows" R =I00 mm, r =25 mm, a =50 mm, thickness of rigid center and outer ring 20 mm. For a limiting load of F s =F n ~ 5000 N and M A = 3 0 0 N-m we get from (i) that h =3.8 mm, while (2) and (3) give the maximum strain as ~ffi 0 . 4 1 m m and e = 0.ii ~ Clearly, the strains are reasonably small. FKPA foil gauges of baseline I0 m m w e r e used. The device was connected to an 8ANCh-7M measuring system, a shunt box, and an R-155 resistance box ~ogether with an N-II5 oscillograph. The relationship between the readout h i and the load was linear. The coefficients of (4)-(6) defined by calibration were as follows: m, =m3 =40 N/mm, m2 =4 N.m/mm; kx = --0.059 m, k2 = --0.196, k3 = --9.29 i/m. Tests showed that the method is sound and that the device is convenient; it gives ~apid and precise measurements of the three force components of an off-axis load.

685

LITERATURE CITED i. 2.

3. 4.

G. F. Malikov et al., Design of Elastic Strain-Gauge Components [in Russian], Mashinostroenie, Moscow (1964). S. P. Timoshenko, Plates and Shells [in Russian], GTI, Moscow--Leningrad (1948). F. M. Dimentberg, Vestn. Inzh. Tekh., No. 7 (1938). N. M. Belyaev, Resistance of Materials [in Russian], Nauka, Moscow (1976).

PULSE-PHASE TORQUEMETER UDC 621.3.016.1.08

A. L. Krainev and Yu. V. Klevtsov

The most effective means of measuring and monitoring loads in transmission systems are provided by magnetically coupled devices attached to the shafts; a device of this type has been developed at the Urals Automobile Plant, which converts the angle of torsion to a phase shift between pulses. The device includes the pulse transducer and an electronic phasemeter. The transducer (Fig. i) consists of the elastic shaft i, whose ends bear two ferromagnetic toothed disks 6 with outside teeth, while the body 7 is driven by a belt drive from the motor 8 and bears two ferromagnetic toothed disks 5 with internal teeth. These disks 5 and 6 are set up in pairs with gaps between the crests of the teeth of 0.12-0.25 mm. The magnetizing windings 3 and working windings 4 are mounted on the immobile magnetic cores 2. Permanent magnets may be used instead of magnetizing windings. The windings 3 are supplied with d.c. and set up a field that passes through the gaps between the teeth on disks 5 and 6. When shaft 1 rotates, the magnetic impedance of the gaps alters, and a pulsating emf is induced into the windings 4. The phase shift between the pulses is governed by the angle of torsion of the shaft and thus by the torque applied to it. Statis calibration and measurement when the shaft is immobile or rotating slowly (less than 500 rpm) are provided by rotating the body 7, which causes a pulsating emf to pass to the phasemeter. The latter (Fig. 2) includes the amplifiers 2 and 9, which receive the pulses from the windings i and i0. The signals pass to the clippers 3 and 8 and then to the differentiators 4 and 7, whose outputs are positive-going sharply-rising pulses. These pass to the flipflop 5, in which the load of one of the transistors is the milliammeter 6. The current through this directly proportional to the phase difference between the pulses and thus to the torque. The average current indicated by the meter is that carried by flip-flop 5:

l a y = !~

AT T

'

where Io is .the current through the open arm of the flip-flop, AT is the pulse length, and T is the pulse repetition period.

2 3~56

~ ~ !

Fig. i

2

Fig. 2

Translated from Izmeritel'naya Tekhnika, No. 6, pp. 34-35, June, 1979.

686

0543-1972/79/2206-0686507.50

9 1979 Plenum Publishing Corporation