MECHANICAL MEASUREMENTS

HIGH-SPEED WEIGHING SYSTEM WITH A MULTICOMPONENT STRAIN-GAUGE DYNAMOMETER V. V. Bogdanov, A. S. Romashkin,

and B. A. Derkach

UDC 681.26:531.787.2:519.2

The high-speed multicomponent weighing system (WS) is meant for measuring and recording the components of the resultant aerodynamic force and moment acting on a model in installations of short-time action. The duration of the working process in these installations is counted in hundredths and thousandths of a fraction. The operating conditions of the weighing system are made complicated by the fact that the strain-gauge dynamometer body experiences the effect of vibrations during the experiment. A multicomponent strain-gauge dynamometer of high rigidity is used as the primary transducer. Dynamic characteristics of the dynamometer with the model are selected so as to meet contradictory requirements, i.e., to provide for high sensitivity and high natural frequencies necessary for enhancing the high-speed response of the system. In this, the measured deformations are in the 0.5-50"10 -6 range. Silicon resistance strain gauges are used to compensate for the loss of sensitivity. Strain-sensitivity of these gauges are 50 times more than that of the wire and foil gauges. The high-temperature sensitivity of these gauges does not substantially affect measurement accuracy since the duration of the aerodynamic experiment is very brief. Moreover, enhancement of the short-time action is facilitated by inclusion of an inertial compensation device (ICD) and optimum low-pass filter (LPF) in the system. The ICD consists of strain-measuring accelerometers rigidly connected to the model and a summator block. The dynamometer is mounted on a vibration damping platform to reduce the level of body vibrations. The block diagram of the WS is given in Fig. i, where A is the amplifier with its output connected with the recorder (R). The high-speed action of the weighing system is based on using inertial compensation for the vibration components of the output signals of the dynamometer. Its principle is based on independent measurement of the elastic and inertia force vectors and their subsequent summation with determined coefficients. The advantage of this, as opposed to usual methods of filtering, lies in increased high-speed action and the possibility of producing a wide-band output signal. We examine the operating principle of the ICD in an example of a single-stage dynamometer consisting of a load of mass m fixed on an elastic element of rigidity c. The point of suspension of the elastic element is displaced in conformity with the law x s = xs(t). The accelerometer is mounted at the load center. The requirement is to measure the variable force F = F(t) applied on the load. There is no damping. The equation of motion of the load will be mx + c(x - x s) = F, where x is displacement of the load relative to the fixed system of coordinates. The output signal of the dynamometer s d is proportionate to the elastic force F e = c(x - Xs), so that E d = aF e and the output signal of the accelerometer ea, to acceleration x, i.e., E a = bx (a and b are constant conversion factors). The signal ~c = Sd + AEa = a[c(x - x s) + (b/a)Ax] is formed with the help of the ICD. Here, A is a variable weighted factor of the accelerometer signal. It is possible to select A such that (b/~)A = m and then E c = a[c(x - x s) + mx] = aF, i.e., the compensated signal Sc is proportionate only to the measured force F and is independent of inertia forces occurring as a result of displacement of the point of suspension and natural vibrations of the elastic system. Actually, signals s d and E a are fed to the summator input with the controlled weighted factor of the accelerometer signal. The natural vibraitons of the dynamometer are required to be excited for tuning the ICD and, by varying the amplitude of the signal Sa, full compensation achieved for the dynamic component in the output signal Sc" In this, there is Translated from Izmeritel'naya Tekhnika, No. 7, pp. 27-28, July, 1990.

0543-1972/90/3307-0673512.50

9 1991 Plenum Publishing Corporation

673

"

CM

OC

tag

[

'

'

J

_,

Fig. 1

Fig. 2

no need foe exact measurement of the value of load acceleration and for accounting for the actual sensitivity of the accelerometer. The measurement error will be mainly determined by the dynamometer error since the dynamic component of the signal caused by inertia forces is suppressed practically to the level of the equipment noise. In a general case, the dynamometer has six degrees of freedom. However, when the center of mass of the model coincides with the dynamometer axis, the problem of total compensation breaks down into the corresponding problems in the vertical (components Y and M z) and horizontal (Z, My) planes, and the problem of compensation along and around the dynamometer axis (components X and M x) [i]. The solution of the problem of compensation in the vertical plane is represented in Fig. 2, where

A1y-AI Mz - -

Xa2--xa I

Xa2 _ *"al

m; A,2y~ m/A;

Xa~ ,_--Xal" ra;

,4~Mz.-

.~a_o --xal

mfe..

Here, Xal is the coordinate of the point of fixing of the first accelerometer relative to the origin of coordinates (OC); Xa2 is the coordinate of the point of fixing of the second acceleromater; ~o is the distance between points OC and CM (center of mass); P0 is the radius of inertia of the model; m is the mass of the model. It is evident that a similar solution extends to the components Z, My and X, Mx, which leads to the solution of the complete problem of compensation in a case when the CM of the model lies on the dynamometer axis. As is seen from the relationships given above, inertia parameters of the model are part of the weighted coefficients. Hence, retuning of the ICD is required on changing the model. For this, a method of tuning has been developed which realizes the algorithm for iterative solution of the compensation equation with unknown inertia parameters of the model. This method reduces to a process of successive adjustments. The practical circuit of the ICD was constructed based on the positions discussed earlier. It confirmed the possibility of inertia compensation for the signals of the components. Along with this, it was observed that total compensation in the higher frequency region is not possible without accounting for the actual properties of the accelerometers used. Primarily, these are the amplitude- and phase-frequency characteristics. Phase equalizing circuits connected before the ICD and specially calculated LPF following immediately after the ICD were introduced in the WS for better suppression of the high-frequency inertia components.

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The fact that the spectrum of the signal obtained from the dynamometer is significantly nonuniform was considered in selecting the LPF. Its maximums correspond to the first (w01) , second (m02), and other higher frequencies of natural vibrations of the model - dynamometer dynamic system while only small noise components of the signal lie between these frequencies. Since the drawbacks in the operation of the ICD as discussed earlier begin to tell only at sufficiently high frequencies of vibrations, starting from ~02, it was decided to use the type 5.2.10.10 LPF [2] for suppressing noise and higher frequencies of vibrations and a fuse-filter included in series with it for suppressing the frequency ~0~. Since each model possesses its own size and mass, provision should be made for easy retuning of the fuse-filter to the specific frequency m02 in each experiment. Practical realization of such a LPF, its design, and experimental testing are discussed in detail in [3]. Based on the above, a weighing system with a three-component dynamometer was developed and tested. The system is meant for measuring short-time loads of 0.005-sec duration. Dynamic characteristics of the system and its elements were investigated on a specially designed stand which facilitates the application of a step-by-step load at any given point of the model with an error of not more than 1%. The reaction itself of the dynamometer to the stepped input action contains the vibration component. Its level can be significantly more than the measured signal [4]. The ICD and LPF made it possible to reduce the level of the vibration component in the input signal of the WS by more than i00 times. The characteristics

of the system are as follows:

Number of measured components, Range of measured loads:

3.

X = 0-20 N, Y = 0-20 N, M z = 0-0.25 N.m.

Reaction time of system to a stepped load (setting error of 1%): 2~.172 rad/sec and ~02 = 27.456 rad/sec. rms error of measurements,

0.0025 sec at ~0~ =

~1%.

Resolving power of the setup adjusted for the input, 1 ~V. Effectiveness of ICD operation: the 20-500 Hz range.

decrease in sensitivity to vibration of >40 dB in

Natural frequency of the vibration damping platform,

30 Hz.

The weighing system facilitates reliable measurements of short-time loads of about 0.005 sec duration with a steep leading edge. LITERATURE CITED i. 2. 3.

4.

V. V. Bogdanov, J. Jess and H. B. A. Derkach, Moscow (1985), V. V. Bogdanov

Izmer. Tekh., No. Ii, 50 (1979). W. Schussler, IEEE Trans. on C.T., ST-12, No. 3, 393 (1965). Theoretical and Experimental Study of Fluid and Gas Motions [in Russian], p. 63. et al., Izmer. Tekh., No. 5, 24 (1985).

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