MECHANICAL MEASUREMENTS

A P P L I C A T I O N OF PRESSURE T R A N S D U C E R S S U B J E C T E D

TO LARGE V I B R A T I O N S

I . I . M i l ' s h t e i n , V. N. P i n e s , A. E. Z h u k o v s k i i , a n d G. A. T e r e k h o v

UDC 531.787.09

The operation of pressure transducers is often affected by destabi l iz ing factors, such as high temperature of the measured medium or vibrations. In order to protect the transducer from these effects, the measuring system should be provided with appropriate elements. In a general case the system is then made more complex and provided with a min imum of the following structural eiements: a device intended for protecting the transducer's sensing element

from temperature effects and consisting, for instance, of a pipeline which also protects the transducer from the ef- fect of strong vibrations (insulation from vibrations); a damping device for protecting the transducer from the effect of shocks and vibrations.

The presence of these addi t ional elements, especiaLLy of the pipeline for conveying pressure to the transducer requires the study of their effect on the dynamic characterist ics of the measuring system.

The transfer function of the measuring channel is determined as

~v = Wp "~vtr -Wms-~Vr , (1)

where Wp is the transfer function of the pipeline channel which connects the mains to the transducer, Wtr is the transfer function of the transducer proper, Wms is the transfer function of the transducer's measuring channel, Wr is the transfer function of the recorder.

The to ta t spectrum of vibrations which affect the transducer can be represented by the relationship

n

where X AV g~ t= l

n n

X4,,= o,X % / = 1 i = I

(2)

is the spectrum of vibrations accelerat ions existing in the units and mains of the tested object, Wa i

is the to ta l transfer function of the damping device.

In the system under consideration (Fig. 1) notation Ms represents the transducer's measuring channel, P is the pipel ine, R is the recorder, and Tr is the transducer. It should be noted that such an arrangement can be used with

a pipel ine for measuring re la t ive ly high pressures (according to our data above 2 MN/mZ). Experiments have shown that the use of pipelines for connecting the transducer to the mains whose pressure varies from 0 to 2 MN/m z pro-

duces inadmissibly high random errors in measuring dynamic processes. Therefore, let us examine a system used for measuring re la t ive ly high pressures.

Dynamic response requirements of the pressure measuring system make it necessary to determine with high precision the transfer functions (frequency characteristics) of separate system elements. Let us note that the fre- quency characterist ics of the secondary conversion equipment and the recorders can be evaluated with adequate pre- cision by means of e l ec t r i ca l methods. The transducer's dynamic response is determined by the natural frequency of the mechanica l system. For the s train-gauge pressure transducers in use this frequency amounts to 10-15 kHz.

Translated from Izmer i t e l ' naya Teldlnika, No. 10, pp. 23-25, October, 1969. Original ar t ic le submitted June 4, 1969.

@1970 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New

York, N. Y. 10011. All rights reserved. This artic.~e cannot be reproduced for any purpose whatsoever

without permission of the publisher. ,4 cop), of this article is available from the publisher for $15.00.

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Fig. 1 Fig. 2

ls

K

o,,

~a

o,e

dl

o 200 000 600 800 1000 1200 f#O0 1600 2200 3~00

Fig. 3

,A, ,!,t 1800 2000 Hz

Therefore, the e'lement which determines the dynamic response of the measuring system consists of the feeding pipe- line channel. The precision in determining the transfer function of the measuring system will depend on the pre- cision in evaluating the dynamic properties of this channel.

The computation of the dynamic (frequency) charccteristics of interconnecting pipeline channels is usually made by the method of lumped parameters, since the application of more precise and complex relationships, for in- stance, of the impedance method, is inadvisable, because calculations by means of various techniques produce the same results in the frequency range from 0 to the first resonance of the system.

The design schematic is shown in Fig. 2, where d 1 is the internal diameter of the pipelinechanne[ (0.4 cm), d a is the diameter of the transducer's membrane (1.8 cm), l 1 is the pipeline channel length of 50 cm, and I z is the length of the transducer's reception cavity channel (0.2 cm),

The modulus of the pipeline relative transfer function is

1 A =

/ ( 1 - - T2o~)2 +(TIco) ~

The lagging (phase shift) depends on the oscillatory frequency and amounts to

T1 03 --r 1 - - T 2~2

The coefficients T 1 and T~ in the differential equation of the system's movements are determined as

Tt = 8alx lx Vx ' see, T~ -- lx pVx sec 2, kf~ kf

where w is the angular velocity of oscillations, f is the cycle frequency, p is the dynamic viscosity coefficient, p, is the density, Vp. is the total volume of the hydraulic system, k is the compressibility factor.

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TABLE 1

f, H z

10 20 30 40 50 80

100

p=O, 84 - 10 - 6 ,

I - t=1 ,52" 10 - 8

p = 0 , 9 . 1 0 _ 7 ,

~x=2,68- 1 0 - - 1 0

,7 e Tre s

! 1 , 0 0 o I , 0 0 1 , 0 0 " 0 i I ,00 0 1 , 0 0 00 1 , 0 1 1 , 0 2 <1 ~

5 0 0 H z 90 ~ I

p = 1 , 2 2 . 1 0 - 6 ,

g = 1 , 2 . 1 0 _ 7

0 0 0

.~ ~o . ; 1 0 ~ .~25 ~ < 60 ~

~0 ire s

1 , 0 ) 0 l , 0 ) 0 1 , 0 ) 0 1 , 0 ~ 0 a 1 , 2 I , 3 - < 2 ~ 1 ,5 ,.;5 ~

1 , 0 0 1 , 0 0 1 , 0 0 1 , 2 1 , 8 2 , 2 3 , 6

I r e s

f m s 4 9 0 H z 200 H z 120 H z I r e s 90 ~ 2 2 0 H z 90 ~ I [ 3 0 H 2

For evaluating agreement between the computat ion and exper imenta l results, the following relationship is sometimes used:

i , / / 2r -r, rres-- V ,

where fres is the first resonance frequency of the hydraulic system.

A detai led computat ion was carried out up to 100 Hz (the relevant frequency range for our experiments was 20-30 Hz). The computat ion results are summarized in Table 1.

The trustworthiness of computat ion was est imated by the agreement between the ca lcula ted resonant frequen- cy and the "noise" frequency recorded by the transducer incorporated in the system for measuring the pressure of the given component.

It will be seen from Table 1 that the agreement is fair ly good. Therefore, in analyzing the computed values of the system's ampli tude distortion factor and the phase delay factor, we find that they are negligibly smal l in the range of 20-30 Hz, which is of interest to us.

The recording of dynamic processes with character is t ic durations of 0.05-0.03 sec is not distorted appreciably by connecting pipelines to the transducers which are used for measuring re la t ive ly high pressures. As far as the low pressures are concerned, the processing of the readings of a reference and tested transducer has confirmed the pre- viously expressed assumption about the inadmissibl i ty of using pipelines in low-pressure measuring systems. The ap-

pl icat ion of frequency relationships to such systems is also inadmissible, owing to the considerable nonlinear distor- tions whichexist in the pipel ine-transducer channel and result in spontaneous exci ta t ion of oscillations with con- siderable ampli tudes and the appearance of the frequency fractioning effect.

The particular feature of our pipeline consists of a smal l internal resistance and, therefore, a smal l damping of the osci l latory processes. This is why the column of the component inside the pipeline is l iable to amplify con- siderabty the pressure pulsations at natural frequencies (from t50 to 500 Hz). These "stray" frequencies are e l i - minated by means of e l ec t r i ca l filters, thus raising considerably the quali ty in recording the measured parameters and reducing the errors in processing information.

The transducer is protected from the effect of vibrations and shocks by the damping system which includes a

pipel ine and standard meta t l i zed- rubber shock absorbers. Owing to the difficulty of calculat ing the transfer func- t ion Wa i, it was determined exper imenta l ly by vibration testing of a system on an e lec t r i ca l vibration rack. The relationship of the modulus of Wa i to the vibration frequency is shown in Fig. 3. Since the maximum amplitudes which affect the v ibra t ion-acce le ra t ion system fall within the range of 200-2500 Hz, it is obvious that even for v i - brations with 400-600 g the transducer is affected by vibration loads with ampli tudes of 20-200 g.

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C O N C L U S I O N S

The appl ica t ion of the above system for protecting the means of measurement from appreciably destabi l izing effects ensures that the required s ta t is t ical measurement precision is obtained, trustworthy information about the dynamic processes (in measuring re la t ive ly high pressures) which occur over periods exceeding 0.03 sec is provided, and a higher re l iab i l i ty for the normal functioning of a measurement channel is ensured with its possible future u t i l iza t ion for controlling the working objects with a speed of operation exceeding that of existing control systems.

In principle the above system for protecting pressure transducers from destabi l iz ing effects can be extended to the measurement of lower pressures and processes with characteris t ic durations down to 0.01 sec. This entails reduc- ing the pipeline length and preserving at the same t ime the vibration properties of the system.

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