1、A Guide for the DynamicCalibration of PressureTransducersApproved 21 November 2002ISA-37.16.01-2002 STANDARDISA The Instrumentation,Systems, andAutomation Society TMISA37.16.012002A Guide for the Dynamic Calibration of Pressure TransducersISBN: 1-55617-838-7Copyright 2002 by ISA The Instrumentation,
2、 Systems, and Automation Society. All rights reserved.Not for resale. Printed in the United States of America. 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, recording, or otherwise), witho
3、ut the prior written permission of the Publisher.ISA67 Alexander DriveP. O. Box 12277Research Triangle Park, North Carolina 27709- 3 - ISA-37.16.01-2002PrefaceThis preface, as well as all footnotes and annexes, is included for information purposes and is not part ofISA-37.16.01-2002.This document ha
4、s been prepared as part of the service of ISA The Instrumentation, Systems, andAutomation Society toward a goal of uniformity in the field of instrumentation. To be of real value, thisdocument should not be static but should be subject to periodic review. Toward this end, the Societywelcomes all com
5、ments and criticisms and asks that they be addressed to the Secretary, Standards andPractices Board; ISA; 67 Alexander Drive; P. O. Box 12277; Research Triangle Park, NC 27709;Telephone (919) 549-8411; Fax (919) 549-8288; E-mail: standardsisa.org.The ISA Standards and Practices Department is aware o
6、f the growing need for attention to the metricsystem of units in general, and the International System of Units (SI) in particular, in the preparation ofinstrumentation standards. The Department is further aware of the benefits to USA users of ISAstandards of incorporating suitable references to the
7、 SI (and the metric system) in their business andprofessional dealings with other countries. Toward this end, this Department will endeavor to introduceSI-acceptable metric units in all new and revised standards, recommended practices, and technicalreports to the greatest extent possible. Standard f
8、or Use of the International System of Units (SI): TheModern Metric System, published by the American Society for Testing an overdamped (aperiodic) system comes to rest without overshoot; and a criticallydamped system is at the point of change between the underdamped and the overdamped conditions.4.4
9、.3 Damping ratio (z )The ratio of the actual damping to the damping required for critical damping. In Equation 4.2, thecoefficient z is the damping ratio. Typical dynamic pressure transducers have damping ratios much lessthan unity; consequently values of wdand wrvery nearly coincide. The damping ra
10、tio is definedspecifically for a linear second-order system. Transducers with more resonances are approximated byassociating a “damping ratio” with each resonant frequency.The damping ratio is a useful parameter in both the time and frequency domain. In the time domain, z isrelated to the amount of
11、overshoot (see Figure 2) and influences the number of ringing cycles presentafter a shock excitation. In the amplitude response, z is related to the height of the peak at the resonantfrequency.4.4.4 Rise timeThe length of time required for the output of a transducer to rise from 10% of its initial v
12、alue to 90% of itsfinal value when excited by a step change in measurand. Rise time is related to transducer frequencyresponse.4.4.5 OvershootThe amount of output measured beyond the final steady output value in response to a step change in themeasurand. The maximum theoretical overshoot of an ideal
13、 second-order transducer is 100 percent; thisoccurs when z is zero. Overshoot is determined as(Eq. 4.6)z-zp-=21e100overshootfor the condition z 0.1.4.4.6 Settling timeThe time required after the application of a step change in measurand for the transducer output to settlewithin a small specified per
14、centage (5 percent) of its final value. For the ideal second-order transducerwith small z(Eq. 4.7)d2s13twzz-=The settling time increases with smaller z and wd. The number of oscillations at wdrequired to settle within5 percent of final value for the ideal second-order transducer isISA-37.16.01-2002
15、- 22 -(Eq. 4.8)zpz-=213N24.4.7 Discharge time constant (DTC)Time required for a transducer or measuring system to discharge its signal to 37% of the original valuefrom a step-change measurand. It relates to low-frequency measuring capability for both transient andsinusoidal events.5 Dynamic pressure
16、 generatorsThe dynamic calibration of pressure transducers requires that the measurand produced by a dynamicpressure generator varies in time in both a known and an appropriate manner. With some generators, thepressure-time relationship can be predicted quite accurately. With others, the pressure-ti
17、me relationshipcan be established accurately only with the aid of comparison to referenced pressure transducers. Whilereproducibility is a highly desirable characteristic of the dynamic pressure generator, it is not an essentialcharacteristic. When such a characteristic is lacking in a generator, fu
18、ll dependence on the referencetransducer is required.Dynamic-pressure generators fall into two basic classes: aperiodic and periodic. The aperiodic generatorsare characterized by the pulse shapes they produce, such as the step or the peaking pulse. Quick-opening valve devices and pulse generators pr
19、oduce pressure rise times generally in the milli-secondrange or less. The rise times and the pressure amplitudes generated by these devices vary markedly fromone type of aperiodic pressure generator to another. The shock tube, for example, is capable ofgenerating pressure steps having rise times in
20、the nanosecond range. A number of the dynamiccalibrators described in this clause are now commercial products.Pressure step, as used in this document, is defined as a change in measurand in which the rise time isless than one-fifth the rise time of the transducer measuring it.Sinusoidal pressure gen
21、erators, which require the use of a transfer standard, are the most useful of thevarious periodic pressure generators available, however, and these devices are limited as to useablerange of frequency dynamic pressure ratio and dynamic amplitude. Nonsinusoidal pressure generatorsof significant useful
22、ness include the square wave or rectangular wave generators, which may beconsidered as a special case of the aperiodic or step-function generators. Figures 4 and 5 present asummary of the capabilities of the dynamic pressure generators.5.1 Shock tubeA shock tube, in its simplest form, consists of tw
23、o sections of tubing separated by a thin diaphragm. Whenthese two sections are pressurized to different pressure levels, and the diaphragm is suddenly ruptured,the higher-pressure gas will immediately begin to flow and compress the gas at a lower pressure(References 56, 57, 58).It should be noted th
24、at most cold-gas, shock-tube-development work occurred in or before the 1960s.However, in 1997, a shock tube was designed and built at a university for a transducer manufacturer. Thedevelopment report for this new shock tube, Reference 64, also updates the literature through theintervening time peri
25、od.At a distance of approximately 10 to 15 tube diameters downstream from the diaphragm, a well-formedshock wave is established. This shock wave continues to move through the remainder of the gas in thelow-pressure section at approximately a constant velocity. Behind the shock wave, the pressure sud
26、denlyrises to a new value, resulting in a positive pressure step. The length of time the pressure remainsconstant behind the shock wave depends on the dimensions of the shock tube, the position in the low- 23 - ISA-37.16.01-2002pressure section at which the pressure is being monitored, the degree of
27、 smoothness of the inner walls ofthe low-pressure section, the type and design of the diaphragm, and the type, temperature, and initialpressure of the gas in each section. Air or helium and air in combination are commonly used gases.When a shock tube is utilized for pressure transducer calibration,
28、several parameters must be measuredbefore the amplitude of the pressure step can be ascertained. These parameters include the shock-wavevelocity, Vs, and the initial absolute pressure, P1, and temperature, T1, of the gas in the low-pressuresection.5.1.1 Sidewall transducer mountingIf a pressure tran
29、sducer is mounted flush in the sidewall of the low-pressure section, it will sense achange in pressure, D P, when the shock wave passes over it. This is commonly referred to as “incident“pressure. The equilibrium pressure and particle velocity behind the shock wave are determined from theRankine-Hug
30、oniot relations (References 2, 6, 24, 25, 26, 27, 28, and 58). When air is used as the workinggas (low-pressure section), the amplitude of the pressure step can be computed from the followingequations:(Eq. 5.1) ()1MP67P2s1-=Dand(Eq. 5.2)+=1ssT2732985.344VMwhere Vsis expressed in meters per second, T
31、1is gas temperature in degrees, C, P1is absolute pressure,and Msis the shock-wave Mach number. When gases other than air are used, Equations 5.1 and 5.2 donot apply. (See References 2, 24, and 25 for further information.)Since the working-gas temperature must be known, the convenient method of deter
32、mining thetemperature is from a measurement of the static-wall temperature of the shock tube. Except at very lowpressures, the temperature of the working gas closely approaches that of the wall in less than oneminute.The shock-wave velocity, Vs, is determined by measuring the shock-wave transit time
33、 between pointsspaced a known distance apart along the path of the velocity vector. Because the velocity of the shockwave tends to decrease with distance, the last pair of points should be in close proximity (less than 1 tubediameter) to the transducer undergoing calibration. Several different types
34、 of sensors are used to detectthe passage of the shock wave past these points; the most common being pressure transducers, thin-filmheat-transfer gages, and light screens. The shock-wave transit time, D ts, between pairs of sensors, ismeasured with digital timing. The shock-wave velocity, Vs, is cal
35、culated using the equation Vs = spacingbetween sensors/D t s. Because of the squared relationship between Vs and D P, an uncertainty of 0.5percent in the measurement of the shock-wave velocity produces an uncertainty of at least 1 percent inthe determination of pressure-step amplitude.When the press
36、ure transducer is mounted flush in the sidewall of the shock tube, the rise time of thepressure step resulting from the passage of the shock wave is dependent on both the shock-wavevelocity and the transverse length of the transducer diaphragm, d, in the direction of shock-wavepropagation. Consequen
37、tly, pressure transducers with the fastest rise time and smallest diameterdiaphragm should be used. Commercially available micro-sized pressure transducers with a 1mmeffective area reduce transient time across the diaphragm to 2 to 3 microseconds.ISA-37.16.01-2002 - 24 -The time required for the pre
38、ssure on the transducer to change from P1to P2 (P2= P1+ D P) is given by theexpression(Eq. 5.3)sVdt =Figure 4 Aperiodic generators- 25 - ISA-37.16.01-2002Figure 5 Periodic generatorsISA-37.16.01-2002 - 26 -The maximum theoretical rise time, tr, for pressure transducers with circular diaphragms mount
39、ed flush inthe sidewall of a shock tube can be shown to be(Eq. 5.4)srVd687.0t =The side-mounted mode of operation is recommended1) when this is the manner in which the transducer will be used in application;2) when maximum accuracy in the determination of the pressure-step amplitude is desired;3) wh
40、en it is desirable to minimize transducer ringing; and4) when the incident wave is considerably “cleaner” than the reflected wave.5.1.2 End-wall transducer mountingIf the end of the low-pressure section of the shock tube is sealed off with an end plate, the moving shockwave, in striking the plate, w
41、ill reflect from it. This is commonly referred to as a “reflected“ shock wave. Apressure transducer mounted flush in the end plate will detect only the reflected shock wave. Thereflected shock wave is characterized by a much shorter rise time (usually nanoseconds) and a higherpressure as compared wi
42、th the incident shock wave (sidewall measurement). The rise time of thepressure step associated with the reflected shock wave is sufficiently short to excite all the ringingfrequencies associated with virtually all flush-mounted pressure transducers. A tourmaline pressure bartransducer specially des
43、igned for reflected shock-wave measurements has an 0.2 m sec rise time andnonresonant response (References 57, 58). When air is used as the work gas, the amplitude of thepressure step behind the reflected shock wave is(Eq. 5.5) ()+-=D2s2s2s1M5M421MP37Pwhere Msand P1are defined as in Equations 5.1 an
44、d 5.2.Because of the complex relationship between D P and Msin Equation 5.5, any uncertainty in themeasurement of the shock-wave propagation Msmay produce an uncertainty in the determination of thepressure amplitude D P several times larger. (Reference 2 provides a convenient source of workingequati
45、ons when gases other than air are used.)The pressure behind the incident and reflected shock waves remains constant for a period of time, whichis dependent on the design of the shock tube and on the type, temperature, and pressure of the gasesinitially in the two sections. For a given shock-tube geo
46、metry, the longest duration of constant pressurebehind the reflected shock wave is obtained when the shock tube is operated under tailored conditions,as described in References 2, 10, and 26. Depending on the operating conditions and shock-tubegeometry, the period of constant pressure behind the ref
47、lected shock wave may vary from a few hundredmicroseconds to several milliseconds.The end-plate mounted mode of operation is recommendeda) for the determination of transducer ringing frequencies;b) when this is the manner in which the transducer is to be used in application;- 27 - ISA-37.16.01-2002c
48、) when the maximum pressure step amplitude is required in calibration;d) when the maximum duration of constant pressure behind the shock wave is desired; ande) when determination of ringing frequency of gas passage is associated with transducer recess mount.5.1.3 Other considerationsAcceleration of
49、the walls and end plate of a shock tube occurs during operation of the device. In order todetermine the effect of this “ground shock” acceleration on the transducer output, the sensing end of thetransducer must be blanked off from the pressure wave without significantly altering the accelerationcomponents. Acceleration effects can be minimized by utilizing heavy-walled tubing for the low-pressuresection of the shock tube, by using a heavy end plate, and by shock-mounting the tube. Modern miniatureacceleration-compensated transducers are less susceptible to mechanical vi
