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NBS TECHNICAL NOTE 914

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

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- Located at Boulder, Colorado 80302.
A New Dynamic Pressure Source for the

Calibration of Pressure Transducers

OF STANDARDS

LIBRARY JUL 7 1976

r\.o~t • exec-. - Cc i?5l

Carol F. Vezzetti

John S. Hilten

J. Franklin Mayo-Wells, and

Paul S. Lederer

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by:

NASA Langley Research Center Hampton, Va. 23365

°f£AU Of *

u:

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued June 1976
National Bureau of Standards Technical Note 914

Nat. Bur. Stand. (U.S.), Tech. Note 914, 35 pages (June 1976) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order hy SD Catalog No. C13.46:914). Price 85 cents (Add 25 percent additional for other than U.S. mailing).
FOREWORD

The work described was performed as a task within the Electromechanical Transducer Project. This is a continuing project for the

development of calibration and evaluation methods for electromechanical transducers, supported by a number of Government agencies. This

task was funded by the National Aeronautics and Space Administration

through the Langley Research Center under order number L-88319.

Paul S. Lederer

Acting Chief

Components and Applications Section

in

A NEW DYNAMIC PRESSURE SOURCE FOR

THE CALIBRATION OF PRESSURE TRANSDUCERS

CONTENTS

Page

1. Introduction 1 2. Experimental Development of Source 2

2.1 Theoretical Considerations 2

2.1.1 Pressure Amplitude 3

2.1.2 Natural Frequency 3

2.2 Preliminary Investigations 5 2.3 Background for Use of Steel Balls as Column Packing ... 6

2.4 Design and Description of Dynamic Pressure Source .... 6

2.4.1 Column Design 7

2.4.2 Column Description 7

2.4.3 Tests to Determine Column Packing

and Source Repeatability ... 8

3. Cal ibration 9

3.1 Calibration Procedure 9

3.2 Error Analysis 11 3.3 Results from the Calibration of Six Transducers 11 4. Conclusions 14

5. Recommendations 15

6. Acknowledgements 16

7. References 16

LIST OF TABLES

Table 1

Table

Table

Table

Table

Working Liquids Used in Preliminary Investigations

of Damping 17

Reference Transducer E Output 18

Factors Contributing to Transducer Calibration Error . . 19

Transducer Characteristics 20

Transducer Experimental Calibration Data 21

LIST OF FIGURES

Figure 1: Columns and Filters of Various Geometries Used In Preliminary Experiments 22

Figure 2: The Dynamic Pressure Source in Use to Calibrate

a Pressure Transducer 23

Figure 3: Cross Section of Dynamic Pressure Source 24

Figure 4: Oscilloscope Traces Showing Peak-to-Peak Output (mV)

from Reference Transducer E as a Function of Frequency

(kHz) for Three Quantities of Balls, as Described in

the Text 2 5
Page

Figure 5: Schematic of Apparatus Used to Fill the Source

with Liquid Under Weak Vacuum 26

Figure 6: Oscilloscope Traces Showing Corresponding

Frequency-Response Curves for Test Transducer

(Left) and Reference Transducer E (Right) 27

Figure ~J : Oscilloscope Traces Showing Frequency-Response

Curves for the Undamped Source with Test

Transducer A-l (Trace A), B (Trace B)

C (Trace C) , and D (Trace D) 28

Figure 8: Test Transducer B Output (mV rms) as a Function

of Frequency (Log Hz) with the Pressure Level Held

Constant, as Described in Text 29

VI
A New Dynamic Pressure Source for the

Calibration of Pressure Transducers

Carol F. Vezzetti, John S. Hilten,

J. Franklin Mayo-Wells and Paul S. Lederer

A dynamic pressure source is described for producing sinusoidal ly

varying pressures of up to 3^ kPa zero-to-peak, over the frequency

range of approximately 50 Hz to 2 kHz. The source is intended for

the dynamic calibration of pressure transducers and consists of a liquid-filled cylindrical vessel, 11 cm in height, mounted upright

on the armature of a vibration exciter which is driven by an amplified sinusoidal ly varying voltage. The transducer to be calibrated

is mounted near the base of the thick-walled aluminum tube forming

the vessel so that the pressure-sensitive element is in contact with

the liquid in the tube. A section of the tube is filled with small

steel balls to damp the motion of the 10-St dimethyl siloxane working fluid in order to extend the useful frequency range to higher

frequencies than would be provided by an undamped system.

The dynamic response of six transducers provided by the sponsor

was evaluated using the pressure sources; the results of these calibrations are given.

Key words: calibration; dynamic; dynamic calibration; dynamic

pressure; dynamic pressure source; liquid column; pressure; pressure

source; pressure transducer; sinusoidal pressure; transducer.

1. INTRODUCTION

Increased use of electromechanical transducers for measurement of dynamic pressures in complex processes arising in diverse

fields has increased the importance of determining the dynamic

characteristics of such transducers. Dynamic pressure-calibration

systems now in existence do not meet all the amplitude or frequency range requirements of present technology.
In 1971 the National Bureau of Standards Instrumentation

Applications Section'1' developed a method for generating sinusoidal ly varying pressures constant in amplitude within +5% over a frequency range of a few Hertz to about 1 kHz [1]**. In the

current work, this method has been modified and extended [2,

3] in both amplitude and frequency capability to result in a source of sinusoidal ly varying pressures of up to 3^ kPa zero- to-peak (about 5 psi zero-to-peak), over the frequency range of

approximately 50 Hz to 2 kHz. The source is intended for the

dynamic calibration of pressure transducers and consists of a liquid-filled cylindrical vessel, 11 cm in height, mounted upright on the armature of a vibration exciter which is driven by an amplified sinusoidal ly varying voltage. The transducer to

be calibrated is mounted near the base of the thick-walled aluminum tube forming the vessel so that the pressure-sensitive element

is in contact with the liquid in the tube. A section of the tube

is filled with small steel balls to damp the motion of the 10-St

dimethyl siloxane working fluid in order to extend the useful frequency range to higher frequencies than would be provided by an undamped system. Both the natural frequency and the degree of

damping of the combined 1 iquid-col umn-and-transducer structure

determine the useful upper frequency limit.

EXPERIMENTAL DEVELOPMENT OF SOURCE

2.1 Theoretical Considerations

For the geometry described, both the amplitude of the sinusoidal ly varying pressure and the natural frequency of the liquid

column may be calculated to first approximations by simple re- lations to permit comparison with experimental results.

The Section is now the Components and Applications Section.

^Figures in brackets indicate the literature references listed in

section 7.
Damping is also an important consideration because a damped

system may have a higher useful frequency range than the same system undamped. With an undamped, single-degree-of-f reedom

system, the amplitude-frequency response remains constant within

+5% up to approximately 20% of the natural frequency. In a system with optimum damping (a damping ratio of about 0.6 of critical), the amplitude-frequency response remains constant within

+5% to about 80% of the natural frequency [3, A] . To maintain

a flat response to 2 kHz thus requires an undamped system with a natural frequency of 10 kHz, an optimally damped system with a natural frequency of 2.5 kHz, or a non-optimal ly damped system

with a natural frequency between 2.5 and 10 kHz, with the exact

natural frequency required dependent on the degree of damping.

2.1.1 Pressure Ampl itude - The factors that in combination

determine the pressure levels attainable over the frequency range

of interest are (1) the force and displacement capabilities of

the vibration exciter, (2) the density of available working fluids,

(3) the height of the liquid column, and (k) the degree of damping.

This last factor interacts with the others and depends on geometry,

on the bulk modulus and viscosity of the fluid. As noted above,

damping need not be considered at frequencies below about 20% of

the system natural frequency because the amplitude-frequency re- sponse is flat up to this limit. Up to the stated limit, the

amplitude of the sinusoidal pressure generated within the liquid

column and acting on the transducer is given by [1],

P - ah p c where

P = pressure (Pa zero-to-peak)

. a = acceleration amplitude (gn zero-to-peak )

h c= liquid-column height above the center of the

transducer diaphragm (m) , and

p = density of liquid (kg/m3 )

As an example, for the source to be described in this paper, h. =

0.1m and p = 972 kg/m3 . At an acceleration of 36 gn zero-to-peak,

the pressure is calculated to be 3^ kPa zero-to-peak, and at 20 gn zero-to-peak, 19 kPa.

2.1.2 Natural Frequency - The natural frequency of a liquid

column is directly proportional to the square root of the velocity

of sound in the liquid and inversely proportional to the height of

f The symbol gn represents the unit of acceleration equal to the

standard value of the acceleration of gravity at the earth's surface
the column. For an infinitely stiff, open-topped vessel containing

the liquid, the system has one degree of freedom with a natural frequency given by [1]

'n - ••« * « *

*

where

f

n = natural frequency (Hz),

h = total height of liquid column (m) , and

B = bulk modulus (Pa)

The quotient of B and p is proportional to the velocity of sound in

the liquid. For the dynamic pressure source, h = 0.11 m and B = 9.^7 x 10 8 Pa, the value given by the supplier for 10-St dimethyl

siloxane. The undamped natural frequency is calculated to be 2.24

kHz.

In practice the tube is not infinitely stiff, but has some elasticity. For other than thin-walled vessels, a volume change in

the tube itself is usually small enough compared to other volume

changes that it may be neglected for practical calibrations. More

importantly, the transducer diaphragm forms part of the tube wall,

and since this diaphragm is displaced in response to pressure, an overall volume change occurs. The effect of this change is to

lower the natural frequency as the effective bulk modulus is reduced

The effective bulk modulus may be defined by the relation [1]

B- Y_

V

B + dV

t where

B

1 = effective bulk modulus (Pa),

V = volume of liquid in the tube (m 3

) , and

dV t = change of volume resulting from unit pressure change

(m 3 /Pa).

As an example, transducer B introduces a volume change of 9.14 x 10" 15 m

3 /Pa, as calculated from information supplied by the manufacturer.

With this transducer installed in the source, the effective bulk

modulus is calculated to be 7-03 x 10 8 Pa and the natural frequency

is lowered to 1 .93 kHz.

In the source, steel balls are used for damping and the volume

of the liquid is reduced by an amount equal to the total volume of

the balls, although the column height remains unchanged. As an example, consider that 15% of the volume of the liquid is replaced by

the balls (as was done in some of the experiments). The effective
bulk modulus would then be given by 6.73 x 10 8 Pa, and the undamped

natural frequency would become 1.89 kHz. If the balls were to occupy

50% of the available volume, the calculated natural frequency would

be 1.72 kHz, which is significantly lower than the 2-kHz goal.

Combining the results of the above discussion, the natural frequency is given by

1 B(Vr

' V

f = 0.25 A £

n h

h

p(VCD- V. + BdVj

t

where

V

c = volume available for liquid with no balls present (m 3

)

Vl = volume occupied by balls (m 3

)

, and

h, B, p, and dV are as given above.

2.2 Preliminary Investigations

Preliminary experiments described in the progress reports [ 3 ] were conducted to investigate approaches for improving the frequency

range of the method developed earlier. These experiments involved

a variety of working liquids, including water, tetrabromoethane,

petroleum oils, a fluorocarbon liquid, dimethyl siloxane liquid of

various viscosities, glycerine, and mercury. These candidate liquids

were chosen because of specific physical properties given in table 1 and on the basis of experience. Chemical reactivity and the criterion

of ready availability also governed the choice of liquids. For example,

water was chosen because it has a relatively high bulk modulus and be- cause its use in the earlier work permitted intercomparison of experimental results. Tetrabromoethane, the fluorocarbon liquid, and es- pecially mercury have high densities and therefore should confer highpressure capability with short columns of liquid. Mercury has been

used in related work with a closed-tube dynamic pressure source* [5].

Dimethyl siloxane liquids and petroleum oils are available in a wide

range of viscosities; glycerine possesses a combination of high viscosity and high bulk modulus.

The damping provided by a number of column geometries was also

investigated experimentally with the various liquids, as shown in

table 1. Among these experiments, which were designed to increase

the available wetted surface compared to that of the interior of a simple tube, were trials with columns of various cross-sections (including columns with vertical fins, spiral fins, and multiple channels)

and with columns packed with various materials (including bundles of

smal 1 -diameter tubes, sintered metal filters, and sea sand). A se- lection of columns is shown in figure 1. Damping of a magnetic liquid

by means of a coil electromagnet wound around the outside of the column

was also attempted.

5
The results of these investigations tended to single out 10-St

dimethyl siloxane as the liquid possessing the best combination of

properties, including handling quality, of those liquids tried. The

principal reasons for rejecting the other liquids may be summarized

as follows: water and tetrabromoethane -- low viscosity precludes

achievement of effective damping; petroleum oils -- viscosity is

highly temperature dependent; fluorocarbon liquid -- bulk modulus

too low; glycerine -- presence of dissolved gas (which could not be

removed reliably by the vacuum filling procedures described in an earlier report [3] reduced bulk modulus to too low a value; and

mercury -- viscosity too low.

2.3 Background for Use of Steel Balls as Column Packing

At an early stage of the work, the use of a material such as sea sand had been proposed as a means of increasing the column wetted

surface, and hence the degree of damping, by a very large factor.

However, experimental difficulties and inconclusive results discouraged further work along these lines at the time. The comparative

success achieved with a column packed with small tubes (inside diameter 0.16 cm) and filled with 10-St dimethyl siloxane encouraged a search for other geometries offering still greater wetted surface

(without the insuperable filling problems which had precluded the use of tubes substantially smaller than 0.16 cm i.d.). The use of

small objects as a column packing was again considered, with the re- quirement that the objects not absorb or be soluble in the dimethyl

siloxane. If suitable objects could be found in a selection of sizes,

a range of wetted areas would be available for experiment. The

polished steel balls produced for use in ball bearings are readily

available in a range of sizes and do not interact with dimethyl siloxane, and were therefore tried as a column packing. These trials (described in 2) were successful in that the project goals for the source were met (sinusoidal ly varying pressures of at least 3** kPa zero-topeak, flat to within +5% from approximately 50 Hz to 2 kHz), and development of the source was considered complete for the intended purposes.

2.k Design and Description of Dynamic Pressure Source

An overall view of the dynamic pressure source and associated

instrumentation is shown in figure 2. Mounted on the armature of the

vibration exciter (C) is the source column (A) with the reference

transducer (B) screwed into the base. The position for the transducer

to be calibrated is on the opposite side of the column from (B) and is

not shown. The controller (D) for the vibration exciter supplies the

driving signal and can be programmed to sweep over the frequency range

of interest at constant acceleration, displacement, or velocity. The

vibration exciter system has a displacement capability of 1.3 cm peakto-peak and can impart accelerations of 25 gn to an 1

1 -kg mass at

frequencies of 30 Hz and above.
A digital voltmeter iE) may be switched to read the output of

the test transducer, the reference transducer, or the accelerometer

mounted in the armature of the vibration exciter. Transducer excitation power supplies are denoted by (F) and (G) , and (H) is the accelerometer amplifier. Pressure transducer output as a function of frequency is displayed on the oscilloscope (l), which is equipped with a recording camera.

2.4.1 Column Design - In order to accommodate the ball packing,

the column required modification with respect to earlier columns used.

The following considerations governed the design: (1) the balls must

not be allowed to contact and thus damage the transducer diaphragm,

(2) the balls must not be permitted to move in relation to one another

or to the column to any significant degree (ball movement would result

In uncontrolled changes in damping), (3) a method for conveniently

varying the ball loading (ball size and number) is required, and (4)

the amount of liquid displaced by the balls should not be so great as to lower the natural frequency below acceptable limits, that is, as shown in 2.1.2, the balls should occupy less than half of the available volume.

The design that was selected utilized pierced circular plates

to clamp the balls in a section of the bore near the bottom of the

column. The geometry of the plates was subject to the following con- siderations: (1) the plates should have the maximum practicable

amount of open area so as not to impede the movement of the dimethyl

siloxane liquid (thus not to change the damping characteristics or

the natural frequency appreciably), (2) the holes should be small

enough to retain the smallest balls envisaged, (3) the distance between the holes should be less than the diameter of the smallest ball

envisaged (to prevent balls from blocking all the holes), and (4) the

plates should be thick enough to provide adequate rigidity.

2.4.2 Column Description - The construction that was chosen to

satisfy the varying requirements is shown in a cross-sectional sketch,

figure 3. Steel balls (K) are clamped tightly in place by two 0.48-

cm-thick pierced steel plates (L) . The outer diameter of the plates

loosely fits the inner diameter of the aluminum column; forty-five

0. 13-cm-diameter holes drilled through each plate perpendicular to the

faces account for approximately one-third of the face area and provide

for free movement of the liquid. The bottom plate rests on a machined

shoulder 1.6 cm above the bottom of the column bore. The top plate

clamps down on the ball packing, the clamping force being transmitted

to the plate from a vented, threaded plug (M) by means of a brass re- tainer tube (N) which is a loose fit in the main bore (J) . This tube

has an outside diameter of 1.6 cm and a 0.16-cm wall thickness. The

plug engages threads machined into an upper section of the bore. The

volume of the column bore available for ball packing may be adjusted

through the use of retainer tubes of various lengths combined with
various positions of the threaded plug. Threaded holes for mounting the reference transducer (B) and the transducer to be calibrated

(0) are provided in two machine flats near the base of the column.

The centerline of these holes is 1 cm above the bottom of the bore.

The column is fastened to the vibration exciter armature by means of

four machine screws passing through holes (not shown) in the column

flange.

2.4.3 Tests to Determine Column Packing and Source Repeatability - The output of reference transducer E was used to determine an acceptable column packing in terms of ball diameter and length of section

packed with balls. Balls with diameters of 0.24, 0.28, 0.32, 0.40,

and 0.48 cm were available for these tests with selected section lengths

of 2.0, 2.7, 3-0, 6.0, and 8.0 cm.

The procedure used was as follows. Transducer E was mounted on

the column and the controller for the vibration exciter set to sweep

the excitation frequency from 35 Hz to 3 kHz at an arbitrary constant

acceleration. Three swept-f requency response curves of transducer E output were generated on the oscilloscope screen and photographically

recorded: (1) with the column empty of liquid, plates, etc., (2) with

the column filled with 10-St dimethyl siloxane to the 1

1 -cm level, and

(3) with the column filled with dimethyl siloxane as in (2) and the

plates, retainer tube, and plug in place (the plates separated by means

of a spacer tube, since no balls were used). The curve from run (1) is

the transverse vibrational response of transducer E. From the run (2)

curve, the resonance frequency and damping characteristics of the basic

system may be determined. Resonance was at 2.35 kHz, and the damping

ratio approximately 0.03 of critical. The curve from run (3) shows a resonance frequency of 2.20 kHz and a damping ratio of 0.10 of critical, which was considered to be acceptable.

The experimental value of resonance frequency from run (2) is

higher than the calculated value of 2.24 kHz obtained in 2.1.2. The

difference may result from several sources, including an inexact knowledge of the bulk modulus for the 10-St dimethyl siloxane used and imprecision in the determination of resonance frequency. It is also

possible that the theory is deficient. Another factor, not considered

in the analysis of 2.1.2, that can affect the resonance frequency is

the presence in the liquid of absorbed gases and other impurities.

The presence of gases always results in a lowered resonance frequency,

and the presence of impurities usually does.

Other swept-f requency response curves of transducer E output

were then generated and recorded with various sized balls and various

section heights. These tests showed that damping could be varied over

a wide range (from very under damped to very over damped) and that,

regardless of ball size, the resonance frequency is lowered significantly when either 6.0- or 8.0-cm section lengths are used. The probable

reason for this lowered resonance frequency is that with these quantities

of balls the volume available for liquid (filled to the 1

1 -cm level) is

8
reduced enough to produce a significant reduction in the value of the

effective bulk modulus, as discussed in 2.1.2.

Examples of the results obtained using 0.2^-cm balls are shown

in figure ^4. With a ball section 3.0 cm in length, the pressure am- plitude is seen to decrease with increased frequency (top trace), indicating that the calibrator system is overdamped. With a 2.0-cm

section, the pressure amplitude is seen to rise to a maximum between

2.1 and l.k kHz (center trace), indicating that the column is underdamped (estimated to be 0.38 of

critical) . The most nearly flat re- sponse was obtained with the 2.7 _ cm section, for which the pressure

amplitude is seen to remain almost constant to approximately 2.k kHz

(bottom trace). The small resonances near 1.1 and 1 .*t kHz are believed to result from mechanical resonances of the column assembly,

and data near these frequencies are not used.

As described in 3«3, reference transducer E was used in 16 calibrations of other transducers. In particular, 30 measurements were

made with a constant acceleration of 20 gn at two frequencies, 35 and

50 Hz, for which the output should be the same. Two computed values

are also available. The data and statistics are given in table 2.

The computed coefficient of variation of 1.1% is considered to demonstrate the acceptable repeatability of the source. Sources of both

systematic and random errors are discussed in 3.2.

3. CALIBRATION

3.1 Calibration Procedure

Before calibration of a pressure transducer can be carried out

using the source, the size of the contribution to zero shift from the

transducer transverse acceleration response is checked. The transducer

is mounted on the empty column, and the vibration exciter driven at the

intended test level, usually 20 gn zero-to-peak. For all transducers

tested in the study, the transverse response was not significant, i.e.,

contributed to less than 0.02% of the transducer response.

For the calibration itself, the column must be loaded with balls

and filled. The procedure is as follows:

1. Mount the transducer to be calibrated and the reference

transducer (or, if not used, a plug) in the holes provided

at the base of the column.

2. Position the restraining plates, steel balls, and retainer

tube in the column.

3. Place the column in a suitable bell jar, as shown in figure

5. The bell jar should have a tube passing through its top

and be equipped with a ball valve (Q)
k. Attach a suitable flask to the ball valve with the upper

opening unstoppered. One type of suitable flask is a leveling bulb. The flask should have a volume of at least

twice the volume of the empty column.

5. Close the valve.

6. Pour at least enough 10-St dimethyl siloxane into the flask

to fill the empty column.

7. Connect the bell jar lower port and the upper opening of the

flask to a mechanical vacuum pump and operate the pump until

the liquid in the flask does not bubble (fifteen minutes is usually sufficient).

8. Open the valve until the column is filled approximately to

the desired level; then close the valve.

9. Slowly release the vacuum in the bell jar.

10. Remove the column from the jar.

11. Mount the column on the armature of the vibration exciter.

12. Use a suitable depth micrometer to measure the liquid level.

The lowest setting of the micrometer at which a drop of

liquid adheres to the end of the micrometer probe is taken

as the distance between the liquid surface and the top of

the column.

13. Adjust the level by adding or removing a few drops with a suitable instrument, such as an eye dropper, until the desired level is attained.

14. Screw the threaded plug into the fixture and torque to the

recommended value of from 16 to 19 N*m (12 to \k pound-force

•ft). This completes the filling procedure.

Following filling, the controller of the Vibration exciter is set to

sweep the frequency of the driving signal from 35 Hz to 3 kHz at a given acceleration, usually 20 gn zero-to-peak.

An acceleration of 36 gn zero-to-peak is required to generate

pressures of 3** kPa zero-to-Peak with a 10-cm column of 10-St dimethyl

siloxane. However, as 36 gn zero-to-peak is close to the upper acceleration level capability of the vibration exciter with the column as load,

and operation of the exciter at that level resulted in occasional overtravel alarms, the majority of the calibrations reported in this paper were made using an acceleration of 20 gn zero-to-peak, resulting in

pressures of 19 kPa zero-to-peak over the frequency range of 35 Hz to

3 kHz. One test was run at an acceleration of 36 gn zero-to-peak over

a frequency range of 50 Hz to 3 kHz to demonstrate the higher pressure

capability of the method. In this test, the lower frequency limit of

50 Hz was imposed by the displacement limits of the armature of the

vibration exciter.

10
During a dynamic calibration run, readings on the digital

voltmeter of the transducer outputs are recorded at selected f re-

quencies, and curves of transducer response vs frequency are re- corded by photographing the oscilloscope display of the test (and

reference, if desired) transducer outputs as the fixture is vibrated

at a constant acceleration over the frequency range of interest.

Static calibrations of d-c responding transducers are made with

the transducer mounted in the liquid-filled fixture by imposing known

pneumatic pressures on the top of the liquid column and measuring the

resulting transducer output with the digital voltmeter. A liquidhead correction is made. Static pressures are produced with a precision bellows and read with a dial gage.

3.2 Error Analysis

The dynamic pressure source provides capabilities not before

available. There is no "standard transducer" that can be used to

evaluate the source performance. The best that can be done is to

carry out repetitive measurements on a transducer for which theory

predicts that the frequency response should be flat beyond the frequency range of interest. Such a series of measurements was carried

out with the piezoelectric quartz crystal reference transducer E; the results are given in 2.^.3. Because there is no "standard transducer," it is instructive to analyze the potential sources of error.

Factors contributing to the uncertainty of the pressure available from the source include (1) uncertainty in the height of the

liquid column resulting from meniscus effects and from machining inaccuracies, (2) uncertainty in the knowledge of the true density of

the liquid resulting from variations in temperature, (3) uncertainty

in the acceleration produced by the vibration exciter and measured

by its accelerometer , (k) uncertainties in various voltage measurements, and (5) electrical noise. For the dynamic calibration as a whole, uncertainty in the amount of transducer output resulting from

transverse vibrational response, additional voltage-measurement un- certainties, and additional electrical noise should be added to the

uncertainties listed above. For static calibrations, uncertainty in

the knowledge of the additional pressure applied to the liquid in

the column must be considered.

Estimated values for these uncertainties are given in table 3.

The overall estimated uncertainty for dynamic calibration measurements

is ±h.\% of the true value and for static calibration measurements

+0.k% of the true value.

3-3 Results from the Calibration of Six Transducers

Six pressure transducers were supplied by the project sponsor for

dynamic calibration using the dynamic pressure source. The character11
istics of these test transducers and of reference transducer E are

given in table 4. Three of the transducers (Al , A2, and A3) are of

the same model and have a silicon diaphragm into which a Wheatstone

bridge circuit has been diffused. The other three (B, C, and D) are bidirectional unbonded strain-gage types. Reference transducer E,

used as a control in all tests, is a piezoelectric quartz crystal

transducer, as has been noted.

Three calibration runs each were made of transducers Al, A2, A3,

C, and D using a 20 gn zero-to-peak acceleration level from 35 Hz to

3 kHz. Transducer B was calibrated in only one run (calibration No. 10)

and at a level of only 10 gn zero-to-peak. The reason for the change

in procedure was that transducer B was accidentally overranged in

preliminary resonance tests and damaged as a result. After the damage

had occurred, the output waveform of the transducer was distorted when

full-scale sinusoidal pressure was applied. Calibration at approximately

one-half the full-scale pressure was attempted and resulted in good waveform; therefore, calibration was completed at that level.* The test

transducer and the reference transducer E outputs were monitored on an oscilloscope whose horizontal deflection system was driven by a sweptfrequency sine-wave generator from 35 Hz to 3 kHz. In addition, the

outputs were monitored with a digital voltmeter at 35, 50, 75, 100, 200,

300, and 400 Hz for all calibrations and at 500 Hz and 1, 1.5, 2, and

2.5 kHz for selected calibrations. Reference transducer E was included

as a control in all 16 of the calibration runs.

The frequency-response curve for transducer Al , shown in figure 6A,

is different from that of transducer E and shows evidence of overdamping. The curves for transducers A2 and A3 are similar. The manufacturer

was asked to supply details of the design. It was reported that this

model of transducer has a protective diaphragm 0.015~cm thick in front

of the sensing diaphragm, with an air space of 0.015 to 0.033 cm between

the two diaphragms. Small holes, 0.013 to 0.015 cm in diameter, around

the periphery of the protective diaphragm admit the pressure to the

sensing diaphragm. It seems likely that this arrangement significantly

affects the damping characteristics of the transducer.

For a given transducer, it is expected that all measurements made

at 35 Hz and 50 Hz would agree. For the three transducers Al, A2, and

A3, the mean values of the six measurements (two measurements in each

of the three calibration runs for each transducer) are 21.232, 21.483,

and 23 . 427 mV rms , respectively. The maximum deviations from these means

are 0.3%, 0.2%, and 0.7%, with sample standard deviations of 0.059, 0.031,

and 0.111 mV rms. Comparison of the static calibration output measurement

with the above mean values showed differences of 3-7%> 2.9%, and 2.k% for

transducers Al, A2, and A3, respectively. The data are given in table 5.

^The oscilloscope trace shown in figure 6B was recorded using an acceleration of 18 gn zero-to-peak before the damage occurred. (18 gn gives fullscale pressure variations for this transducer.)

12
Figures 6B, 6C, and 6D are of the frequency response curves

for transducers B, C, and D. The mean values of the six measurements made at 35 Hz'and 50 Hz for transducers C and D are 10.67

and 3.550 mV rms , respectively. The maximum percent deviations from

these means are 0.**% and 0.8%, with sample standard deviations of

0.027 and 0.015 mV rms. No statistics are given for transducer B,

which was* cal ibrated in only one run. Comparison of the static calibration output measurement with the above mean values showed differences of 2.6% and 2.4% for transducers C and D, respectively . Comparison of the mean of the two measurements at 35 Hz and 50 Hz for

transducer B with the static calibration output measurement for this

transducer showed a difference of 0.8%. These reported differences

between static and low-frequency dynamic calibrations probably result

from the uncertainties involved in determining the height of the

liquid column. It is not possible to perform a static calibration on reference transducer E, as this transducer has no response to static

pressure.

If the test transducer natural frequency is high, the undamped

resonance frequency of the source-transducer combination will not be

appreciably affected: this is the case for transducer Al (and A2 and

A3), as is shown by the frequency-response curve in figure 7A. The

vertical axis scale (transducer output) is arbitrary. If the test

transducer natural frequency is relatively low, as it is for transducers B, C, and D (3.5 kHz, 5 kHz, and 8.5 kHz, respectively), the

calibrator system resonance will be lowered. The frequency-response

curves in figures 7B, 7C, and 7D show the resonance frequency of the

source-transducer combination as being about 1.3, 1.7, and 2.2 kHz,

respectively. These curves and values were obtained with the column

filled with dimethyl siloxane only, balls and plates having been re- moved. For calibrations of transducers with low natural frequencies,

not only is the resonance frequency lowered, but the degree of damping is also altered; 0.28-, 0.32-, and 0.48-cm-d iameter balls were

required for transducers B, C, and D, respectively, when the length

of the section of balls was held to 2.7 cm. (For transducer B, it

appears that balls of about 0.44-cm diameter would have given a more uniform response but were not available; the height of the section of

balls could have been changed but for the sake of consistency was not.)

Consideration of test transducer natural frequencies is useful in an evaluation of transducer dynamic performance as shown in curves such

as those of figure 6. Pressure transducers are commonly not used to

measure pressures varying at frequencies beyond approximately 20% of

the natural frequency of the instrument. For transducers B, C, and D,

this 20% limit is approximately 700 Hz, 1.0 kHz, and 1.7 kHz, respectively. As may be seen by examination, the response of transducers C and D is reasonably flat up to their respective limits. The response

of transducer B up to its 20% limit is somewhat less flat.

in a final experiment, the output of the reference transducer

was both recorded and used to provide an input signal for the controller for the vibration exciter with the power to the exciter continuously

adjusted to maintain the reference transducer output at a constant level,

13
The output of the test transducer under these conditions was recorded.

A plot is shown in figure 8 for transducer B. The curve suggests agreement with the manufacturer's specified natural frequency of 3-5 kHz and

should represent the frequency response of the transducer with no interpretation required. Further work is required to validate this technique.

k. CONCLUSIONS

The useful frequency range of the liquid-column sinusoidal pres- sure calibration source has been increased considerably by damping the

liquid column. The use of steel balls with 10-St dimethyl siloxane

liquid to achieve this damping is simpler and more versatile than

other damping schemes considered. The result is a dynamic pressure

source capable of generating pressure levels of up to 3^ kPa over a frequency range from approximately 50 Hz to 2 kHz, flat to within

+5%. At frequencies below 50 Hz the pressure amplitude is limited

by the displacement capability of the vibration exciter used. The

estimated total calibration measurement error using the source with

a typical transducer is +ji.]%.

It is important to note that a flat frequency response can be

achieved over a frequency range of up to a maximum of about 80% of the

natural frequency of the liquid column-transducer combination, and

that this natural frequency is lower than that of the component with

the lowest natural frequency.

The wetted surface area required to damp adequately a particular

liquid column and transducer combination is dependent on the natural

frequency of the combination. Combinations with high natural frequencies

require larger wetted surface areas than those with low natural frequencies. The wetted surface area may be adjusted easily by changing ball

size, ball quantity, or both.

Over a frequency range of up to 20% of the resonance frequency

of the liquid-column transducer combination, the dynamic pressure source provides an absolute calibration to within 5% of the true pressure supplied in the sense that this pressure is calculable on the basis of

mechanical parameters that can be measured and on the basis of knowledge of the acceleration imparted to the column, which acceleration can

be measured with instruments that may be traced in calibration to basic

standards. For the remainder of the frequency range, a reference transducer with a flat response over that range is required both for setting

and monitoring the degree of damping.

Another calibration technique using the source has been the subject of several experiments and requires further development. In this

technique, a signal derived from the reference-transducer output is

supplied as a control input to the vibration-exciter control, and the

acceleration of the column is continuously adjusted to maintain the pressure amplitude at a constant level as the frequency is swept over the

desired range. In principle, the only frequency limitations should be

14
imposed by the frequency responses of the reference transducer and

the exciter system.

5. RECOMMENDATIONS

The following recommendations for future work are based on the

experience gained during the development of the dynamic pressure

source and during the various calibrations.

1. A number of different high-natural-frequency, flush-diaphragm

pressure transducers should be calibrated with the dynamic pressure

source to determine if the degree of damping is approximately constant.

2. The number and size of balls should be more widely varied

and curves generated showing the relationship between these parameters

and column resonance frequency and damping characteristics.

3. The effect of temperature changes 6n the degree of damping

should be investigated.

k. Calibrations using the source should be attempted on transducers with low natural frequencies, with a constant-level-control

servo used to maintain the reference transducer output constant with

frequency. This technique should be developed and validated.

5. The use of columns with larger bores to reduce the percent

contribution of dVt (see 2.1.2) should be investigated. This recom- mendation is particularly aimed at calibrations of transducers with

large dVt values, usually transducers with low natural frequencies.

6. The use of short columns (with high resonance frequencies)

should be investigated without damping over a frequency range of up

to 20% of the resonance frequency of the column-transducer combination.

7. The presence of the retainer tube used to transmit force

from the threaded plug to the upper plate has been found to complicate

measurement of the height of the liquid column. A modified design

eliminating the retainer tube would be desirable. It has been suggested that the upper plate could itself be threaded into the bore.

8. Any new columns should be fabricated without the flats

machined near the base into which the transducer mounting holes are

bored. The presence of the slots formed by the flats reduces column

stiffness.

9. The discrepancy between the theoretical predictions for

natural frequency and the experimental values achieved requires further examination. Experiments with several fluids, dimensions, and

degrees of damping should provide data for further analysis.

15
6. ACKNOWLEDGEMENTS

Kurt Muhlberg designed and supervised construction of the

mechanical components of the various development versions of calibrators .

7. REFERENCES

[1] Hilten, J. S., Lederer, P. S. , and Sethian, J. D. , A Simple Hydraulic Sinusoidal Pressure Calibrator, NBS Tech. Note 720 (April

1972).

[2] Lederer, P. S., Development of a Dynamic Pressure Calibration Technique - A Progress Report for the Period June 15, 1973 to September 15, 1973, NBSIR 73-290 (October 1973) . (Available as COM 74-10974

from the National Technical Information Services, Springfield, VA 22161.)

[3] Vezzetti, C. F. , Lederer, P. S., and Hilten, J. S. , Development of

a Dynamic Pressure Calibration Technique - A Progress Report for

the Period February 15, 1 97^ to August 15, 197 1*, NBSIR 75-708

(June 1975). (Available as COM 75-10817 from the National Technical

Information Services, Springfield, VA 22161.)

[4] Bradley, W. , (and Eller, E. E., Introduction to Shock and Vibration

Measurements, Book, Shock and Vibration Handbook, Vol. 1, Eds.

C. M. Harris and C. E. Crede, pp. 12-1 -- 12-24 (McGraw-Hill Book

Company, New York, NY, 1 96 1 )

[5] Hilten, J. S. , Lederer, P. S., Vezzetti, C. F. , and Mayo-Wells,

J. F. , Development of Dynamic Calibration Methods for Pogo Pres- sure Transducers, NBS Tech. Note (to be published in 1976).

16
TABLE 1

Working Liquids Used in Preliminary Investigations of Damping

Liquid Viscosity Density

(St) (kg/m 3

)

Bulk Modulus

(Pa)

Velocity

of

Sound

(ra/s)

Advantages Disadvantages Experiments

Column Description

I.D. Height Material

(cm) (cm)

Damping Amplitude

Ratio*

0.009 1.00 x 10 3 20.9 x 10 9 1460 High bulk modulus, and velocity of

sound; non-toxic; inexpensive

Low viscosity;

high vapor

pressure; corrosive to steel

2.2

1.3

1.3 1.2

Brass Smooth wall 14 Brass Smooth wall 12 Copper Spiral fins 15 Brass Woven -metal mesh filter

8.0

Copper Multiple

channels

9.0

Copper Interlacing fins **

Brass Smooth wall 5.0 Brass Woven-metal mesh filter

**

Brass Sintered-metal

fi 1 ter

**

Copper Multiple channel s 3.7

Tetrabromo- 0.080 2.95 x 10 3 29.3 x 10 9 1007 ethaneHigh density; non-toxic

Low viscosity;

high vapor

pressure; corrosive to steel , aluminum

and other metals

and rubber

2.2

1.2

1.2

Fluorocarbon 0.026 1.88 x 10 3 9.8 x 10 9 730 High density; Low viscosity; non-toxic low bulk modulus

Smooth wall 9.0

Mercury 0.001 13.6 x 10 3 265 x 10 9 1410 High density, Low viscosity;

bulk modulus, dissolves most

and velocity metals, health

of sound hazard

1.1 Stainless

steel

Glycerine 7.50 1.26 x 10 3 44.8 x 10 9 1904 High viscosity, bulk modulus, and velocity of sound; non- toxic

Hygroscopic Smooth wall 5.2

Petroleum

Oils 0.5 0.86 x 10 3 15.2 x 10 9 1340 925°C

15

(?25 C

High viscos- Low density;

ity and viscosity

velocity of temperature

sound dependent

2.2

2.2 Brass Smooth wall 16 Brass Woven-metal filter

mesh 3.8

Copper Multiple che nnel! 4.5 Brass Smooth wall 12 Copper Multiple cha nnel; 1.1

Brass Smooth wall 13 Brass Smooth wall 8.0 Aluminum Smooth wall 3.3

and glass

Brass Smooth wall 13.0 Brass Smooth wall 20 Brass Smooth wall 33 Brass Smooth wall 27 Aluminum Smooth wall 7.4

and glass Aluminum Smooth wall 2.8

and glass Aluminum Smooth wall 1.4 and glass Aluminum Smooth wall ** and glass

Brass Multi-tube Response

fixture flat to ±5% from

40 Hz to

75t Hz

Dimethyl 0.97 x 10 3 9.28 x 10 9 987 High

viscosity; non-toxic

Low bulk modulus

and density

300 125

10

2.4

1.1 0.50

2.4

2.4 2.4

1.1 0.50

0.40

0.20

0.15

0.16

*For a given value of acceleration, amplitude ratio is here defined as the ratio of measured maximum amplitude (at resonance) to the average of the amplitudes measured over 35-50 Hz. "Data not obtainable.

17
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18
TABLE 3

Factors Contributing to Transducer Calibration Error

Factor Systematic Error

(% of measured value) Random Error

(% of measured value)

DYNAMIC

Liquid Column

Height of liquid column Variation of liquid density with temperature

Acceleration Applied

Calibration of exciter control accelerometer

with reference accelerometer and precision of reading

Transducer Output

Voltmeter calibration of precision of reading Noise Trarcverse acceleration response of transducer

±0.1

±1.0

±0.3 d

±0.02 9

±1.0

±0.2

±0.1

±0.05

±0.1 /

TOTAL RMS ±1.05 ±1.03

Estimated Error = RMS systematic + 3 RMS random = ±4.14%

STATIC

Pressure Applied

Pressure gage calibration and precision of reading ±0.07

Transducer Output

Voltmeter calibration and precision of reading

Noise

±0.07

±0.06

±0.03

±0.07

TOTAL RMS ±0.099 ±0.097

Estimated Error = RMS systematic + 3 RMS random = ±0.39%

Typical calibration values for the source are acceleration, 20 gn zero-to-peak and liquid column height above centerline of transducer, 10 cm using 10-St dimethyl si loxane with a bulk modulus of

9.47 x 10 8 m

3 /Pa.

d

Estimate based on manufacturer's value of 0.098%/°C and variation of ±2°C. Estimate based on least count of ±1 mV for measurement of 1000 mV. Manufacturer's value for range of 20 mV.

e Estimate based on least count of ±0.01 mV for measurement of 20 mV. ^ This figure corresponds to ±0.02 mV for a typical calibration.

9 This value represents a maximum value for any of the transducers listed in table 4. h Manufacturer's value for range of 17 kPa (5 psi).

1 Estimate based on least count of ±0.2 kPa (±0.03 psi) for measurement of 17 kPa.

3 Manufacturer's value for range of 30 mV.

v Estimate based on least count of ±0.1 mV for measurement of 30 mV. This figure corresponds to ±0.02 mV for a typical calibration.

19
TABLE 4

Transducer Characteristics*

Transducer Type Range

(kPa zero- to peak)

Natural

Frequency

(kHz)

'

Diaphragm

Diameter

(cm)

Full -Range

Deflection of

Diaphragm

at Center**

(cm)

A-l,A-2,A-3 Silicon

diaphragm

with bonded

Wheatstone

bridge

34 45

B Unbonded

straingage

17 3.5

C Unbonded

straingage

34 5.0

D Unbonded

straingage

102 8.5

E(Reference)

Piezoelectric

quartz

crystal

54,400 100

0.22 2.5 x 10-^

1.26

1.26

1.26

0.953

3.8 x 10" 4

3.8 x 10" 14

3.8 x lO" 4

Data not

available

from

manufacturer

*From manufacturer's data.

**The manufacturers specify these deflections as maximum values

20
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23
Figure 3: Cross section of dynamic pressure source. Shown are reference

transducer port (B) , liquid-column chamber with 1 .7~cm-diameter

bore (J) , steel balls (K) , pierced steel plates (l_) , threaded

plug (M) with vent, retainer tube (N) , and test transducer

port (0).

24
9

Figure h: Oscilloscope traces showing peak-to-peak output (mV) from

reference transducer E as a function of frequency (kHz) for

three quantities of balls, as described in the text. The

top trace shows the source-transducer combination as being

overdamped; the center trace, underdamped; and the bottom

trace, near optimum damping. The vertical scale is 20 mV

peak-to-peak per division, and the horizontal scale is 0.3

kHz per division. The left-hand edge of each trace begins

at 35 Hz; the sweep range is 3 kHz.

25
Figure 5' Schematic of apparatus used to fill the source with liquid

under a weak vacuum. Q is a ball valve in the line between

bell jar and flask. Line R is connected to a source of vacuum,

26
OB I!

c

Figure 6 Oscil'oscope traces showing corresponding frequency-response

curves for test transducer (left) and reference transducer E (right). Of interest is the frequency range over which

transducer output is at a relatively constant level. Trace A:

test transducer A-l ; vertical scale for both transducers is

20 mV , peak-to-peak, per division. Trace B: test transducer

B; vertical scale for both transducers is 10 mV, peak-to-peak,

per division. Trace C: test transducer C; vertical scale for

both transducers is 10 mV, peak-to-peak, per division. Trace

D: test transducer D; vertical scale for D is 2 mV, peak-to-peak,

per division and for E, 10 mV, peak-to-peak, per division. The

horizontal scale for all traces is 0.3 kHz per division.

27
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29
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS Technical Note 914

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A New Dynamic Pressure Source for the Calibration of

Pressure Transducers

5. Publication Date June 1976

6. Performing Organization Code

7. author(S) Carol F. Vezzetti , John S. Hi 1 ten,

J. Franklin Mayo-Wells, and Paul S. Lederer

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4253456

11. Contract/Grant No.

NASA Order L-88319

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

NASA Langley Research Center

Hampton, VA 23365

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) A dynamic pressure source is described for producing sinusoidal ly varying

pressures of up to 34 kPa zero-to-peak, over the frequency range of approximately

50 Hz to 2 kHz. The source is intended for the dynamic calibration of pressure

transducers and consists of a liquid-filled cylindrical vessel, 11 cm in height,

mounted upright on the armature of a vibration exciter which is driven by an amplified sinusoidally varying voltage. The transducer to be calibrated is

mounted near the base of the thick-walled aluminum tube forming the vessel so that the pressure-sensitive element is in contact with the liquid in the tube.

A section of the tube is filled with small steel balls to damp the motion of the

10-St dimethyl siloxane working fluid in order to extend the useful frequency

range to higher frequencies than would be provided by an undamped system.

The dynamic response of six transducers provided by the sponsor was evaluated using the pressure sources; the results of these calibrations are

given.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated 6y sem/co/ons; Calibration; dynamic; dynamic calibration; dynamic pressure;

dynamic pressure source; liquid column; pressure; pressure source; pressure

transducer; sinusoidal pressure; transducer.

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J For Official Distribution. Do Not Release to NTIS

\ \ Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CU TOftT

_J Order From National Technical Information Service (NTIS)

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UNCLASSIFIED

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21. NO. OF PAGES I

35

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