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NBS TECHNICAL NOTE 927

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Development of

Dynamic Calibration Methods

or Pogo Pressure Transducers
NATIONAL BUREAU OF STANDARDS

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torn of stmdam

o 1976

Development of Dynamic Calibration Methods

for Pogo Pressure Transducers

John S. Hilten, Paul S. Lederer, Carol F. Vezzetti, and

J. Franklin Mayo-Wells

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by:

National Aeronautics and Space Administration G. C. Marshall Space Flight Center

Huntsville, Alabama 35812

^T 0F «*

°*EAU Of

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

Edward O. Vetter, Under Secretary

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director -\

Issued November 1976
National Bureau of Standards Technical Note 927

Nat. Bur. Stand. (U.S.), Tech. Note 927, 58 pages (Nov. 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 by SD Catalog No. C13.46:927). Stock No. 003-003- Price $1.15

(Add 25 percent additional for other than U.S. mailing).
FOREWORD

The work described was performed as a task within the InterAgency

Transducer Project. This is a continuing project for the development of calibration and evaluation techniques for electromechanical

transducers, and is supported by the National Bureau of Standards

and a number of other Government agencies. This task was largely

funded by the National Aeronautics and Space Administration through

the G. C. Marshall Space Flight Center under order number H-92100A.

Paul S. Lederer

Acting Chief

Components and Applications Section

i i i

DEVELOPMENT OF DYNAMIC CALIBRATION METHODS

FOR POGO PRESSURE TRANSDUCERS

CONTENTS

Page

1. Introduction 1 2. Experimental Development 2

2.1 Background: Discussion of Calibration Using

Open-Tube Source 2

2.2 Development of Closed-Tube Source 3 2.2.1 Pressure Halving in a Closed-Tube 3

2.2.2 Inertial Effects 4

2.2.3 Column Design and Construction . 7

2.2.4 Working Fluids 7 2.2.5 Effect of Variations in Bias Pressure ...... 8

2.2.6 Source Repeatability 9

2.3 Development of Windmill Source 9

2.4 Other Source Designs Using Working Liauids 12

2.4.1 Extensions of the Open-Tube Source 12

2.4.2 Other Source Schemes 13

3. Cal ibration 13

3.1 Filling the Column 13

3.1.1 Filling Procedure 13

3.1.2 Resonance Measurements 15

3.2 Calibration Procedures for Closed-Tube Sources 16

3.2.1 Calibration on Vibration Exciter .... 16

3.2.2 Calibration of Windmill Apparatus 17

3-3 Error Analysis 20

4. Measurements on Seven Pogo Pressure Transducers 21

4.1 Frequency-Response Measurements 21

4.2 Phase-Shift Measurements 23

4.3 Repeatability Measurements 24

4.4 Acceleration Linearity Measurements 24

4.5 Vibration Response Measurements 24

5. Conclusions 24

6. Recommendations 25

7. Acknowledgment 25

8. References 26

LIST OF TABLES

Table 1: Calculated Pressure Capability of a Closed-Tube LiquidColumn Source for Two Working Fluids at Constant

Displacement 27

Table 2: Effect of Bias-Pressure Variation on Transducer

Response with Silicone Oil as the Working Fluid .... 28
Table 3: Closed-Tube Source Repeatability as Determined

with Two Transducers 29

Table 4: Resonance Frequency as a Function of Closed-Tube

Column Bias Pressure for Mercury and Silicone Oil . . 30

Table 5: Factors Contributing to Estimated Transducer

Cal ibration Error 31

Table 6: Phase Shift Between Pressure and Transducer-Output

Waveforms for Transducer 537 on Windmill Apparatus . . 32

Table 7

'• Acceleration Linearity Measurements for Two

Transducers 33

Table 8: Vibration Response Measurements for Two Transducers . 34

LIST OF FIGURES

Figure 1: Two Source Columns Used in Early Experiments 35

Figure 2: Transducer Output (mV rms) at Constant Acceleration

Plotted as a Function of Frequency (Hz) for Two

Transducer Locations and for Open- and Closed-Tube

Configurations 36

Figure 3: The Developed Closed-Tube Column, with the Transducer

(A) at the Top, or Free End 37

Figure 4: Engineering Sketch of Closed-Tube Column

Construction 38

Figure 5- Engineering Sketch of Two-Piece Fixture Used to Mount

the Column (Shown in Figure 3) Inverted 39

Figure 6: Closed-Tube Column with Provisions for Mounting a Test Transducer (A) at Each End for an Experimental

Investigation of Inertial Effects as Described in

the Text 40

Figure ~]

: Transducer Sensitivity (mV/kPa) as a Function of Added

Mass (g) and of a Quantity (g) Equal to the Sum of the

Added Mass and One-Half the Distributed Mass 41

Figure 8: Apparatus Used in the Calibration of Pressure

Transducers for Pogo Measurements 42

Figure 3: The Windmill Source, Consisting of the Closed-Tube

Column Mounted on the Windmill Apparatus 43

Figure 10: Close-Up View of the Rotating Assembly of the

Windmill Apparatus 44

Figure 11: Photographs of Oscilloscope Traces of Waveforms from

a Test Transducer Calibrated on the Windmill Source

and on the Oscillating Source at Several Frequencies . 45

Figure 12: Schematic Elevation of Apparatus Used to Fill

Closed-Tube Column 46

Figure 13: Column Resonance Frequency (Hz) Plotted as a Function

of Bias Pressure (MPa) for Mercury and Silicone Oil as Working Liquids 47

Figure 14: Transducer Response Ratio Plotted as a Function

of Frequency on a Three-Cycle Logarithmic Scale

(Hz) at Bias Pressures of 7 MPa and 55 MPa, for

Transducer 537 48
Figure 15: Dynamic Sensitivity (%) Plotted as a Function of

Bias Pressure (MPa) , for Three Transducers kS

Figure 16: Transducer Response Ratio Plotted as a Function

of Frequency on a Three-Cycle Logarithmic Scale

(Hz) with Working Liquids of Mercury and Silicone

Oil, for Transducers 859 and 858 50

Figure 17: Dynamic Sensitivity {%) Plotted as a Function of

Bias Pressure (MPa), for Transducers 858 and 857 ... 51

VI 1

Development of Dynamic Calibration Methods

for Pogo Pressure Transducers

John S. Hilten, Paul S. Lederer,

Carol F. Vezzetti, and J. Franklin Mayo-Wells

Two dynamic pressure sources are described for the calibration of

pogo pressure transducers used to measure oscillatory pressures generated

in the propulsion system of the space shuttle. Rotation of a mercuryfilled tube in a vertical plane at frequencies below 5 Hz generates sinusoidal pressures up to 48 kPa, peak-to-peak; vibrating the same mercuryfilled tube sinusoidal ly in the vertical plane extends the frequency re- sponse from 5 Hz to 100 Hz at pressures up to 140 kPa, peak-to-peak.

The sinusoidal pressure fluctuations can be generated by both methods in

the presence of high pressures (bias) up to 55 MPa.

Calibration procedures are given in detail for the use of both

sources. The dynamic performance of selected transducers was evaluated

using these procedures; the results of these calibrations are presented.

Calibrations made with the two sources near 5 Hz agree to within 3% of

each other.

Key Words: 3ias pressure; calibration; dynamic calibration; dynamic

pressure; high pressure; liquid medium; pogo pressure; pressure source;

pressure transducer; sinusoidal; space shuttle; transducer.

1. INTRODUCTION

This report describes the development of dynamic pressure sources

and associated calibration methods for pogo pressure transducers used to measure oscillatory pressures generated in the propulsion system of the

space shuttle. These pressure transducers are intended to make measurements over a full-scale range of 140 kPa peak-to-peak in the presence of

high static (bias) pressures of up to 55 MPa over a frequency range from

1 Hz to 100 Hz.*

A method for transducer calibration was available using a pressure

source consisting of a liquid-filled tube mounted on the armature of a vibration exciter [1].** This method was chosen as a starting point for

the present work [2,3,4].

*1 kPa = 0.145 psi ; 1 MPa = 145 psi.

**Figures in brackets indicate the literature references, section 8,

1
Whether a given transducer in the shuttle propulsion system is re- sponding to gas pressure, to liquid pressure, or to the pressure of a mixture of phases will depend both on its detailed location in the oxidizer or propel lant flow stream and on the flow conditions at any given

moment. The use of a liquid-filled tube as opposed to a gas-filled tube

does not affect the operating principle of flush-diaphragm-type pressure

transducers, although the manner in which differential types respond may

be different for gaseous than for liquid media over the frequency range

of interest.

2. EXPERIMENTAL DEVELOPMENT

2.1 Background: Discussion of Calibration Using Open-Tube Source

A considerable amount of work has been carried out on the development of a dynamic pressure source and associated calibration method using

a liquid medium for pressure transducers with low full-scale ranges [5].

This hydraulic s i nusoidal -pressure source consists of a rigid cylindrical

vessel, or tube, closed at the bottom and open at the top, mounted ver- tically on the table of an electrodynamic vibration exciter. The pres- sure transducer under test is mounted with its diaphragm in a vertical

plane near the bottom of the liquid-filled tube. A vertical orientation

of the diaphragm is chosen to minimize the effect of vibration on transducer response. Over that part of the frequency range for which the

pressure amplitude is considered to be flat (i.e., frequencies below

20% of the natural frequency of the filled tube and transducer taken

together), the effects of damping need not be considered. With this

frequency constraint, the amplitude of the sinusoidal pressure generated

within the liquid column and acting on the transducer when the table is

driven at a zero-to-peak acceleration of a is given by:

P = ah

c

p,

where

P = pressure (Pa zero-to-peak)

,

a = zero-to-peak acceleration (gn )*,

h c = liquid-column height (m) above the center of the transducer

diaphragm, and

p = density of liquid (kg/cm 3 ).

With the exciter table at rest, the static pressure acting on the transducer diaphragm is equal to hc p , a quantity referred to as "liquid head."

Thus, if the tube is vibrated sinusoidally in a vertical direction with

a peak acceleration of exactly 1 g n , the pressure seen by the transducer

will vary sinusoidally from a maximum of twice the liquid head to near

: The symbol gn represents the unit of acceleration equal to the standard

value of the acceleration of gravity at the earth's surface: gn =

9.8l m/s 2

, to three significant figures.

2
zero. There is a theoretical limitation on the pressure amplitude

generated; an acceleration level sufficiently high to reduce the liquid

pressure to zero can never be reached, but only some value near the

vapor pressure of the liquid. Operation at higher levels of acceleration will produce wave-shape distortion.

Over the flat range of frequency response, the dynamic pressure

source as described serves as a source of calibrated pressure known to

within 5%. The source is an absolute calibration source in the sense

that the pressure is calculable from mechanical parameters that can be

measured and knowledge of the acceleration imparted to the column. Thh

acceleration, in turn, can be measured with instruments that may be

traced through calibration to basic standards.

If the transducer diaphragm is sensitive to vibration, such sensitivity would have the effect of widening any discrepancy between static

and dynamic calibrations. Experimental data indicate that correlation

between static and dynamic calibrations of a pressure transducer using

this source may be expected to be on the order of ±0.1%.

2.2 Development of Closed-Tube Source

During the development of the open-tube source, exploratory tests were conducted which indicated that the source could be, modified into a closed-tube configuration to accommodate a comparatively high-level bias

pressure. This concept served as the basis from which was developed the

present vi brat ing-tube pressure source for calibration of transducers designed to measure small pressure fluctuations in the presence of large

static pressures.

A prototype closed-tube column was constructed from an open-tube

design. The converted tube is shown in figure 1, left. This tube accom- modates two transducers (A) screwed into mounting plates (B) . At (C) is

the valve which permits the tube to be filled under pressure. The tube

is closed at the top by threaded plug (D)

.

2.2.1 Pressure Halving in a Closed Tube - During several early

experiments with the closed-tube configuration, it was observed that the

output of the pressure transducer mounted on the source was substantially

less than the output expected on the basis of P = ahc p. At the same time,

the natural frequency of the closed configuration was determined to be

approximately double that of the same tube in open configuration. For

investigating these results, a closed-tube column 31~cm long was con- structed with mounting plates for transducers near the bottom and 6.1

and 11.9 cm above the bottom (approximately 20 and k0% of the column

length from the bottom, respectively). This tube is shown in figure 1,

right. The results of tests at constant acceleration with the same transducer mounted at the middle and highest level and with the tube both

open and closed are shown graphically in figure 2.
If the transducer is mounted near the bottom end of the tube so that the center of the diaphragm is at a distance, r, from the end, the

pressure amplitude P generated in open-tube configuration is given by

P = a(h - r)p,

where

h = h c + r = the length of the tube containing liquid, in meters.

With the same tube closed, the pressure amplitude P c experienced by

the transducer will be

Pc = a(|- r) p.

For example, a transducer mounted very close to the bottom end of the

tube sees approximately twice the pressure in the open-tube configuration that it sees in the closed configuration; mounted at a point k0% of

the length from the bottom of the tube it sees approximately six times

the pressure in the open-tube configuration that it sees in the closed

conf igurat ion.

An analysis of these results was conducted and a theoretical explanation developed, reported in detail in [6]. In an open tube, the upper

surface of the liquid is unconstrained and therefore becomes the locus

of a pressure node. At the lower end of the tube, the velocity of the

liquid is constrained to be zero, but acceleration amplitude (and conse- quently pressure amplitude) is at a maximum value. The result is that

pressure amplitude is proportional to distance from the node at the open

end. When the tube is closed at both ends, the upper surface of the

liquid is also constrained to zero velocity, and pressure maxima of equal

amplitude occur at the ends. From symmetry considerations, it can be seen that the pressure node must be located halfway between the ends so that the pressure amplitudes in the liquid column will range from zero

at the center to equal maxima, determined by the acceleration amplitude,

at the ends. These maxima, resulting from an effective liquid head of

one-half of the tube length, are thus one-half of the single maximum for

the corresponding open tube. A similar analysis leads to a doubling of resonance frequence of the closed-tube configuration relative to the

open configuration.

In summary, a vertical tube completely filled with liquid and closed

at both ends behaves like a vertical tube open at the top and of half the

height of the closed tube when the tubes are subjected to sinusoidal ly

varying acceleration along their axes.

2.2.2 Inertial Effects - The analysis given above, predicting

equal pressure amplitudes at both ends of a closed tube, does not take

into account effects which tend to deform any real, non- inf in i tely-st i ff

tube. Further, the desirability of using a closed-tube column that could

be mounted on either a vibration exciter or the windmill apparatus

k
(described in 2.3) suggested a tube design in which the transducer would

be mounted at the upper end with the result that the tube would be loaded

by the mass of transducer and mount.

To investigate the size of the inertial effect, two series of experiments were performed. In the first, a closed-tube column representative

of the final experimental transducer-at-the-top design was mounted on the

vibration exciter in its intended orientation and then, by means of a special fixture, upside down. The column and fixture are shown in figure 3> with engineering sketches of the column and fixture in figures h

and 5, respectively. The response of a selected pressure transducer was measured over a range of frequencies and showed a significant, consistent

difference between the transducer at top and transducer at bottom. !n all cases the response when the transducer was in the bottom position

was the larger. On the basis of this experiment, a more detailed experiment was planned. The closed-tube column constructed for these tests is

shown in figure 6. Identical transducer-mounting blocks are incorporated

into each end of the column, with the filling connection (hidden in the

figure) at the mid-plane of the column. A blind, tapped hole at each

end of the column permits it to be mounted on the vibration exciter by means of a threaded stud. Loading masses, shown at the left in figure

6, are attached to whichever end is the free end of the column by means

of a machine screw.

In the tests, two similar piezoelectric pressure transducers (identification numbers 535 and 536) were mounted, one on each end of the

column. The column was filled with silicone oil at the test pressure of

either 7-1 or 55 MPa. The filled column was mounted on the exciter

table and driven with an acceleration amplitude of 5 ffn at 50 Hz. Tests were conducted with first one end of the column up and then the other

for loading masses in steps of 100 g from to 600 g. The outputs of the

two transducers were measured and recorded and sensitivities calculated.

Figure 7 shows the results, with sensitivities (mV/kPa) plotted as a function of the added mass (g) and the sum of the added mass and one-half

the mass of the column (g). This sum is chosen because the product of

the acceleration and this sum represents the compressive force applied

to the column, as explained below.

The results of the experiments are qualitatively consistent with

excitation of an axial compression mode in the column. The pressure

seen by either transducer is the sum of the component generated by

volume changes of the column, which are in turn the result of acceleration of the column.

For a column of uniform cross section and wall thickness, and con- sidering only the axial mode, the compressive force will be the product

of half the column mass and the acceleration, since the mass is assumed

to be distributed uniformly over the length. The change in volume is

proportional to the compliances of the column and of the fluid. The

contribution of column vibration for frequencies sufficiently far below

resonance is in phase with the fluid acceleration component of pressure
at the column end nearest the exciter table and, consequently, out of

phase at the free end. The components will, therefore, add and subtract,

respectively, at the two ends. At the midpoint of the column, where the

component contributed by column acceleration is zero, only the component

•contributed by the fluid acceleration is present to a first-order

approximat ion.

Adding additional mass at the free end of the column increases proportionally the compressive forces acting on the column (at twice the

rate of an equal change in distributed column mass). Referring to fig- ure 7, the indication of the transducer at the mounted (bottom) end in- creases in a linear manner with increasing mass and that of the transducer at the free (upper) end decreases at the same rate with increasing

mass, consistent with the analysis. If the readings are extrapolated to

lower mass, the two curves intersect at zero mass at a pressure sensitivity corresponding to the pressure component generated by the fluid

acceleration alone.

Other vibrational modes such as flexure and radial distension modes,

which are much more difficult to analyze, can be suppressed in practice

by increasing wall thickness. Increased wall thickness also has the

effect of adding mass to the column end, but to a first-order approximation greater thickness does not change the contribution of the distributed mass.

The above analysis requires that a correction factor C for inertial

effects be incorporated into the expression for the pressure amplitude

in a closed-tube column:

Pc = C a ( y

- r ) p

For the column design shown in figure 3, C is determined by measuring and recording transducer output at a convenient constant acceleration

amplitude at 11 frequencies (15, 20, 25, 30, kO, 50, 60, 70, 80, 90, and

100 Hz) with the transducer first at the top and then, with the inverting

fixture, at the bottom of the column. The average of the 11 values for

each transducer position is calculated. C may then be calculated empirically as

P + P top bottom

2 P"top

where

P = average of transducer measurements with transducer in

top . •«.. A _ top position, and

P, = average of transducer measurements with transducer in

bottom bottom position.

6
Note that for the design shown in figure 3, r = and the expression for

pressure amplitude simplifies to

P c =}cahp. .

2.2.3 Column Design and Construction - On the basis of experience

with the prototype and other columns, a new closed-tube column was con- structed to meet the following design considerations:

1. Material of construction to withstand attack by corrosive

liquids and be suitable for use with mercury,

2. Column to be of reduced overall weight to limit loading of

vibration exciter or windmill apparatus at low frequencies,

especially in 3 to 10 Hz range,

3. Tube to have increased wall thickness to permit bias pres- sures of up to 55 MPa , and

k. Design to incorporate a minimum number of fluid connections

to 1 imi t leaks.

In addition, the design was to be simple to machine and suitable for use

on the windmill apparatus. The column is shown in figure 3- The tube

is type 321 stainless steel, with an outside diameter of 2.5** cm and a wall thickness of 0.45 cm. A closure is welded into the tube at each

end; a blind hole is drilled and tapped into the lower closure for a mounting stud and a through hole is drilled and tapped into the upper

closure to mount the pressure transducer. The filling-pressurizing

valve is mounted on the side of the tube by means of a short nipple of

pipe.

Weight reduction is chiefly achieved in this design by eliminating

transducer mounting plates and the relatively massive column end block.

One consequence is that the transducer diaphragm is perpendicular to the

applied acceleration and hence the transducer response is more likely to

be affected than in a right-angle mounting. This disadvantage is more

than balanced by the fact that the diaphragm sees a uniform pressure

(instead of a pressure gradient) at the end of the tube with r = 0. The

other consequence is that only one transducer may be mounted; however,

multiple mounting is used only for development purposes and serves no purpose in the source configuration recommended for use.

l.l.h Working Fluids - Experience with the open-tube pressure

source suggested the use of either silicone oil or mercury as the working fluid. Petroleum oil was also used in a few tests, but showed no advantages over silicone oil and some disadvantages (such as a highly

temperature-dependent viscosity); the use of petroleum oil was therefore not pursued.
For a given liquid-column height and a given vibration-exciter capability, the specific density of the working fluid determines the maximum

pressure and amplitude attainable, and the velocity of sound transmission

determines the column natural frequency and therefore the maximum useful

frequency attainable. Mercury has a high specific density (13-55), a relatively high velocity of sound transmission (l^tlO m/s) , and is a hazardous material to handle. The maximum peak-to-peak sinusoidal pressures

that can be generated by a closed-tube source with a mercury column

height of 36.8 cm and with a double-amplitude displacement of 1.25 cm are given in table 1 for various frequencies.

The silicone oil selected for use has a comparatively low specific

density (0.97), a moderate velocity of sound transmission (987 m/s), and

is nontoxic. In addition the silicone oil has good damping characteristics, with a viscosity of 10 St at room temperature. The most significant disadvantage is the low density, which limits the pressure amplitudes available at frequencies below 20 Hz because of the low acceleration levels produced by the exciter below this limit (see table 1).

2.2.5 Effect of Variations in Bias Pressure - Small changes in

temperature have been observed to produce large changes in bias pressure.

For example, the warmth of an experimenter's hand applied to a closedtube column with zero bias pressure for approximately two minutes re- sulted in a positive change in bias pressure of 3^0 kPa . A tube also at zero bias pressure cooled slightly below its filling temperature behaved

in the erratic manner of a tube with a void. These effects are presumably the result of unequal expansion of fluid and tube and are less severe at high bias pressures than low.

To determine the order of magnitude of the effect of bias-pressure

variation on pressure-transducer response, an experiment was conducted

with a single transducer (identification number 537) in which the bias

pressure was varied from 6.89 MPa to 0.21 MPa in the steps shown in

table 2 and the transducer output measured and recorded. The acceleration was held constant at 10 gn peak-to-peak, at 50 Hz. The data in the

table indicate the presence of a small, though real ,/ effect of biaspressure variation on transducer output. However, the maximum deviations

from the calculated average of 32.425 mV rms (+0.175, -0.305 mV rms) are

less than 1% of the average value and thus within the estimated limits

of error (see 3- 3)

.

The measured resonance frequency of the source-transducer system is

also given in table 2 for each bias pressure, as this measurement for

silicone oil provides an indication of bias-pressure changes to within

an estimated 170 kPa. Resonance frequency determinations are made at an acceleration of 1 g n peak-to-peak, a level chosen to prevent overranging

the test transducer. This technique of monitoring bias pressure cannot

be used with mercury as the working fluid, because a mercury-filled tube

exhibits little change in resonance frequency with change in bias

pressure.
2.2.6 Source Repeatability - Because no apparatus for calibrating

transducers for pogo pressure measurements existed prior to the development of the sources described in this report, wel 1 -character ized pressure

transducers were not available to make measurements of source repeatability. Accordingly, two of the transducers to be calibrated (identification numbers 537 and 859) were selected for these measurements. The

results are summarized in table 3, which shows the coefficient of variation of pressure measurements made with the two transducers at various

frequencies. No way is available to distinguish the contribution to the

observed variations resulting from source fluctuations from that resulting from time-variant changes in transducer performance. However, the source is probably at least as repeatable in performance as the mean of

the coefficients of variation for transducer No. 859, on the order of

0.2%.

2.3 Development of Windmill Source

The vibration-exciter system used in this work has a displacement

capability of 1.3 cm peak-to-peak and can impart accelerations of 25 <3x\ to an 1

1 -kg mass at frequencies of 30 Hz and above. With the closedtube column shown in figure 3> these capabilities do not permit the

achievement of sufficient pressure amplitudes over the frequency range

of 1 to 3 Hz, which is of particular importance in the pogo application.

For example, with mercury as the working fluid, a pressure amplitude of

1 kPa is attainable at 1 Hz and 5 kPa at 2 Hz. These amplitudes are very much smaller than the 1 40 kPa desired.

To permit pogo calibrations at low frequencies, a new source was designed to be used in conjunction with the closed-tube vibrating column

described in 2.2. The source consists of a closed-tube column which is

rotated about one end in a vertical plane in the earth's gravitational

field so that the column experiences a sinusoidal ly varying acceleration

of ±1 gn

. The configuration gives rise to the name windmill source and

is based on earlier work with an earth's field calibrator for accelerometers [7]- The design uses the same physical column used in the

vibrat ing-column source, with the transducer at the outer, or free, end

of the tube.

When the tube is rotated at constant angular velocity, the transducer experiences a pressure with two components: a sinusoidal ly varying

component (A Pqrav ) produced by the interaction of the rotating mass of

fluid and the earth's gravitational field, and a constant component

(Pcen t) resulting from the action of centrifugal force on the mass of

the fluid. In addition, the transducer sees any constant bias pressure

present.

The force applied to the outer end closure by the mercury is equal

to the force required to restrain a mass rotating with the same angular

velocity as the mercury, equal to the mass of the mercury, and having

the same radial distance to the center of mass as the mercury. Since
the distribution of mercury per unit length of the tube is uniform, the

center of mass is located at h/2 from the center of rotation, and

Fcent ° m &>< 2

'

p m co 2 h io 2 h

2

p •cent 2A " 2

where

m = mass of mercury (kg)

,

a) = 2tt x rotational frequency (rad/s) , and

A = cross-sectional area of tube (m 2

)

.

The maximum pressure is seen by the transducer when it is "down" in

the rotational cycle and the minimum when it is "up." Experimental observations show that the difference between these two pressures is

A p = r a h P A r grav u n

where

a = peak-to-peak acceleration in units of gn

.

This result is consistent with that obtained from the same closed-tube

column on the vibration exciter. While it has not been demonstrated

rigorously, the suggestion is made that the time-varying acceleration

field seen by the fluid in each configuration is equivalent when the

acceleration varies from +1 gn to -1 gn

, and that the pressures produced

in the column on the windmill apparatus are subject to boundary conditions equivalent to those produced on the vibration exciter. To a first

approximation, the empirical correction factor C has been taken to be

the same as that used before and is defined in the same manner.

The relative magnitudes of P cen t and A Pg ra v ma y be compared by means of the following example. Consider a mercury-filled tube 36-cm

long and with a cross-sectional area of 1 cm2. The mass of the mercury

is approximately 0.5 kg, and at a rotational velocity of 2 revolutions

per second (rps), the bias pressure P C ent at the outer end is approximately 1 kO kPa. The effective acceleration is approximately 3 g^ > an d

the dynamic pressure A Pgrav ' s approximately kS kPa

.

An important design goal imposed in the windmill apparatus is that

the arm formed by the closed-tube column and the counterbalance rotate

smoothly at constant known angular velocity with a.minimum of vibration.

Also, there should be a minimum amount of energy dissipated in the mainshaft bearings. If these conditions are not met by the apparatus to a sufficient degree, irregularities in rotational motion will result which

will in turn produce a distorted pressure waveform.

10
Figure 8 shows the apparatus evolved (A), its supporting electronics

(B), and the vibration-exciter system (C) . A more detailed view of the

apparatus is given in figure 9. with a close-up of the rotating assembly

in figure 10.

Air bearings mounted in blocks (D) support the 3-8-cm-d iameter main

shaft. The front of the shaft carries a two-piece clamping block (E)

into which the windmill arm is mounted. This arm is composed of the

closed-tube column (F) and the counterbalance-tube assembly (G) to which

it is mounted by a threaded stud. The counterbalance tube has the same outer diameter as that of the column and carries at its free end a weight

(H) adjustable in position radially for single-plane static balancing.

As noted earlier, the transducer under test (I) is mounted on the free

end of the column. Electrical connection to the transducer is made

through slip rings (J) mounted at the rear end of the main shaft. The

shaft and variable-speed drive motor (K) are each equipped with toothed

pulleys (L) ; rotational motion is transmitted from the motor to the

rotating assembly by means of these pulleys and cog-belt (M) . The source

of power for the motor is a rack-mounted d-c power supply (N)

.

Angular velocity is monitored by counting the number of holes in a disk (0) that pass betv/een a lamp and a photoelectric cell in a given

interval of time. The disk is fixed to the shaft at a position immediately behind the windmill arm and has 100 equ id istant ly spaced through

holes drilled on a slightly smaller circle than that of the disk itself.

A pulse is generated and counted for each hole passage; the resulting

count is displayed on a counter (P) , which has an adjustable counting

interval. A second photocell assembly detects the number of times a single hole in the disk (at a slightly different radius from the center

of the disk than the others) passes between lamp and photocell. This

hole, used to provide phase-reference information, is positioned so that

it is sensed when the windmill arm is in one of its two horizontal orientations. Photocells and lamps are mounted in block (Q_) .

The motor drive can be used to produce angular velocities of approximately 0.5 to 5 rps. The upper limit is primarily determined by how

well the windmill arm is balanced; however, both limits depend on the

degree of smoothness of motor operation at low frequencies. With the

drive belt removed, the arm may easily be swung manually up to approximately 2 rps. The low-friction air bearings permit a well-balanced arm

to spin freely so that at 1 rps as many as six or seven revolutions may occur with no change in the displayed count of 100/s.

Figure 11 shows the output waveforms from a transducer mounted on the closed-tube column on the windmill apparatus manually spun at 1 Hz

(A) and motor-driven at 5 Hz (B) . The stepped effect of the waveform at

5 Hz is attributable to the cog-belt drive and to relatively few poles

in the motor. For comparison, waveforms are also shown for the same transducer-column combination on the vibration exciter. The waveform at

(C) represents 10 Hz and exhibits some distortion, notably near the

peaks. By 25 Hz (D) , little distortion is evident, although close

11
examination of the peaks reveals a lack of symmetry. At 100 Hz (E) , no distortion is detectable.

2.k Other Source Designs Using Working Liquids

Because there was no a pr ior i guarantee of success with the closedtube source, several other methods for generating pressures were investigated in parallel until the closed-tube column on vibration exciter and

windmill apparatus showed clear superiority with respect to feasibility,

simplicity, or the like.

2.4.1 Extensions of the Open-Tube Source - Since the pressure amplitude generated in an open-tube column depends on the acceleration imparted to the column, on the length of the liquid column, and on the

density of the liquid, increasing any one or combination of these quantities will result in an increased pressure amplitude. Trade offs — increasing one quantity at the expense of another -- are also to be con- sidered as long as the ahp product is thereby increased. Restrictions

imposed by parameters such as resonance frequency, maximum available

exciter displacement at a given load and given frequency, and vapor pressure of the liquid are examples of practical considerations that must

also be taken into account.

The use of mercury as contrasted with water or a silicone oil is an example of increasing p, and no practicable denser fluids are known.

Attempts were made to construct sources with open-tube columns by

manipulating the other two parameters: a column for use on the vibration

exciter with a liquid height of 137 cm, 4.5 times that of the usual

column, and a similar long column mechanically driven through large displacements. In the experiments with the vibration exciter, water was

used as the working liquid for convenience, and the column was driven

over the range of frequencies from 5 to approximately 20 Hz. A piezoresistive pressure transducer was mounted with the center of its diaphragm one diaphragm radius from the bottom of the tube. Below 5 Hz,

the output waveform of this transducer became grossly distorted. Above

20 Hz, the effect of the low resonance frequency of approximately 240 Hz

limited useful response.

Because of the very limited range of frequencies over which the

pressure amplitude of the long column is flat to a useful degree (for

example, limits of ±5% of the pressure amplitude are often used to define "flat"), no further work is contemplated or recommended with a long

column on the vibration exciter.

Experiments were also conducted in which a vertical long column was driven up and down through various displacements by. means of an eccentric

and connecting rod. This mechanical drive was intended to extend the displacement range considerably over that provided by the exciter, with the

adjustable eccentric mounted on the drive motor providing peak-to-peak

12
displacements of 5-1 to 11.4 cm in approximately 1.3 - cm steps. When the

column was set into motion, the signal from a pressure transducer mounted

near the bottom of the tube proved to be sufficiently noisy to mask the

sinusoidal pressure signal desired, in spite of the fact that considerable attention had been paid to the selection and installation of bearings in which the connecting rod and column were supported. With the

drive disconnected, the tube was manually displaced, and a cleaner signal

from the transducer was observed.

Analysis indicated that a considerable refinement of the mechanical

drive would be required to reduce the noise level, even with a shorter

column. The long column is subject to a similar upper-frequency limit

imposed by the natural frequency to that of the column described above.

For these reasons, no further work is contemplated on mechanical drive

systems.

2.4.2 Other Source Schemes - Two other schemes were investigated

for producing pressures suitable for calibrating pogo transducers. One

of these was the use of a closed-tube column on a dual centrifuge which

was available for experiment [8]. On the basis of the preliminary work,

it was determined that the presence of electrical noise, especially at

frequencies on the order of a few hertz, militates against using this

form of dynamic pressure source, as does the somewhat exotic nature of

the dual centrifuge itself. The other scheme was to use a double-acting

piston in a closed-tube column mounted on a vibration exciter. An em- bodiment of this source was constructed, and limited tests carried out.

Despite redesign of the apparatus to reduce the effects of a number of

mechanical problems which tended to degrade the pressure waveform, no satisfactory waveform was obtained.

CALIBRATION

3.1 Fi 1

1

ing the Column

Experience has shown that filling and pressurizing the closed-tube

column so that the working liquid occupies all the available space without any inclusions of gas (air) or other liquids is vital to proper

operation of the source. The presence of even small voids alters the

behavior of the closed-tube source in the direction of an open-tube

source in an unpredictable manner.

3.1.1 Filling Procedure - A schematic elevation of the system used

to fill the column with both silicone oil and mercury is shown in figure 12. Initially the column is not connected to the filling system. A

valve-position chart, indicating the sequence of valve operations after

the filling system is connected to the column, is also given. To prepare the system for use, the following procedure should be followed:

13
1. Close valves A, B, C, and D.

2. Remove the cap from the liquid reservoir and pour liquid

into the reservoir. Pour enough liquid into the reservoir

to fill the connecting tubes of the system and the column

itself, with a substantial reserve.

Note - A trial run with water may be used to

determine the volume of liquid required to fill

the system. Be sure the system is dry before

filling it with the working liquid.

3. To catch the liquid released in step 5, place a suitable

vessel under the free end of the tubing which will later

be attached to valve E.

h. Open Valve C.

5- Momentarily open valve B; then close it.

Note - The purpose of this step is to purge air

from the short connection between the liquid

reservoir and valve B. As a result of manipulating valve B, a small quantity of liquid will fall

into the vessel. If the liquid has a density

near that of water, some of it will be discharged

into house vacuum; if the liquid is mercury, the

entire slug of liquid will land in the vessel.

6. Clean the closed-tube column with a suitable solvent to remove grease and other contaminants; then dry. Install

the test transducer.

7- Connect the free end of the tubing to E. Open valve E if

it is not already open.

8. Set the oil piston gage to the required pressure for bias.

9- Follow the sequence of valve operations given in figure 12.

10. After the last step, "Close Down System," disconnect the

tubing from valve E.

If the same liquid is to be used the next time a column is to be

filled, and if the liquid is not mercury, the filling system may be left

as is until that use. At that time, new liquid should be added to the

reservoir if required, and the filling operation entered at step 6. If

a different liquid is to be used the next time a column is to be filled,

or if the liquid is mercury, the filling system should be emptied and

cl eaned

.

14
3.1.2 Resonance Measurements - A resonance method is used to monitor the adequacy of column filling. The filled column is mounted on the

table of the vibration exciter, and the exciter control system set to

maintain the acceleration level at ±1 gn peak-to-peak. The driving frequency is continuously increased from a few hertz until resonance in the

test transducer pressure signal is observed. The resonance peak value

should be at least 5 times the level at which the signal is flat to

within a few percent over a range of frequencies; for this purpose

smaller resonances are to be ignored.- Experience has shown that the resonance frequency measurement for a given column fill should be repeatable to within 25 Hz of the calculated value.

As reported earlier [h] , the piezoelectric type of pressure transducer appears to be the most suitable of those commercially available

types evaluated for pogo application. For piezoelectric transducers,

the diaphragm is relatively stiff and the increase in volume of the

closed-tube column contributed by a piezoelectric transducer when the

column is pressurized to as much as 55 MPa is negligible. Thus, for

tests on piezoelectric transducers using a given column, liquid, and bias

pressure, the resonance frequency range representing satisfactory filling

may be determined on the basis of a few carefully performed fillings and

corresponding measurements. For a given column, liquid, and bias pressure, a higher measured resonance frequency indicates a more satisfactory

filling, with the proviso that it is desirable for the bias pressure to

be sufficiently high that bias pressure drift resulting from temperature

changes is no more than 1 or 2%.

This proviso is more important for liquids with low bulk moduli

(such as 10-St silicone oil or water) than high (such as mercury). For

example, the maximum measured drift in a closed experimental tube with a silicone-oil column 29 - cm long and pressurized to approximately 65 kPa was over 100 kPa for one 20-min run. The tube was standing free on a bench in the laboratory; although a strain-gage pressure transducer re- quiring excitation was used (and hence the transducer heated the oil

slightly), the transducer had been energized for some 12 hours prior to

the test to permit temperatures to stablilize. Ten measurements with

piezoelectric quartz-crystal transducer identification number 858 mounted

on the closed-tube column showed a variation in resonance frequency from

Another way of stating this is that the resonance amplitude ratio

should be at least 5- (For the purposes of this report, resonance amplitude ratio is defined as the ratio of the measured maximum amplitude

of the pressure transducer signal, at resonance, to the measured amplitude at frequencies below the natural frequency over which the frequencyresponse plot exhibits no significant departure from a straight line

parallel to the frequency axis.) With no damping, the resonance and

natural frequencies are the same. With the little degree of damping

present in the column, these two frequencies are nearly enough the same

to permit the substitution of "measured resonance frequency" for

"natural frequency" in the definition above.

15
1359 to 1598 Hz with silicone oil bias pressures of 3-5 to k] MPa.

Thirty-three measurements with four similiar transducers including identification number 858 over a mercury bias pressure range of 3-5 to 55 MPa

showed a variation in measured resonance frequency of 1615 to 1662 Hz.

A single transducer with the same type of design (identification number

311)- showed resonances of 1717 and 1 7 1 8 Hz at 55 MPa in mercury. The

detailed data are given in table k. Figure 13 shows that the shift in resonance frequency with bias pressure is very nearly linear for silicone

oil and constant within the estimated measurement error for mercury over

the range of bias pressures used. The data points for each plot in some cases represent averages of measurements taken at a given frequency.

The silicone data were measured with transducer identification number

858 and the mercury, with 857-

3.2 Calibration Procedures for Closed-Tube Sources

The following procedures are those developed as a result of experience with using the two sources to calibrate pressure transducers for

pogo measurements. The starting point is that the column has been

cleaned, the test transducer installed, and the column filled and pressurized to the desired bias pressure. A general caution relates to the

sensitivity of bias pressure to temperature, especially at lower bias

pressures for which the percentage change will be greater. Because of

this sensitivity, calibrations should be conducted expediently, with no more than 15 min allowed to elapse between the conclusion of measurements

on the vibration exciter and the beginning of measurements on the windmill apparatus. Direct contact between the filled column and any thermal source (including hands) should be avoided. If possible, calibrations

should be scheduled for times when the work space in which they are carried out is not subject to large changes in temperature.

3.2.1 Calibration on Vibration Exciter

1. Mount the column, transducer up, securely to the exciter

table by means of a threaded stud.

2. Connect the output of the transducer to whatever instrument (such as storage oscilloscope, digital voltmeter,

etc.) is to be used to measure the electrical pressure

s ignal .

Note - It has been found convenient to make

low-frequency measurements up to the neighborhood of 1 Hz by direct measurement of the

trace displayed on the screen of a storage

oscilloscope or by measurement of a photograph of the trace displayed on either a storage or non-storage oscilloscope. Above

1 Hz, a true-rms digital voltmeter was used,

as this was the lower frequency limit of the

16
instrument available, and the signal waveform

deviated little from a true sine wave. If

phase information is desired, it is useful to

photograph traces showing both the pressure

signal and the signal from the monitor accelerometer of the exciter at selected frequencies over the entire range.

3. Connect other components of the system as required. Energize any equipment requiring a warm-up period.

k. Following the longest specified warm-up period for any item

of equipment in use, determine the column resonance frequency as indicated in 3-1.2.

5. if the result of this measurement indicates the column is

satisfactorily filled, continue with step 6. Otherwise,

refill the column according to the procedure given in

3.1.1, or according to other accepted procedure. Following refill, begin the calibration procedure again at step

1 of 3-2.1.

6. Set the exciter controller to drive the exciter table at

the required acceleration level to generate the desired

test pressure. Set the frequency selector to the lowest

(test) frequency desired.

Note - The lower frequency limit is determined

by the exciter capability.

7. With the exciter energized, measure and record the amplitude of the pressure signal. Record the acceleration level

and frequency at which the column was driven. Photograph

the signal trace if desired.

8. Set the frequency selector to the next desired test frequency.

9. Repeat steps 7 and 8 until the pressure signal has been measured at all intended test frequencies.

Note - The upper frequency limit should not exceed

approximately 20% of the measured resonance frequency if measurements in only the flat portion

of the amplitude-frequency response are desired.

To avoid damage to the test transducer, or to the

exciter, or to both, do not drive the column near resonance at more than ±1 gn

.

3.2.2 Calibration on Windmill Apparatus - The procedure given below reflects the specific design of the apparatus, for example in detail

ing the manner in which the air supply to the bearings is varied. This

17
information is provided primarily to indicate the kinds of operational

aspects that should be considered. The starting point for this calibration is that the amplitude-frequency response for the test transducer

has been measured on that portion of the desired frequency range covered

by the vibration exciter, and therefore that the column resonance has

been measured as a check on filling.

1. Apply air to the air bearings at a pressure approximately

one-third more than the manufacturer's recommended running

pressure for the calculated load.

Note - For the air bearings used, this higher pres- sure is 415 kPa. The purpose of the higher pressure is to make the bearings stiffer than when run- ning, to prevent damage that might otherwise occur

when shock loads are applied to the main shaft, as during mounting of the arm.

2. If the drive belt is in place on the pulleys, remove it

from the main-shaft pulley so that the shaft is free to

rotate.

3. Assemble the windmill arm by securely mounting the closedtube column to the counterbalance-tube assembly by means

of a threaded stud.

k. ' Install the arm into the two-piece clamping block and

lightly tighten the clamping screws.

5. Connect the output of the transducer to the windmill apparatus leads.

Note - It has been found convenient to wind the

leads in a loose spiral around the column and secure them with tape, as shown in figure 9-

6. Connect the transducer output from the slip rings to whatever instrument is to be used to measure the electrical

pressure s ignal .

Note - The note under step 2 of 3-2.1 applies,

except that phase information for the windmill

apparatus is derived from a comparison of the

pressure signal to the output of the second

photocell, which is recorded as a separate trace.

7. Connect other components of the system as required. Energize any equipment requiring a warm-up period.

8. Balance the arm by moving it back and forth in the clamp

until there is little tendency for the arm to rotate from

any angular position. Tighten the clamping screws.

18
9. Manually spin the arm slowly and allow it to coast to a stop. (Do not touch the arm directly.) If several such

trials indicate a lack of balance by a preferred stopping

position, adjust the balance by means of the movable

weight on the couterbalance tube.

10. Repeat step 9 until the arm appears to stop at random positions around the circle of rotation.

11. Replace the drive belt on the main-shaft pulley, and on the

motor pulley if required.

12. Reduce the air pressure to the air bearings to the recommended

running pressure.

Note - For the air bearings used, this pressure is

300 kPa.

13- Following the longest specified warm-up period for any item

of equipment in use, energize the motor and adjust its con- troller so that the arm rotates at an angular velocity of

approximately 5 rps, as measured by the counter display of

the number of holes passing the photocell per selected unit

of time.

Note - Not shown in the figures is a wooden box

placed around the rotating windmill arm and lined

with polyethylene sheeting. This box served as a safety shield to protect both apparatus and personnel and as a means of containment for small

amounts of mercury that were occasionally leaked

from the column, especially in early experiments

at 55 MPa. The box also served as a baffle to

reduce the amount of air flowing around the tube

from the laboratory heating and ventilation system; no attempt was made to seal the windmill arm

into the box.

14. Measure and record the amplitude of the pressure signal.

Record the angular velocity at which the arm was driven.

15- Readjust the motor controller so that the arm rotates at the

next desired angular velocity.

Note - It is useful to start the calibration on the

windmill apparatus at 5 Hz to check the balance,

even if a higher frequency is intended to be used.

It has been the usual practice with the windmill

apparatus to start the calibration with a measurement at 5 Hz and then to reduce the frequency for

each successive measurement. In the region of

19
1 Hz, the drive belt is removed and the arm spun

manually for this and lower frequencies.

16. Repeat steps 14 and 15 until a frequency of 1 Hz is reached.

17- Remove the drive belt from the main-shaft pulley.

Note - The detailed design of the drive system

will dictate whether the air-bearing pressure

should be raised for this step.

18. Manually spin the arm. When the counter display indicates

that the arm is rotating with the desired angular velocity, measure and record the amplitude of the pressure signal.

Record the angular velocity.

19- Repeat step 18 until the pressure signal has been measured

at all intended test frequencies.

20. Disconnect the column from all instrumentation. Dismount

the column from the windmill apparatus.

21. Using suitable precautions, vent the column slowly by opening the value slightly.

22. Remove and clean the test transducer; drain the column.

3-3 Error Analysis

The two dynamic pressure sources described in this report combine to

provide a capability not before available. There is no "standard pogo

transducer" that can be used to evaluate source performance. Repetitive

measurements with one or more transducers that experience has shown to be

relatively well-behaved provide some measure of source repeatability, as indicated in 2.2.6. It is also possible to calculate transducer dynamic

sensitivity at zero bias pressure by other methods and to compare these

results with a plot of dynamic sensitivity as a function of bias pressure,

the plot data being derived from calibration measurements using the closedtube sources; an example of this type of analysis is given in 4.1.

Factors contributing to the uncertainty of the pressure available

from both sources include (1) uncertainty in the length of the liquid

column resulting from machining and measurement inaccuracies; (2) uncer- tainty in the knowledge of the true density of the working liquid resulting from variations in temperature; (3) uncerta i nt ies in the bias pressure

resulting from variations in temperature and, to a lesser extent, from

the operation of the oil piston gage; (4) uncertainties in the knowledge

of the correction factor for inertial effects; (5) uncertainties in various voltage measurements; and (6) electrical noise. To these must be

added uncertainty in the acceleration produced by the vibration exciter

20
and measured by its accelerometer and the effects of unbalance in the

windmill apparatus. In addition, the pressure amplitude in the closedtube column is enhanced as a function of frequency, as is the case with

any s ing le-degree-of-f reedom system. For example, with a typical column resonance frequency of on the order of 1500 Hz, the pressure amplitude

enhancement is 0.1% at 25 Hz and 0.5% at 100 Hz. For dynamic calibrations

as a whole, uncertainty in the amount of transducer output resulting from

transverse or longitudinal vibrational response, additional voltagemeasurement uncertainties, and additional electrical noise should be

added to the uncertainties listed above.

Estimated values for these uncertainties are given in table 5 for

two calibration conditions. The overall estimated uncertainty for dynamic

calibration measurements using the oscillating source is ±5-8% (calculated at 25 Hz) of the true value and using the windmill source is ±3-7%

(calculated at 2 Hz) of the true value. For both estimates, the test

transducer was assumed to have an output of 1 V rms at ±1 g n

; the error

resulting from noise will be substantially larger for transducers with

significantly lower output.

k. MEASUREMENTS ON SEVEN P0G0 PRESSURE TRANSDUCERS

Calibrations using the two closed-tube sources and other measurements were conducted to characterize the behavior of seven candidate

pressure transducers for pogo measurements. The data from some of these

measurements also provide information on the calibrations themselves.

All transducers evaluated are of the piezoelectric type, with quartzcrystal sensing elements and integral solid-state impedance-conversion

circuits. Six of the transducers selected for evaluation were produced

by one manufacturer and carry NBS-assigned identification numbers 535,

536, 537, 857, 858, and 859- The remaining transducer is assigned identification number 311 and is also a commercial product, from a different

company. This transducer has a significantly smaller diaphragm and lower

specified sensitivity than the others.

For the tests, two transducers were mounted successively in the

closed-tube column shown in figure 1, left; all other transducers were mounted on the developed column shown in figure 3- Calibrations over

the frequency range 0.2 to 5 Hz were carried out with the column mounted

on the windmill apparatus and over 5 ~ 100 Hz with the column mounted on the vibration exciter. The measurement of column resonance frequency,

as described in 3-1-2, was used for all tests as a means of detecting

the presence of voids.

h.\ Frequency-Response Measurements

As an example, plots of response ratio as a function of frequency on

a logarithmic scale are shown in figure ]k for transducer 537 at two bias

pressures. The working fluid was mercury. Response ratio represents the

21
output of the pressure transducer normalized to a reference value

equal to the average of the values of transducer output measured

at eight frequencies in the range 2 to 25 Hz, including at the end

points 2 and 25 Hz. The shape of the curves would be the same if

the transducer output as measured in millivolts rms were plotted.

Curves for both bias pressures show a low-frequency roll-off of

approximately 3 db at 0.25 Hz. The calibration agreement between the

two sources at the juncture point of 5 Hz is within 0.2% of the refer- ence value for the calibration at 55 MPa, and within 2.8% for the calibration at 7 MPa.

Examination of the plot shown in figure 15 of dynamic sensitivity

as a function of bias pressure for transducer. 537 (plots are also shown

for 535 and 536) shows that a change of nearly k% of the reference sensitivity measured at a bias-pressure level of 55 MPa occurs with a bias

pressure change from 7 to \k MPa. Sensitivity is a calculated value

(transducer output per unit pressure) based on calibration measurements and is expressed in figure 15 as a percentage of the reference

value. This observed change in sensitivity may be responsible for at

least some of the difference between calibrations made with the rotating

source and the oscillating source at 5 Hz. Calibration runs with the

windmill source probably tend to cool the column below ambient because

of the motion of the column through the expanding air discharged from

the air bearings. Cooling the column reduces the bias pressure. In contrast, there appears to be a slight tendency for the column on the

vibration exciter to be warmed with respect to ambient, even though the

exciter-table temperature is thermostatically controlled. The differences shown in figure \k , then, are probably functions of the calibrations and not primarily of the transducer under test, although a transducer property may give rise to them.

The means for varying the bias pressure for the measurements of

figure 15 are of interest. An L-shaped length of rigid tubing is mounted

to the column valve with the long arm of the L extending upwards parallel

to the (filled) column. The column with tube is then placed in a bell

jar and the tube filled with the same working liquid as the column, using

the procedure given in [5] for filling an open-tube column. The column

is mounted on the exciter table and an oil piston gage connected to the

open end of the L-tube by means of a short length of flexible tubing and

a three-way valve, which is used for bleeding the oil from the piston

gage to eliminate air. The purpose of the L-tube is to prevent oil from

the piston gage from contaminating the working fluid and to minimize the

possibility of air bubbles' being introduced into the column. Following

bleeding, the piston gage is set at the bias pressure of the column and

the column valve opened. The piston gage may then be reset to the new desired bias pressure; after approximately 5 min, the column valve is

closed. It is desirable to remove the L-tube before the exciter is energized, but calibrations have been made with the connections all in place

at small exciter displacements and with movement of the connecting tubing

restrained or damped. Calibrations were made at frequencies of 20, 25,

30, hO, and 50 Hz and at an acceleration level of ±2.5 ffr\ • The bias

22
pressure was usually changed in increments of 7 MPa and occasionally re- turned to a previous level as a check.

Further examples of response rat io-vs-f requency , or frequency re- sponse, are given in figure 16 for transducers 858 and 859 at a bias

pressure of 41 MPa. The working fluid used was mercury throughout for

transducer 859 and for calibration over the low-frequency range up to

20 Hz for 858. At 20 Hz and above, calibration for 858 was conducted

with both silicone oil and mercury. (The low frequency limit for sili- cone oil is imposed by the combination of the acceleration capability of

the exciter and the static head provided by the oil; the calibration was carried out at ±10 g n with oil and ±2.5 g n with mercury.) The agreement between calibration with oil and with mercury is on the order of 2% of the

reference output value.

Plots of dynamic sensitivity as a function of bias pressure are

given in figure 17 for transducers 857 and 858 with the data originating

from three types of calibration: (1) at zero bias pressure with the NBS

quick-opening-valve pressure source, with a rise time of approximately

1 ms [9]; (2) calibration perforce at zero bias pressure with the opentube source; and (3) calibration at selected bias pressures from 3-5 to

k\ MPa, inclusive, with the oscillating closed-tube source. Sensitivity

is expressed as percent of the reference sensitivity measured at k\ MPa.

For transducer 857> an extrapolated point for calibration with the oscillating closed-tube source at zero bias would fall between 111 and 112%;

for 858, between 107 and 108%. These extrapolated values and the measured values at zero bias therefore agree to within approximately 3% of

the reference sensitivity.

It should be noted that no static calibrations were attempted with

the selected test transducers because of the short time constants asso- ciated with piezoelectric instruments.

k.2 Phase-Shift Measurements

Measurements of the phase shift between the waveform of the driving

signal and the waveform of the transducer pressure signal were made to

monitor the presence of anomalies. The phase shift of a well-behaved

system should be small and monotonic except in the neighborhood of the resonance frequency. Measurements of the phase shift of transducer 537

for a calibration using the windmill source are given as a typical ex- ample in table 6. The phase shift changes in a monotonic manner from

30 deg at 0.5 Hz to near deg at 5-0 Hz. The phase shift for the same transducer for calibrations using the oscillating source was measured

from 10 to 100 Hz and found to be approximately deg. Experience indicates that the phase-shift measurement can be made within ±3 deg of the

actual value.

23
4.3 Repeatability Measurements

As described in 2.2.6 (which see), two transducers were calibrated

repetitively at 1, 3, 5, 10, 25, and 100 Hz and at bias pressures of 41

(transducer 859) and 55 (transducer 537) MPa. For 537, coefficients of

variation ranged from 0.03 to 0.14% (six measurements each) and for 859,

from 0.08 (six measurements) to 0.33% (seven measurements). The data are

given in table 3.

4.4 Acceleration Linearity Measurements

The same two transducers used in 2.2.6 and 4.3 were also calibrated

at two acceleration levels at 10 Hz and five at 25 Hz by means of the

oscillating source. The bias pressures were again 41 (transducer 859)

and 55 (transducer 537) MPa. The data are given in table 7-

4.5 Vibration Response Measurements

The transverse (perpendicular to imparted motion) and longitudinal

(along direction of imparted motion) vibration response was measured for one transducer from each of the two manufacturers represented. These

measurements were made with the transducer mounted in an aluminum block

in turn mounted to the table of the vibration exciter. The acceleration

levels used equaled or exceeded the estimated levels to be found in the

space shuttle and were as follows: (1) peak-to-peak displacement- of

1.3 cm (1.3-cm double amplitude), from 5 to 30 Hz; ±15 g'rn from 30 to

900 Hz; and ±70 gu , from 900 to 3000 Hz. Transducer 311 showed a maximum

response of 39 kPa, or approximately 28% of the 140-kPa measurement

range; transducer 537 showed a maximum response of 3 kPa, or approximately 2% of the measurement range. Other data are given in table 8.

5. CONCLUSIONS

Two dynamic sinusoidal ly varying pressure sources have been described by means of which candidate transducers for pogo measurements may

be calibrated. These sources provide 48 kPa peak-to-peak from 0.2 to

5-0 Hz (windmill source) and up to 140 kPa peak-to-peak from 5-0 to 100

Hz (oscillating source using vibration exciter) in the presence of a d-c

bias pressure of up to 55 MPa. Overall calibration uncertainties are a function of both frequency and pressure amplitude, but are probably no more than ±6% and may be on the order of ±k% for calibrations with the

windmi 1 1 source.

A peak-to-peak displacement is conventionally specified in this frequency range instead of an acceleration level per se , because the accel

eration levels are low, while the displacements are large.

24
The requirements on the working liquid are such that mercury is the

only recommended liquid for calibrations at frequencies of 20 Hz and below, although mercury's density, toxicity, and surface-tension properties

render it a difficult liquid to handle safely. Above 20 Hz, silicone

oil is recommended.

Variations in bias pressure with temperature require that care be

taken to minimize the amount of thermal energy transferred into or away

from a filled column. The lower the bias pressure, the more important

this consideration becomes. Handling problems relating to column temperature changes begin to intensify below the neighborhood of 7 MPa, although calibrations have been made at as low as 0.21 MPa.

6. RECOMMENDATIONS

As has been pointed out, no standard transducers exist to serve as references for the calibration measurements. A comparison between the

output signals of two transducers exposed simultaneously to as nearly as possible the same pressure amplitudes would provide corroborative data

now lacking. The recommendation is therefore made that a new column with

ports for two test transducers be constructed and evaluated.

Means for maintaining the filled column temperature at a stable

value at least for the 30 min or so that is required for a calibration

using both sources should be investigated. Possibilities include a thermally insulated column and either deliberate heating or cooling of

the column.

7. ACKNOWLEDGMENT

During the development of the dynamic pressure sources, the design

and construction of the mechanical components was the responsibility of

Kurt Muhlberg. Useful information concerning the performance of liquidcolumn sources was supplied by Harlan S. Harman of the NASA G. C. Marshall Space Flight Center. Richard Kraft of the Mathematical Analysis

Section, NBS, provided the theoretical verification of the pressurehalving phenomenon observed with the closed-tube source. The authors

gratefully acknowledge the contributions of these people.

25
8. 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] Hilten, J. S., and Lederer, P. S., Space Shuttle Pogo Pressure Measuring System - A Progress Report Covering Period January 15, 1973 to

September 15, 1973, NBS I R 74-562 (July 197*0.

[3] Hilten, J. S., and Lederer, P. S., Space Shuttle Pogo Pressure Measuring System - A Progress Report Covering Period December 15, 1973 to

June 15, 197^, NBS 1 R 74-604 (December 1974).

[4] Lederer, P. S., and Hilten, J. S., Space Shuttle Pogo Pressure Measuring System - A Progress Report Covering Period September 15, 1973 to

December 15, 1973, NBSIR 75-650 (March 1975).

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

A New Dynamic Pressure Source for the Calibration of Pressure Transducers,

NBS Tech. Note 914 (June 1976).

[6] Kraft, R., Note on a Vibratory Phenomenon Arising in Transducer Calibration,

NBS Tech. Note 856 (February 1975).

[7] Hilten, J. S., Accel erometer Calibration with the Earth's Field Dynamic

Calibrator, NBS Tech. Note 517 (March 1970).

[8] Smith, R. 0., Willis, E. A., and Hilten, J. S., A Dual Centrifuge for

Generating Low-Frequency ' S

i

nusoidal Accelerations, J. Res. Nat. Bur.

Stand. (U. S.) 66C , No. 4, 357-362 (1962).

[9] Lederer, P. S., Step- Function Pressure Calibrator, U. S. Patent No.

3,034,332 (May 15, 1962).

26
TABLE 1

Calculated Pressure Capability of a Closed-Tube Liquid-Column Source

for Two Working Fluids at a Constant Displacement

Liquid-Column Height: 36.8 cm Displacement: 1.25 cm (double amplitude)

Vibration

Frequency

(Hz)

5

6

7

8

9

10

15

20

25

30

Acceleration Generated Pressure"

40

0.6

0.9

1.3

1.6

2.1

2.6

5.7

10

16

23

41

Mercury

as Working Fluid

(kPa) (psi)

Si 1 icone Oi

1

as Working Fluid

(kPa) (psi)

31 4.5 2.2 0.32

45 6.5 3.2 0.46

61 8.9 4.3 0.63

80 11.6 5.7 0.82

100 14.7 7.1 1.04

130 18.1 9.2 1.29

280 44.7 19.9 3.17

500 73.4 35.5 5.21

780 113 55.4 8.02

1120 163 79.5 11.6

2000 290 142 20.6

Pressure values given are peak-to-peak,

27
TABLE 2

Effect of Bias-Pressure Variation on Transducer Response

with Silicone Oil as the Working Fluid

Acceleration: 10 g peak-to-peak

Acceleration Frequency: 50 Hz

Transducer: No. 537

Bias Pressure

(MPa)

Measured

Resonance Frequency

(Hz)

6.89 2227

6.21 2224

5-52 2222

4.83 2217

4.14 2212

3.45 2208

2.76 2206

2.07 2200

1 .38 2196

0.69 2193

0.21 2188

6.89 2233

Transducer Output

(mV rms)

32.12

32.28

. 32.38

32.46

32.56

32.60

32.58

32.52

32.50

32.42

32.36

32.32

av 32.425

28
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29
TABLE k

RESONANCE FREQUENCY AS A FUNCTION OF CLOSED-TUBE

COLUMN BIAS PRESSURE FOR MERCURY AND SILICONE OIL

Length of Liquid Column: 36.8 cm

Transducer Identification

Number 537

Resonance Freq

(Hz)

857

uency

858 859

Bias Pressure

(MPa)

3.5 1650 1651 1359*

7 1624

1624

1631

1625

1650

1649

1652 1383*

14 1652 1653 1429*

21 1647 1652

1651

1478*

1471*

28 1650 1652 1513*

34 1655 1653 1550*

41 1655 1623

1622

1613

1627

1652

1652

1572*

1578*

1598*

1618

1615

1629

311

48 1660

55 1627 1718

1636 1717

1631

1662

* Denotes use of silicone oil, all other measurements are for mercury.

30
TABLE 5

Factors Contributing to Estimated Transducer Calibration Error

Oscillating Source^ Wi ndmi 1 1 Source

Factor

Sys temat i c Error (% of measured

va 1 ue)

Random

Error

{% of measured

value)

Systematic

Error {% of measured

va 1 ue)

Random

Error

(% of measured

val ue)

Liquid column

Height of liquid column ±0.1 Variation of liquid density with temperature

Uncertainties due to bias pressure variations'^

Variation of bias pressure

with temperature/

Oil piston gage Variation caused by

centrifugal force

Acceleration Applied

Calibration of exciter control

accel erometer with refer- ence accelerometer and precision of reading ±1.0 Knowledge of earth's field Unbalance of windmill source

Frequency enhancement ±0.1

Transducer output

±0.1

±0.04

±1.0

±0.02

±0.1-

±0.1

±0.1

±0.01

±0.1

±0.04

±1.0 ±0.02

±0.1

precision of reading ±0.3 ±0.1" ±1.0 Longitudinal acceleration

±0.03 J response - ±0

Noise ±o.i

k Waveform distortion ±0.5

TOTAL RMS :1 .05 = 1 - 111 1.01

Estimated error = RMS systematic + 3 RMS Random

+ k.5% + k.k%

±o.r

±0.1 ±0.5

±1.14

For typical calibration using a 36-8-cm column of mercury at a bias pressure of 55 MPa.

at a frequency of 25 Hz.

at a frequency of 2 Hz.

Estimate based on coefficient of expansion of mercury of 0.000182/°C

and variation of + 2°C.

The magnitude of the effect of bias pressure variation on transducer

output depends on the linearity of the transducer response; values given are

for transducer 537-

JfEstimated to be + 3-5 MPa.

Estimate based on least count of 1 mV for measurement of 1000 mV. hManufacturer's value for range of 20 mV at frequencies above 10 Hz.

Manufacturer's value for measurements at frequencies from I to 10 Hz.

Depends on transducer; value given is for transducer 537

-

This figure corresponds to 1 mV for a typical calibration.

31
TABLE 6

PHASE SHIFT BETWEEN PRESSURE AND TRANSDUCER-OUTPUT WAVEFORMS FOR

TRANSDUCER 537 ON WINDMILL APPARATUS

Working Liquid: Mercury

Bias Pressure: 55 Mpa

Frequency Phase Shift

(Hz) (deg)

0.5 30

0.8 19

1.0 16

1 .2 12

1.5 10

1.8 8.0

2.0 6.0

2.5 5.0

3.0 k.S

k.O 3.5

5.0 ^ 0.0

32
TABLE 7

Acceleration Linearity Measurements for Two Transducers

Acceleration Relative Transducer Output

(g

n peak-to-peak) h Transducer 859 Transducer 537

(mV rms/g ) (mV rms/g ) at 1 H z

0.5 639.1 19.19

1.0 638.4 18.95

at 2 5 H z

0.5 645-1 19-35

1.0 644.9 19.13

1.5 644.8 19.09

2.0 644.7 19.09

2.5 647.2 19.08

The bias pressure for these measurements with Transducer 859 was 41 MPa

The bias pressure for these measurements with Transducer 537 was 55 MPa

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34
Figure 1. Two source columns used in early experiments. That on the

left is a conversion from an open-tube design. The column

on the right was constructed to permit source pressure

measurements at several heights on the column, as described

in the text. Identified are pressure transducers (A),

transducer mounting plates (B), column valves for filling

and pressurizing (C), and removable plugs (D), used to permit

operation in either closed- or open-tube configurations.

35
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Figure 2,

20 40 60

FREQUENCY (Hz)

80 100

Transducer output (mV rms) at constant acceleration plotted

as a function of frequency (Hz) for two transducer locations

and for open- and closed-tube configurations. The upper

plot shows transducer pressure sensitivity (mV/kPa or mV/psi)

as a function of frequency (Hz). Triangles indicate measurements made with the transducer 6.1 cm (20%) from the bottom

and circles, 11.9 cm (40%) from the bottom. The open symbols

represent open-tube measurements and the filled symbols,

closed-tube measurements.

36
Figure 3. The developed closed-tube column, with the transducer (A)

at the top, or free, end. The fixture at the left permits

operation with the column inverted.

37
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38
/

V

IL

Figure 5. Engineering sketch of two-piece fixture used to mount the

column (shown in figure 3) inverted. The two clamping surfaces (A) in the cap and main body act on the outside surface

of the column, with the effective bore diameter matching the

column diameter. The step at (B) limits the depth to which

the column is inserted, to provide clearance for the test

transducer. Four clamping screws pass through clearance

holes (C) in the cap and thread into the main body; the

clear holes (D) are for mounting screws.

39
Figure 6. Closed-tube column with provisions for mounting a test transducer (A) at each end for an experimental investigation of

inertial effects, as described in the text. The port for the

column valve [position indicated by (B)] is on the hidden

side of the column; the valve was not mounted when the photograph was taken. The loading masses used in the experiments

are shown at the left of the column.

ko
ADDED MASS (g)

200 400 600

4.00

£ 3.50

3.00

= 2.50

00

2.00

MOUNTED

END

(free

A I END

_L _L I J_ 200 400 600 800 1000 1200

Y2 DISTRIBUTED MASS+ADDED MASS (g)

1400

Figure 7. Transducer sensitivity (mV/kPa) as

(g) and of a quantity (g) equal to

and one-half the distributed mass,

the mass of the column shown in fig

for two transducers mounted in turn

Circles identify measurements taken

535; and triangles, with transducer

sensitivity at zero mass correspond

nent generated by the acceleration

in the text.

a function of added mass

the sum of the added mass

the distributed mass being

ure 6. Plots are shown

at each end of the column,

with transducer number

536. The extrapolated

s to the pressure compoof the liquid, as described

k]
Figure 8. Apparatus used in the calibration of pressure transducers

for pogo measurements. The windmill source is shown at (A)

with supporting electronics in rack (B). The vibrationexciter system which forms part of the oscillating source

is at (C).

hi
Figure 9. The windmill source, consisting of the closed-tube column

mounted on the windmill apparatus. Identifications of the

various components are given in the text.

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Figure 11. Photographs of oscilloscope traces of waveforms from a test

transducer calibrated on the windmill source [(A) and (B)]

and on the oscillating source [(C), (D), and (E)], at several

frequencies. Photograph (A) is of a trace taken at 1 Hz

(angular velocity of 1 rps) with the windmill arm manually

spun. Photograph (B), of a trace taken at 5 Hz, shows

stepping in the waveform attributable to the cog-belt drive

and to poles in the drive motor. Distortion in photographed

trace (C), taken at 10 Hz, results from deterioration of the

acceleration waveform of the vibration exciter at low frequencies, particularly near its displacement limits. At

25 Hz, the acceleration waveform of the exciter has little

distortion as revealed in the transducer output waveform,

trace photograph (D). At 100 Hz, no distortion is detectable,

trace photograph (E).

h5
<:

LIQUID

RESERVOIR

H u3,

TO OIL PISTON GAGE

(:>> 0*

D =©=1

B

CLOSED-TUBE COLUMN

TO

VACUUM

Qc

UP

VALVE POSTION CHART

A B C D E

Step

Evacuate System closed closed open open open

Fill System closed open 2 closed 1 open open

Pressurize System open 2 closed 1 closed open open

Close Calibrator Valve open closed closed open closed

Vent Oil Piston Gage

to Atmospheric Pressure open closed ciosed open closed

Close Down System closed closed closed closed closed

Invert; Empty Mercury

Reservoir closed closed closed closed closed

Figure 12. Schematic elevation of apparatus used to fill closed-tube

column. Valves in the filling system are indicated by (A),

(B), (C), and (D). Valve (E) is the column valve. The

filling procedure, incorporating the sequence of valve operations given in the chart, is described in the text. Numbers

1 and 2 refer to the sequence of valve operation within the

step.

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14 21 BIAS PRESSURE (MPa)

Figure 17. Dynamic sensitivity [%) plotted as a function of bias pressure

(MPa), for transducers 858 (top plot) and 857 (bottom plot).

Dynamic sensitivity is expressed as a percentage of that

measured at 41 MPa. The data points at zero bias pressure

are from measurements with a quick-opening-valve apparatus

(squares) and with the open-tube dynamic pressure source

(triangles). The other data points were taken with the

oscillating source (column on vibration exciter). The filled

circles at 21 and 41 MPa on each plot represent repeated

measurements, the second measurement at 21 MPa follwoing the

first at 41 MPa, and the second measurement at 41 MPa following the second at 21 MPa. As with the plots of figure 15,

the general character of the plots is seen to be linear.

The agreement at zero bias pressure with the other data is

particularly noteworthy in the case of transducer 857.

51
-*"*S-TI4A IREV.-T.73I

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. TN - 927

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Development of Dynamic Calibration Methods for Pogo

Pressure Transducers

5. Publication Date November 1976

6. Performing Organization Code

7. author(S) Jonn s Hilten, Paul S. Lederer, Carol F. Vezzetti , and J. Franklin Mayn-Wplls

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. 1*253^8

11. Contract/Grant No. NASA Order #H92100A

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

National Aeronautics and Space Administration

G. C. Marshall Space Flight Center

Huntsville, Alabama 35812

13. Type of Report & Period CoveredFinal

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less tactual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.)

Two dynamic pressure sources are described for the calibration of pogo

pressure transducers used to measure oscillatory pressures generated in the

propulsion system of the space shuttle. Rotation of a mercury-filled tube

in a vertical plane at frequencies below 5 Hz generates sinusoidal pressures

up to kS kPa, peak-to-peak; vibrating the same mercury-filled tube sinusoidally in the vertical plane extends the frequency response from 5 Hz to 100 Hz at pressures up to IkO kPa, peak-to-peak. The sinusoidal pressure fluctuations can be generated by both methods in the presence of high pressure

(bias) up to 55 MPa

.

Calibration procedures are given in detail for the use of both sources. The dynamic performance of selected transducers was evaluated using these

procedures; the results of these calibrations are presented. Calibrations

made with the two sources near 5 Hz agree to within 3 % of each other.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Bias pressure; calibration; dynamic calibration; dynamic pressure; high pressure;

liquid medium; pogo pressure; pressure source; pressure transducer; sinusoidal;

space shuttle; transducer.

18. AVAILABILITY [^~| Unlimited

^2 For Official Distribution. Do Not Release to NTIS

Washington, D.C. 20402, SD Cat. No. C13

Printing Ol

. Lb :927

J Order From National Technical Information Service (NTIS)

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19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

58

22. Price $1.15

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