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Calibration of Ballistic Pressure Transducers

by Charles D. Bullock and Arpad A. Juhasz

Current procedures used for the calibration of ballistic pressure transducers at BRL are described. Checks include evaluation of continuity, hysteresis, and zero return characteristics as well as calibration against a dead weight system. Static versus dynamic response behavior is evaluated with the aid of a high pressure dynamic positive step calibrator. For the most exacting measurements, adapters are used permitting calibration of transducers in the same mechanical environment as during measurement. Recommended recalibration intervals are indicated.

Introduction

The mission of the Interior Ballistic Division of BRL includes research on novel ballistic concepts, charge design methodology and advancing the state of the art in interior ballistic computations. These efforts are supported by a variety of combustion, interior ballistic and ballistic simulator firings. Central to all these experiments is the measurement of pressure. Pressures may range from a few hundred pounds per square inch (psi) to a hundred thousand psi full scale depending on the experiment. The quality of the measured pressures, in large scale, is dependent upon the methodology, care and accuracy of the calibration process.

The primary function of the calibration procedures is to determine transducer response characteristics and to act as a screening tool to help weed out problem transducers before they can do damage. A secondary but vital function is to help solve measurement related problems and assure that the devices perform as required under the conditions of service. The purpose of this paper is to discuss the procedures which have evolved over the past twenty five years at BRL for the calibration, selection and use of high pressure transducers for ballistic applications. It will include a discussion of the most important characteristics of high pressure transducers, BRL's calibration and evaluation procedures and a look at potential problem areas.

Discussion

Transducers Used
Ballistic pressure transducers in routine use at BRL fall into two categories, piezoelectric element and single arm strain sensors. The commonly used piezoelectric transducers (gages) are obtained commercially. The strain sensor transducers are made privately for BRL. All of the above are used daily to measure pressures up to 100,000 psi. The gages have a fast response (10-90 percent response times on the order of 10 microseconds). The events measured range from the sub-millisecond to several hundred millisecond time frames.

High pressure transducers can, with adequate care in calibration and use, be successfully employed to make measurements under 1000 psi. This requires special calibration procedures, however, which will be discussed later. In addition to high pressure transducers, good low pressure, fast response transducers are also commercially available and find applications in ignition simulators and the like. At the other end of the spectrum, a current development effort is aimed at providing a ballistic pressure transducer capable of measuring pressures to 200,000 psi.

Calibration Procedures
The purpose of pressure calibration is to determine the response of the transducers to known pressures, to verify the response specified by the manufacturer, and to show repeatability. During the calibration procedure for a given transducer the following questions are considered:
Initial Screening
Calibration typically begins with an examination of the continuity, hysteresis and zero return properties of a transducer over the pressure range intended for use. A schematic of the main calibration system in use at BRL is given in Figure 1. The output of the test transducer is plotted (Y-axis) against the output of a stable reference strain gage transducer of known characteristics (X-axis) while the system is pressurized and depressurized over the desired pressure range. Pressurization is accomplished using the air pump/intensifier portions of the system. The response curve of the transducer is used as an indicator of its overall quality.
Continuity
Examples of "good" and "bad" continuity response are given in Figure 2. In this case, both plots were obtained from the same transducer but at different times, indicating degradation in performance as a function of use. Normally, when discontinuities of this type are encountered, the transducer is retired.
Hysteresis
Examples of "good" and "bad" hysteresis characteristics are shown in Figure 3. In the plot on the left the ascending and descending portions of the curve coincide. In the plot on the right the transducer appears to take a "set" on depressurization. Normally, a maximum hysteresis level of 1-2 percent of full scale is thought to be acceptable. Excessive hysteresis would make interpretation of the up and down slope portions of ballistic data difficult to interpret.
Zero Return
Examples of "good" and "poor" zero return properties of a transducer are given in Figure 4. In this case, the transducer exhibits a residual output after the pressure loading is removed. Normally, the maximum error in zero return deemed acceptable is one percent of full scale.

A final characterization made at this point involves a comparison of the first and subsequent cycles of transducer output. With certain transducers, response characteristics change between the first and subsequent pressurization for a given installation. This could lead to serious problems in measurements, especially in cases involving cyclic events such as multi-shot bursts. Examples of "good" and "bad" first vs. second cycle output are given in Figure 5. Normally, a difference of less than one percent full scale variation of cyclic output is found to be acceptable.

Quantitative Procedures
Quantitative transducer response characteristics are obtained using a dead weight system. A simplified schematic of a dead weight system is given in Figure 6. The principle of operation is simple. At the point of equilibrium, that is, where the mass/piston combination is exactly balanced by pressure in the fluid, the hydrostatic pressure throughout the fluid may be calculated by dividing the total mass ("weight" plus piston) by the piston area. The output of the test transducer is measured at a series of float points corresponding to various mass loadings. The static dead weight calibration method has both advantages and disadvantages; it is the most accurate and repeatable source of calibration pressures. Its principal disadvantage for ballistic applications is that it needs dynamic verification.

The dead weight calibrator used at BRL is a 100 Kpsi Astra model D100KS.1 In this device the pressurizing fluid balances the force of a series of calibrated masses transmitted through a piston of precisely known area. A thin film of hydraulic fluid separates the piston from the cylinder wall and the piston is oscillated about its axis to reduce the effects of static friction. Various combinations of masses permit the generation of pressures at intervals as small as 100 psi up to a maximum pressure of 100,000 psi. In the "at rest" position, all the masses are loaded onto the yoke. A series of air operated lifters is used to download respective masses to yield the desired pressures. The tare pressure (due to the weight of the yoke alone) is three thousand psi, representing the minimum pressure attainable with this system. Common calibration intervals are 5 Kpsi and above.

For the most accurate work with deadweight calibrators, corrections need to be made for the effects of gravity, buoyancy of air, and effective piston area of the calibration system.2 The maximum error from all these sources for our facility is less than 0.25 percent, as measured by cross-floating our device against a Harwood controlled clearance deadweight calibrator. The precision of the Astra gage as used is 0.15 percent. Our data analysis program is currently being revised to include the buoyancy and gravity corrections. Once this is complete, the accuracy of the system is expected to move closer to its precision.

The dead weight device as used in our main calibration station is given in Figure 1. The pressure generating source is an hydraulic intensifier (pressure multiplier) of 16:1 ratio, capable of producing over 100 Kpsi. The low pressure side is driven by a 10 Kpsi air pump. The normal high pressure medium is plexol 201 (now Monoplex), a synthetic lubricant. A check valve, relief valve, additional valving and hydraulic reservoir complete the system.

Transducers are calibrated over the range at which they will be used. Typically, if the expected maximum pressure for an experiment is 100 Kpsi, a series of points at 20 Kpsi intervals is chosen for calibration. For a test series with an expected maximum pressure of 25 Kpsi, 5 Kpsi intervals are used. Output values from both the upward and downward portions of the calibration cycle are included, giving typically 11 points for curve fitting purposes. In Table 1 the values Y1, Y2 and Y3 are voltage reading representing transducer output which are averaged (Y) and converted to gage output units (PCB), in this case picocoulombs. The data are fitted via a least squares method to a first degree equation. Curve fitting is done both in terms of transducer response vs. pressure and pressure vs. transducer response (which is used in computerized data reduction programs). Due to the slight curvature in even "good" pressure transducers, users generally prefer the second order fit for computerized data analysis purposes. For the sake of simplicity, however, they prefer the first order fits to make the amplifier settings.
 
Table 1. Gage Calibration Record for Piezoelectric Gage
PT
KPSI
Y1
Y2
Y3
Y
PCB
1
0
0.0000
0.0000
0.0000
0.0000
0.0
2
20
0.2673
0.2673
0.2673
0.2673
2673.0
3
40
0.5399
0.5399
0.5399
0.5399
5399.0
4
60
0.8183
0.8183
0.8183
0.8183
8183.0
5
80
1.1069
1.1069
1.1069
1.1069
11069.0
6
100
1.4010
1.4010
1.4010
1.4010
14010.0
7
80
1.1090
1.1090
1.1090
1.1090
11090.0
8
60
0.8219
0.8219
0.8219
0.8219
8219.0
9
40
0.5435
0.5435
0.5435
0.5435
5435.0
10
30
0.2700
0.2700
0.2700
0.2700
2700.0
11
0
0.0006
0.0006
0.006
0.0006
6.0
 
 
First Degree Fits
PCB =
8.6081E+01
1.3946E-01
*  PSI 
 
 
 
PSI =
-6.3059E+02
7.1683E+00
* PCB
 
 
 
MPA =
-4.3489E+00
4.9436E-02
* PCB
 
 
 
Correlation Coefficient = 0.99985
Second Degree Fit
PSI = 
-4.6285E+02
7.5573E+00
* PCB
-2.9739E-05
* PCB
2
MPA = 
-3.1921E-01
5.2119E-02
* PCB
-2.0510E-07
* PCB
2
Correlation Coefficient = 0.99999
When high pressure transducers are to be used in low pressure measurements, special precautions are needed. Certain makes and models of high pressure transducers appear to have superior low pressure linearity and torque sensitivity properties. These transducers are first prescreened using the conventional technique. The best of these units are calibrated against a 10 Kpsi dead weight system using the negative going pressure step method. That is, the deadweight system is floated at a given pressure against the gage and the pressure is released to zero. (The signal generated is equal to but opposite in sign to the output during actual pressure measurement). The amplifier is zeroed just prior to the pressure step, the whole process taking approximately one second. This fast procedure helps to reduce the effect of drift which can be a significant problem in using high pressure transducers at their low end. For calibrations under 0.15 Kpsi a commercial air operated dynamic calibrator is used.

Problem areas and solutions
Among the practical transducer problems of interest to ballisticians are changes in response characteristics as a function of use, poor dynamic performance, response changes with calibration range, difficulties involving concentricity and depth tolerances in gage ports, and differential pressure measurements. The purpose of this section is to highlight some of these areas and to point out procedures which may help to prevent difficulties before they occur.
Change of response characteristics with use.
It is normal for transducer sensitivity to change with use. Typically, gage response decreases, and linearity and hysteresis properties may be adversely affected. Presumably this is due to a gradual degradation of the sensing element. This need not be a problem, however. Regularly scheduled recalibration is used to keep track of these changes, users changing calibration constants as appropriate. For high pressure firings (90-100 Kpsi) recalibrations are recommended at 5-10 round intervals. At lower pressures, say 60 Kpsi, recalibration after 25-50 rounds is recommended. In extreme cases, degradation can be sufficient to affect the continuity of response of the transducer (see Figure 2). In such cases the device is immediately retired. In other cases gages are retained until they fall outside of acceptable hysteresis or zero return characteristics.
Dynamic Performance.
Questions of the dynamic vs. static response behavior of ballistic pressure transducers have concerned ballisticians for some time. In an effort to address this problem, BRL in conjunction with the Harwood Engineering Company has developed a 150 Kpsi positive step calibrator.3 The device has been used to assess transducer dynamic performance properties. In most cases static and dynamic properties have agreed quite well. Occasionally, however, problems have occurred. Figure 7 illustrates examples of "good" and "bad" dynamic response behavior. In the bad response case the signal from the transducer is showing an upward creep over many milliseconds. Similar, but shorter term, instances have also been observed where the 10-90 percent response appear to be normal but the last 10 percent of the response curve takes several milliseconds. It is thought that seal movement and air bubbles under the strain patch may have caused some of these problems. Other cases where dynamic response problems have occurred have involved eccentric loading of gages due to mismatch between transducer and mounting cavity, see below.
Calibration over the Wrong Range
A common error among project engineers is to use calibration data obtained over one range in analyzing the results of experiments over a significantly different pressure range. Table 2 illustrates this point. The gage in question was calibrated to 100,000 psi and the calibration data fitted to a first and a second order equation. The error columns indicate the the difference between the fitted equation and the measured calibration points. The greatest derivation from the curves comes at the low pressure end. Use of this calibration data for measurements made over the 0-20 Kpsi range, for instance, could introduce as much as six to seven percent error in the interpreted data. This error can be dramatically reduced by recalibrating the transducer over the 0-20 Kpsi range, see Table 3.
 
Table 2. Examples of Potential Errors Introduced at the Low Pressure and in Calibration Over a Wide Pressure Range
PT
PSI
PCB
1ST
ERROR %
2ND
ERROR %
2
20000
2673.000
19160.83
4.20
19988.22
0.06
3
40000
5399.000
38701.59
3.25
39935.09
0.16
4
60000
8183.000
58658.10
2.24
59850.15
0.25
5
80000
11069.000
79345.78
0.82
80008.23
0.01
6
100000
14010.000
100427.72
0.43
100040.83
0.04
7
80000
11090.000
79496.32
0.63
80153.10
0.19
8
60000
8219.000
58916.16
1.81
60104.66
0.17
9
40000
5435.000
38959.65
2.60
40195.55
0.49
10
20000
2700.000
19354.38
3.23
20187.96
0.94
 
Table 3. Examples of Improvement in Error Levels Due to Calibration Over the Range of Test Pressure
PT
PSI
PCB
1ST
ERROR %
2ND
ERROR %
2
5000
651.000
4902.81
1.94
4969.78
0.60
3
10000
1311.000
9873.40
1.27
9979.62
0.20
4
15000
1975.000
14874.11
0.84
14990.72
0.06
5
20000
2642.000
19897.42
0.51
1995.06
0.02
6
25000
3313.000
24950.86
0.20
24999.70
0.00
7
30000
3990.000
30049.48
0.16
30018.87
0.06
8
25000
3320.000
25003.57
0.01
25051.75
0.21
9
20000
2651.000
19965.20
0.17
20062.39
0.31
10
15000
1986.000
14956.96
0.29
15073.49
0.49
11
10000
1322.000
9956.24
0.44
10062.87
0.63
12
5000
662.000
4985.65
0.29
5053.51
1.07
 
Mounting Problems
Figure 8 and Figure 9 present two common problems in transducer/mounting cavity interactions. A lack of concentricity in either transducer or the mounting hole can result in eccentric loading. The curves may look "normal" but the response may be far out of line. Similar results can be noted if the sensing element touches the bottom of the mounting cavity. In the case of one popular commercial transducer, for instance, seal rings of two thickness, steel (0.010 inch) or copper (0.020 inch), are available. The cavities are dimensioned according to the intended seal thickness. Substitution of the thinner steel seal for the originally intended copper, for instance, can cause the transducer to "bottom" giving false, often high, readings. While this may seem, on the surface, trivial, such problems are often hard to track down in practice due to the depth and inaccessibility of gage cavities. A related problem where tolerances are close is the flexing of the fixture in such a way as to introduce transient mechanical loading on the transducer. Some mounting problems may indicate their presence during installation. If the "feel" of the transducer being screwed into the cavity is "too tight" chances are that there is a concentricity problem. Alternatively, recording electronics may be connected to the gage prior to installation to see if excessive signals are generated during the mounting procedure.
Differential Pressure Measurements
One of the most exacting pressure measurement problems in gun ballistics involves so called differential pressure measurements. Typically, the objective is to measure pressure differences between the fore and aft ends of the breech section in the early portion of the ballistic cycle to detect the formation of pressure waves which may have ill effects on gun performance. The problem is that whereas the event may have a maximum pressure of 80-90 Kpsi, the region critical to pressure wave formation is often below 10 Kpsi. The pressure differencing needs to be accurate at the low end of the range, where gage errors are greatest. For these measurements, transducers are preselected for the best linearity and hysteresis characteristics. In addition, two and sometimes three sets of calibrations data are used for the same transducer depending on the pressure range are used for the same transducer depending on the pressure range being probed. For instance, calibration data for 10 Kpsi maximum may be used to interpret the low pressure end of the data while calibration data for 100 Kpsi maximum are used to interpret the overall character of the full pressure-time curve. An additional technique used to obtain quality pressure difference data involves the use of mounting adapters, see below.
Mounting Adapters
One effective way of minimizing mounting problems is by use of an adapter. A typical example appears in Figure 10. The small size of the adapter permits easier machining and quality checks of the cavity dimensions. A further advantage is that calibration can be done in the adapter, making transducer remounting unnecessary. The adapter, in effect, protects the transducer from mounting strains in the fixture. If necessary, the measurement system, gage and amplifier can be calibrated together, further refining the data. This can result in excellent performance and repeatability. Figure 11 shows the response behavior of a transducer in its adapter over three calibration cycles. The lines are indistinguishable. The impressive fact about this data is that the transducer had been used to make measurements between the calibration cycles.

Summary and Conclusion

The procedures in use at BRL are aimed at preventing problem transducers from entering the system and weeding out those whose useful life is past. Continuity, linearity, hysteresis, and repeatability characteristics are evaluated for new transducers and for transducers submitted for recalibration. Numerical data are derived using a dead weight calibration system. Static vs. dynamic performance differences, when suspected, are evaluated using a high pressure, dynamic positive step calibration system. Calibrations are recommended at 5-10 round intervals when pressure in the range of 90-100 Kpsi are to be measured. For pressures in the 60 Kpsi regime recalibration is recommended at 25-50 round intervals. Calibration of transducers for the expected pressure range is strongly recommended, since needless large errors may be introduced at the low pressure end by the fitted curve. Mounting adapters not only help to eliminate undesirable mounting effects on the measurements but permit calibration of the transducer in the mechanical environment of the actual measurement. This procedure has been especially useful in exacting measurement applications such as differential pressure measurements.

Acknowledgments

We wish to thank Mr. D. Dykstra, mentor t one of us (CDB), who was responsible for setting up the original calibration system. Further thanks go to Harwood Engineering Company, for their assistance with the controlled clearance measurements and the dynamic positive step calibrator. Final appreciation goes to R. Tompkins and J. Newberry for their assistance with this report.

References

1. Thirteenth Transducer Workshop, Monterey, CA
2. The Piston Gage as a Precise Pressure Measuring Instrument; Harwood Engineering Company, Walpole, MA
3. Astron Gage Manual; Pressure Products Industries, Warminster, PA
4. Handbook of Transducers for Electronic Measuring Systems; Harz No. Norton, Prentice Hall Inc., Englewood Cliffs, NJ
Harwood Engineering Company, Incorporated – © July, 1999
455 South Street, Walpole, Massachusetts 02081
phone: 508-668-3600
fax: 508-660-2276
http://www.ultranet.com/~harwood/
email: harwood@ma.ultranet.com