MEASUREMENTS OF DEAD WEIGHT TESTER
PERFORMANCE USING HIGH RESOLUTION
QUARTZ CRYSTAL PRESSURE TRANSDUCERS

Laboratory users and manufactures of primary pressure standards are interested in evaluating dead weight tester performance and making cross comparisons between different standards.  Quartz crystal pressure transducers have been developed which may be used to make high speed, high resolution measurements of dead weight tester performance.  Transducer resolution of parts per billion of full scale output allows observation of piston-cylinder non-uniformity and taper equivalent to changes in diameter of one molecular layer.  Pressure fluctuations associated with dead weight tester rotation, weight bounce, drive mechanism imperfections, and piston flexing are easily measured.  Errors from these fluctuations can be minimized by choosing an appropriate averaging time.  These observations have implications for proper design and use of dead weight tester systems. 

Inherently digital pressure transducers employing quartz crystal frequency output sensors have been developed for use in applications requiring high resolution and precision.  Although these transducers are described in more detail in Reference 1, the following is a brief summary of the construction, operation, and performance of the Digiquartz Pressure Instrumentation manufactured by Paroscientific, Inc. 

The key sensing element in these transducers is a vibrating quartz crystal whose resonant frequency changes with pressure-induced stress.  Figure 1 shows a resonator of the double-ended tuning fork (DETF) design.  It consists of two identical beams flexing 180 degrees out of phase to cancel the opposing forces and moments, thus transmitting very little energy to the mounting pads.  Even though the quartz crystal has a high Q and a long-lasting resonance, a small amount of energy must be supplied to achieve and maintain oscillation of the DETF.  Surface electrodes piezoelectrically drive and detect the resonant frequency through an external oscillator circuit.  The electrode pattern is produced as an integral part of the photolithographic and chemical milling methods used in DETF manufacturing (Reference 2).  The resonant frequency of the tines is a function of the dimensions, composition, and applied load.  As with a violin string, the frequency of oscillation increases under tension and decreases with compressive loading.  As described in References 3 and 4, the resonators must be carefully designed to minimize energy losses and to avoid spurious resonances, which can produce discontinuities in the frequency versus load relationship.

Figure 1. Double-Ended Fork

The DETF is insensitive to temperature because the crystallographic orientation and force producing structure were designed to minimize thermal effects (Reference 5).  The remaining temperature sensitivity is readily compensated using a quartz crystal thermometer.  A quartz resonator that is sensitive only to temperature (not load) is shown in figure 2.  It consists of two torsionally oscillating tines connected to a mounting pad through a mechanical isolation system (Reference 6).  The dimensions of the temperature sensitive quartz resonator must be carefully chosen to avoid spurious modes of oscillation (Reference 7).  These temperature sensors are manufactured with the same photolithographic, chemical milling techniques used to make the DETF resonators.  An oscillator piezoeletrically excites and detects the torsional tine vibrations.  The change in resonant frequency of the temperature sensitive quartz resonator can conveniently be used to compensate for thermal effects in the DETF force sensor and pressure transducer mechanism. 

The pressure-induced load applied to the force sensitive resonator may be generated by a bellows, diaphragm, or Bourdon tube.  The higher range designs generally employ a Bourdon tube as the pressure-to-load converter (Reference 8).  Figure 3 shows a single-turn Bourdon tube restrained by the DETF resonator. Applied internal pressure tends to uncoil the Bourdon tube, thus placing the crystal under tension and increasing the resonator’s frequency of oscillation.  An integral torsional tuning fork temperature sensor is used for thermal compensation.  Small, adjustable masses are positioned such that the center of gravity of the mechanism coincides with the effective pivot or center of rotation of the Bourdon mechanism.  Thus inertial forces and torques are reduced to zero and the transducer has a low sensitivity to linear acceleration and vibration.  A hermetically sealed case encloses the internal vacuum in which the resonators operate, thus eliminating air damping and contamination while ensuring high Q values and a stable reference for the absolute pressure transducers. 

Figure 3. Quartz Crystal Pressure Transducer

The quartz crystal transducer can be mated with a special digital interface board to produce an intelligent transmitter. Each pressure transducer provides two continuous frequency output signals, one corresponding to the pressure and the other to the sensor’s internal temperature.  The digital board measures the period of these two signals and calculates fully corrected pressure and temperature. 

As shown in Figure 4, the digital board has a microprocessor-controlled counter and RS232 port.  The microprocessor operating program is stored in permanent memory (EPROM) and user controllable parameters are stored in user writable memory (EEPROM).  The user interacts with the transmitter via the two-way RS232 interface.  These transmitters output fully temperature corrected pressure information on a two way addressable RS232 bus that can be interfaced to a computer or stand-alone readout display. 

The RS232 interface allows complete remote configuration and control of all operating parameters of the intelligent transmitter, including resolution, sample rate, integration time, and baud rate.  Resolution is programmable from 0.04 to 100 parts per million depending on system requirements.  Baud rate is user selectable from 150 to 19,200.  Pressure data are available in eight different selectable standard engineering units.  Up to 15 data readings per second can be obtained with normal sampling commands.  More than 100 samples per second can be obtained with special burst sampling commands. 

The ability to control the transmitter’s resolution and integration time is important in developing a practical instrument to measure dead weight tester performance. 

The first step in processing the output of the quartz crystal pressure transducer is to measure its resonant frequency with a period averaging technique.  The output from the resonator gates a high frequency clock and the clock pulses are counted.  With an unsophisticated counter-timer scheme, there is uncertainty of +/- 1 count out of the total number of clock pulses. The total number of clock pulses equals the clock frequency multiplied by the integration time ( number of resonator periods averaged multiplied by the resonator period).  For example, integrating for one second with a 15 MHz clock yields a frequency resolution of the resonator’s output of 0.07 parts per million (ppm).  The quartz crystal pressure transducer is designed to produce a 10% change in resonator frequency from zero to full scale applied pressure.  Thus only 10% of the counts are related to pressure and the pressure resolution would be 0.7 ppm using a 15 MHz clock and update time of 1 second.  Higher resolution, interpolating start-stop counters are available with equivalent clock frequency close to the GHz range.  With this improved counting system, the resolution was found to be limited by a small amount (about 30 nsec) of phase jitter on the pressure signal waveform caused by cross-talk from the temperature oscillator.  Although this phase jitter is smaller than the time base resolution of most counters, the transducer electronics were modified to provide gating for the temperature oscillator.  With the temperature oscillator gated off while measuring the pressure signal, resolution was improved by more than a factor of 4 for any integration time and was least count limited by the interpolating start-stop counter.  Actual sensor performance may be even better than listed in Table 1.  

  Table 1. Pressure Resolution Temperature Resolution Gated Off

Tests were then run to show that the transducers can measure real pressure changes that exceed the noise levels shown in Table 1.  Figure 5 shows a 15,000 psia (103 MPa) transducer tracking small “weight wobble” pressure fluctuations on a DH Instruments primary dead weight pressure standard.  Sensor output was integrated for 0.1 sec.  Pressure fluctuations of a few parts in 10⁷ are readily resolved. 

An even more remarkable set of measurements is shown in Figure 6 in which small atmospheric pressure changes over a five minute interval are tracked simultaneously with a barometer and with a 10,000 psi (69 MPa) transducer.  Real pressure changes of the order of 0.00005 psi (5 parts per billion full scale) are being tracked with a 10,000 psi transducer!  Counter integration time was 10 seconds.

To demonstrate the high resolution capabilities of the quartz crystal pressure transducers, they were used to study the performance of the DH Instruments primary dead weight pressure standard. 

Figure 7 shows the piston area variation with float height for three different pistons, as determined from pressure measurements as a function of height.  About 15 minutes were required for three profiles on a single piston.  A few parts in 10⁷ changes in piston area with height are easily resolved, corresponding to an equivalent change in diameter of one molecular layer.  The 100 psi/kg piston is remarkably uniform in area along its length, varying less than 1 ppm in the central 0.5 cm.   Not surprisingly, the smaller diameter, higher pressure pistons tend to show greater variation in area.  The data suggests some interesting applications for screening pistons and monitoring wear patterns with time.  For example, is the 5 ppm relative dip in the central region of the 20,000 psi piston caused by piston wear?  This is a steel piston in a carbide cylinder and so would wear to a smaller effective area.  Although these are all very high quality pistons, with variations less than one percent of a wavelength of light, their minute departures from perfection are readily measured with the quartz crystal pressure transducers.  Less expensive pistons from other manufacturers frequently show changes of 200 ppm in area along the piston. 

DH Instruments provided three well used pistons of different ranges.  Normally, one compares piston areas by cross-floating using two dead weight standards.  By switching a transducer back and forth between two dead weight testers using valves, one would be able quickly to compare two pistons to one part per million; however, as only one dead weight standard was available, a much more difficult procedure was attempted.  Pressure was applied at 8,500 psia with the first piston and measured with two of the quartz crystal pressure transducers as transfer standards.  The system was depressurized, the piston was changed, and the measurements were repeated with the remaining two pistons in turn.  The total measured spread among the three pistons (after allowing for differences in nominal piston area using the manufacturer’s data) was 12.9 ppm, even though two of the pistons had not been calibrated in two or three years.  This represents the total cumulative error from the manufacturer’s original area measurement, wear with time, mass errors, and transfer sensor errors.

The pressure output of primary dead weight pressure standards is not precisely constant in time.  High quality standards typically have short period pressure fluctuations of 10 ppm.  Less accurate standards may have fluctuations of 100 ppm or more. 

Figures 8, 9, 10, and 11 show fluctuations observed for various pistons at pressure from 6000 psia to 35,000 psia.  The dead weight standard used is a DH Instruments Model 5306, which is representative of a premium class standard.  Output pressure was measured with Paroscientific Inc, Model 15K quartz crystal pressure transducers; read out with a HP 5384A counter, with an integration time of 0.1 seconds.  For optimum resolution, data were taken with the sensor temperature oscillator gated off.  Each run consisted of 100 consecutive period measurements taken at a rate of approximately 4 points per second. 

Figure 8. DWT Fluctuations at 6,000 PSIA Piston  S/N 1339

Figure 9. DWT Fluctuations at 10,000 PSIA Piston S/N 1064

Figure 10. DWT Fluctuations at 30,000 PSIA Piston S/N 1340

Figure 11. DWT Fluctuations at 35,000 PSIA Piston S/N 1340

The observed fluctuations often occur at periods associated with weight rotation, weight bounce, or pendulum oscillations of the weights flexing the piston.  Note that the Figures 10 and 11 show a pronounced response at the weight rotation frequency and its second harmonic, but that other runs show more varied frequency content.  Some show pronounced changes in amplitude with time. 

Although more data are needed, indications are that the dead weight standard short period fluctuations result primarily from the weight drive and weight suspension mechanisms.  Now that sensors are available that can measure these fluctuations, it should be possible to develop primary pressure standards with improved performance. 

Current premium class primary dead weight testers have variations in output pressure with float height and time, which are readily measured with quartz crystal pressure transducers.  With these new sensors as a testing tool, it should be possible to develop primary pressure standards with improved performance.  The sensors also make it easier to cross-check piston sets against a master reference piston and to screen them for nonuniformity. 

1. Busse,  D.W., “Quartz Transducers for Precision Under Pressure”, Mechanical Engineering, Vol. 109, No. 5, May 1987.

2. EerNisse, E.P., “Minature Quartz Resonator Force Transducer”, U.S. Patent  4,215,570 Aug. 5, 1980.

3. Paros, J.M. and Busse, D.W., “Longitudinal Isolation System for Flexurally Vibrating Force Transducers” U.S. Patent 4,321,173 Mar. 23, 1982.

4. EerNisse, E.P and Paros, J.M., “Resonator Force Transducer” U.S. Patent 4,372,173 Feb. 8,1983.

5. Paros, J.M., “Isolating And Temperature Compensating System For Resonators”, U.S. Patent 4,406,966 Sept. 27, 1983.

6. Paros, J.M., Wearn, R.B., and Tonn, J.F., “Mounting and Isolating System for Tuning Fork Temperature Sensor”, U.S. Patent 4,706,259 Nov. 10, 1987.  

7. EerNisse, E.P. and Wiggens, R.B., “Resonator Temperature Transducer”, U.S. Patent 4,593,663 June 3, 1986

8. Paros, J.M., “Digital Pressure Transducer”, U.S. Patent  4,455,874 June 26, 1984.

©2007 Paroscientific, Inc.