A. Luper

Las Cruces, NM NASA-JSC-WSTF

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Aeronautics and Astronautics

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Af AA-93-1866 DATA REDUCTION FOR A SMALL SOLD ROCKET MOTOR TEST

BY FAST FOURIER TRANSFORM

Alton Luper NASA White Sands Test Facility

Las Cruces, New Mexico

Abstract

A fast Fourier transform (FFT) technique has been refined and applied to data from a small solid rocket motor test stand to extract the motor thrust data from the noise and stand impulse response. The technique employs the FFT both to determine and apply the stand transfer function, and to allow digital test data filtering. The transfer function is applied to the first 0.1 second of the thrust data to remove the stand response to the igniter charge and rocket propellent ignition transient. Digital filtering is applied to the remaining thrust data to remove noise and the stand damped impulse re- sponse. The paper addresses the practica1 consider- ations and methods in applying this technique.

Introduction

This work was completed at White Sands Test Facility (WSTF) located on White Sands Missile Range in southcentral New Mexico. WSTF, a remote test site of the National Aeronautics and Space Administration (NASA), Johnson Space Center in Houston Texas, con- ducts materials, components, and rocket engine tests. This particular project resulted from the flight safety requirement to provide an escape mechanism for the Space Shuttle astronauts. One of the mechanisms investigated was the implementation of a small solid rocket motor to pull each astronaut through the access hatch and out beyond the Shuttle’s wing. The motors under consideration were in common use for crew extraction from high-performance jet aircraft, however, the thrust and torque produced had not been measured adequately to satisfy all engineering requirements. Thus, WSTF was requested to accomplish these mea- surements. The type of thrust measurements (axial to approximately 2 klb, rS.9 kN] and torque to approxi- mately 300 in-lb, [34 Nm] simultaneously) and the small physical size of the motor forced the design and fabrication of a thrust stand unique to WSTF. Th is test program presented some difficult measurement prob- lems which the methods addressed in this paper re- solved.

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A FFT was used to allow the application of a digital filtering technique and the stand transfer function, to the digitized data, attenuating the additive response of the stand. This allowed recovery of the test motor data to the required accuracy and minimized the design and instrumentation expense.

Test Article

The tractor rocket motor (TRM) consists of a solid propellent rocket motor containing 6.5 pounds (1 1 kg) of pdysulfidelammonium perchlorate, and rocket igniter shown in figure 1. The igniter is located at the left end of the rocket body, just inboard of the clevis. The clevis doubles as the attach point for the extraction payload and the rocket igniter. The exhaust nozzles, one is shown in figure 2, are located at the right end of the body, with the exhaust directed back along the body angled away.

Thrust Stand

The thrust stand was constructed to measure 6 degrees of freedom (6DOF), however only two (x-axis thrust and torque about the x-axis) are of interest in this test series. Figure 3 is a side view of the stand showing three of the six strain gage load cells. The three thrust (x-axis) load cells are mounted at the bottom of the stand, shown in figure 4. The rods, figure 3, connect- ing these load cells to the thrust plate are of varying diameter for maximum strength and minimum side load transmission. The threaded hole in the center of the thrust plate, shown in figures 5 and 6, was the mount- ing point of the TRM. A clevis pull device was mounted to the thrust pIate to eliminate my bias to the thrust data from a “grounded” pull on the rocket. A downward pull would activate the rocket igniter. A shroud was installed over the sta-ud, figure 7, to protect the instrumentation and stand structure from the ex- haust. This stand is similar in operation to the Wiancko hi-Symmetric Six-Component Thrust Stand, and the same mathematics are used to derive the rocket forces. The thrust stand was bolted to a large concrete pad near

WSTF Test Stand 405 to facilitate data and control system access.

Instrumentation and Controls

The instrumentation and control cables were routed to the stand through covered cable trays. This precluded cable damage during set up and calibration, and also provided protection from the racket exhaust. Instru- mentation consisted of the strain gage load cells, chamber pressure transducers, thermocouples, bum through through wires, normal and high-speed video, and cine cameras. Each load ceIl contained two strain gages, thus a total of twelve force measurements were made.

Control systems consisted of remote operated gaseous nitrogen valves controlling the clevis pull device.

at 60 ips, was 40,000 Hz. This provided a good backup for the digital data system which has a 500 Hz Nyquist frequency.

The digital data system was composed of an analogue to digital (A/D) converter and a pair of minicomputers with peripherals. The A/D converter has an aggregate scan rate capability of 80,000 samples per second, and sampled each load cell at 1,OOO samples per second. The AID converter can scan a total of 1,075 channels’, however, this test required only about 50 channelg. The digitized data stream was passed to one of a pair of minicomputers. One computer is dedicated to data acquisition and storage, while the second is dedicated to test control. This configuration records time tagged data to hard disc with a minimum resolution of 1 millis- second .’

Test Procedure Data System

The data system consisted of a chain of devices. The load cells at the thrust stand were connected to the signal conditioning in the bunker, which provided k5 volts to the analogue to digital converter and the frequency modulated (FM) tape recorder.

The six strain gage load cells were of standard con- struction and are available off the shelf. Each load cell contained two electrically independent strain gages configured to provide an output proportional to the force exerted on the load cell sensing column. Figure 8 depicts the typical load cell used. These load cells have a maximum usable frequency response of approxi- mately 1,500 hertz (Hz), and a maximum force rating of 5 klbf (22.25 kNn6

The signal conditioning provided 10 volts excitation independentIy to the bridge of each load cell. The signals from the quarter bridge measurements were amplified without filtering by a factor of approximately 166 (30 millivoIts full scale to 5 volts full scale). The 3 dB down point of the amplifiers is approximately 30 kHz. Modeling of the tractor motor suggested that the data frequency would be limited to less than 200 Hz, therefore no problems were expected from aliasing the computer data.4 The analogue data was, however, recorded at a higher band width.

All load cell and various other measurements were recorded on R 42 track FM Wide Band Group I record- er. The 0.5 dB dowa point for this recorder, operated

The test procedure required approximately 2 days to complete. The six strain gauge load cells were calibrat- ed in-place both dynamically and statically to measure axial thrust and torque. The stand was excited with a modal hammer providing up to 1 klb, (4.45 kN) in the form of an impulse delivered axially and then radially. The force input to the stand and each load cell response was recorded on FM tape, and later analyzed in the frequency domain. Pneumatic cylinders in conjunction with transfer standard load cells were utilized to csti- brate the DC response of the stand. An axial pneumatic cylinder, figure 7, was niounted to the concrete pad, and exerted a force on the thrust plate when activated. This force was measured both by the transfer standard, and the three thrust load cells, This data was recorded by the computer and used to generate engineering unit curves for the three thrust load cells. A similar method was applied to the torque load cells using the static torque calibration apparatus shown in figure 9. The pneumatic cylinder and transfer standard were mounted in each of three positions around the stand, to collect data which was used both to calibrate the torque measurement and eliminate the bending moment gener- ated during the calibration runs. The actual test TRM was then installed with the remining instrumentation. All cameras were aligned on the test article and the area cleared for pyrotechnic arming. This was accomplished 20 to 30 minutes before the firing. A final system electronic calibration was completed after the TRM was armed. A final countdown was started, the TRM fired, and then data reduction began.

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Data Reduction

The data reduction process began with the calibration data analysis. The frequency domain analysis of the dynamic calibration data was employed to develop the transfer function of the stand and the background noise characteristics. The input and output are both measured quantities in the time domain. The two mearmred values are first transformed into the frequency domain with the FFT. The transfer function is then determined from the following equation4:

Y ( f ) = X(f) H(f) where Y(f ) is the output of the particular load cell

X(f) is the input to the stand from the modal hammer

H ( f , is the transfer function

Two basic problems must be resolved at this point. Gibb's Phenomena introduces an error of 8.95 percent of the difference in the starting and ending points in the inverse Fourier transformed (IFT) data3. A procedure was developed in which the frequency domain data was examined for an excursion in the amplitude at the end of the window which was not derived from the lime domain data. If such an excursion was detected it was set to zero in the frequency domain before the IFT was applied. This resulted in the elimination of the highest frequency data. This was not a problem for this test the data of interest occurred at much lower frequencies. A second problem with the transfer function was division by zero. A routine was written which eliminat- ed all zeros from the transfer function. These were set to a user defined small number, typically O.oooO1. This resulted in low level time domain noise. The zero replacement number was adjusted for each case to optimize this noise to an acceptable level. The determi- nation of the transfer function could then continue with an element by element division with the output being divided by the input, and the amplitude and phase Components remaining segregated. This resulting transfer function can now be applied to data with a number of restrictions:

1. The data must be from the same load cell channel configured in the same way.

The data FFT must produce the same number of elements as make up the transfer function.

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3. Any physical change to the stand will invalidate the transfer function to some degree, requiring a new function to be developed.

The time consuming computer intensive nature of the application of the transfer functions forced their use only when necessary.

The strip chart and digital data were reviewed to determine the exact time at which the test O C C U K ~ . This time minus 3 milliseconds was set 0n.m IRIG-B decoder, which would provide a 1 microsecond wide pulse when this time passed on the wide-band tape. The recorder channel(s) of interest and the decoder trigger were patched to a digitat osciHoscope. The oscilloscope was typically set to sample at 20 micro- second intervals. This provides a Nyquist frequency4

of 25 kHz. This frequency is approximately 100 times the highest expected data frequency, thus providing acceptable signal accuracy in the time domain'. The digital oscilloscope stored the acquired data in bubble memory to allow the quick capture of several windows. The bubble memory contents were later transferred to a 80286 based computer for analysis and plotting. The oscilloscope data was stored on the computer as a ".PRN" fiIe, which was imported to a spreadsheet. This spreadsheet data was graphed on the screen to aid in setting the final data window.

Data Window

There were two considerations in setting the data window. The final number of data points has to be a power of two, i.e., 1024,2048, or 4096, for use in the FFTIIFT routine. The latter was generally precluded due to computer memory limitations. The reason for this limitation will be described in more detail later. The second window consideration was an effort to eliminate phase relationship problems. Each window had to start the same number of points before the firing. This windowing condition simplified the array handling described later. This windowed data was then saved as a second ".PRN" file in preparation for the FFT. Each measurement to be operated on in the frequency domain (either filtered or the transfer function applied) was preprocessed in this manner. The FFT and IFT were accomplished with a Microsoft Quick Basic program converted from a decimation in frequency type FORTRAN program4.

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Data Analysis Techniaue

There are several things to consider in the application of this FFT/IFT technique. If the time domain win- dowing is "correct" as described above, the matrix operations are greatly simplified. The FFT part of this routine produces a 2 by "x" matrix where "XI is the number of data points in the time domain array. The first column of the frequency domain matrix i s the amplitude at a given frequency, and the second co[urnn is the phase angle normalized to 180 degrees, If the data was to be digitally filtered, botb the amplitude and the phase information were set to zero for the undesired frequencies. When the transfer function was applied, the measured load cell output amplitude was divided by the transfer function ampIitude. The test data phase information was preserved and recombined with the "transferred" frequency domain amplitudes before the IFT was applied. This is acceptable only because the window phase with mpt to the data was held con- stant throughout at1 operations. At this point, the same two problems (Gibb's Phenomena and division by zero) occurred as in the transfer function determination phase, and were resolved in the same manner.

Apdications

This technique was applied to thrust stand evaluation. A rough modal analysis was conducted to determine the resonant frequencies of the thrust stand. The stand was struck with a modal hammer to excite "all" frequencies. Each load cell signal was recorded on magnetic tape and digitized as described above. The FFT was applied to this digital data to reveal any frequencies excited by the impulse. These resonant frequencies were exam- ined to determine if they could be easily designed out of the system. If not, the transfer function would be used to remove them from the test data. The chamcter- istic damping of the stand was also checkd. If the data is attenuated before it gets to the rscorder the ease of reconstructing it with any accuracy vanes from difficult to impossible. However, if the damping is well charac- terized this reconstruction may also be possible through the application of the transfer function.

The transfer function was applied in two modes. The full application mode was tried but not implemented due to computer memory limitations. A longer digitizing interval was required to limit the number of data points and still include all of the 0.5 to 0.7 second duration firing. This reduced the Nyquist frequency below that applicable to firing data. The partial application mode

utilized a time window much smaller than the test duration, digitizing only the start up response. This resulted in data errors introduced from Gibb's phenom- ena, which were dealt with as described above.

Conclusions

These techniques allowed posttest recovery of the TRM data, however, in this particular case the digital filtering technique produced data only slightly less noisy than conventional electronic analogue filtering. Figure 10 depicts the unfiltered torque data as it was recorded, and figure 11 is the same data after the stand transfer function was applied. The frequency of the TRM thrust data was sufficiently low relative to the stand response, that conventional fiItering removed the stand effects with a minimal loss of thrust data. The technique did allow discovery of a high-frequency ringing which developed near the end of each firing which was attributed to an acoustic standing wave in the motor casing. This did not effectively change the thrust and was of academic interest only.

The availability of the transfer function technique allowed fewer of the test project resources to be spent constructing and commissioning the stand. This technique permitted the simpler criteria of designing the stand strong enough to damp any harmonics which might be generated during the firing. Less sophisticat- ed design and mechanical tuning of the stand was required, knowing that the undesirable stand response could be removed mathematically from the data postt- est. Also there was no requirement for real time decisions based on thrust levels, therefore the data was simply stored for later processing. Instead of building a stand to test a particular small motor, a general purpose stand was constructed, which can be used for any solid motor with less than 5 Hbf (22.25 kN) thrust. Without this tecbnique the stand would have to be tuned to the particular motor, possibly requiring one or two firings for tuning to an unknown motor. This technique aIlows mounting and firing a relatively unknown motor, and removing the stand effects from the data posttest.

The data reduction and analysis steps of these tech- niques were very l a b r intensive, due primarily to the equipment available. A PCAT (80286) compatible, with 1 megabyte of memory, was used for this work. The computer must hold 6 arrays of 4,096 points for a sample interval of 0.1 milliseconds and 0.5 second duration firing. A 2 to 4 megabyte machine would permit greater frequency resolution and/or longer data

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windows. The greater memory WilI also underscore the greater times required to compute iin 8,192 or 16,384 poini FFT/lFT*

A 4,096 point FFT rcquum 20-30 seconds to run on the 286 machine, and at least two FF"/IF" conversions per data channel are requ id . The use of an 80386 compatible machine cut this time by a factor of 10, however the array manipulations are still time wmming.

WSTF found these techniques quite useful for this unusual type of test (short firing duration and high thrust to weight ratio). The stand evaluation phasa of the technique has been used a number of times since, however, the full application has not been used due to the long test duration of the typical nxket test.

References

1. Daystrom-Wiatm Engineering Company, "The Design of High-Accuracy Rocket Thrust Stands and Calibrators", Daystrom-Wianco Engineering Company Report WSC-SA-7D, March 1961

2. J. Mulhollaad, Tractor Rocket System Test Project u

TD-525-001, 1987

3. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing, Prentice-Hall, he., 1975

4. R. W. Ramirez, The FFT Fundamentals and Con- cepts, Prentice-Hafl, Inc., 1985

5. J. Taylor, Fundamentals of Measurement Error, Neff Instrument Corp., 1988

6. Toroid Corp. Series 36 Load Cell Specification She& CS1-1002B

7. WSTF Engineering, Propulsion T& Area Data Acquisition System Handbook PROP-DAS401, NASA-WSTF, 1989

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Fig. 1. Tractor Rocket Motor

Fig. 2. Tractor Rocket Motor Operation

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Fig. 4. Plan View B-B Thrust Axis Load Cells

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Fig. 5. Plan View A-A Thrust PIate

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Fig. 6. Plan View C-C Torque Load Cells !

Fig. 7. 6DOF Thrust Stand Exhaust Shroud

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Fig. 8. Typical h a d Cell

Fig. 9, Static Torque Calibration Apparatus

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