HIGH FIDELITY-LOW FREQUENCY SENSOR

I have shown in previous reports the response of the SE1000-HI high fidelity transducer in the frequency range between 7 to 400Khz. This is the frequency range which we have traceability to NIST. As it turns out this transducer also exhibits high sensitivity and high fidelity at the lower frequencies. Figure 1 shows the calibration between 1 and 3 Khz for a SE1000-HI. The calibration system is only setup to automatically record the data down to 1Khz. Manual measurements were made down to 100Hz with no noticeable change in the sensitivity or flatness shown by figure 1.

I was not certain exactly what was being measured in figure 1. Since the frequency range shown is below the spring mass resonance of the transducer, it would lead one to believe that the output shown would correspond to acceleration and not displacement. I began to search for a method to resolve this and contacted Marvin Hamstad at NIST in Boulder. He informed me of a finite element program at NIST that he and co-workers had developed for the study of stress waves in rods (ref. 1). We collaborated on an experiment which involved attaching a SE1000-HI transducer to the end of a 51 inch long, 3/4 inch diameter aluminum rod which I happened to have available. 0.3mm pencil lead breaks were made on the opposite end of the rod and the signals were digitized and recorded. Hamstad had previously determined the magnitude of the energy output of the 0.3mm pencil lead. Using the dimensions of the aluminum rod and its elastic constants a finite element program was written and executed at NIST Boulder to determine the displacement at the end of the rod.

Figure 2 shows the finite element results on the aluminum rod. The upper trace in figure 2 is the calculated displacement at the end of the rod and the lower trace is the first derivative of the displacement curve which gives the velocity response. Note that there is no correction for attenuation in the program, therefore the signal due to the reflection in the rod is the same amplitude as the first signal. The vertical scale in figure 2 is nanometers and the horizontal scale is microseconds.

In a recent report (ref 2) on earthquake prediction I discussed using a pointed waveguide attached to a displacement transducer to measure the displacement of the granite in a deep bore hole instead of using strong motion sensors or accelerometers for measuring seismic events . It was suggested in that report that measurements in the picometer range of displacements would be possible, which would allow for detecting higher frequencies and therefore the smaller seismic events that are precursors to larger events. With this in mind a 1/4 inch stainless steel waveguide 4.5 inches long with a pointed end was attached to a SE1000-HI transducer. The pointed end of the waveguide was placed in the center of the aluminum rod at one end and measurements of the displacement at the end of the rod was made with this arrangement in addition to using the SE1000-HI directly coupled with petroleum jelly.

Figure 3 shows the results obtained from both configurations in response to the 0.3mm pencil lead break at the opposite end. Note the similarity between figure 3b for the experimental results and the finite element calculations for displacement shown by the upper trace of figure 2. The curves are almost identical with exception that the reflection of the wave at approximately 800 microseconds for the experimental results shows some attenuation as opposed to the results in figure 2 as would be expected. Figure 3a shows the results of the displacement measured with the pointed waveguide. Note that the time of arrival for the wave is somewhat longer which represents the additional distance traveled due to the 4.5 inch waveguide. Both the initial wave and the reflection are clearly shown with very little attenuation due to the waveguide. This illustrates that a pointed waveguide can be used without couplant for accurately measuring very small displacements. There is distortion between the initial and reflected wave due to multiple reflections occurring in the waveguide, but the initial portion of the wave is uncompromised. Comparison of the upper trace in figure 2 which shows a peak displacement of 4 nanometer, and figure 3b which shows a peak voltage of 1.5 volts indicates that the sensitivity for this configuration is approximately 0 .4 volts/nanometer.

Another experiment that was performed involved placing a DECI SE375-MI at the end of the aluminum rod and measuring its response to the 0.3 mm pencil lead break. The SE375-MI is the integral electronics version of this transducer. The internal amplification of the signal was the same as used in the SE1000-HI, (10dB) with the exception that it was designed with a 20Khz hipass filter. Figure 4 shows the results of this experiment. Note that the response compares favorably with the velocity response calculation of the finite element analysis shown by the lower trace of figure 2. Note the change in vertical scale between figure's 3 and 4.

The calibration curve in figure 1 shows sensitivity of approximately 100 volts/micrometer in the lower frequency ranges for the SE1000-HI used in these experiments. This represents a sensitivity of 0.1V/Nanometer which is a difference of 4 to 1 between the two measurements. This difference indicates that extrapolation of the NIST calibration below the 10Khz spring-mass resonance would result in an error of approximately 12dB. Therefore the finite element calibration shown by figure 2 appears to be a better way of calibrating the low frequency response of the SE1000-HI.

Only 10dB of gain was used by the internal electronics of the SE1000-HI to produce the signals shown by figure 3. An additional 70dB of amplification could be utilized while still maintaining a favorable signal to noise ratio. Therefore the additional amplification would allow one to measure displacements in the picometer range over a wide range of frequencies..

CONCLUSIONS

These results have shown excellent correlation between finite element calculations of the displacement at the end of a 3/4 inch diameter aluminum rod 51 inches long from a 0.3mm pencil lead break at the opposite end, and experimental measurements made with a DECI SE1000-HI displacement transducer. It is shown that a waveguide with a sharp point integrally mounted to a DECI SE1000-HI transducer can be used to measure these same displacements with very little loss of sensitivity. This will have important implications in the earthquake monitoring applications at low frequencies, and could have equally important applications in leak monitoring of high temperature pressure vessels and piping. My intuition tells me that high pressure leaks should produce low frequency flexure waves in the walls of pressure vessels and piping that will result in large displacements that can easily be measured by a pointed waveguide mounted on a DECI SE1000-HI transducer in the 20-80Khz range of frequencies. A future experiment will be designed to find out if a typical leak acts as an in-plane(IP) or out-of-place (OOP) source for AE signals. If anyone knows someone that has already made this study Please let me know.

I would like to acknowledge with special thanks Marvin Hamstad, Abby O'Gallagher and John Gary of NIST Boulder for their efforts in running the finite element analysis program and supplying the data in figure 2.

REFERENCES

1. Gary, John and Hamstad, Marvin A. "On the Far Field Structure of Waves Generated by a Pencil Lead Break on a Thin Plate" Journal of Acoustic Emission Vol. 12 pp 157-170

2. Dunegan, Harold L., "Prediction of Earthquakes with AE/MS? Why Not" Proceedings of 6th Conference on AE/MS Activity in Geologic Structures and Materials" Pennsylvania State University, June 11-13, 1996.