System and method for generation of a tachometer signal and reduction of jitter
A system and method for generating a tachometer signal from a vibration sensor is disclosed in which an approximately idealized band pass filter is used along with a fast Fourier transform (FFT) to create a sufficient analytic signal to derive the tachometer signal for a shaft or other rotating component. In addition, jitter in the generated tachometer signal, or any tachometer signal, can be reduced by using an approximately idealized low pass filter and then transforming the filtered signal using a real FFT. These processes can be performed using a smart vibration sensor, which facilitates improved vibration analysis on rotating equipment where in the past the addition of a tachometer would be prohibitive due to cost, weight, certification requirements, or physical impracticality.
1. A method of generating a tachometer signal with reduced jitter comprising the steps of:
receiving vibration data from a vibration sensor that monitors a rotating component;
applying a band pass filter to the vibration data;
using a fast Fourier transform to filter the vibration data;
producing a tachometer signal from the transformed, filtered vibration data;
applying a low band pass filter to the tachometer signal;
fast Fourier transforming the filtered tachometer signal; and
reconstructing a reconstructed tachometer signal with reduced jitter from the transformed, filtered tachometer signal.
2. The method of claim 1 wherein the step of producing a tachometer signal includes taking a pseudo integral.
3. The method of claim 1 wherein the step of producing a tachometer signal includes taking an inverse fast Fourier transform.
4. The method of claim 1 further including a step of normalizing tachometer zero crossing times by a sample rate of the vibration data.
5. The method of claim 1 further including a step of identifying variations on the tachometer signal unrelated to jitter.
6. A system of generating a tachometer signal comprising:
a vibration sensor that produces a vibration signal representative of a spectral content of vibration of a rotating component, wherein the vibration signal includes n data points; and
a controller that receives the signal from the sensor, wherein the controller generates a tachometer signal from the vibration signal by:
determining a low bandwidth cutoff and a high bandwidth cutoff based on a gear mesh frequency,
calculating a radix-2 length that is a closest larger value to n,
zero padding the vibration data from n to the radix-2 length,
taking a fast Fourier transform of the zero padded vibration data,
zeroing the vibration data for which the fast Fourier transform was taken from zero to the low bandwidth cutoff and from the high bandwidth cutoff to the radix-2 length,
taking an inverse fast Fourier transform of the zeroed, transformed vibration data, and
normalizing the inverse-transformed vibration data.
7. The system according to claim 6 , wherein the controller normalizes the generated tachometer signal to tachometer zero crossing times.
8. The system according to claim 6 , wherein the controller interpolates a number of indexes for every 2π radians.
9. The system according to claim 6 , wherein the controller normalizes a time series of radians by a number of teeth of a gear of the component assuming a first harmonic.
10. The system according to claim 6 , wherein the controller normalizes a time series of radians by a number of teeth of a gear of the component assuming a second harmonic.
11. The system according to claim 6 , wherein the controller normalizes a time series of radians by a number of teeth of a gear of the component assuming a third harmonic.
12. A method of reducing jitter in a tachometer signal comprising:
receiving a tachometer signal;
applying a low band pass filter to the tachometer signal;
taking a fast Fourier transform of the filtered tachometer signal; and
reconstructing, from the transformed, filtered tachometer signal, a reconstructed tachometer signal that includes less jitter than the received tachometer signal.
13. The method of reducing jitter in a tachometer signal according to claim 12 further including a step of taking a pseudo derivative of the tachometer signal, wherein the resulting pseudo derivative has a length n.
14. The method of reducing jitter in a tachometer signal according to claim 13 further including a step of determining a closest larger radix-2 value to n.
15. The method of reducing jitter in a tachometer signal according to claim 14 further including a step of creating an array of values of the resulting pseudo derivative values and zeros from n to the radix-2 value.
16. The method of reducing jitter in a tachometer signal according to claim 15 further including a step of calculating a bandwidth index.
17. The method of reducing jitter in a tachometer signal according to claim 16 further including a step of taking a fast Fourier transform of the array.
18. The method of reducing jitter in a tachometer signal according to claim 17 further including a step of setting real and imaginary parts of the transformed array from the bandwidth index to the radix-2 value.
19. The method of reducing jitter in a tachometer signal according to claim 18 further including a step of taking an inverse fast Fourier transform of the transformed array.
20. The method of reducing jitter in a tachometer signal according to claim 19 further including a step of taking a pseudo integral of the inverse transformed array.