# A Comparison of Frequency Demodulation Methods to Determine the Instantaneous Angular Speed of a Machine

## Abstract

The instantaneous speed of a machine can be accurately determined by frequency demodulation of a tacho or shaft encoder signal, but can often be determined by frequency demodulation of a machine shaft order in a response vibration signal. It has recently been realised that the latter is not necessarily the same as the speed variation of the machine, as it varies depending on whether displacement, velocity or acceleration is being measured, and whether the band being demodulated falls on a spring line or mass line of the frequency response function. A widely used procedure for performing frequency demodulation of a signal using the Teager Kaiser energy operator (TKEO) actually gives an estimate of the frequency modulation of the derivative of the signal, and this paper discusses alternative more accurate ways of extracting the frequency modulation of the signal itself, and the errors involved in the different estimation methods. The discussion is illustrated using simulated signals, and measurements made on a variable speed gear test rig, with accelerometer response measurements as well as a tacho signal.

## Keywords

Instantaneous machine speed Instantaneous angular velocity Frequency demodulation Energy operators TKEO Hilbert transform techniques Non-causal signal processing## References

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