Tacho-less automatic rotational speed estimation (TARSE) for a mechanical system with gear pair under non-stationary conditions

The condition monitoring of mechanical systems by vibration analysis becomes a problem whenever the rotational speed varies and is unknown. This work proposes an algorithm to automatically estimate the rotational speed from the vibration generated by a gear pair. The algorithm is based on the decomposition of the vibration signal into mono-component signals and the detection of amplitude modulations. Singular Spectrum Decomposition was used for decomposing the vibration signal into the mono-component signals, and a non-quadratic phase coupling analysis was applied in order to detect the amplitude modulations. The algorithm is validated by working with simulated and true signals resulting from the application of different speed profiles. Finally, two practical cases are presented: (1) the implementation of order tracking through the rotational angle estimated by the new algorithm; and (2) the identification of the first harmonic of gear-mesh frequency from a time-frequency representation of the vibration signal.