Spectrum and Cepstrum Based Speed Determination of Stepper Motors

Accurate rotational speed determination for rotary machines tends to be allocated high priority in technical applications. It is not easy to measure shaft speed directly in some cases. Vibration diagnostic tools can offer an alternative solution to the problem posed by direct rotational speed measurement. Using calculated spectra and cepstra can help to determine rotational speed of stepper motor driven systems easily and accurately. This paper summarizes the theoretical background of discrete spectrum and cepstrum based methodologies and shows results of practical experiments. Equations for each method to calculate the possible speed estimation error are also shown. A novel vibration based hybrid spectral speed estimation logic can be defined, which uses the presented equations to decide which spectral method results in the most accurate output. Numerous vibration measurements have been made to test the hybrid methods reliability. The hybrid spectral speed determination method has been successfully applied on various type of electromotive drives, as well as spark- and compression-ignition internal combustion engines.