Impact of the non-uniform angular sampling on mechanical signals

• We recall the angular and temporal sampling principle and show their limits.
• We study the impact of these limits by using the non-uniform sampling model.
• We show that non-uniform sampling introduces second order cyclostationarity.
• We show that non-uniform sampling can act like an anti-aliasing filter.
• A test bench was used to corroborate some conclusions.

Angular sampling is a useful tool to study cyclic rotating machine vibrations. It can be implemented by using computer order tracking, directly, or by extracting position information from an acceleration signal. Instantaneous speed can also be angularly sampled using a counter technique. Angular sampling is sensitive to hardware imperfections (optical encoder precision, electrical perturbation, etc.). Angular sampled signal quantification step or sampling frequency determination is not identical to time domain. Angular sampling is also not adapted to study time domain signals like impulse response. Some of these imperfections can be viewed as non-uniform sampling.Non-uniform sampling consists in introducing a jitter in an angular sampling position. This jitter is random and different for every position. This jitter can be caused physically by some inaccuracies in position sensor measurements. Sampling a time domain relative signal against the angle can also be viewed as a non-uniform sampling. In this case the jitter is caused by speed fluctuation (constant speed case). Non-uniform sampling introduces an additional noise (that can be cyclostationary at order 2 if the original signal is cyclostationary at order 1). Non-uniform sampling also acts as a low pass filter. Its cut-off frequency depends on jitter standard deviation.An experimental bench was built. This bench uses a synchronous data acquisition board, an arbitrary generator, and a non-uniform clock generator. Experimentations are performed using various jitter values (from 0.1% to 20%) and are corroborated by previous theoretical studies.