Abstract

The regularity of the vibration signals measured from a rotating machine is often affected by the condition of the machine. The fractional order of regularity can be measured using the definition of Hölder continuity. In this paper, we review the connection between the pointwise Hölder regularity of a signal and its wavelet transform. We calculate the wavelet transform modulus of acceleration measurements from a test rig. The effects of different faults were recorded, such as unbalance, the coupling misalignment of a claw clutch, the absence of lubrication in a ball bearing, the absence of the bearing’s cage, and their combinations. An analysis of the estimated isolated pointwise regularities from the wavelet transform modulus maxima ridges shows that the faults often cause irregularities in the signals and that their locations and frequencies can be used in diagnosing the faults. Coupling misalignment and the absence of lubrication in a ball bearing both cause impact-like vibrations, but these impacts have positive and negative regularities in the case of a coupling misalignment and mainly negative in the case of a dry bearing. Unbalance is best diagnosed from the integrals of the acceleration signals using traditional methods. In diagnosing the misalignment, bearing problems and simultaneous faults, the local regularity analysis outperforms the use of high order norms of differentiated acceleration measurements (i.e. jerk and snap signals). Using just three features (the number of local irregularities in an acceleration signal, their mean Hölder regularity and the arithmetic mean of the absolute values of a velocity signal), a quadratic classifier can be constructed whose estimated classification error is only 0.3%.