A study on waviness induced vibration of ball bearings based on signal coherence theory

This paper focuses on the effects of waviness on vibration of ball bearings. An experimental analysis method is developed by adopting signal coherence theory of multiple-inputs/single-output (MISO) system. The inputs are waviness excitations of the inner and outer races, and the output is vibration response of the outer ring. Waviness excitation signals are first derived from the manufacturing deviations, and found to be strongly coherent in low frequency range. Virtual input signals are then introduced by the method of orthogonalization. In both cases of vibration acceleration and speed responses, the cumulated virtual input–output coherence function verifies that the first peak region of vibration spectrum is mainly induced by the waviness excitations. In order to distinguish the contributions of the inner and outer races, coherence functions of the virtual inputs with real inputs are calculated, and the results indicate that the outer race waviness contributes more to vibration than the inner race waviness does in the example. Further, a multi-body dynamic model is constructed and employed to frequency response analyses. It is discovered that the waviness induced spectral peak frequency is close to the natural frequency of bearing.