Based on the rolling bearing vibration measurement principle in ISO standard, a nonlinear dynamic model of ball bearing is built and motion equations of the inner ring, outer ring, and rolling elements are derived by using Lagrange’s equation. The ball bearing model includes the influence of waviness, rotational speed, external load, arbor supporting stiffness and arbor eccentricity. Ball bearing high-speed vibration tests are performed and used to verify the theoretical results. Simulated results showed that specific waviness orders produced the principal frequencies that were proportional to rotational speed. Rotational speed mainly affected the value of the natural frequency of the bearing system, and RMS (Root Mean Square) of the full band had a great fluctuation with the increase of rotational speed. In the experiment, spectrum and RMS of 2fs-30 kHz (fs: the rotational frequency of inner ring/arbor) under high speed could include not only the influence of rotational speed but also principal frequencies produced by waviness, which could cover the part of requirements of the standard bearing vibration measurement.

Buzz, squeak and rattle (BSR) noise has become apparent in vehicles due to the significant reductions in engine noise and road noise. The BSR often occurs in driving condition with many interference signals. Thus, the automatic BSR detection remains a challenge for vehicle engineers. In this paper, a rattle signal denoising and enhancing method is proposed to extract the rattle components from in-vehicle background noise. The proposed method combines the advantages of wavelet packet decomposition and mathematical morphology filter. The critical frequency band and the information entropy are introduced to improve the wavelet packet threshold denoising method. A rattle component enhancing method based on multi-scale compound morphological filter is proposed, and the kurtosis values are introduced to determine the best parameters of the filter. To examine the feasibility of the proposed algorithm, synthetic brake caliper rattle signals with various SNR ratios are prepared to verify the algorithm. In the validation analysis, the proposed method can well remove the disturbance background noise in the signal and extract the rattle components with well SNR ratios. It is believed that the algorithm discussed in this paper can be further applied to facilitate the detection of the vehicle rattle noise in industry.