Vibration Spectrum Analysis of Rolling Bearings Based on Nonlinear Stiffness Model

This paper addresses the issue of fault diagnosis in high-speed train bogie bearings under complex working conditions and proposes a method for calculating the characteristic frequency of rolling bearings that takes into account the influence of radial clearance. By establishing a five-degree-of-freedom nonlinear dynamic model, this study systematically analyzes the modulation mechanism of radial clearance on the fault characteristic frequency of bearings and verifies the findings through an experimental platform. The results indicate that an increase in clearance not only leads to significant attenuation of the fault characteristic frequency amplitude, but also induces sideband modulation effects, thereby interfering with fault diagnosis accuracy. The experimental data show good agreement with the theoretical calculations, verifying the effectiveness of the proposed method. Specifically, the nonlinear stiffness-based characteristic frequency calculation reduces the prediction error from 6.9–5.7% under traditional theory to 2.3–3.4% across a wide range of rotational speeds. Meanwhile, the clearance-induced amplitude attenuation predicted by the model is also experimentally confirmed, with measured amplitude reductions of 35–42% as clearance increases from 0.2 μm to 0.5 μm. These results not only demonstrate the accuracy and engineering applicability of the method but also provide new theoretical foundations and practical references for health monitoring and early fault diagnosis of high-speed train bearings.