An Analysis of Hertzian Contact and Inner Race Crack-Induced Vibrations in a Coupled Shaft-Bearing System

Résumé

A dynamic model of a coupled shaft-bearing system was developed to examine the vibrational behavior caused by Hertzian contact mechanics and localized defects on the inner race. The model integrates mechanical energy balance, nonlinear Hertzian contact stiffness, and the Lagrangian formalism, considering the radial loads, system damping, and geometric characteristics. Numerical simulations executed via the fourth-order Runge–Kutta method reveal distinct vibrational signatures between the healthy and cracked bearing conditions. Under healthy operating conditions, broadband spectral energy is observed without significant peaks, indicating a uniform vibration behavior. The introduction of an inner race crack generates amplitude modulation, increased vibration levels, and pronounced spectral peaks between 600 Hz and 800 Hz. These peaks are consistent with defect-passing frequencies and nonlinear impact phenomena. This study reveals that the local defects significantly impact the dynamic response by producing complex, nonstationary vibration patterns that can be detected through time-domain analysis and power spectral density estimation using the power spectrum of the Fast Fourier Transform (FFT) technique.

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