Multi-Domain Vibration Diagnosis of Gear Pitting Using a Coupled Torsional-Lateral Spur Gear-Cardan Shaft Model

¹ Department of Industrial Engineering, Operation Management and Mechanical Engineering, Vaal University of Technology, Andries Potgieter Blvd, 1900 | Private Bag X021, Vanderbijlpark, 1911, South Africa.
² Department of Industrial Engineering, Operation Management and Mechanical Engineering, Vaal University of Technology, Andries Potgieter Blvd, 1900 | Private Bag X021, Vanderbijlpark, 1911, South Africa.

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 14 January 2026

Abstract

This study proposes an in-depth investigation of pitting failures in a complex mechanical transmission system, based on vibration analysis. This system incorporates a spur gear and a Cardan shaft that shows an angular misalignment. A torsionally-laterally coupled dynamic model of 13 degrees of freedom (DOF) is developed using the Lagrangian formulation. This approach accurately represents the dynamic interactions between mesh excitations and kinematic fluctuations induced by the universal joint. The model explicitly incorporates the progressive degradation of mesh stiffness caused by pit distribution on the tooth surface. The dynamic response of the system is numerically simulated under healthy and then defective operating conditions (pitting affecting 25% of the tooth surface). Multi-domain diagnostic analysis is then performed. This method employs time-domain waveform analysis, Fourier transform (FFT) spectral analysis, time-frequency representations (spectrograms), and visualization of lateral displacement orbits. The results clearly highlight the signature of pitting defects: increased vibration amplitude and amplitude modulation in the time-domain signal, the appearance of characteristic sidebands in the frequency spectrum, and a diffuse structure with energy scattered in the time-frequency plane. Crucially, the combined analysis of lateral and torsional responses demonstrates the effective transmission of defect-generated excitations from the gear subsystem to the Cardan shaft subsystem.