Coupled Nonlinear Dynamic Modeling and Experimental Investigation of Gear Transmission Error for Enhanced Fault Diagnosis in Single-Stage Spur Gear Systems

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems.