Parametric Simulation of Tooth-Level Barreling Distribution Effects on Transmission Error Modulation and Spectral Characteristics in a Single Gear Pair

Transmission error (TE) is a major excitation source in geared systems, but microgeometry deviations are usually evaluated through nominal amplitudes rather than their tooth-to-tooth spatial distribution. This study investigates how different tooth-level barreling deviation patterns influence TE modulation and spectral characteristics in a controlled single helical gear-pair model. The nominal barreling value was kept constant, while four deviation patterns were imposed on the 23-tooth pinion: harmonic, phase-shifted harmonic, clustered with an outlier, and random. The TE response was evaluated in the time domain and by Fast Fourier Transform (FFT)-based spectral analysis, with particular attention to the gear mesh frequency (GMF) and shaft-frequency-spaced sidebands. The results show that identical nominal barreling levels can produce different TE waveforms and spectral signatures. Harmonic distributions mainly preserve a regular response, whereas phase-shifted and clustered patterns increase waveform asymmetry and sideband activity. The clustered outlier case produced the most fault-like response. The findings indicate that tooth-level spatial distribution should be considered explicitly in simulation-based gear microgeometry and noise, vibration, and harshness (NVH) sensitivity studies.