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This paper proposes a method to estimate the loaded static transmission error (STE) waveform by vibration measurement under operating load conditions of a gearbox. The proposed method is based on the understanding that vibration is determined by the loaded STE and frequency response function (FRF) of the gearbox. The loaded STE is calculated by dividing the measured vibration by the FRF. The FRF is derived by continuously combining the measured vibration response curves of mesh fundamental and harmonic frequency components with the calculated FRF by using a dynamic model of the gearbox. By employing parameter optimization for constructing a dynamic model that has the best fit with the measured vibration response curve, it becomes possible to accurately estimate the loaded STE. Because the objective function is multimodal, we solved this optimization problem by using a real-coded genetic algorithm (RCGA). The proposed method was performed on a single-stage helical gear vibration test rig. The estimated results are then compared to the calculated loaded STE by tooth contact analysis. This comparison shows good qualitative and quantitative agreement between the estimated and the calculated loaded STE waveforms. Our findings confirmed that the loaded STE can be estimated accurately by vibration measurement and that the effectiveness of the proposed method was verified experimentally.

Estimation of loaded static transmission error of helical gears by vibration measurement under operating load conditions