Design and analysis of herringbone gear with sixth-order transmission error based on meshing vibration optimization

To reduce the herringbone gear transmission vibration and noise, an optimization design method about the meshing vibration of herringbone gear is provided with a controllable sixth-order polynomial function of transmission error. First, the polynomial coefficients of sixth-order polynomial function of transmission error curves can be determined by optimizing the aim at minimum root mean square value of herringbone gear meshing vibration acceleration based on loaded tooth contact analysis method and herringbone gear vibration model. Second, because of the existence of second-order frequency factors in the amplitude of loaded transmission error, the root mean square value of meshing vibration acceleration under the optimization of amplitude of loaded transmission error is worse than the value under the optimization of meshing vibration acceleration in resonant frequency. Third, a numerical simulation of example based on herringbone gear with different order transmission errors is performed, which proves that the herringbone gear train with sixthorder polynomial function of transmission error has the lowest root mean square value of meshing vibration acceleration in the design loads' range. This study provides evidence that the proposed herringbone gear train with sixth-order polynomial function of transmission error has the significantly better performances in vibration reduction and smooth transmission than that with fourth-order polynomial function of transmission error and second-order parabolic function of transmission error.