Time-varying mesh stiffness (TVMS) and gear errors include short-term and long-term components are the two main internal dynamic excitations for gear transmission. The coupling relationship between the two factors is usually neglected in the traditional quasi-static and dynamic behaviors analysis of gear system. This paper investigates the influence of short-term and long-term components of manufacturing errors on quasi-static and dynamic behaviors of helical gear system considering the coupling relationship between TVMS and gear errors. The TVMS, loaded static transmission error (LSTE) and loaded composite mesh error (LCMS) are determined using an improved loaded tooth contact analysis (LTCA) model. Considering the structure of shaft, as well as the direction of power flow and bearing location, a precise generalized finite element dynamic model of helical gear system is developed, and the dynamic responses of the system are obtained by numerical integration method. The results suggest that lighter loading conditions result in smaller mesh stiffness and stronger vibration, and the corresponding resonance speeds of the system become lower. Long-term components of manufacturing errors lead to the appearance of sideband frequency components in frequency spectrum of dynamic responses. The sideband frequency components are predominant under light loading conditions. With the increase of output torque, the mesh frequency and its harmonics components tend to be enhanced relative to sideband frequency components. This study can provide effective reference for low noise design of gear transmission.

A generalized finite element dynamic model of helical gear system considering time-varying mesh stiffness and loaded composite mesh error is developed. Bias modification is introduced into this model, and the corresponding time-varying mesh stiffness and loaded composite mesh error are determined based on improved loaded tooth contact analysis model. By introducing vibration exciting force, the time-variant differential equations of the system are transformed into time-invariant differential equations which can be solved faster by Fourier series method. Meanwhile, the internal excitation of the system can be captured clearly. Aiming to reduce vibration of the system, optimization method of bias modification is proposed with the objective of minimizing fluctuation of the vibration exciting force. The global optimal modification parameters are obtained using brute force optimization method. The sensitivity of dynamic response of the modified helical gear system to gear misalignment is then investigated. Simulation results suggest that bias modification has little effect on time-varying mesh stiffness but reduces system vibration significantly. Increasing gear misalignment will decrease time-varying mesh stiffness and increase the system vibration. Bias modification shows a well robustness in reducing vibration of helical gear system when gear misalignment is not too large.

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

Mesh misalignment in mating the gear tooth surface is common and difficult to be determined accurately because of system deformation and bearing clearances, as well as manufacturing and assembly errors. It is not appropriate to consider the mesh misalignment as a constant value or even completely ignore it in the tooth surface modification design. Aiming to minimize the expectation and variance of static transmission error (STE) fluctuations in consideration of mesh misalignment tolerance, a multiobjective optimization model of tooth surface modification parameters is proposed through coupling the NSGA‐II algorithm and an efficient loaded tooth contact analysis (LTCA) model. The modified tooth flank of helical gear pairs is defined using 6 design variables which are related to profile modification, lead modification, and bias modification. The influences of mesh misalignment on time‐dependent meshing stiffness (TDMS) and STE of unmodified and modified helical gear pairs are investigated. Then, the dynamic transmission error (DTE) of modified helical gears in consideration of mesh misalignment is discussed. The results indicate that the designed modified tooth surface shows good robustness to mesh misalignment.