He et al. extended the two-stage gear reducer dynamics model on the single-stage gear dynamics model, and studied the influence of gear eccentricity on the system response and the frequency modulation phenomenon of meshing multiple frequency sideband considering the bearing elastic support effect. Based on the 6-DOF dynamics mathematical model, Dadon et al. proposed a new general gear dynamics model, which successfully simulated the acceleration signals of real gear pairs considering the broken teeth and global geometric errors. At the same time, the modified model and analytical equation of local tooth surface fault caused by the local contact loss of contact line due to the failure geometry are proposed, which can be used for modeling simulation and fault diagnosis and identification of the whole tooth surface fault in the whole contact area. Mqczak et al. studied the signal response during gear tooth mating in the presence of manufacturing and assembly errors, and used to detect gear tooth fatigue damage and sensitivity of signal recognition.
Based on this mathematical model of spur gear elastic support dynamics, Wang et al. extended it to a helical gear meshing analysis model considering helical deviation. By comprehensively considering the calculation method of helical gear tooth meshing stiffness and meshing vibration, the LTCA (Load Contact Analysis;) was rearranged according to the coincidence degree and tooth pitch deviation. According to the numbering rules of middle gear teeth, the actual analysis of gear pitch deviation causes unstable response, such as the increase of transmission error, the increase of meshing vibration acceleration amplitude, the decrease of resonance frequency and so on. Cui et al. proposed an improved 6-DOF dynamic model with tooth cracks, and analyzed the influence of different crack action lines (parabola or straight line) and variable Angle cracks on vibration response in time domain and frequency domain. Skrickij et al. % proposed an accurate mathematical transfer model with center distance as a variable, defined center distance error, tooth clearance and elastic support of bearings, and studied the effects on meshing stiffness and spur gear dynamics. The research results can be used for comparing response data of later gear box diagnosis.
Cui et al., by monitoring the different influence indexes of the vibration response of the broken tooth, such as RMS and kurtosis, can achieve the analysis ability of dynamic fault detection indexes. He et al. developed a semi-analytical single or multiple harmonic balance method to effectively construct frequency responses to predict meshing forces, frictions, and large and small gear dislocations (along the LOA and OLOA directions), taking into account the analysis model of multi-degree-of-freedom nonlinear systems with friction. Vedmar analysis results based on the bending torsional model such as the only important mode of vibration is found that the gear contact of gear tooth deformation mode of vibration, bearing force will receive other vibration patterns and obvious change, the frictional force on the gear meshing action line direction of gear contact force and bearing force has no obvious dynamic effect, but the vibration in the direction of friction bearing force changes obviously. Xue, developed the FEA method to calculate gear meshing stiffness of gear center distance changes and as considering gear group dynamics analysis model of flexible supporting input parameters, using Newmark method numerical integral differential equation of motion, and concludes that previously ignored the gear center distance change as a result, the dynamic response of structure dynamic design and optimization for further development of new ideas and new methods.