Zhou Sun

Reliable vibration prediction for gear systems requires calibration of uncertain mesh and bearing parameters. Previous gear physics-informed machine learning (PIML) studies mainly estimated time-varying meshing stiffness (TVMS) or calibrated gearbox dynamics for fault diagnosis or response reconstruction. Yet identifying multiple key parameters from limited data remains challenging. This work develops a PIML-based dynamic parameter inversion method using limited housing-surface vibration acceleration measurements. A gear-shaft-bearing-housing system dynamic model is embedded directly in the optimization loop, and automatic differentiation provides gradients for updating selected parameters without training a separate response-prediction network. A weighted meshing harmonics complex-spectrum loss penalizes amplitude and phase differences, focusing calibration on mesh-related vibration. Numerical studies show that the method reconstructs time- and frequency-domain response features across speeds and initial estimates, and principal features remain discernible with 20% added noise. In experiments, with mesh and bearing stiffnesses fixed at theoretical values, the first two harmonics of static transmission error (STE), mesh damping, and bearing damping are identified from measurements at a single resonant speed of 3100 r/min. The calibrated model reproduces dominant harmonics at 2400 r/min and captures major resonance peaks across the tested speed range, providing a basis for identifying key dynamic parameters from limited vibration data.

In the aerospace industry, thin-web gears are preferred for achieving high power-density transmission. However, thin-webbed structures always lead to out-of-plane resonance during the transmission process, which commonly happens in helical gears, manifesting as severe vibration at a specific rotational speed. To address this, a shaft–web–ring dynamic model is proposed. The shaft, gear web, and gear ring are modelled based on the Timoshenko straight beam, Mindlin plate, and Timoshenko bent beam theory. Simultaneously, the potential energy caused by the time-varying meshing stiffness is coupled to the gear ring. The kinetic and potential energies of each discretized finite element of the components are derived based on elastic deformation theory, and the governing equations of each element are obtained using Hamilton’s principle. The model is verified through a modal experiment. The comparison with traditional rotor-gear models has demonstrated the significance of gear body flexibility in helical gears with thin webs. The effects of the web thickness and helix angle on dynamic response are studied, revealing that gear web elasticity and an appropriately high helix angle can effectively reduce vibrations at the support bearing, prevent excessive vibrations, and contribute to vibration and noise reduction in the transmission system.

Gear modification, which involves the removal of material from the theoretical surface to improve the contact characteristics of the gear face, is widely applied in gear vibration reduction and noise optimization design. This paper establishes a dynamic model of the straight bevel gear (SBG) transmission system to accurately and efficiently evaluate the effects of different modification strategies on the vibrational characteristics of SBGs. Initially, the time-varying meshing stiffness (TVMS) of standard SBGs was calculated, and methods such as the slicing method and deformation coordination equations were used to calculate the TVMS under tooth profile modification (TPM), Lead crown relief (LCR), and comprehensive modification (CM), which were then validated against finite element method (FEM) calculations. Subsequently, taking into account the impact of time-varying meshing point vectors and the degree of contact overlap, a finite element node dynamic model of the SBG transmission system was established. Finally, by comparing the dynamic characteristics under different modification conditions, the study further elucidates that selecting the appropriate modification method and amount according to different service scenarios is an effective means to suppress gear transmission vibration. This research provides a theoretical basis for the design of gear modification and vibration control for SBGs.

Under high-speed and heavy-load conditions, the influence of temperature on the gear system is extremely important. Basically, the current work on the effect of temperature mostly considers the flash temperature or the overall temperature field to cause expansion at the meshing point and then affects nonlinear factors such as time-varying meshing stiffness, which lead to the deterioration of the dynamic transmission. This work considers the effect of temperature on the material’s elastic modulus and Poisson’s ratio and relates the temperature to the time-varying meshing stiffness. The effects of temperature on the elastic modulus and Poisson’s ratio are expressed as functions and brought into the improved energy method stiffness calculation formula. Then, the dynamic characteristics of the gear system are analyzed. With the bifurcation diagram, phase, Poincaré, and fast Fourier transform plots of the gear system, the influence of temperature on the nonlinear dynamics of the gear system is discussed. The numerical analysis results show that as the temperature increases, the dynamic response of the system in the middle-speed region gradually changes from periodic motion to chaos.