An Inverse Method For Friction Coefficients Of Spur Gears Based On Radial Basis Function

The research on the characteristics and regularity of gear friction is of great significance to reduce tooth surface wear,vibration,noise,improve transmission performance and fatigue life.Friction coefficient is the most important and intuitive parameter in many parameters that characterize tooth surface friction.Based on the radial basis function model and the multi-island genetic algorithm,the tooth surface friction coefficient of the spur gear is inverse.The influence of lubrication state and working parameters on the friction coefficient of tooth surface is analyzed.(1)Geometry model and finite element model of spur gear are established.According to the principle of gear engagement and generating method,the curve equation of tooth profile was obtained.Based on MATLAB and hybrid modeling method of ANSYS/APDL,parameterized modeling of gear was finished and its finite element model is established.Besides that,the tooth root bending stress was calculated.(2)Finite element analysis and measuring of bending strength for spur gear are performed.According to load sharing coefficient of a spur gear pair,load distribution along the line of action was obtained.Tooth deformation along the face width,distribution of tooth bending stress and variation curve of tooth stress in the direction of tooth depth along the line of action were also obtained at uniformly distributed loading.The rotation speed,torque and root strain are measured respectively by the gear test bench with electric-closed loading and LabVIEW.The finite element results of tooth root bending stress are compared with the results of dynamic testing that verified validity of the finite element model.(3)An inverse method for friction coefficient of spur gears based on the radial basis function is developed.Taking latin hypercube method to design experiment and employing radial basis function to establish the agent model.The object function is established by the variables of bending stresses from finite element calculation and experiment results,the friction coefficient in mesh process is inversed baed on multi-island genetic algorithm.To verify the validity of the calculation method,the results is compared with other formulas by published papers.(4)The effects of various parameters on friction coefficient are investigated.Without considering the gear tooth temperature and the transmission errors,the influences of rational speed and torsion on friction coefficient are analyzed.The friction coefficient is calculated and analyzed with lubricant or without lubricant.The effect of speed on the friction coefficient is small and the torque has a great influence on the friction coefficient.The friction coefficient decreases with increasing speed and increases as the torque increases.This is consistent with other researchers’conclusions about the tooth surface friction coefficient.