Stress And Strain Analysis In Hyperboloidal-type Normal Circular-arc Gears Using Finite Element Method

Hyperboloidal-type normal circular-arc gear(HNCG)is a latest transmission by expending the application of circular-arc tooth profile into the gear transmission with cross axes.It inherits the advantages of conventional W-N gear with parallel axes,and has the following special advantages in the cross-axis gear transmission: higher contact ratio,lower sensitivity to error,larger range of gear ratio,and so on.The meshing principle of HNCGs,the design criteria of tooth profile and the processing technology had been solved in the past study,and the conclusions presented a theoretical basis for further research.For this novel gear,which still lies at the state of theory research,its transmission performances,such as carrying capacity,vibration properties and service life,have a direct impact on its potential application,and the stress and strain of gear teeth under load are important factors to determine the transmission performance.In order to reveal the relationship between the stress/strain of HNCGs and the design parameters of gear pair,based on constructing the tooth profile with point contact,the variation rules of stress and strain of gear teeth in HNCGs had been explored by using the finite element method,which provides the guidance for the optimizationdesign and the health diagnostics of HNCGs.The main works of this paper include:(1)On the direction of the transmission principle of HNCGs,the design method of HNCGs with point contact were presented based on the mismatched theory of teeth,the vector radius of the directrix of the tooth surface was deduced,and the complete equation of the tooth surface was determined.The geometric characteristics of tooth surface in HNCGs were analyzed,and the induced curvature of conjugate tooth surfaces was calculated.(2)Based on Hertz contact theory,the instantaneous contact area and the instantaneous load of acting teeth were determined,and the formula of theoretical contact stress was deduced.The solution of finite element model of HNCGs was conducted,and its results was compared with the theoretical contact stress to verify the feasibility of the finite element method.(3)The relative sliding of acting teeth was analyzed by the considerations of the tooth surface and the directrix of tooth surface,respectively,and the directrix-based equation of sliding rate was deduced.Using numerical computation,the rules of the sliding rate were explored,and the sliding characteristics of HNCGs were analyzed.(4)Considering the influences of the tooth number,modulus,the radius difference of tooth profiles,the pressure angle and the radius of fillet arc at the root of pinion,the contact stress and the strain of gear pairs at different meshing positions under load and constraint were calculated using finite element method,and the influences of these design parameters on the stress and strain of gear teeth in the meshing cycle were analyzed.In summary,using accurate finite element models of HNCGs,the relationships between the main design parameters and the stress and strain of gear teeth were studied.This work presents an important theoretical basis for the optimal design and the health diagnostics ofhyperboloidal-type normal circular-arc gears.