Calculation methods of load distribution ratio for spiral bevel gear

The tooth strength of spiral bevel gear is compromised with decreased tooth thickness along the cone distance to transfer power between intersected axes. Its stress condition and transmission performance are generally studied by approximating the meshing process as an equivalent spur gear pair. This paper developed a mathematical model to bridge the meshing characteristics of spiral bevel gear and its basic parameters with no approximate simplification in the derivation process. It is constituted with the equations for the calculation of contact ratio, determining the track of contact areas, and describe the primary geometric parameters. The meshing model indicates that the contact profile of the teeth pair is determined by the spiral angle in certain working conditions. The multi-state meshing characteristic and stress condition of spiral bevel gear are analysed by dividing the tooth surface into different meshing regions. A calculation method of load distribution ratio for spiral bevel gear is proposed while two methods are developed for analysis and comparison based on the length of the contact line and the potential energy principle, respectively. They are suitable for different working conditions. The results show that the stability of the spiral bevel gear drive is sensitive to the alternating of the meshing state, which is generally believed only appear in the gear drive with straight teeth. Additionally, an excitation source from the varying length of the contact line has been unveiled exists in the spiral bevel gear drive. The two types of excitations will occur simultaneously in some cases and become apparent with the increase of the meshing stiffness. The distribution law of the load is obtained and illustrated on the tooth surface. It provides a theoretical basis for the dynamic analysis and optimal designs of spiral bevel gear.