Accurate Modeling Of Helical Bevel Gear And Calculation Of Initial Value

Spiral bevel gears have been widely used in automobiles, aircraft, and other industrial fields because of transmission stability and large carrying capacity. At present, the transmission quality, machining efficiency and precision of the demand is higher and higher, therefore, the in-depth study on the spiral bevel gears has some practical value in engineering. This paper introduced the model of spiral bevel gears and studied the calculation method of the initial value in tooth contact analysis, mainly includes the following aspects:(1) Calculation of pinions’ machine tool adjustment parametersFor a given gear’s machine tool adjustment parameters, a point is selected to meet the central point of contact ratio on the big gear, then pinion gear tooth surface curvature and the main direction is solved. Pinion is generated by the method of FG, the local synthesis method is used to calculate its machine tool adjustment parameters.(2) Derivation of the mathematical equation of tooth surfaceBased on the generative principle of spiral bevel gear, format was carried out on the right-hand gear, left-handed pinion is used by Generated. Parabolic cutting tools are applied for gear, and linear for pinion. Mathematical model of cutting tool(including blade edge) is established, through the homogeneous coordinate transformation based on space meshing theory, using the calculation of cutter and machine tool adjustment parameters, tooth surface equation of gear and pinion is derived(3) Setting up the entity modelThe tooth surface boundary is determined in the plane of gear shaft,coordinate transform and matrix is applied in MATLAB software. Tooth surface concave and convex data points are get by solving the nonlinear equations, and imported through a certain format into Pro/E, then the model of spiral bevel gear is established by using rich surface modeling function in Pro/E.(4) The calculation method of the initial valueA new method of calculating initial value is put forward, the points of toothsurface are dispersed into points of the cutting tool. Considering both matching points minimum distance and minimum tooth surface deviation factor, a weighted factor is applied, contact points under different weighted factor are given, and gear tooth surface contact trajectory and the motion error of curve is given.