# Analysis of influence law of contact characteristics and control parameters of spiral bevel gear

It can be seen from the figure that with the increase of the inclination angle of the large and small wheel cutters of the spiral bevel gear, the length of the instantaneous contact ellipse on the concave and convex sides of the spiral bevel gear is significantly shortened, and the amplitude of the transmission error is significantly increased. The inclination angle of the large wheel cutter of spiral bevel gear has a great influence on the diagonal direction of the contact area, and the inclination angle of the small wheel cutter of spiral bevel gear has a small influence. With the change of the curvature of the cutting edge of the large and small wheels, the diagonal direction of the contact area on the concave and convex sides of the spiral bevel gear and the amplitude of the transmission error change obviously. The blade curvature increases in the positive direction, the diagonal direction and transmission error amplitude increase, the blade curvature increases in the negative direction, and the transmission error amplitude in the diagonal direction decreases. The blade curvature of the large wheel of spiral bevel gear has a great influence on the length of the instantaneous contact ellipse, and the blade curvature of the small wheel of spiral bevel gear has little influence. With the change of the number of teeth of the small wheel, the shape of the contact area does not change obviously, but the shape of the transmission error curve changes; The number of teeth of spiral bevel gear is reduced, and the point with transmission error of 0 is offset to the tooth root; The number of teeth of spiral bevel gear pinion increases, and the point with transmission error of 0 is offset to the tooth top. The above analysis shows that:

(1) The end face hobbing method of spiral bevel gear adopts the double-sided cutter head to process the concave convex two tooth surfaces at the same time, and the cutter inclination affects the contact state of the two tooth surfaces at the same time. The length of the contact area of the concave convex two surfaces cannot be specified at will, but basically the same value should be specified.

(2) The length of contact area, the diagonal direction of contact area and the amplitude of transmission error restrict each other. When choosing a smaller length of contact area and a larger diagonal direction of contact area, the amplitude of transmission error should also choose a larger value.

(3) Among the seven control parameters, the change of the number of teeth of spiral bevel gear has little effect on the curvature parameters of tooth surface contact reference point. The influence of the inclination angle of the large and small wheel cutters and the blade curvature parameters of the paired tooth surface machining cutters on the characteristics of the contact area is basically the same.

Therefore, there are not enough effective independent variables in the above six nonlinear equations constructed by the curvature parameters of the concave convex contact reference points of the spiral bevel gear pinion, which belong to the overdetermined equations and cannot be solved directly. The optimization method can be used to take the inclination angle of large and small wheel cutters and the curvature of large and small wheel blades of spiral bevel gears as independent variables to solve the approximate solution.

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