Dynamic stability analysis of hemispherical bevel gear system

The stability of hemispherical bevel gear is one of the important factors to be considered in the design of gear transmission system. The stability of hemispherical bevel gears is evaluated by the degree of coincidence.

The coincidence degree of the hemispherical bevel gear is characterized by the joint meshing time of the two adjacent teeth. The simulation result data of the joint meshing time of the two adjacent teeth of the hemispherical bevel gear pair is shown in the table.

Axis intersection angle/(°)	Diameter 30 mm	Diameter 45 mm	Diameter 60 mm	Diameter 75 mm	Diameter 90 mm	Diameter 120 mm	Diameter 150 mm
50	0.008	0.013	0.019	0.030	0.046	0.064	0.116
55	0.004	0.007	0.014	0.014	0.014	0.068	0.112
60	0.004	0.003	0.009	0.017	0.030	0.071	0.112
65	0.003	0.003	0.005	0.013	0.024	0.069	0.103
70	0.003	0.003	0.004	0.008	0.020	0.067	0.096
75	0.003	0.003	0.003	0.005	0.015	0.061	0.061
80	0.002	0.002	0.003	0.003	0.012	0.057	0.060

The fitting analysis of the data results shows that the surface fitting of the joint meshing time length of two adjacent teeth under a certain load is as shown in the figure.

The curve fitting formula for the length of the joint meshing of two adjacent teeth on the tooth surface of the hemispherical bevel gear is:

It can be seen from the figure that the meshing time of the two adjacent teeth is greater than 0, and with the increase of the angle of the intersecting axis of the hemispherical bevel gear pair, the meshing time of the two adjacent teeth decreases slightly and then increases; With the increase of the pitch radius of the hemispherical bevel gear, the meshing time of the two adjacent teeth shows a gradual decline, especially when the angle of intersection is greater than 90 °. It can be seen from the analysis diagram that the hemispherical bevel gear is in continuous meshing motion, and the coincidence degree is greater than 1. With the increase of the intersection angle of the secondary shaft of the hemispherical bevel gear, the coincidence degree of the hemispherical bevel gear decreases slightly at first and then increases gradually; With the increase of the pitch diameter of the hemispherical bevel gear, the coincidence degree of the hemispherical bevel gear decreases gradually.