For, pitch curve is circular, and each tooth is the same. During machining, the starting position of the gear blank to be cut can be any position, and the rotation angle is also fixed. The four degrees of freedom are: the axial movement and rotation of the milling cutter head, and the axial movement of the wheel blank to be cut. For non-circular bevel gears, the pitch curve is a special curve on the spherical surface, and each tooth is different in each cycle (for example, Fig. 1 shows a pair of pitch curves of meshed non bevel gears, the transmission ratio is a sinusoidal periodic curve, and Fig. 2 is a non-circular spur bevel gear) In addition, the instantaneous transmission ratio is different during transmission. Therefore, the starting position, rotation angle and rotation speed of each tooth of the wheel blank to be cut are different. The instantaneous positions of the wheel blank and the cutter need to be accurately calculated according to the pure rolling principle of the two pitch curves. Therefore, the processing method is much more complicated, and the relevant contents have not been found yet.
In theory, it needs five axis machine tool to complete: in addition to the axial (z) movement and rotation around the axis of the milling cutter head, it also needs the lateral (x) and longitudinal (y) movement, as well as the rotation of the wheel blank to be cut and the rotation caused by the change of pitch cone angle. If the pitch curve of non bevel gear is known, the machining method can be obtained according to the meshing principle.
Therefore, a series of real-time milling cutter head positions Xi, Yi, Zi and the axle angle α I and the shaft rotation angle φ I of the wheel blank to be cut are obtained. The pitch cone angle minus the root cone angle is the angle of the wheel axle when the cutting wheel blank is processed. According to these parameters, the movement coordination of the five axis machine tool in each degree of freedom is controlled to achieve the purpose of correctly machining the designed noncircular bevel gear.
In addition, the initial position, end position and each position of the middle interval step of each tooth should be calculated. Therefore, the processing parameters of non-circular bevel gear with spiral tooth should be obtained according to the spiral angle of spiral tooth.