According to the space meshing theory, the mathematics model of conjugate surfaces is constructed. Based on the coordinate transformation of this model, the mathematical solution of the wheel and pinion tooth surfaces is obtained. On the basis of surface synthesis, the construction method of gradient surface (Ease-off) for tooth modification is given. Taking the rotating projection plane of the tooth surface as the coordinate plane, the normal deviation of the modified tooth surface from the conjugate tooth surfaces for pinions is calculated, and the Ease-off surface of the spiral bevel gear is obtained. Based on analysis of the Ease-off surface, the complete contact morphological characteristics of tooth surface are obtained: the contact line-off, contact path, transmission error, etc., which are highly consistent with the actual contact pattern of the tooth surface. The above findings provide an accurate and feasible method for the topology design and meshing simulation of complex tooth surfaces.
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