Abstract: Self-intersect curve is often existent in the profile of forming cutter computed by the helicoid with cusp, which leads to form the big size of transition surface at the location of cusp of the helicoid processed by the cutter. Therefore, a method of discreting the cusp vector is proposed. It firstly defines a point and its normal vector as “point vector”, and discrete the two point vectors formed by the two intersection curves at the location of cusp, which brings more information of the cusp into the computation process of profile for the accuracy improvement. Then, an algorithm for the minimization of transition surface is put forward. The discrete cusp vectors and the four point vectors on the cusp sides are used to compute the points which forming the profile of cutter. The cusp of the cutter and other four nearby points are obtained after the self-intersect is eliminated, which are used in the inverse calculation to gain the transition surface. The evaluation standard of transition surface is developed to optimize the installation angle of cutter within a certain range aiming at the minimization of transition surface. At last, the method is applied in the relief grinding for the double circular-arc gear hob. The actual processing result verifies that the method is helpful to reduce the size of transition surface effectively and also applicable to optimize the forming processing of helicoid with cusp.

Key words: Cusp, Form grinding, Grinding wheel, Helicoid, Optimization, Transitional surface