Abstract:
As contact line solved by analytic method is difficult to be parameterized in 3-D design software, it has not been applied in 3-D modeling for helical groove of rotary solid tools. A geometric method based on limit thought to get contact line in grinding tool helical groove is proposed. First, the mathematical principle of the geometric method is addressed, and then the derived conditional equation based on limit thought for conjugate surfaces is compared to equation derived based on envelope principle. The result show that the two equations are completely the same in form validates the reliability of the geometric method to solve contact line. Moreover, the concrete implementation steps of the new method are stated. At last, through an example of 3-D modeling a flat end mill with four teeth, the application of the limit geometric method to solve contact line in grinding helical groove is illustrated. Based on the conjugation theory of space surface, the vector relation of gear cutting is ensured