Abstract: This paper shows that the "grind ability" of curved surface is an important conception. To make clear the grindability of curved surface as the point of departure, in this paper that the curved surfaces with special shape are generally ungrindable is analysed. So they can only be substituted by the approximate curved surfaces ground out, and the key problem is how to. Grind out the approximate curved surfaces satisfying the accuracy grade in engineering fore the required special shaped curved surf aces. In order to slove this problem, the principle of anomalous conjugation is presented in this article. Applying this principle can make the ground approximate curved surfaces substitute the required curved surfaces optimumly. It has been tested and verified that the principle of anomalous conjugation has been applied successfully now in the area for grinding some complex curved surfaces on cutting tools.

Key words: 铲削, 齿面, 共轭, 滚刀, 磨削, 曲面拟合/廓形计算