A mathematical model for the evaluation of conically tapered parts

This paper mainly defines and solves minimum circumscribed and maximum inscribed cones which are used to evaluate the contact surface of conically tapered parts. The optimal model of the minimum circumscribed cone employs the concept of the minimum volume cone, and the maximum inscribed cone uses the maximum volume cone. Examples are given to verify that the model is admissible and reliable. The results show that the optimization procedures presented in this paper provide exact values of minimum circumscribed and maximum inscribed cones. The mathematical model is superior to the existing method in terms of computation time in material processing and mechanical assembly.