Article details

Title: The Third Order Development of the Sculptured Surfaces and the Third Order Contact in 5-Axis Machining
Author(s): Huran Liu               

Abstract: In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; the best contact condition between tool and the surfaces was researched. Through analysis, the contact degree of the intersection line of the cutter and the surfaces is known. In comparison to previous studies, the theory of this paper is more restricted going beyond second order parameters into the third order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The research process is very clear: first, suppose that there is a surface of third order, the coefficients of which are arbitrary. Then, find out the best posture of the circle so that the circle and the surface will most closely contact with each other at the origin position. Finally, develop the surface into a 3-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. The equations are easy to solve and clear in concept.

Keywords: surface, contact, NC machining.

[1] S. MIYAZAWA, K. TAKADA – Micro Milling of Three-Dimensional Surface, Journal of the Japan Society of Precision Engineering, Vol. 47, No. 2, pp. 234-239, Feb. 1981 (in Japanese)
[2] T. KISHINAMI, H. SUZUKI, K. SAITO – A Theoretical Analysis of Cutting Speed Components on the Rake Face of Circular Cutting Edge Ball End Mill: A Study of Cutting Mechanism of Circular Cutting Edge Ball End Mill (1st Report), Journal of the Japan Society of Precision Engineering, Vol. 46, No. 10, pp. 1303-1310, Oct. 1980 (in Japanese)
[3] Y. FUJII, H. IWABE – Relationship between Cutting Force Curve and Working Accuracy with Ball-Nose End Mills, Journal of the Japan Society of Precision Engineering, Vol. 48, No. 5, pp. 649-654, May 1982 (in Japanese)