Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (Ⅰ): Third-order approximation of tool envelope surface  

作　　者：ZHU LiMin1, DING Han2 & XIONG YouLun2 1 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China 2 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China 

出　　处：《Science China(Technological Sciences)》2010年第7期1904-1912,共9页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 50835004, 50775147);the National Basic Research Program of China ("973" Program) (Grant No. 2005CB724103);the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)

摘　　要：In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.

关 键 词：FIVE-AXIS NC machining ROTARY CUTTER CUTTER ENVELOPE surface normal CURVATURE THIRD-ORDER point contact 

分 类 号：TG711[金属学及工艺—刀具与模具]