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.
ZHU LiMin1, DING Han2 & XIONG YouLun2 1 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
Based on the mathematical model describing the third-order approximation of the cutter envelope surface according to one given cutter location(CL),a tool positioning strategy is proposed for efficiently machining free-form surfaces with non-ball-end cutters.The optimal CL is obtained by adjusting the inclination and tilt angles of the cutter until its envelope surface and the design surface have the third-order contact at the cutter contact(CC)point,which results in a wide machining strip.The strategy can handle the constraints of machine joint angle limits,global collision avoidance and tool path smoothness in a nature way,and can be applied to general rotary cutters and complex surfaces.Numerical examples demonstrate that the third-order point contact approach can improve the machining strip width greatly as compared with the recently reported second-order one.
ZHU LiMin 1 ,DING Han 2 &XIONG YouLun 2 1State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University,Shanghai 200240,China
