中文摘要：

针对球头铣刀三维曲面加工，提出一种考虑进给方向和刀具切触界面任意变化的铣削力预报方法。基于微分的思想，将曲面加工中单个齿频周期内的切削过程看成是切削条件恒定的微小稳态加工，进而将整个三维曲面加工视为一系列微小稳态加工的组合。根据各微小稳态加工的始、末刀位点坐标，建立进给转向角和进给倾斜角模型，刀具切触界面应用基于逻辑数组的Zmap方法确定，并修改了未变形切屑厚度模型的参数，使其适应三维曲面加工中刀具切触界面和进给方向的任意变化。分别进行凸圆弧曲面、凹圆弧曲面和自由曲面三个铣削加工试验，数值计算及试验测量结果表明，提出的方法能够很好地描述曲面加工中进给方向及刀具切触界面的变化，预报的铣削力和试验测量结果在幅值和变化趋势上都吻合良好，从而验证了该铣削力预报方法的有效性。

英文摘要：

An approach of milling force prediction for ball-end milling of 3D curved surfaces is presented. Based on the idea of differential, in one tooth period the cutting process of curved surface machining is considered as steady-state cut, in this case the whole process of curved surfaces machining can be treated as combination of small steady-state cuts. According to the coordinates of start/end cutter position of each small cut, the mathematical models of feed turning angle and feed inclination angle, which are taken to characterize feed direction, are proposedl The cutter engagement area is determined by a logical array based Zmap method. In addition, the parameter of undeformed chip thickness model is modified for fitting the variation of feed direction and cutter engagement in 3D curved surfaces machining. Three experiments for ball-end milling of convex arc surface, concave arc surface and freeform surface machining are operated. The results of numerical and experiments show that the feed direction and cutter engagement can be described well, and the predicted cutting forces are according with the measurements both in magnitude and in variation trend. Thus, the validity of proposed approach is confirmed.