等间距法直线逼近非圆曲线的误差控制

Error Control on Equidistant Interpolation of Linear Approximation Non-circle Curve

非圆曲线轮廓是机械零件常见的轮廓要素之一,绝大多数数控机床只具备直线插补和圆弧插补功能。因此,在这些数控机床上加工非圆曲线只能用很多直线段或圆弧段来逼近非圆曲线,其中直线逼近法中的等间距法由于数学处理简单而被编程人员广泛采用。但是对于如何合理地确定间距的大小,很多编程人员往往采用经验法或估算法,结果不是加工精度达不到要求就是节点太多而使加工时间过长。本文从数学的角度详细地介绍了如何根据编程允差合理地确定间距的一种新方法。

Non-circle curve is one of familiar outlines, but most numerical control machine tools only have linear interpolation and circular interpolation. Therefore, non-circle curve only can be machined on the machine by linear approximation or circular approximation. Equidistant interpolation of the linear approximation is widely adopted by programmers because of simple data processing. But the problem perplexing the programmers is how to determine the size of step. Many programmers usually depend on their experience or estimation, As a result, the machining error is bigger than tolerance error or machining time is long because of too much nodes, the paper introduces in detail a new approach to determine step size properly from mathematical point of view.