等弓高误差变步长算法求取刀触点的优化

2018-09-21

作者：丁鹏，杜娟，刘鹏程，白晏霏单位：太原科技大学

摘要：传统的等弓高误差是假设步长内所有点的曲率半径相等，然后根据已知刀触点的曲率半径来求取步长，得到下一个刀触点。但由于曲线的曲率在不断变化，所以传统方法得到的刀触点可能会超出弓高允许误差或取得保守，在拐点附近的刀触点更会出现严重失真问题。为了解决传统的等弓高误差的缺点，本文将在此基础上进行改进，提出了新的方法，通过迭代计算，直到实际弦高逼近弓高误差，实现真正意义上的等弓高变步长。校核时运用了几何关系，求出的实际弓高误差更精确，进一步缩小了误差。最后通过MATLAB进行验证，得出算法的可靠性。

关键词：刀触点；等弓高误差；变步长

中图分类号：TG707；TH161文献标志码：A

Optimization of CutterContact Point by Variable Forward Step Algorithmwith Constant Chord Error

Ding Peng，Du Juan，Liu Pengcheng，Bai Yanfei

Abstract:The traditional constant chord error error is that assuming that the curvature radius of all the points in the step are equal，then the step length is obtained according to the radius of curvature of the known cuttercontact point，and then the next cuttercontact point is obtained.However，as the curvature of the curve is constantly changing，cuttercontact point obtained by the conventional method may exceed allowable bow tolerances or are conservative，resulting in serious distortion problems at the cuttercontact point near the inflection point.In order to solve the traditional shortcomings of constant chord error，this article will be based on this improvement，proposed a new method，iterative calculation，until the actual chord height close to the chord error，to achieve the true sense of the constant chord error of forward step.The geometric relationship was used in the verification，and the actual bow height error was found to be more accurate，further reducing the error.Finally verified by MATLAB，coming to the reliability of the algorithm.

Keywords:cuttercontact point；constant chord error；forward step