中文摘要：

针对五坐标数控加工中刀位误差计算效率较低的问题,提出了一种基于包络原理的刀位误差快速计算方法。首先,通过描述刀位误差与最短距离线段的关系建立两者的关系式。其次,将工件曲面沿进给方向离散成若干条截型线,基于包络原理推导出工件曲面截型线到刀具曲面的距离最短点应满足的基本方程,通过求解该方程获得最短距离线段和刀位误差,建立误差分布曲线。最后,分析了W形和V形误差分布曲线的特点,对曲面截型线离散精度的确定方法进行了研究。在此基础上,设计了计算流程,开发了计算程序,算例结果表明：所提方法与原方法相比,计算效率有了很大的提高。

英文摘要：

In order to improve the low calculation efficiency of tool position error in the programming of 5-axis numerical control（NC） machining,a quick calculation method of tool position error based on envelope theory is proposed.First,a relationship equation is established between the shortest distance line and the tool position error.Then,the workpiece surface is discretized into a number of sectional curves along the feed direction.With the tangent condition of the envelope theory,another basic equation is presented to calculate the shortest distances between the tool surface and the workpiece surface sectional curves.The shortest distance line and tool position error can be obtained through the equation.Then the error distribution curves can be established.Finally,the problem of surface sectional curve discretization is studied through analyzing the characteristics of different error distribution curves.On this basis,calculation flows are designed,and programs developed.Calculation examples are given in this paper in which the calculation efficiency of the new method is compared with that of the previous method.It is shown that the new method can greatly improve the calculation efficiency of the shortest distance pair.