数控技术中曲线曲面算法.docx

曲线、曲面的等距算法及其在数控加工中的应用 摘要：主要的传统插补算法(直线、圆弧插补)已经越来越不能满足现代高速高精加工的需求,本文通过对数控加工的研究,发现数控插补算法是制约高速AO精加工的关键因素,NURBS曲线能统一地表达自山曲线曲面和解析曲线曲面,其直接插补能避免传统插补算法的很多问题,有效解决插补算法与现代高速高精加丁的矛盾。推导了NURBS曲线、曲面的各阶导矢、等距曲线曲面的各阶导矢及其曲率的计算公式,分析了参数曲线曲面线性插值误差,讨论了插值等距曲线曲面上点的采样原则,B样条形式表达的插值曲线曲面的求解方式以及减少B样条形式表达的插值曲线曲面的数据冗余的方法, 并将上述理论应用于两轴联动行切加工的刀位计算。 关键字：数控技术;五轴联动;NURBS曲线插补;NURBS曲线曲面;等距曲线曲面;误差分析;数控加工 Abstract: the main traditional interpolation algorithms ( linear, circularinterpolation ) cant meet the modern high speed and high precision machiningrequirements more and more.Based on the CNC machining research, we find that thekey factors to restrict high speed and high precision machining is the interpolationalgorithm. NURBS curve can express the free-form curve and surface, and analyticcurve and surface by uniform. Based on the fact that NURBS curve directlyinterpolation technology can avoid traditional interpolation algorithm for manyproblems, it can effectively solve the contradictory between the interpolationalgorithm and modern high speed and high precision machining. Derived NURBS curves and surfaces of each order derivative vector, offset curves and surfaces of the first derivative of the curvature vector and its formula, parametric curves and surfaces analyzed linear interpolation error is discussed interpolation points on curves and surfaces equidistant sampling principles, expressed in the form of B-spline curves and surfaces to solve the interpolation methods and reduce the expression of B-spline interpolation of curves and surfaces in the form of data redundancy method, and the theory is applied to two-axis machining tool knife-bit computing. 1.绪论 数控技术是支持现代装备制造业的关键性技术，决定着制造装备的功能和性能。其中，参数曲线、参数曲面插补是现代数控系统的标志性功能。作为数控技术的核心，插补技术尤其是参数曲线、参数曲面插补及加减速控制算法的运算精度和速度对现代数控系统性能优劣起着决定性作用。本文就这两方面问题进行深入的理论和应用研究。 以一、二阶泰勒展开式参数曲线插补算法和平面参数曲线插补算法研究为基础，提出引入误差补偿值的复杂空间参数曲线高精度插补算法以实现空间曲线的高精度插补。通过引入误差补偿值以提高参数曲线插补点的求解精度，在求解过程中对误差补偿值进行合理简化以降低插补计算量。Nurbs曲线仿真实例证明在满足实时性的前提下，该算法所计算的插补点参数值误差精度有明显提高。 在对参数线法加工曲面研究的基础上，提出引入误差补偿值的