自由曲面加工刀具路径轨迹规划算法研究
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摘要
自由曲面零件以其优良的空气动力学、流体动力学和热力学等特性，广泛应用于航空航天、造船、汽车、模具制造等领域。自由曲面造型技术已经比较成熟，但是相对而言，自由曲面的加工技术发展稍显落后，随着多轴联动加工中心的发展，自由曲面的数控编程，作为自由曲面设计和多轴联动加工自由曲面的桥梁，越来越凸显出其重要性，特别是其刀具路径轨迹规划技术研究成为该领域内的一个研究热点和难点。
论文系统地研究了国内外关于自由曲面加工刀具路径轨迹规划的研究进展，以提高自由曲面的表面加工质量和加工效率为目标，对自由曲面加工的刀具路径轨迹规划的若干关键技术进行了深入研究，提出了自由曲面加工的多刀具组合自动优化算法、等弓高误差变步长算法、基于等残余高度线的刀具路径轨迹规划算法和基于关键刀触点提取的样条曲线插补加工刀具路径轨迹生成算法等。
论文的主要研究成果和创新点总结如下：
提出了一种自由曲面加工多刀具组合自动优化算法。改进了遗传算法，为适应自由曲面的主曲率特性，设计了一种新的非线性自适应度函数，给出了新的复制规则，求取自由曲面上的最大主曲率点，以获取满足无曲率干涉加工自由曲面的最大刀具尺寸；提出了自由曲面加工局部干涉区域边界追踪算法，用于曲面分区域划分，然后分区域规划刀具路径轨迹，建立了刀具路径轨迹总长度和刀具尺寸之间的函数关系式，采用遗传算法求取使得加工效率最高的多刀具组合。
提出了一种等弓高误差变步长算法。算法给出了步长范围内弓高误差的计算方法，然后将黄金分割法应用到最大弓高误差的求取和变步长参数点的求取，给出了基于曲率半径符号判别的弓高误差校核方法，避免了弓高误差中点校核法可能的错误判断，最后给出了完整的等弓高误差变步长算法。
提出了一种基于等残余高度线的刀具路径轨迹规划算法。由当前刀具路径轨迹计算等残余高度线，根据等残余高度线计算相邻刀具路径轨迹，循环下去直到结束；给出了计算投影点的Newton-Raphson迭代法和计算等残余高度点、相邻刀具路径轨迹刀位点的Newton迭代法；给出了根据自由曲面在步距方向的曲率半径和刀具尺寸计算迭代角度初值的方法，与二分法相比提高了计算效率；最后给出了完整的算法流程图。
提出了基于关键刀触点提取的样条曲线插补加工刀具路径轨迹生成算法。首先根据离散曲率极值点提取初始关键刀触点，提出了基于偏差分析的多点调整算法，用于确定每次需要新增关键刀触点的个数，然后基于形状指数分析提取出新增关键刀触点；提出了根据提取的所有关键刀触点建立节点矢量的新方法，采用最小二乘法进行B样条曲线逼近；定义了一种新的五轴联动双NURBS样条曲线插补G代码格式，并给出了根据前述刀具路径轨迹规划结果直接生成五轴联动双NURBS样条曲线插补G代码的方法。
Free-form surfaces are widely used in the shipbuilding, automotive, mould, aeronautic andastronautic areas and many other industries for their special functional or aesthetic feature. Comparedwith the maturate free-form surface modeling, free-form surface machining is dropped behind for along time. As a bridge built between the free-form surface designing and machining, NC program offree-form surface is becoming more and more important with the development of multi-axismachining center. As key technology of NC program, tool path planning of free-form surfacemachining is a research hotspot and difficulty in this field.
According to the research progress at home and abroad in the field of tool path planning forfree-form surface machining, key technologies of tool path planning for free-form surface machiningare studied and implemented aiming at improving the machining efficiency and quality. Severalalgorithms are proposed, including the algorithm of automatic optimum of multi-cutters combinationfor free-form surface machining, the algorithm of variable forward step with constant chord error intool path planning, the tool path planning algorithm based on constant scallop curve(CSC) forfree-form surface machining, and the algorithm of tool path planning for spline curve interpolationbased on the selection of key cutter contact (CC) points.
A new algorithm of automatic optimum of multi-cutters combination is proposed. After a novelnon-linear automatic fitness function is designed according to the feature of the principal curvature,and new selection rules of the units to be copied are given, the maximum principal curvature of thefree-form surface is calculated by the new proposed improved genetic algorithm(IGA). The biggestcutter to machining the free-form surface with no curvature interference is selected according to theglobal maximum principal curvature. New interference area boundary tracing algorithm is proposed toclassify the free-form surface into different areas. Tool paths are generated in different areas withdifferent cutter, so the function can be constructed according to the total tool path length and the cuttersize. The optimal combination of multi-cutters are solved by using the genetic algorithm (GA). Themaximum of machining efficiency and avoidance of curvature interference are realized.
A new algorithm of variable forward step with constant chord error in tool path planning isproposed. Calculation method of the chord error in forward step is proposed. Golden section methodis applied to calculate the maximum chord error and the parameter in every variable forward step.New method of chord error verification based on the sign of the curvature radius is presented to avoidthe wrong verification with mid-point verification method. Full description of the algorithm ofvariable forward step with constant chord error is given at last.
A new kind of CSC algorithm for free-form surface machining is proposed. The constant scallopcurve is calculated according to the current CC path and the next CC path is calculated according tothe constant scallop curve. This processes are repeated until the free-form surface is covered entirelywith tool paths. Newton-Raphson iterative algorithm to calculate the projection point and the Newtoniterative algorithm to calculate the constant scallop point and the cutter location point are proposed.Calculation method of the initial angle to calculate the side step according to the curvature radius andthe cutter size is presented to improve the calculation efficiency compared that of bisection method.Full description of CSC algorithm is given at last.
A new algorithm of tool path planning for spline curve interpolation based on the selection of keycutter contact (CC) points is proposed. The initial key points are selected according to the discretecurvature extrema, and the new key points are selected by the analysis of shape index. Number of thenew key points to be added is identified according to the proposed multi-point adjusting algorithmbased on the calculated deviation. The knot vectors are constructed according to the selected keypoints and the corresponding parameters, and least-square method is employed to approximate the CCpoints with least number of control points within the tolerance requirement by the new proposedalgorithm. A new kind of double NURBS curve interpolation G code is defined, and the method togenerate the double NURBS curve interpolation G code from the tool path directly is proposed.
论文系统地研究了国内外关于自由曲面加工刀具路径轨迹规划的研究进展，以提高自由曲面的表面加工质量和加工效率为目标，对自由曲面加工的刀具路径轨迹规划的若干关键技术进行了深入研究，提出了自由曲面加工的多刀具组合自动优化算法、等弓高误差变步长算法、基于等残余高度线的刀具路径轨迹规划算法和基于关键刀触点提取的样条曲线插补加工刀具路径轨迹生成算法等。
论文的主要研究成果和创新点总结如下：
提出了一种自由曲面加工多刀具组合自动优化算法。改进了遗传算法，为适应自由曲面的主曲率特性，设计了一种新的非线性自适应度函数，给出了新的复制规则，求取自由曲面上的最大主曲率点，以获取满足无曲率干涉加工自由曲面的最大刀具尺寸；提出了自由曲面加工局部干涉区域边界追踪算法，用于曲面分区域划分，然后分区域规划刀具路径轨迹，建立了刀具路径轨迹总长度和刀具尺寸之间的函数关系式，采用遗传算法求取使得加工效率最高的多刀具组合。
提出了一种等弓高误差变步长算法。算法给出了步长范围内弓高误差的计算方法，然后将黄金分割法应用到最大弓高误差的求取和变步长参数点的求取，给出了基于曲率半径符号判别的弓高误差校核方法，避免了弓高误差中点校核法可能的错误判断，最后给出了完整的等弓高误差变步长算法。
提出了一种基于等残余高度线的刀具路径轨迹规划算法。由当前刀具路径轨迹计算等残余高度线，根据等残余高度线计算相邻刀具路径轨迹，循环下去直到结束；给出了计算投影点的Newton-Raphson迭代法和计算等残余高度点、相邻刀具路径轨迹刀位点的Newton迭代法；给出了根据自由曲面在步距方向的曲率半径和刀具尺寸计算迭代角度初值的方法，与二分法相比提高了计算效率；最后给出了完整的算法流程图。
提出了基于关键刀触点提取的样条曲线插补加工刀具路径轨迹生成算法。首先根据离散曲率极值点提取初始关键刀触点，提出了基于偏差分析的多点调整算法，用于确定每次需要新增关键刀触点的个数，然后基于形状指数分析提取出新增关键刀触点；提出了根据提取的所有关键刀触点建立节点矢量的新方法，采用最小二乘法进行B样条曲线逼近；定义了一种新的五轴联动双NURBS样条曲线插补G代码格式，并给出了根据前述刀具路径轨迹规划结果直接生成五轴联动双NURBS样条曲线插补G代码的方法。
Free-form surfaces are widely used in the shipbuilding, automotive, mould, aeronautic andastronautic areas and many other industries for their special functional or aesthetic feature. Comparedwith the maturate free-form surface modeling, free-form surface machining is dropped behind for along time. As a bridge built between the free-form surface designing and machining, NC program offree-form surface is becoming more and more important with the development of multi-axismachining center. As key technology of NC program, tool path planning of free-form surfacemachining is a research hotspot and difficulty in this field.
According to the research progress at home and abroad in the field of tool path planning forfree-form surface machining, key technologies of tool path planning for free-form surface machiningare studied and implemented aiming at improving the machining efficiency and quality. Severalalgorithms are proposed, including the algorithm of automatic optimum of multi-cutters combinationfor free-form surface machining, the algorithm of variable forward step with constant chord error intool path planning, the tool path planning algorithm based on constant scallop curve(CSC) forfree-form surface machining, and the algorithm of tool path planning for spline curve interpolationbased on the selection of key cutter contact (CC) points.
A new algorithm of automatic optimum of multi-cutters combination is proposed. After a novelnon-linear automatic fitness function is designed according to the feature of the principal curvature,and new selection rules of the units to be copied are given, the maximum principal curvature of thefree-form surface is calculated by the new proposed improved genetic algorithm(IGA). The biggestcutter to machining the free-form surface with no curvature interference is selected according to theglobal maximum principal curvature. New interference area boundary tracing algorithm is proposed toclassify the free-form surface into different areas. Tool paths are generated in different areas withdifferent cutter, so the function can be constructed according to the total tool path length and the cuttersize. The optimal combination of multi-cutters are solved by using the genetic algorithm (GA). Themaximum of machining efficiency and avoidance of curvature interference are realized.
A new algorithm of variable forward step with constant chord error in tool path planning isproposed. Calculation method of the chord error in forward step is proposed. Golden section methodis applied to calculate the maximum chord error and the parameter in every variable forward step.New method of chord error verification based on the sign of the curvature radius is presented to avoidthe wrong verification with mid-point verification method. Full description of the algorithm ofvariable forward step with constant chord error is given at last.
A new kind of CSC algorithm for free-form surface machining is proposed. The constant scallopcurve is calculated according to the current CC path and the next CC path is calculated according tothe constant scallop curve. This processes are repeated until the free-form surface is covered entirelywith tool paths. Newton-Raphson iterative algorithm to calculate the projection point and the Newtoniterative algorithm to calculate the constant scallop point and the cutter location point are proposed.Calculation method of the initial angle to calculate the side step according to the curvature radius andthe cutter size is presented to improve the calculation efficiency compared that of bisection method.Full description of CSC algorithm is given at last.
A new algorithm of tool path planning for spline curve interpolation based on the selection of keycutter contact (CC) points is proposed. The initial key points are selected according to the discretecurvature extrema, and the new key points are selected by the analysis of shape index. Number of thenew key points to be added is identified according to the proposed multi-point adjusting algorithmbased on the calculated deviation. The knot vectors are constructed according to the selected keypoints and the corresponding parameters, and least-square method is employed to approximate the CCpoints with least number of control points within the tolerance requirement by the new proposedalgorithm. A new kind of double NURBS curve interpolation G code is defined, and the method togenerate the double NURBS curve interpolation G code from the tool path directly is proposed.
引文
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