数控机床NURBS曲线插补轮廓误差自动控制

针对伺服滞后对高速高精度数控系统加工精度的影响,在圆弧插补时对工件轮廓误差进行理论分析,在此基础上设计了一种NURBS曲线插补轮廓误差自动控制算法,该算法能简化计算,提高数控系统插补计算的实时性.在给定轮廓误差的条件下对算法进行仿真.仿真结果显示,该算法能有效的根据NURBS曲线的曲率半径实时获取适当的进给速率以控制实际轮廓误差,控制效果比较好,可有效减小数控机床NURBS曲线插补的轮廓误差.     

高档数控机床NURBS曲线Newton Rapson迭代的插补算法

为了解决NURBS曲线在Taylor一阶、二阶展开式求解曲线插补坐标点ui+1,存在计算量大、插补时间长等问题,提出一种Newton-Rapson迭代法的NURBS插补算法。该插补算法可以减少插补计算量和插补时间,提高插补精度,并提高曲线加工的效率。仿真实验结果表明,Newton-Rapson迭代法的NURBS插补算法计算过程简单、切实有效,具有可行性和实用性,满足数控系统实时、高速、高效率插补的要求,在其他数控插补的过程中具有很强的借鉴意义。     

基于NURBS曲线的扩径头模块插补算法

在分析三次非均匀有理B样条(NURBS)曲线原理的基础上,提出了NURBS曲线的实时插补算法.该算法通过插补预处理以及合理的近似计算,大大减小了插补计算的时间;并且列出了插补误差和进给步长自适应控制,从而实现高速高精度插补加工.     

椭圆曲线回转类零件NURBS插补算法研究

针对激光熔覆加工中椭圆曲线回转类零件,提出了利用NURBS曲线直接对椭圆曲线零件拟合、插补的算法。在NURBS曲线建模的理论基础上,利用一阶泰勒展开式对插补点进行迭代运算,结合可控弓高误差插补理论,对刀轨曲线进给速度进行了规划。插补加工实例说明,对于椭圆曲线回转类零件,所提出方法满足加工精度要求,达到了预期的加工目标。     

基于牛顿迭代法的NURBS曲线插补算法

通过分析数控机床加工中样条曲线插补原理,提出了一种基于牛顿迭代法的非均匀有理B样条(NURBS)曲线插补算法.该算法首先进行速度控制,保证了加工精度,然后利用牛顿迭代法来计算插补参数,避免了传统方法的大量求导运算.通过将二阶泰勒展开式化成简单的线性递推方程来预测插补参数的迭代初值,进一步减小了运算开销.仿真对比实验表明,该算法稳定性好,运算精度高,能够满足实时插补的要求,且能够将实时插补产生的速度波动限制到理想的水平.     

NURBS曲线插补算法及加减速控制研究

针对复杂零件高速高精密加工的需求,提出了一种基于阿当姆斯微分方程的NURBS曲线实时插补算法。通过对算法的合理简化与近似,保证了算法的实时性。此算法基于轮廓误差和法向进给加速度控制,使进给速度能随曲线曲率自适应调整。与之相适应,配合此插补算法,利用NURBS曲线的对称性预测减速点,提出了一种新的插补前抛物线-直线-抛物线S形加减速控制方法。该方法具有位置精度高、速度无突变、过渡平滑、计算简便等优点。通过采用MATLAB对插补轨迹仿真和实例分析,证明了插补算法和加减速控制方法的正确、合理、有效性。     

NURBS曲线插补的运动规划与自适应速度插补

文章整合了以基于曲率速度插补算法与自适应速度插补规划算法,分析了NURBS曲线的特点和NURBS曲线插补的参数值的求取方法;构建了基于曲线几何特性与动力学特征插补器,几何模块提出如何决定NURBS曲线的速度尖点,并根据速度尖点信息将NURBS曲线划分为曲线段,依据弓高误差及曲线曲率规划进给速度;机床动力学模块依据每段曲线长度对加加速度控制,对于每段曲线采取相应的加减速控制规划,实现了基于S形速度曲线的加速度平滑处理,与传统插补方法相比,该插补器能够保持高速度和高精度加工性能,而且能够抑制在插补过程当中产生的轮廓误差和速度波动.     

基于FPGA的NURBS曲线插补设计与实现

基于现场可编程门阵列(FPGA),以Cox-de Boor递推插补算法为基础,对NURBS曲线插补的FPGA实现方法做了深入探究。将基于Cox-de Boor的NURBS曲线插补映射到FPGA中实现,同时注重并行处理和流水线等基本设计技巧,相比基于PC或者DSP结构的串行计算,极大地提高了NURBS插补的运算速度。在不改变算法结构的前提下,该方法也可用于B样条曲线和Bezier曲线。仿真和实验结果表明,利用FPGA可显著改善NURBS插补的运算速度。     

基于NURBS插补算法的汽轮机叶片数控加工

为了提高汽轮机叶片的加工精度,文章通过分析汽轮机叶片的结构特点,采用一种NURBS曲线插补算法对其进行插补仿真。文章所采用算法由两部分组成:速度规划和参数计算。首先速度规划采用简化的五段S曲线加减速控制方法,保证了叶片在高速加工过程中加速度的连续,使机床运行平稳,然后利用牛顿迭代法来计算插补参数,得到更精确的插补参数,进一步提高了叶片的加工精度和加工速度。汽轮机叶片的插补仿真表明,该算法有高的稳定性和运算精度,并且使机床振动减小,速度波动小,保证了叶片的高质量加工。     

基于NURBS曲线的五轴数控插补算法研究

针对复杂曲而实际加工中五轴线性插补存在的不足,研究一种基于双NURBS曲线的五轴联动插补算法,能有效提高零件加工效率与表面精度;同时.对插补前进行三次样条曲线加咸速处理,减小加速阶性变化对机床造成的往复振动;通过UG二次开发生成双NURBS样条代码实例,表明其具有显著的优越性.     

涡轮叶片造型方法的研究

对涡轮片进行精确的数学描述是对其进行数控加工的前提，本文讨论了在给定叶片沿叶高方向上截面数据的情况下，采用双三次B样条拟合法和三次NURBS曲面插值法构造叶片曲面的具体算法，分析了两种方法的优缺点，并给出了具体的算法和公式，深入探讨了叶片构造过程中遇到的部分网格确定，插值曲面构造，圆弧的二次NURBS曲线精确表示，NURBS曲线节点插入算法及其升降阶等关键性技术问题。     

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.     

基于Cox-de Boor递推的任意次NURBS曲线插补算法的研究与仿真

论文基于Cox-de Boor递推算法实现了任意次NURBS曲线的插补,利用差分插补方法来预估参数,结合机床实际加工过程中所必需满足的条件,将进给速度,机床最大加速度,最大弓高误差分别约束的参数进行比较,优化出最佳参数值,实现了速度自适应控制。论述了控制顶点、节点矢量、权因子对NURBS的影响,利用二分法线性搜索节点区间,给出了系统生成的NURBS曲线插补的NC代码形式,列出了整个插补算法的流程框图,在C++builder开发环境下完成了对任意次NURBS曲线的插补仿真,验证了算法的可行性。     

基于De_Boor递推算法的速度自适应NURBS曲线分段插补算法研究

针对现有大多数NURBS曲线插补算法不能同时满足插补精度和机床加减速性能要求的问题,提出一种基于De_Boor递推算法的速度自适应NURBS分段插补算法。通过前瞻预处理完成插补分段和减速点确定,通过速度修正完成减速段最终插补。MATLAB仿真结果表明,该算法能够同时满足插补精度和机床加减速性能要求。     

A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints

Feedrate scheduling is crucial for CNC systems to generate a smooth movement which is able to satisfy increasing requirements on machining quality and efficiency. In this paper, a novel adaptive feedrate interpolation method is proposed for NURBS tool path with drive constraints. The tool path is first expressed in NURBS form, and then the satisfaction conditions of drive constraints are derived according to the kinematic and geometric characteristics of the NURBS tool path. On this base, a proportional adjustment algorithm, which can quantitatively reduce the accelerations and jerks of drive axes at the sensitive regions of feed profile, is proposed to achieve the new positions of violated sampling points. After each adjustment, a curve evolution strategy is used to ensure the feed profile is locally or globally deformed to the target positions with a good smoothness of path curve and the avoidance of re-interpolation. Through the iterative adjustment, a smooth feed profile with limited velocities, accelerations and jerks of drive axes is thus yielded along the entire tool path. Finally, performances of the proposed method are validated by performing both simulations and experiments on two freeform NURBS curves. The results show the effectiveness and reliability of the proposed feedrate interpolation method.     

Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics

This paper develops a comprehensive interpolation scheme for non-uniform rational B-spline (NURBS) curves, which does not only simultaneously meet the requirements of both constant feedrate and chord accuracy, but also real-time integrates machining dynamics in the interpolation stage. Although the existing work in this regard has realized the importance to simultaneously consider chord error and machining dynamics, none has really incorporated these in one complete interpolation scheme. In this paper, machining dynamics is considered for three aspects: sharp corners or feedrate sensitive corners on the curves, components with high frequencies or frequencies matching machine natural ones and high jerks. A look-ahead module was developed for detecting and adaptively adjusting the feedrate at the sharp corners. By Fast Fourier Transform (FFT) analysis with a moving window in the interpolation stage identified were some special frequency components such as those containing high frequencies or with frequencies matching machine natural ones. Then, the notch filtering or time spacing method was used to eliminate these components. To more completely reduce feedrate and acceleration fluctuations, the jerk-limited algorithm was also developed. Finally, the interpolated feedrate was further smoothened with B-spline fitting method and the NURBS curves were re-interpolated with the smoothened feedrate. During the interpolation, the chord error was repeatedly checked and confined in the prescribed tolerance. Two NURBS curves were used as examples to test the feasibility of the developed interpolation scheme.     

基于NURBS的航空发动机叶片焊接修复的轨迹规划

由于航空发动机叶片截面形状复杂,焊接修复精度高,采用基于非均匀有理B样条曲线(non-uniform rational B-spline,NURBS)方法进行轨迹规划.利用NURBS曲线分别表示叶片截面的前缘、尾缘、叶盆和叶背等四部分曲线,经过升阶整合处理,获得统一表达式,从而进行基于NURBS的曲线插补.综合弓高误差、法向加速度和编程进给速度对焊接速度和精度的影响,实现了进给速度的自适应控制.提出了一种分段前瞻控制,简化了前瞻算法,提高了前瞻效率.最后通过仿真试验验证该算法的可行性和焊接精度.结果表明,该算法是可行的,具有良好的焊接精度.     

NURBS-based fast geometric error compensation for CNC machine tools

In this paper, a novel method for the compensation of geometric errors of CNC machine tools is presented. The key idea is to use the basis functions of the setting NURBS path to approximate its error compensation function and to generate a new compensated NURBS path. In this way, both the setting and the compensated NURBS path have the same NURBS form. More importantly, the control points of the error compensation function can be obtained by simply calculating the positioning deviations of the control points of the setting NURBS path using the error model. A high compensation accuracy can be achieved through the systematic insertion of new knots, which creates new control points and raises the flexibility of NURBS in representing the error compensation function. The real-time interpolation of the compensated NURBS path completes the error compensation automatically. Simulations and experiments have shown that the new method delivers the same positioning accuracy as a model-based real-time geometric error compensation method does, but without additional real-time CPU loading. The proposed method can also be implemented in the post-processor of a CAM system for off-line compensation.