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[1] Zhu Hao, Liu Jingnan, Yang Ankang, et al. An adaptive generation method for free curve trajectorybased on NURBS [J]. Journal of Southeast University (English Edition), 2014, 30 (3): 296-301. [doi:10.3969/j.issn.1003-7985.2014.03.007]
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An adaptive generation method for free curve trajectorybased on NURBS()
基于NURBS模型的自由曲线加工轨迹自适应生成方法
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
30
Issue:
2014 3
Page:
296-301
Research Field:
Automation
Publishing date:
2014-09-30

Info

Title:
An adaptive generation method for free curve trajectorybased on NURBS
基于NURBS模型的自由曲线加工轨迹自适应生成方法
Author(s):
Zhu Hao1 2 Liu Jingnan1 Yang Ankang1 Wang Mulan2
1School of Automation, Southeast University, Nanjing 210096, China
2 Jiangsu Key Laboratory of Advanced Numerical Control Technology, Nanjing Institute of Technology, Nanjing 211167, China
朱昊1 2 刘京南1 杨安康1 汪木兰2
1东南大学自动化学院, 南京210096; 2南京工程学院先进数控技术江苏省重点实验室, 南京211167
Keywords:
free curve NURBS(non-uniform rational B-spline) sigmoid function Adams algorithm
自由曲线 NURBS sigmoid函数 Adams算法
PACS:
TP237
DOI:
10.3969/j.issn.1003-7985.2014.03.007
Abstract:
To realize the high precision and real-time interpolation of the NURBS(non-uniform rational B-spline)curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.
为实现NURBS曲面快速高精度实时差补, 提出了基于修正型sigmoid函数的动力学模型, 给出了最大速度、弓高误差、加工曲线的曲率半径和插补周期之间的约束条件.该模型在满足jerk、加速度、速度均连续的前提下, 将常用的三次多项式S型以及三角多项式S型动力学模型的15个分段数减少至3个.在此基础上, 提出采用差商代替导数的优化Adams算法, 避免了常用的Taylor展开所遇到的高阶求导计算, 求取了差补周期参数.最后通过减少低次零值B样条基函数的计算, 对De Boor-Cox递推算法进行了简化设计, 提出了精简型De Boor-Cox算法, 缩减了计算量.仿真分析表明, 所提算法可根据加工路径有效控制进给速度, 在保证加工精度的同时, 使计算量得到减少, 提高了运算速度.实验结果显示本加工方法可以正确计算目标参数, 并适合应用于实际加工系统.

References:

[1] Zhang Liyan, Bian Yuchao, Chen Hu, et al. Implementation of a CNC NURBS curve interpolator based on control of speed and precision [J]. International Journal of Production Research, 2009, 47(6):1505-1519.
[2] Sekar M, Narayanan V N, Yang S-H. Design of jerk bounded feedrate with ripple effect for adaptive NURBS interpolator [J]. The International Journal of Advanced Manufacturing Technology, 2008, 37(5/6):545-552.
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Memo

Memo:
Biographies: Zhu Hao(1980—), male, graduate, associate professor; Liu Jingnan(corresponding author), male, doctor, processor, liujn@seu.edu.cn.
Foundation items: The Doctoral Fund of Ministry of Education of China(No. 20090092110052), the Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No. 12KJA460002), College Industrialization Project of Jiangsu Province(No. JHB2012-21).
Citation: Zhu Hao, Liu Jingnan, Yang Ankang, et al. An adaptive generation method for free curve trajectory based on NURBS[J].Journal of Southeast University(English Edition), 2014, 30(3):296-301.[doi:10.3969/j.issn.1003-7985.2014.03.007]
Last Update: 2014-09-20