Hermite算法的收敛性分析及其改进

王瑞秋; 边永梅; 陈五一

Hermite算法的收敛性分析及其改进

1.
北京航空航天大学机械工程及自动化学院, 北京 100083
2. 安徽理工大学机械工程系, 淮南 232001

基金项目: 中国航空第一集团创新基金资助项目(CX03007)

详细信息

作者简介:
王瑞秋(1981-),男,安徽淮北人,博士生, wrq work@126.com.

中图分类号: TH 112
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- 被引次数: 0
出版历程
- 收稿日期: 2004-11-22
- 网络出版日期: 2006-02-28

Hermite method convergence analyses and improvement

1.
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
2. Department of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China

摘要

摘要: 为了提高多点切触加工算法的计算效率,对其中的Hermite算法进行了改进,并且对改进后的Hermite算法的收敛性进行了理论分析,推导了改进后算法的局部收敛条件,同时给出算法的Steffensen加速迭代公式并新提出了一种基于试算的待定系数迭代法.分析和实例表明,改进后的Hermite算法属于线性收敛的算法,而待定系数迭代法则有接近二阶的收敛速度.综合应用上述算法,可以满足一般性自由曲面多点切触加工刀位计算的要求.
- 数值方法收敛性 /
- 算法 /
- 刀具控制 /
- 加工 /
- 计算机辅助制造 /
- 迭代方法
Abstract: To make multi-points tangent contact machining have higher computational efficiency, an improved algorithm based on Hermite method was proposed. Theoretical analyses were given on the convergence of the improved algorithm, and the constraints for local convergence of the new algorithm were also derived. Then the formula of steffensen accelerated iterative method was applied on the algorithm. Another novel algorithm called iterative method of undetermined coefficient based on trial method was developed. The results show that the improved algorithm based on Hermite method acts as a linear convergence method, while the iterative method of undetermined coefficient algorithm has the same convergence speed with square convergence method approximately. Then it can meet the demand for the tool path generating computation of general sculpture surface by combining all the above-mentioned algorithms applied on them.
- convergence of numerical methods /
- algorithms /
- cutting tools control /
- machining /
- computer aided manufacturing /
- iterative methods

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参考文献(1)

[1] Max Engeli, Jorg Waldvogel, Thomas Schnider. Method for processing work pieces by removing material . United States Patent:US 6,485,236,2002-11-26 [2] Wang Ruiqiu, Chen Wuyi. Application of the hermite method on tool path generation . In:Chen Wuyi, Yamane Yasuo, Fan Rui, et al, eds. Proceedings of the Seventh International Conference on Progress of Machining Technology . Beijing:Avitation Industry Press, 2004.943~948 [3] 封建湖,车刚明,聂玉峰. 数值分析原理 [M] 北京:科学出版社,2001. 185~198 Feng Jianhu, Che Gangming, Nie Yufeng. The principle of numerical method analysis [M] Beijing:Science Press, 2001.185~198(in Chinese) [4] Warkentin A, Ismail F, Bedi S. Multi-point tool positioning strategy for 5-axis machining of sculptured surfaces [J] Computer Aid Geometric Design, 2000,17:83~100

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