Orthogonal polynomial approximation method for stability prediction in milling
Orthogonal polynomial approximation method for stability prediction in milling
复制标题
铣削稳定性预测的正交多项式逼近法
DOI：
10.1007/s00170-017-0067-x
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发表时间：
2017-02
期刊：
影响因子：
--
通讯作者：
liu zhibing
中科院分区：
文献类型：
--
作者：
yan zhenghu;liu zhibing
基于正交多项式逼近格式，提出了几种利用不同类型的正交多项式进行稳定性预测的方法。用时间周期延迟微分方程(DDES)描述了考虑再生效应的铣削动力学。首先，本文使用经典的勒让德多项式和切比雪夫多项式来逼近状态项、延迟项和周期系数矩阵。利用直接积分法(DIS)，得到了反映当前齿型与前一齿型之间动力响应映射关系的状态转移矩阵。利用勒让德和切比雪夫多项式逼近法生成了单自由度和两自由度铣削模型的稳定叶图。比较了勒让德和切比雪夫多项式方法与基准一阶半离散化方法(1stSDM)的收敛速度。结果表明，勒让德多项式方法和切比雪夫多项式方法的收敛速度和数值稳定性都有待提高。为了开发基于DIS的高收敛速度和数值稳定性的新方法，利用Gram-Schmidt正交化来逼近状态项、延迟项和周期系数矩阵，构造了一元正交多项式序列。通过与基准算法1stSDM的比较，评价了基于一元正交多项式的算法的收敛速度和计算效率。结果表明，基于一元正交多项式的方法在收敛速度和数值稳定性方面具有优势。将基于一次正交多项式的方法得到的单自由度和两个自由度的铣削模型的稳定叶图与用一阶SDM方法得到的稳定叶图进行了比较。最后，证明了基于一元正交多项式的方法是预测铣削稳定性的有效方法。
Based on orthogonal polynomial approximation scheme, this paper presents several stability prediction methods using different kinds of orthogonal polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delay-differential equations (DDEs). Firstly, this work employs the classical Legendre and Chebyshev polynomials to approximate the state term, delayed term, and periodic-coefficient matrix. With the help of direct integration scheme (DIS), the state transition matrixes which indicate the mapping relations of the dynamic response between the current tooth pass and the previous tooth pass are obtained. The stability lobe diagrams for single degree of freedom (DOF) and two DOF milling models are generated by using the Legendre and Chebyshev polynomial approximation-based methods. The rate of convergence of the Legendre and Chebyshev polynomial-based methods is compared with that of the benchmark first-order semi-discretization method (1stSDM). The comparison results indicate that the rate of convergence and the numerical stability of the Legendre and Chebyshev polynomial-based methods are both need to be improved. In order to develop new methods with high rate of convergence and numerical stability base on DIS, the monic orthogonal polynomial sequences are constructed by using Gram-Schmidt orthogonalization to approximate the state term, delayed term, and periodic-coefficient matrix. The rate of convergence and the computational efficiency of the monic orthogonal polynomial-based methods are evaluated by comparing with those of the benchmark 1stSDM. The results turn out that the monic orthogonal polynomial-based methods are advantageous in terms of the rate of convergence and numerical stability. The stability lobe diagrams for single DOF and two DOF milling models obtained by the monic orthogonal polynomial-based methods are compared with those obtained by the 1stSDM. Finally, the monic orthogonal polynomial-based methods are proved to be the effective and efficient methods to predict the milling stability.
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DOI：
10.1007/978-3-540-46783-0
发表时间：
1992-05
期刊：
--
影响因子：
--
作者：
D. Funaro
通讯作者：
D. Funaro
DOI：
10.1007/bf01845689
发表时间：
1996-09
期刊：
The International Journal of Advanced Manufacturing Technology
影响因子：
--
作者：
Michael J. Shorr;S. Liang
通讯作者：
Michael J. Shorr;S. Liang
影响因子：
2
作者：
E. Butcher;Oleg A. Bobrenkov;E. Bueler;Praveen Nindujarla
通讯作者：
E. Butcher;Oleg A. Bobrenkov;E. Bueler;Praveen Nindujarla
DOI：
10.1016/j.ijmachtools.2010.01.003
发表时间：
2010-05-01
影响因子：
14
作者：
Ding, Ye;Zhu, LiMin;Ding, Han
通讯作者：
Ding, Han
DOI：
10.1115/1.1556860
发表时间：
2003-05
影响因子：
4
作者：
P. Bayly;J. Halley;B. Mann;M. Davies
通讯作者：
P. Bayly;J. Halley;B. Mann;M. Davies