基于改进完全离散化法铣削系统稳定性研究

doi:10.3901/JME.2023.15.162

机械工程学报 ›› 2023, Vol. 59 ›› Issue (15): 162-173.doi: 10.3901/JME.2023.15.162

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基于改进完全离散化法铣削系统稳定性研究

刘春景¹, 唐敦兵², 陈兴强¹, 魏天路¹

1. 蚌埠学院机械与车辆工程学院蚌埠 233030;
2. 南京航空航天大学机电学院南京 210016

收稿日期:2022-08-10 修回日期:2022-11-02 出版日期:2023-08-05 发布日期:2023-09-27
通讯作者: 刘春景(通信作者),男,1975年出生,博士,教授。主要研究方向为智能制造技术。E-mail:liusun7575@163.com
作者简介:唐敦兵,男,1972年出生,博士,教授,博士研究生导师。主要研究方向为智能制造系统、智能制造技术与装备。E-mail:d.tang@nuaa.edu.cn
基金资助:
江苏省重点研发计划资助项目(BE2021091)

Research on Stability of Milling System Based on Updated Complete Discretization Method

LIU Chunjing¹, TANG Dunbing², CHEN Xingqiang¹, WEI Tianlu¹

1. College of Mechanical and Vehicle Engineering, College of Bengbu, Bengbu 233030;
2. College of Mechanical and Electronic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016

Received:2022-08-10 Revised:2022-11-02 Online:2023-08-05 Published:2023-09-27

摘要/Abstract

摘要： 颤振是影响铣削质量和切削效率的重要因素之一。为提高铣削颤振预测精度,提出一种改进的完全离散化方法(U-FDM),基于二阶Lagrange多项式对刀具-工件铣削动力学系统时滞微分方程的延迟项和状态项进行数值迭代,根据Floquet原理构建出了高精度的颤振稳定域叶瓣图。单自由度特征值收敛特性分析表明,当离散化间隔数大于50时,二阶完全离散化方法(2-FDM)与一阶完全离散化方法(1-FDM)的收敛速度基本相同,U-FDM收敛特性最优;经叶瓣图对比分析可知,改进的完全离散化方法具有较高的拟合精度,计算效率相比半离散方法(SDM)单自由度和两自由度分别提升了70.6%和64.9%。通过试验获取铣削加工响应信号进行时域、频域和同步采样分析,结果表明所提铣削动力学模型和U-FDM算法是有效的,为叶瓣图指导实际加工奠定了基础。

关键词: 铣削动力学, 颤振, 时滞, 完全离散化法, 稳定域叶瓣图

Abstract: Chatter is one of the major limitation factors in the machining process, which affects milling quality and efficiency. In order to improve the prediction accuracy of milling chatter, an updated complete discretization method (U-FDM) is proposed. Based on the second-order Lagrange polynomials, the delay term and state term of the delay differential equation of milling dynamic system are numerically iterated, and the high-precision lobe diagram of chatter stability region is constructed by using Floquet principle. The convergence rate of the second order complete discretization method is almost the same as that of the first order complete discretization method when the number of discretization interval is more than 50. The convergence analysis of eigenvalue for single degree of freedom shows that the U-FDM has the best convergence characteristics. The comparisons of single and two degree of freedom lobes show that the U-FDM algorithm has high fitting accuracy. Compared with semi-discretization method, the computational efficiency is improved by 70.6% and 64.9% respectively. The force response signal of milling process is analyzed in time domain, frequency domain and synchronous sampling. The results prove that the proposed milling dynamic model and U-FDM algorithm are effective, which can give a help for the practical machining.

Key words: milling dynamics, chatter, time delay, complete discrete method, stability lobe diagram

中图分类号:

TH162

刘春景, 唐敦兵, 陈兴强, 魏天路. 基于改进完全离散化法铣削系统稳定性研究[J]. 机械工程学报, 2023, 59(15): 162-173.

LIU Chunjing, TANG Dunbing, CHEN Xingqiang, WEI Tianlu. Research on Stability of Milling System Based on Updated Complete Discretization Method[J]. Journal of Mechanical Engineering, 2023, 59(15): 162-173.

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基于改进完全离散化法铣削系统稳定性研究

Research on Stability of Milling System Based on Updated Complete Discretization Method

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