• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (23): 223-232.doi: 10.3901/JME.2018.23.223

• 制造工艺与装备 • 上一篇    

预测铣削稳定性的隐式Adams方法

智红英1, 闫献国2, 杜娟2, 曹启超2, 张唐圣2   

  1. 1. 太原科技大学应用科学学院 太原 030024;
    2. 太原科技大学机械工程学院 太原 030024
  • 收稿日期:2017-12-10 修回日期:2018-05-28 出版日期:2018-12-05 发布日期:2018-12-05
  • 通讯作者: 闫献国(通信作者),男,1963年出生,博士,教授,博士研究生导师。主要研究方向为金属切削理论与刀具。E-mail:yan_xg2008@126.com
  • 作者简介:智红英,女,1981年出生,博士研究生。主要研究方向为先进制造技术,最优化理论及方法应用。E-mail:tykdzhy@163.com
  • 基金资助:
    国家自然科学基金(51475317)、山西省留学基金(2013-095)和研究生创新基金(20151027)资助项目。

Prediction of the Milling Stability Based on the Implicit Adams Method

ZHI Hongying1, YAN Xianguo2, DU Juan2, CAO Qichao2, ZHANG Tangsheng2   

  1. 1. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024;
    2. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024
  • Received:2017-12-10 Revised:2018-05-28 Online:2018-12-05 Published:2018-12-05

摘要: 针对铣削加工过程中产生的振动现象,提出了一种隐式Adams方法(Implicit Adams method,IAM)来预测铣削加工过程的稳定性。考虑再生颤振的铣削加工动力学方程可以表示为时滞线性微分方程,将刀齿周期可分为自由振动阶段和强迫振动阶段,对强迫振动阶段进行离散,运用IAM方法构建状态传递矩阵,利用Floquet理论,判定系统的稳定性,获得系统的稳定性叶瓣图。Matlab软件仿真结果表明,IAM方法是预测铣削稳定性的一种有效方法。随着离散数的增加,IAM方法的收敛速度要快于一阶半离散法(First-order semi-discretization method,1st-SDM)和二阶全离散法(Second-order full-discretization method,2nd-FDM),离散数较少的IAM方法能达到离散数较多的1st-SDM方法和2nd-FDM方法的局部离散误差。此外,在单自由度和双自由度动力学模型下,三种方法的稳定性叶瓣图显示,IAM方法预测铣削稳定性的预测精度均好于1st-SDM方法和2nd-FDM方法,计算效率远远高于1st-SDM方法,稍高于2nd-FDM方法。切削试验和仿真结果表明,IAM方法的预测精度和可靠度均好于1st-SDM方法和2nd-FDM方法。

关键词: Adams方法, Floquet理论, 稳定性叶瓣图, 铣削加工

Abstract: In view of the vibration phenomenon in the milling process,an implicit Adams method (IAM) is proposed to predict the stability of the milling process.The dynamic equation of milling process with regenerative chatter can be expressed as a delay linear differential equation.The cutter tooth cycle can be divided into the forced and free vibration stages;The forced vibration stage is discretized and the IAM is used to construct state transition matrix;The stability of the system is determined based on Floquet theory,and the stability lobe diagrams are obtained.Matlab simulation results show that IAM is an effective method to predict the stability of milling process. With the increase of discrete number,the convergence rate of the IAM is faster than the first-order semi-discretization method(1st-SDM) and the second-order full-discretization method(2nd-FDM).The IAM with the less discrete number can reach the local discrete error of the 1st-SDM and the 2nd-FDM with more discrete numbers.In addition,in one and two degree-freedom dynamic model,the stability lobes diagrams of three methods shows that the prediction accuracy of the IAM is better than that of 1st-SDM and 2nd-FDM,and the computation efficiency is much higher than the 1st-SDM,slightly higher than the 2nd-FDM.The results of the cutting test and simulation experimental results show that the prediction accuracy and reliability of the IAM are better than that of the 1st-SDM and the 2nd-FDM.

Key words: Adams method, Floquet theory, milling machine, stability lobe diagrams

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