基于三阶牛顿–埃尔米特插值全离散法的铣削稳定性预测  

A Full-Discretization Method for Milling Stability Prediction Based on Third-Order Newton-Hermite Interpolation

作　　者：黄超 杨文安 黄久超[1] 解菲菲 杨有成 HUANG Chao;YANG Wenan;HUANG Jiuchao;XIE Feifei;YANG Youcheng(Shanghai Spaceflight Precision Machinery Institute,Shanghai 201600,China;College of Mechanical and Electrical Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]上海航天精密机械研究所,上海201600 [2]南京航空航天大学机电学院,南京210016

出　　处：《航空制造技术》2021年第8期92-101,共10页Aeronautical Manufacturing Technology

基　　金：南京航空航天大学研究生创新基地(实验室)开放基金项目(KFJJ20180518);国家自然科学基金面上项目(51707501);国防基础科研重点项目(JCKY2016605B006)。

摘　　要：铣削加工过程中的颤振通常会导致加工零件表面质量差、刀具磨损加剧,甚至会降低数控机床寿命。针对基于再生颤振理论构建的铣削动力学模型,提出了一种三阶牛顿–埃尔米特插值全离散法来预测铣削稳定性。考虑再生颤振的动态铣削过程可以表示为时滞微分方程组,运用三阶牛顿插值多项式和三阶埃尔米特插值多项式分别对积分项中的状态项和时滞项进行拟合,从而推导出转移矩阵。利用Floquet理论判断系统的稳定性,进而获得铣削稳定性叶瓣图。大量仿真结果表明,所提出方法的收敛速度要快于一阶全离散法(1stFDM)和改进三阶全离散法(3rdUFDM)。在离散数相同情况下,文中方法的局部离散误差最小。此外,在单自由度动力学模型下,文中方法的计算效率不仅高于1stFDM和3rdUFDM,而且预测精度远好于1stFDM,稍好于3rdUFDM。通过切削试验数据表明,所提出的方法可高效准确地预测铣削稳定性。In milling processes,chatter usually results in poor surface quality,tool wear and even shorten the life of machine tool.In order to build the dynamic model of milling process using regenerative theory,a new full-discretization method based on third-order Newton-Hermite interpolation method is proposed in this study.The dynamic milling process considering regenerative chatter can be expressed as delay differential equations,then the transition matrix is constructed by using third-order Newton and Hermite interpolation of the state item and the time-delay term,respectively.Finally,the stability of the system was determined based on the Floquet theory,and the corresponding stability lobe diagrams are obtained.The numerical results obtained utilizing extensive simulation indicate that the convergence rate of the proposed method is faster than that of the first full-discretization method(1stFDM)and the third-order updated full-discretization method(3rdUFDM),and the discrete error of the proposed method is the smallest at the same of the discrete number.In addition,for single degree of freedom dynamic model,the proposed method is more efficient than the 1stFDM and the 3rdUFDM,and the computation accuracy of the proposed method is better than that of the 1stFDM and the 3rdUFDM.The experimental results show that the proposed method is effective for predicting the milling stability.

关 键 词：三阶牛顿插值 三阶埃尔米特插值 全离散法 稳定性分析 叶瓣图 

分 类 号：TG54[金属学及工艺—金属切削加工及机床]