磁悬浮铣削电主轴时变质量系统动力学模型与切削稳定性分析  

Dynamic model and cutting stability analysis of time-varying mass system for magnetic levitation milling electric spindle

作　　者：席家乐 康辉民[1] 刘厚才[1] 刘思源 段良辉 沈相君 何瑞荣 XI Jiale;KANG Huimin;LIU Houcai;LIU Siyuan;DUAN Lianghui;SHEN Xiangjun;HE Ruirong(School of Mechanical Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411201,China;Numerical Control Processing Branch,Jiangnan Industrial Group Co.,Ltd.,Xiangtan 411207,China)

机构地区：[1]湖南科技大学机电工程学院,湖南湘潭411201 [2]湖南科技大学数学与计算科学学院,湖南湘潭411201 [3]江南工业集团有限公司数控加工分厂,湖南湘潭411207

出　　处：《机电工程》2024年第10期1816-1823,共8页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(51875198);湖南省教育厅重点项目(23A0360);湘潭市科技局科技攻关项目(GX-YB20221004)。

摘　　要：磁悬浮电主轴铣削加工时,由时变切屑质量高速旋转产生的时变不平衡离心力,会导致加工表面形成再生颤振。针对这一问题,采用构建稳定性叶瓣图的方法,对铣削系统进行了稳定性预测。首先,分析并建立了动态铣削力、时变不平衡离心力以及主动磁轴承电磁力的数学模型,构建了磁悬浮电主轴铣削加工系统动力学模型;然后,采用全离散化方法得到了铣削加工系统的稳定性叶瓣图;最后,利用MATLAB数值计算平台对系统的切削稳定性进行了分析,得到了时变质量特性以及磁悬浮轴承电磁力对系统切削稳定性的影响规律。研究结果表明:在叶瓣1、叶瓣2、叶瓣3、叶瓣4处,时变系统的极限轴向切深对比定常系统分别下降了0.005 mm、0.010 mm、0.022 mm、0.033 mm,证明时变不平衡离心力会导致系统的切削稳定性降低,并且主轴转速越高,其影响越大;磁轴承力-位移刚度分别为k_(q)=-2×10^(5) N/m、k_(q)=-2×10^(6) N/m、k_(q)=-2×10^(7) N/m时,系统的极限轴向切深分别为0.37 mm、0.55 mm、1.45 mm,证明通过增大磁轴承的力-位移刚度可使系统的切削稳定性得到增强。Aiming at the problem that the time varying unbalanced centrifugal force due to the time varying chip mass caused the regenerated chatter on the machined surface during the milling of magnetic levitation electric spindle,the stability of the milling system was predicted by constructing the stability lobe diagram.Firstly,by analyzing and establishing the mathematical models of dynamic milling force,time varying unbalanced centrifugal force and active magnetic bearing electromagnetic force,the dynamic model of magnetic levitation electric spindle milling system was established.Then,the stability profile of milling system was obtained by full discretization method.Finally,the cutting stability of the system was analyzed using MATLAB numerical calculation platform,and the influence of time varying mass characteristics and magnetic bearing electromagnetic force on the cutting stability of the system was obtained.The research results indicate that the limit axial cutting depth of the time varying system is respectively decreased by 0.005 mm,0.010 mm,0.022 mm and 0.033 mm,comparing with the constant system at lobe 1,lobe 2,lobe 3 and lobe 4,indicating that the time varying unbalanced centrifugal force can reduce the cutting stability of the system,and the higher the spindle speed,the greater the effect.When the force displacement stiffness of the magnetic levitation bearings is k_(q)=-2×10^(5) N/m、k_(q)=-2×10^(6) N/m、k_(q)=-2×10^(7) N/m,the ultimate axial cutting depth of the system is respectively 0.37 mm,0.55 mm,1.45 mm,indicating that increasing the force displacement stiffness of the magnetic bearing can enhance the cutting stability of the system.

关 键 词：磁悬浮轴承 稳定性叶瓣图 动态铣削力 时变不平衡离心力 主动磁轴承电磁力 数学模型 

分 类 号：TH113[机械工程—机械设计及理论] TG659[金属学及工艺—金属切削加工及机床]