上海交通大学学报

上海交通大学学报 >

2022 , Vol. 56 >Issue 2: 191 - 200

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2020.413

考虑非线性刚度的正交切削系统稳定性

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  • 兰州交通大学 机电工程学院, 兰州 730070
石慧荣(1979-),男,山西省岢岚县人,副教授,主要从事机械振动控制研究.电话(Tel.):0931-4938023;E-mail: shrz98@aliyun.com.

收稿日期: 2020-12-07

  网络出版日期: 2022-03-03

基金资助

国家自然科学基金(11672121);兰州交通大学-天津大学联合创新基金(2020053)

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Stability of Orthogonal Cutting System Considering Nonlinear Stiffness

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  • School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received date: 2020-12-07

  Online published: 2022-03-03

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摘要

为了准确预测圆柱工件正交切削加工的稳定性,建立了考虑工件表面波动以及刀具和工件变形的非线性正交切削系统模型,利用多尺度法对系统进行了求解,分析了切削加工参数和系统参数对主共振和1/2次共振稳定性的影响,根据主共振和次共振的稳定性获得了切削系统的整体稳定性云图,并与线性近似系统的稳定性叶瓣图(lobe图)进行了比较.结果表明:在一定条件下,含有2次和3次非线性刚度的正交切削系统会出现主共振、1/2、1/3及1/4次共振不稳定现象,从而导致系统具有倍周期、准周期和混沌运行行为.通过比较也证明该非线性正交切削运动动力学模型能够准确预测系统的稳定性.

关键词： 颤振; 非线性; 正交切削; 多尺度法

本文引用格式

石慧荣, 王海星, 李宗刚 . 考虑非线性刚度的正交切削系统稳定性[J]. 上海交通大学学报, 2022 , 56(2) : 191 -200 . DOI: 10.16183/j.cnki.jsjtu.2020.413

Abstract

In order to accurately predict the stability of orthogonal cutting of cylindrical workpiece, a nonlinear orthogonal cutting system model is established, which includes the nonlinear stiffness caused by the surface wave of work as well as the deformation of the tool and work. The multi-scale method is used to solve the system. The effect of machining parameters and system parameters on the stability of the primary resonance and 1/2 subresonance is analyzed to gain the overall stability cloud map compared with the lobe diagrams of linear approximation system. The results show that the instability of primary resonance, 1/2, 1/3, and 1/4 subresonance occur in the orthogonal cutting system with the quadratic nonlinearity and cubic nonlinearities stiffness, which makes the system have period-doubling, quasi-periodic, and chaotic operation behavior. The comparison indicates that the dynamics model of nonlinear orthogonal cutting can accurately predict the stability of the system.

Key words： chatter; nonlinearity; orthogonal cutting; multi-scale method

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