考虑非线性刚度的正交切削系统稳定性

doi:10.16183/j.cnki.jsjtu.2020.413

摘要/Abstract

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

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

中图分类号:

TH113
TG54

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.

SHI Huirong, WANG Haixing, LI Zonggang. Stability of Orthogonal Cutting System Considering Nonlinear Stiffness[J]. Journal of Shanghai Jiao Tong University, 2022, 56(2): 191-200.

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参数	取值	参数	取值
ρ₀/(kg·mm^-1)	1000	F₂/kg	5
α₁/(s·mm^-1)	6×10^-4	κ	0.4
α₂/(s·mm^-1)	0.5	β/(°)	61.79
μ	0.5	α/(°)	10
M/(kg·s²·mm^-1)	2×10^-3	d/mm	35
C/(kg·s·mm^-1)	1.45	v_C/(mm·r^-1)	1
K/(kg·mm^-1)	800	b/mm	2
K₁/(kg·mm^-2)	640	s_t/mm	0.5
K₂/(kg·mm^-3)	1600