Dombovari Zoltan, Iglesias Alex, Molnar Tamas G, Habib Giuseppe, Munoa Jokin, Kuske Rachel, Stepan Gabor
Department of Applied Mechanics, Budapest University of Technology and Economics, Muegyetem rkp. 3, H1111 Budapest, Hungary.
IK4-IDEKO Dynamics and Control Department, Arriaga Kalea 2, E20870 Elgoibar, Spain.
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180125. doi: 10.1098/rsta.2018.0125. Epub 2019 Jul 22.
The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attraction of the stable periodic motion that corresponds to the chatter-free cutting process. The mathematical model is a system of time-periodic nonlinear delay differential equations. It is studied by means of a nonlinear extension of the semidiscretization method, which enables the estimation of the parameter ranges where the unsafe (also called bistable) zones appear. The theoretical results are checked with thorough experimental work: first, step-by-step parameter variations are adapted to identify hysteresis loops, then harmonic burst excitations are used to estimate the extents of the unsafe zones. The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters. The experimental results confirm the existence of the bistable parameter regions. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.
加工中的不安全区域是参数空间中的一个区域，在该区域内，对于某些扰动，稳态切削操作可能会转变为再生颤振，反之亦然。在铣削加工过程中，这种现象与不稳定的准周期振荡的存在有关，其内部边界限制了对应于无颤振切削过程的稳定周期运动的吸引域。数学模型是一个时间周期非线性延迟微分方程组。通过半离散化方法的非线性扩展对其进行研究，该方法能够估计不安全（也称为双稳态）区域出现的参数范围。通过全面的实验工作对理论结果进行验证：首先，逐步改变参数以识别滞后环，然后使用谐波突发激励来估计不安全区域的范围。滞后环与与缓慢变化参数的动态效应相关的动态分岔现象能够准确区分开来。实验结果证实了双稳态参数区域的存在。本文是“延迟系统的非线性动力学”主题 issue 的一部分。
