Approximate stability charts for milling processes using semi-discretization
Approximate stability charts for milling processes using semi-discretization
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DOI：
10.1016/j.amc.2005.05.008
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
F. Hartung;T. Insperger;G. Stépán;J. Turi
中科院分区：
文献类型：
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作者：
F. Hartung;T. Insperger;G. Stépán;J. Turi
刀具和工件之间不需要的相对振动是高速加工中的重大挑战。为了避免这一问题，需要指定工艺稳定的系统参数（主轴转速、切削深度）范围，即获得所谓的稳定性图。这种稳定性图表通常只能通过数值方式给出，这在论文中针对铣削的单自由度模型进行了说明。在本文中，我们建立了一类建模铣削过程的延迟方程的半离散逼近方法的收敛性。此外，我们表明半离散化保留了原始方程的渐近稳定性，因此它可以用来获得稳定性图的良好近似。
Unwanted relative vibrations between the tool and the workpiece represent significant challenges in high-speed machining. In order to avoid this problem, one needs to specify ranges for system parameters (spindle speed, depth of cut) for which the process is stable, i.e., to obtain a so-called stability chart. Such stability charts usually can only be given by numerical means which is illustrated in the paper for a single degree of freedom model of milling. In this paper, we establish the convergence of the semi-discretization approximation method for a class of delay equations modeling the milling process. Moreover, we show that semi-discretization preserves asymptotic stability of the original equation, thus it can be used to obtain good approximations for the stability charts.