Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels
Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels
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DOI：
10.1115/1.3124088
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发表时间：
2009-07
影响因子：
2
通讯作者：
E. Butcher;Oleg A. Bobrenkov;E. Bueler;Praveen Nindujarla
中科院分区：
文献类型：
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作者：
E. Butcher;Oleg A. Bobrenkov;E. Bueler;Praveen Nindujarla
本文通过确定主轴转速和切削深度两参数空间中颤振（不稳定）振动发生的区域，通过单自由度模型研究了铣削过程的动态稳定性。像铣削这样的动态系统是用带有时间周期系数的时滞微分方程来建模的。提出了一种新的研究此类系统稳定性的近似方法。该方法基于切比雪夫多项式的性质和解的搭配展开。并置点是高次切比雪夫多项式的极值点。给出了在线性和非线性再生切削力作用下，单齿或双齿上铣削和下铣削的具体切削力分布图和稳定性图。发现了二次Hopf分岔和翻转分岔（翻倍周期）引起的不稳定区域，并对平均切削力变化标志附近的下铣削最佳稳定浸液水平进行了深入研究。DOI: 10.1115/1.3124088
In this paper the dynamic stability of the milling process is investigated through a single degree-of-freedom model by determining the regions where chatter (unstable) vibrations occur in the two-parameter space of spindle speed and depth of cut. Dynamic systems such as milling are modeled by delay-differential equations with time-periodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation expansion of the solution. The collocation points are the extreme points of a Chebyshev polynomial of high degree. Specific cutting force profiles and stability charts are presented for the up- and down-milling cases of one or two cutting teeth and various immersion levels with linear and nonlinear regenerative cutting forces. The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations are found, and an in-depth investigation of the optimal stable immersion levels for down-milling in the vicinity of where the average cutting force changes sign is presented. DOI: 10.1115/1.3124088