Abstract
The shifted Chebyshev polynomials and Floquet theory are both adopted for the prediction regenerative chatter stability and Hopf bifurcation in milling. The influences of the system parameter on the stability of the milling system have been analyzed. The stability lobe diagrams are obtained. The result shows that the shifted Chebyshev polynomials method is more accurate than the semi-discretion scheme for spindle speed lower than 3500 round per minutes. The stability in milling can well be predicted by the cutting depth and feed rate lobes diagrams. Only Hopf bifurcations are detected by the Eigen-value analysis. The stable solution transform from the stable equilibrium point to the quasi-periodic oscillation after Hopf bifurcation.
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