Abstract
Machine tool vibrations in turning processes are analyzed by taking into account the nonlinearity of the cutting force characteristics. Unstable limit cycles are computed for the governing nonlinear delay-differential equation in order to determine the bistable technological parameter region where stable stationary cutting and large-amplitude machine tool vibrations coexist. Simple closed-form formulas are derived for the amplitude of limit cycles and for the size of the bistable region considering a general cutting force characteristics. The analytical results are determined by the method of averaging, which can be used to treat the nonlinearities without their third-order approximation. The results are confirmed by numerical continuation and using Melnikov’s integral.
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