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Periodic cutting motions in a vibration-assisted, regenerative, nonlinear Orthogonal turning system

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Abstract

In this paper, a mathematical model of 2-degrees-of-freedom (2-DOF), vibration-assisted, regenerative, nonlinear orthogonal turning system is developed. The period-1 motions of such a system are predicted through the discrete mapping method. The discrete mapping is constructed by discretization of equations of motion of the machine-tool system. The periodic motions of such a machine tool system are determined through the mapping structures, and the stability and bifurcation conditions of the period-1 motions are determined by eigenvalue analysis. The variation of period-1 motions with respect to active excitation from a servo unit is presented from the bifurcation diagram of periodic nodes. Numerical simulations are carried out for small-amplitude and large-amplitude machine-tool vibration. The machine tool chatter occurs once the horizontal and vertical displacement of the machine-tool are out-of-phase. Such a relation could be used for the chatter detection of vibration-assisted machining.

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Authors and Affiliations

  1. Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA, 93401, USA

    Siyuan Xing

  2. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1805, USA

    Albert C. J. Luo

Authors
  1. Siyuan Xing
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  2. Albert C. J. Luo
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Correspondence to Albert C. J. Luo.

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Xing, S., Luo, A.C.J. Periodic cutting motions in a vibration-assisted, regenerative, nonlinear Orthogonal turning system. Int. J. Dynam. Control 10, 1–12 (2022). https://doi.org/10.1007/s40435-021-00779-3

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  • DOI: https://doi.org/10.1007/s40435-021-00779-3

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