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Suppression of Hopf bifurcation in metal cutting by extrusion machining

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Abstract

Hopf bifurcation is a common phenomenon during the metal cutting process, which results in poor surface finish of the workpiece and inhomogeneous grain structure in materials. Therefore, understanding and controlling Hopf bifurcation in metal cutting are necessary. In this work, the systematic low-speed extrusion machining experiments were conducted to suppress Hopf bifurcation phenomenon. It is found that the suppression of Hopf bifurcation is achieved with the increasing constraint extrusion degree. In order to reveal the mechanism of the suppression of Hopf bifurcation, a new nonlinear dynamic model for extrusion machining is developed where the convection, the diffusion, the extrusion of constraint, the thermal-softening deformation and the fracture-type damage are included. The theoretical predictions are in agreement with the experimental results; therefore, the present theoretical model is effective to characterize the suppression of Hopf bifurcation in metal cutting. Based on the numerical calculation of the theoretical model, the mechanisms underlying in extrusion machining are further revealed: Fracture-type deformation is more important than the thermal-softening-type deformation in low-speed extrusion machining; however, the thermal-softening-type deformation is the primary deformation mode for high-speed extrusion machining.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China (Grant Nos. 11132011 and 11602236), Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-15-101A1), the Opening Fund of State Key Laboratory of Nonlinear Mechanics, China Postdoctoral Science Foundation (Grant No. 2016M591066), the National Basic Research Program of China (Grant No. 2012CB937500) and the CAS/SAFEA International Partnership Program for Creative Research Teams. We are very grateful to the anonymous reviewers for their helpful comments, which have improved our manuscript significantly.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Yao Liu & Xinchun Shang

  2. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Songlin Cai & Lanhong Dai

  3. China Electric Power Research Institute, State Grid Corporation of China, Beijing, 100192, People’s Republic of China

    Songlin Cai

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  1. Yao Liu
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Correspondence to Songlin Cai or Lanhong Dai.

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Liu, Y., Cai, S., Shang, X. et al. Suppression of Hopf bifurcation in metal cutting by extrusion machining. Nonlinear Dyn 88, 433–453 (2017). https://doi.org/10.1007/s11071-016-3251-x

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