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Approximated Dynamics of Chatter in Turning Processes

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Abstract

The nonlinear behaviour of the turning process is analysed, which is described by a one degree-of-freedom dynamical system. The model takes the form of a delay differential equation that is non-smooth when the cutting tool leaves contact with the surface. The delay equation is approximated by means of a power series with respect to the delay to reveal the geometric structure of the relevant dynamics in a low dimensional phase space. The bifurcation diagram of the non-smooth system is calculated and compared to the existing theoretical and experimental results of the literature.

Keywords

  • Chatter
  • Turning
  • Relevant dynamics
  • Lorenz map

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Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Program (FP/2007–2013)/ERC Advanced Grant Agreement No. 340889.

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Correspondence to Bence Beri .

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Beri, B., Stepan, G. (2020). Approximated Dynamics of Chatter in Turning Processes. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) Nonlinear Dynamics of Structures, Systems and Devices. Springer, Cham. https://doi.org/10.1007/978-3-030-34713-0_46

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