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Stability of turning processes for periodic chip formation

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Abstract

The prediction of chatter vibration is influenced by many known complex phenomena and is uncertain. We present a new effect that can significantly change the stability properties of cutting processes. It is shown that the microscopic environment of chip formation can have a large effect on its macroscopic properties. In this work, a combined model of the surface regeneration effect and chip formation is used to predict the stability of turning processes. In a chip segmentation sub-model, the primary shear zone is described with a corresponding material model along layers together with the thermodynamic behavior. The surface regeneration is modeled by the time-delayed differential equation. Numerical simulations show that the time scale of a chip segmentation model is significantly smaller than the time scale of the turning process; therefore, averaging methods can be used. Chip segmentation can decrease the average shear force leading to decreased cutting coefficients because of the non-linear effects. A proper linearization of the equation of motion leads to an improved description of the cutting coefficients. It is shown that chip segmentation may significantly increase the stable domains in the stability charts; furthermore, by selecting proper parameters, unbounded stability domains can be reached.

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Abbreviations

\(a\), \(b\), \(C\) :

Constants in the constitutive equation

\(c\) :

Heat capacity, J/(kg·K)

\(E\) :

Modulus of elasticity, MPa

\(h_{0}\) :

Initial chip thickness, m

\(K\) :

Time scale of chip formation, s

\(L\) :

Acting length of normal stress, m

\(r\) :

Energy ratio

\(T_{i}\) :

Temperature of shear zone band i, K

\(T_{\text{w}}\) :

Temperature of workpiece, K

\(\tilde{t}\) :

Dimensionless time of chip formation

\(\hat{t}\) :

Dimensionless time of turning

\(v\) :

Cutting speed, m/s

\(\delta\) :

Thickness of deformation layer, m

\(\gamma_{i}\) :

Shear strain in shear zone band i

\(\varPhi\) :

Angle of shear plane, rad

\(\varOmega\) :

Angular velocity of workpiece, rad/s

\(\omega_{\text{n}}\) :

Natural frequency of machine-tool system, rad/s

\(\rho\) :

Density, kg/m3

\(\kappa\) :

Relative damping

\(\tau_{\varPhi }\) :

Shear stress in case of continuous chip formation, N/m2

\(\xi\), \(\eta\), \(\zeta\) :

Dimensionless parameters of chip formation

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Acknowledgements

This research study received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013) ERC advanced grant agreement (Grant No. 340889) and was supported by the Hungarian Scientific Research Fund—OTKA PD-112983 and the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gergely Gyebrószki & Daniel Bachrathy

  2. MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary

    Gábor Csernák & Gabor Stepan

Authors
  1. Gergely Gyebrószki
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  2. Daniel Bachrathy
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  3. Gábor Csernák
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  4. Gabor Stepan
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Correspondence to Gergely Gyebrószki.

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Gyebrószki, G., Bachrathy, D., Csernák, G. et al. Stability of turning processes for periodic chip formation. Adv. Manuf. 6, 345–353 (2018). https://doi.org/10.1007/s40436-018-0229-6

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  • DOI: https://doi.org/10.1007/s40436-018-0229-6

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