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Prediction of Surface Roughness in Turning Applying the Model of Nonlinear Oscillator with Complex Deflection

Author

Listed:
  • Richárd Horváth

    (Bánki Donát Faculty of Mechanical and Safety Engineering, Obuda University, 1081 Budapest, Hungary)

  • Livija Cveticanin

    (Bánki Donát Faculty of Mechanical and Safety Engineering, Obuda University, 1081 Budapest, Hungary
    Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia)

  • Ivona Ninkov

    (Bánki Donát Faculty of Mechanical and Safety Engineering, Obuda University, 1081 Budapest, Hungary)

Abstract

This paper deals with prediction of the roughness of a cutting surface in the turning process, applying the vibration data of the system. A new type of dynamic model for a workpiece-cutting tool system, appropriate for vibration simulation, is developed. The workpiece is modelled as a mass-spring system with nonlinear elastic property. The cutting tool acts on the workpiece with the cutting force which causes strong in-plane vibration. Based on the experimentally measured values, the cutting force is analytically described as the function of feed ratio and cutting speed. The mathematical model of the vibrating system is a non-homogenous strong nonlinear differential equation with complex function. A new approximate solution for the nonlinear equation is derived and analytic description of vibration is obtained. The solution depends on parameters of the excitation force, velocity of rotation and nonlinear properties of the system. Increasing the feed ratio at a constant velocity of the working piece, the frequency of vibration decreases and the amplitude of vibration increases; increasing the velocity of working piece for constant feed ratio causes an increase of the frequency and a decrease of the amplitude of vibration. Experiments demonstrate that the analytical solution of the nonlinear vibration model in turning process is in direct correlation with the cutting surface roughness. The predicted surface roughness is approximately (1–2) × 10 −3 times smaller than the amplitude of vibration of the nonlinear model considered in this paper.

Suggested Citation

  • Richárd Horváth & Livija Cveticanin & Ivona Ninkov, 2022. "Prediction of Surface Roughness in Turning Applying the Model of Nonlinear Oscillator with Complex Deflection," Mathematics, MDPI, vol. 10(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3214-:d:907492
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    References listed on IDEAS

    as
    1. Vikas Upadhyay & P.K. Jain & N.K. Mehta, 2013. "Prediction of surface roughness using cutting parameters and vibration signals in minimum quantity coolant assisted turning of Ti-6Al-4V alloy," International Journal of Manufacturing Technology and Management, Inderscience Enterprises Ltd, vol. 27(1/2/3), pages 33-46.
    2. Sukhdev S. Bhogal & Charanjeet Sindhu & Sukhdeep S. Dhami & B. S. Pabla, 2015. "Minimization of Surface Roughness and Tool Vibration in CNC Milling Operation," Journal of Optimization, Hindawi, vol. 2015, pages 1-13, January.
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    Cited by:

    1. Livija Cveticanin, 2023. "Exact Closed-Form Solution for the Oscillator with a New Type of Mixed Nonlinear Restitution Force," Mathematics, MDPI, vol. 11(3), pages 1-11, January.

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