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

Richárd Horváth, Livija Cveticanin () and Ivona Ninkov
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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
Ivona Ninkov: Bánki Donát Faculty of Mechanical and Safety Engineering, Obuda University, 1081 Budapest, Hungary

Mathematics, 2022, vol. 10, issue 17, 1-15

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.

Keywords: surface roughness; cutting force; complex deflection function; nonlinear oscillator; analytic solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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