Modeling and experimental validation of dynamic response of the cutting tool in turning operations

Abstract

The aim through the present paper is to calculate by analytical modelling the dynamic response of the cutting tool in turning processes, where, the general solution of the dynamic response is based on the numerical evaluation of Duhamel's integral and the integration of the measured cutting force signals into calculations. The proposed approach is a mathematical modelling of the cutting tool dynamic formulated in transverse vibrations in tangential and axial direction respectively according to the cutting speed and feedrate direction based on Rayleigh beam theory, which include the effect of rotary inertia. For this, the turning tool is modelled as a cantilever beam with a uniform cross-section, excited with tangential cutting force applied to their free-end to calculate the transverse tool displacements. To validate the analytical results, comparisons are performed against measured transverse tool displacements obtained from measured tool accelerations. Therefore, it is concluded that well agreement between results was demonstrated and was found.

Keywords

• transverse vibrations
• rayleigh beam
• force signal
• dynamic response
• duhamel's integral
• transverse tool displacement