Estimation of average roughness of X200Cr12 steel using displacement from the tool nozzle
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ORIGINAL ARTICLE
Estimation of average roughness of X200Cr12 steel using displacement from the tool nozzle N. Kribes 1 & A. Rezaiguia 1 & N. Ouelaa 2 & M.A. Yallese 2 Received: 2 June 2020 / Accepted: 7 September 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In this work, we present a modeling of the dynamic behavior of a turning tool. The goal is to show that it is possible to estimate the roughness average of the workpiece starting from resulting displacement from the tool nozzle. The tool is modeled by the Euler beam clamped-free, excited by the cutting force at its free end. The formulation of the motion equations of the tool is based on the Hamilton variational principle and their resolutions are carried out by the modal method and the Duhamel integral. As the excitation is unspecified, the integrals are evaluated numerically. The three components of the cutting force, obtained experimentally, permit to calculate the tool nozzle displacements. The comparison of the calculated average roughness with the measured one shows a good agreement. We present also a validation of the experimental results of the resulting displacement of the tool nozzle with the calculated displacement. Keywords Cutting force . Modal analysis . Duhamel’s integral . Vibratory behavior . Roughness
1 Introduction The vibration of cutting tools is a major problem that appears during the process of metal cutting. These vibrations limit severely machine tool performance on the qualitative plan that appears as ripple on the surface finish. The study of the dynamic behavior of machine tools is very complex. It requires simplifications considering only flexibility of the tool, while the machine tool and the workpiece are supposed to be infinitely rigid. Bourdim et al. [1] have developed an approach of dynamic stability for identification of cutting parameters and dynamic characteristics of the machine tool-tool/workpiece system. In the articles of Arfaoui et al. [2] and Anderson and Chiffre [3], the authors present a vibrational modeling of the cutting tool in turning and they have demonstrated that the vibratory behavior of the tool depends mainly from the attack * N. Kribes [email protected] 1
Laboratoire de mécanique appliquée des nouveaux matériaux (LMANM), Department of Mechanical Engineering, Université 8 Mai 1945 Guelma, Box 401, 24000 Guelma, Algeria
2
Laboratoire de mécanique et structures, Department of Mechanical Engineering, Université 8 Mai 1945 Guelma, Box 401, 24000 Guelma, Algeria
and draft angles, feed rate, cut depth, and cutting speed. Kato et al. [4] have investigated the influence of cutting speed on tool grazing vibrations and they proposed an analytical approach by analogy with the Vander Pol model, who assumes that a component of the cutting force is in phase with the vibration speed. The authors used the discredited motion equations and their resolutions by different methods such as finite element method. A new analytical model of chatter vibration in metal cutting is presented by Younes
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