ORIGINAL ARTICLE Modelling of dynamic cutting force coefficients and chatter stability dependent on shear angle oscillation Erol Turkes 1 & Sezan Orak 2 & Süleyman Neşeli 3 & Mumin Sahin 4 & Selcuk Selvi 4 Received: 25 April 2016 /Accepted: 16 November 2016 # Springer-Verlag London 2016 Abstract Productivity of high-speed turning operations is limit- ed by the onset of self-excited vibrations known as chatter. Unless avoided, chatter vibrations may cause large dynamic loads dam- aging the machine spindle, cutting tool or workpiece and leave a poor surface finish behind. Cutting force magnitude is proportion- al to the thickness of the chip removed from the workpiece. This paper presents a new procedure to determine dynamic cutting force coefficients (DCFC) required for process simulation by mechanistic modelling. In this study, a two degree of freedom complex dynamic model of turning with an orthogonal cutting system is considered. The complex dynamic system consists of a dynamic cutting system force model based on shear angle (φ) oscillations and penetration forces caused by the tool flank’ s con- tact with the wavy surface. The dynamic cutting force coefficients are identified by operating a series of cutting tests at the desired frequency, while changing φ oscillations and penetration forces. It is shown that the process damping coefficient increases as the tool is worn, which increases the chatter stability limit in cutting. The chatter stability of a dynamic cutting process is solved using the Nyquist law and time domain simulation (TDS) techniques and compared favourably against experimental results at low cut- ting speeds. Finally, comparisons among the proposed mechanis- tic model and experimental results show a good agreement with the analytically established SLD and, thus, validate the effective- ness of the proposed model. Keywords Chatter stability . Dynamic cutting force . Share angle oscillation . Turning 1 Introduction Machine tool chatter is the self-excited relative oscillation be- tween the cutting tool and the workpiece which is developed under large metal removal rates. It deteriorates the workpiece surface, reduces tool and machine life and may lead to dangerous accidents. Over the last 100 years, research on this problem has produced many analytical theories as the learning and production engineering world paid close attention to it. Among these theories, the regenerative chatter theory and the mode coupling theory were identified as the principle theories by Tobias [1] and Tlusty [2]. Merritt [3] presented an elegant stability theory for orthogonal turning, using system theory terminology. Recently, researchers [4–8] brought forward analysis and control techniques through various models for the prediction of chatter vibrations. However, since the mechanics and dynamics of cutting have not been discussed adequately, a proper and complicated model capable of expressing metal removal dynamics does not exist yet. Analysis of chatter vibrations is achieved by processing linear and nonlinear forces. All chatter analysis techniques begin with models of the machining force process and the tool-workpiece * Süleyman Neşeli sneseli@selcuk.edu.tr Erol Turkes erol.turkes@klu.edu.tr Sezan Orak sorak@ogu.edu.tr Mumin Sahin mumins@trakya.edu.tr Selcuk Selvi selcukselvi@trakya.edu.tr 1 Mechanical Engineering, Kırklareli University, Kırklareli, Turkey 2 Mechanical Engineering, Eskişehir Osmangazi University, Eskişehir, Turkey 3 Mechanical Engineering, Selcuk Universitesi, Konya, Turkey 4 Mechanical Engineering, Trakya University, Edirne, Turkey Int J Adv Manuf Technol DOI 10.1007/s00170-016-9782-y