International Journal of Machine Tools & Manufacture 46 (2006) 1489–1499 Analytical models for high performance milling. Part II: Process dynamics and stability E. Budak à Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey Received 15 July 2005; received in revised form 17 September 2005; accepted 22 September 2005 Available online 10 November 2005 Abstract Chatter is one of the most important limitations on the productivity of milling process. In order to avoid the poor surface quality and potential machine damage due to chatter, the material removal rate is usually reduced. The analysis and modeling of chatter is complicated due to the time varying dynamics of milling chatter which can be avoided without sacrificing the productivity by using analytical methods presented in this paper. r 2005 Elsevier Ltd. All rights reserved. 1. Introduction Productivity and surface quality in milling processes have direct effects on cost, production lead-time and quality of machined parts. Chatter is one of the most common limitations for productivity and part quality in milling operations. Poor surface finish with reduced productivity and decreased tool life are the usual results of chatter. Additional operations, mostly manual, are required to clean the chatter marks left on the surface. Thus, chatter vibrations result in reduced productivity, increased cost and inconsistent product quality. The importance of modeling and predicting stability in milling has further increased within last couple of decades due to the advances in high speed milling technology. At high speeds, the stabilizing effect of process damping diminishes making process more prone to chatter. On the other hand, high stability limits, usually referred to as stability lobes, exist at certain high spindle speeds which can be used to increase chatter-free material removal rate substantially provided that they are predicted accurately. Chatter vibrations develop due to dynamic interactions between the cutting tool and workpiece. Under certain conditions the amplitude of vibrations grows and the cutting system becomes unstable. Although chatter is always associated with vibrations, in fact it is fundamen- tally due to instability in the cutting system. The first accurate modeling of self-excited vibrations in orthogonal cutting was performed by Tlusty [1] and Tobias [2]. They identified the most powerful source of self-excitation, regeneration, which is associated with the dynamics of the machine tool and the feedback between the subsequent cuts on the same cutting surface. The stability analysis of milling is complicated due to the rotating tool, multiple cutting teeth, periodical cutting forces and chip-load directions, and multi-degree-of-freedom structural dy- namics. In the early milling stability analysis, Koenigsber- ger and Tlusty [3] used the orthogonal chatter model [1] considering an average direction and average number of teeth in cut. An improved approximation was performed by Opitz et al. [4]. Sridhar et al. [5,6] performed a comprehensive analysis of milling stability which involved numerical evaluation of the dynamic milling system’s state transition matrix. On a two-degree-of-freedom cutter model with point contact, Minis et al. [7] used Floquet’s theorem and the Fourier series for the formulation of the milling stability, and numerically solved it using the Nyquist criterion. Budak [8] developed a stability method which leads to analytical determination of stability limits in milling. The method was verified by experimental and numerical results [9,10], applied to the stability of ball-end milling [11], and was also extended to 3D milling [12]. The special case of low immersion milling has been investigated ARTICLE IN PRESS www.elsevier.com/locate/ijmactool 0890-6955/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.09.010 à Tel.: +902164839519; fax: +902164839550. E-mail address: ebudak@sabanciuniv.edu.