*Corr. Author’s Address: Autonumus University of Queretaro, Faculty of Engineering, Cerro de las Campanas s/n, Ciudad Universitaria, 76010 Querétaro, Qro., México, jc.jauregui@uaq.mx 693 Strojniški vestnik - Journal of Mechanical Engineering 58(2012)12, 693-700 Paper received: 2012-06-13, paper accepted: 2012-10-17 DOI:10.5545/sv-jme.2012.649 © 2012 Journal of Mechanical Engineering. All rights reserved. 0 INTRODUCTION Grinding technology has an important advantage in terms of productivity and precision in comparison with its competitive machining operations. Innovations in fixed-abrasive tools with enhanced, wear-resistant abrasives and improved bond systems [1] together with higher process capacity [2] have all contributed to this. Centerless grinding process (CGP) is one of the most productive and precise machining operation for manufacturing of rotationally- symmetrical workpieces. The advantage of the CGP is that the workpiece is not clamped, thus enabling high automation and production rates. The disadvantage of having the workpiece not held between centers is that the process is unstable and the workpieces lobed (non- round). In the centerless grinding gap the workpiece is supported at its surface in three points; the grinding wheel, the regulating wheel and the workrest blade, as shown in Fig 1. The function of each one of them is the following: • The grinding wheel removes material from the workpiece diameter. • The regulation wheel controls the workpiece velocity (by friction) and the radial infeed (depending on machine configuration). • The workrest blade supports the workpiece and keeps the set workpiece height. Next to workpiece out-of-roundness, chatter is the most significant problem related to CGP. Chatter (self excited vibrations) can deteriorate both the workpiece and the grinding wheel surfaces. The most obvious errors on the workpiece surface are chatter marks (wavy markings on the workpiece surface) that are rooted in: variation in depth of cut caused by CGP- inherent workpiece center displacement; the existence of a too-large angle of the workrest blade; flexibility of the grinding wheel; high workpiece speed; vibrations transmitted to the machine or caused by a defective drive; the interference between grinding wheel out-of- balance and workpiece waviness [3]. The configuration of the CGP is complex and has a high sensitivity to the grinding gap set-up and process parameters [4] to [7]. Moreover, productivity depends on the process stability. The latter is usually secured by reducing the workpiece speed that ultimately leads to low material removal rates. There are different responses of the CGP as a consequence of the instability: The workpiece looses contact with the workrest blade, presents run-out and chatter [8] to [11]. Many researchers have studied the CGP instability. Some of the first investigations were done by Furukawa et al. [12] and [13], who pointed out that the self-excited vibration is geometrically stable but it changes to an unstable condition as a result of the workpiece regeneration, system dynamic characteristics and low dynamic stiffness due to machine-tool design. Very often, the CGP stability has been analyzed through simulation. Simulations consider the use of kinematic, kinetic and geometric conditions, and mechanical properties of the process. With a simulation it is possible to obtain: Stability maps showing the stable/unstable geometric configurations, the number of lobes that generate unstable conditions, a qualitative determination of the workpiece roundness error, the dynamical displacement, and the predictions Nonlinear Model for the Instability Detection in Centerless Grinding Process Robles-Ocampo, J.B. –Jáuregui-Correa, J.C. –Krajnik, P. –Sevilla-Camacho, P.Y. –Herrera-Ruiz, G. Jose Billerman Robles-Ocampo 1,2 – Juan Carlos Jauregui-Correa 1,* – Peter Krajnik 3 – Perla Yasmin Sevilla-Camacho 1,2 – Gilberto Herrera-Ruiz 1 1 Autonumus University of Queretaro, Faculty of Engineering, Mexico 2 Polytechnic University of Chiapas, México 3 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia In this work a novel nonlinear model for centerless grinding is presented. The model describes the dynamic behavior of the process. The model considers that the system’s stiffness depends on the existence of lobes in the workpiece surface. Lobes geometry is treated as a polygonal shape and it is demonstrated that the system can be represented as a Duffing’s equation. It is shown that there is a critical lobe number, where the systems present an unstable behavior; the critical lobe number is identified through the geometric stability index. Instabilities in the centerless grinding process are analyzed with two methods: the phase diagram and the continuous wavelet transform. The presented results show that the dynamic behavior of the centerless grinding process can be represented with a cubic stiffness function that is obtained from the analysis of the surface topology. Keywords: phase diagram, chatter, nonlinear model, centerless grinding, polygonal shape, instability index