A new perspective on the stability study of centerless grinding process

Regenerative chatter is one of the most complex dynamic processes in machine tools. It is characterized by the presence of self-excited vibrations during machining, limiting the achievable tolerances in the workpieces. In order to predict the set-up conditions that produce these vibrations, it is necessary to model the regenerative mechanism responsible of their appearance accurately, so that the system stability can be studied solving the characteristic equation of the chatter loop. Although the dynamic behavior of machining processes like milling, turning or drilling is governed by a time delayed differential equation with one time delay term, a very particular problem is presented in centerless grinding. In this process, in addition to the dynamic instabilities, geometric instabilities must be analyzed, which are another important factors limiting the workpiece tolerances and lead to three time delay terms in the modeling procedure. This fact complicates its study remarkably, and the resolution of the characteristic roots of the dynamic process of these kinds of machines has not been tackled in the specialized literature as extensively as in other machining processes, being this field a challenging research line. According to this, in this paper an original and efficient method is presented to solve the roots of the characteristic equation of the centerless grinding process, based on the application of the root locus method. The main features of the proposed procedure are its ability to obtain the solutions accurately and that it is capable of determining the origin of the instabilities, so it constitutes a powerful tool to predict machine response for different set-up conditions. These interesting properties are demonstrated through the simulation results presented in this paper.