Extracting the In-Process Structural Dynamics Parameters in Micro-Milling Operations

Stability properties of micro-milling operations are characterized by the Stability Lobe Diagram (SLD). The material removal rates during micro-milling operations depend on the optimal values chosen for the depth of cut and also spindle speed. Theoretically, the stability boundary is calculated having the structural dynamics and the cutting parameters. However, some discrepancies are usually observed between the empirical results and the expected results that the theory supports. The driver of such a gap is that the dynamics is affected during machining operation by parameters such as the spindle speed, cutting loads, thermal changes, feed rate, etc whereas the theory is based on the structural dynamics parameters in the idle state of the machine (zero speed). Consequently, the selection of chatter-free values for cutting depth and spindle speed based on SLD in the idle state of the machine is not reliable. In addition, measuring structural dynamics parameters under cutting conditions is difficult. In this study, a novel approach is introduced to determine in-process structural dynamics parameters based on a multivariate Newton-Raphson method. Having the empirical SLD characterized by experimental data, our method tries to find the structural parameters under which the theory can support the given empirical SLD. Note that the theoretical SLD is usually characterized as a function of the cutting and structural dynamics parameters. Here our method follows the inverse flow and utilizes the empirical SLD to return the underlying parameters. The parameters returned by our method are those supported by the physics-based theories. Therefore, our approach is a hybrid method where the physics-based model is combined with the experimental results. For any given empirical SLD, with the cutting parameters fixed, the in-process structural dynamics parameters are determined using the proposed inverse approach. We use a multivariate Newton-Raphson method approach where through the iterations, an initial guess selected for the set of the parameters is adjusted step-by-step until the final set of the parameters can justify the empirical SLD based upon physics-based models.