A Multivariate Newton-Raphson Method Approach to Extract Structural Dynamics Parameters During Milling Operations

The material removal rates during milling operations are affected by the selection of the cutting parameters. Poor selection of these parameters can result in chatter or suboptimal material removal rates. Stability lobe diagrams (SLDs) are often used to select appropriate values for the cutting parameters. The stability lobe diagram is generated using the structural dynamics and cutting parameters. Structural dynamics or Frequency Response Function (FRF) is determined in the idle state of the machine (zero speed). However, the dynamics is influenced during machining operation by parameters such as spindle speed, feed rate, thermal changes, cutting loads, etc. Hence, discrepancies are observed between the FRF calculated in zero speed and during machining conditions. As a result of such discrepancies, the selection of chatter-free spindle speed and depth of cut based on stability lobe diagrams 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 new method is proposed to determine in-process structural dynamics parameters based on a multivariate Newton-Raphson method. The idea of this hybrid approach is to combine physics-based process model with the experimental results. By fixing the cutting parameters, the structural dynamics parameters are determined using the proposed inverse approach. An example based on synthetic data is presented to illustrate the inverse approach. Furthermore, results from a sensitivity analysis performed to study the sensitivity of the SLD to each structural dynamics parameter are presented.