Sensitivity Analysis and Monte Carlo Based Uncertainty Quantification of the In-process Modal Parameters in Milling

TL;DR

This paper introduces a novel inverse method combining physics-based models with empirical data to accurately determine in-process structural dynamics parameters for milling, enhancing the reliability of stability predictions and quantifying parameter sensitivities.

Contribution

It proposes a multivariate Newton-Raphson based inverse approach to estimate in-process dynamics, improving stability boundary accuracy over traditional static measurements.

Findings

The inverse method successfully estimates dynamic parameters from synthetic and empirical data.

Sensitivity analysis quantifies how parameter variations affect the stability boundary.

The approach enhances the reliability of stability lobe diagrams during milling operations.

Abstract

The material removal rates during milling operations are affected by the selection of the cutting depth and spindle speed. Poor selection of these parameters can result in chatter or suboptimal material removal rates. Stability Lobe Diagrams (SLDs) are the well-known approach to selecting appropriate chatter-free values for these parameters. The Physics-based stability lobe diagram is usually generated using the structural dynamics and the cutting parameters. However, since the machine dynamics are measured in the static state of the machine (zero speed), the generated SLD is not reliable as the machine behavior may vary during the cutting operations. Besides, measuring structural dynamics parameters under cutting conditions is difficult and needs new equipment. This study proposes a new approach to determining in-process structural dynamics parameters based on a multivariate Newton-Raphson method. The physics-based model is combined with empirical records to extract reliable structural dynamics parameters inversely. Some examples based on synthetic data are presented to illustrate this inverse approach. Also, the performance of the algorithm is evaluated on an empirical data set and its ability to improve the stability boundary is verified. Furthermore, the sensitivity analysis is performed to quantify the exposure of the SLD to the changes in each structural dynamics parameter.