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

M. Hashemitaheri, T. T. Le, T. Khan, H. Cherukuri

TL;DR

This work tackles the mismatch between idle-state stability boundaries and in-process milling behavior by introducing an inverse, data-driven Newton-Raphson approach to identify in-process structural-dynamics parameters. The method couples a physics-based stability diagram—constructed with a Fourier-series Zero-Order model—with empirical stability-lobe data, updating six in-process parameters $(f_{nx}, k_x, \xi_x, f_{ny}, k_y, \xi_y)$ via an $MLAE$-based optimization and sensitivity guidance. Three synthetic tests demonstrate convergence to reference SLDs, and an empirical dataset shows improved stability-boundary alignment when the inferred in-process dynamics are used. Sensitivity analyses (local and Monte Carlo) reveal that the natural frequencies $(f_{nx}, f_{ny})$ are the dominant factors shaping the stability boundary, offering insight into reliable robustness against parameter uncertainty. The work provides a pathway to more accurate, in-process chatter prediction and parameter tuning for milling.

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.

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

TL;DR

This work tackles the mismatch between idle-state stability boundaries and in-process milling behavior by introducing an inverse, data-driven Newton-Raphson approach to identify in-process structural-dynamics parameters. The method couples a physics-based stability diagram—constructed with a Fourier-series Zero-Order model—with empirical stability-lobe data, updating six in-process parameters via an -based optimization and sensitivity guidance. Three synthetic tests demonstrate convergence to reference SLDs, and an empirical dataset shows improved stability-boundary alignment when the inferred in-process dynamics are used. Sensitivity analyses (local and Monte Carlo) reveal that the natural frequencies are the dominant factors shaping the stability boundary, offering insight into reliable robustness against parameter uncertainty. The work provides a pathway to more accurate, in-process chatter prediction and parameter tuning for milling.

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.
Paper Structure (6 sections, 6 equations, 5 figures, 5 tables, 2 algorithms)

This paper contains 6 sections, 6 equations, 5 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results
  4. Newton-Raphson Method
  5. Sensitivity Analysis
  6. Conclusions

Figures (5)

  • Figure 1: The objective function (MLAE) measuring the error terms trough iterations.
  • Figure 2: Some of the steps in Newton-Raphson approach for example 3. The blue curve is the empirical SLD while the orange curve is the guessed SLD at each step.
  • Figure 3: Final SLDs for the three examples. Blue curves are the target SLDs while the orange curve shows the calculated SLD in each example.
  • Figure 4: Stability lobe diagram on empirical data for Newton-Raphson method and methods used in eynian2019process.
  • Figure 5: Sensitivity of the stability lobe diagram to the changes in structural dynamics parameters.