Abstract

The prediction of chatter-free machining parameters is not reliable for industrial applications without guaranteed robustness against modeling uncertainties. Measurement inaccuracies, fitting uncertainties, simplifications and modeling errors typically lead to a mismatch between the mathematical model and the real physical system. This paper presents the robust stability analysis of milling operations based on a pseudospectral approach to take into account the effect of bounded parametric uncertainties both in the cutting coefficients and in the modal parameters. In order to make the predictions more accurate, the operational modal analysis of the spindle during rotation was conducted. The natural frequencies and damping ratios of the dominant vibration modes were identified from the impact tests of the rotating tool at different spindle speeds. The uncertainties of the fitted parameters were included in the computation of the pseudospectral radius of the monodromy operator of the time-periodic system. The solver is tested in a case study and experimental chatter tests are also included for demonstration purposes.

Highlights

  • The continuously increasing demand for competitive, fast, high-quality and economical production forces the manufacturing industry to push the operational conditions of machines to their limit

  • The vibrations in the past are embedded in the surface of the workpiece, which affects every subsequent cut by the modified geometry of the chip that depends on present and past states, too

  • A different robust method called Multi-frequency Solution with Structured Singular Value Analysis is based on the direct perturbation of the measured frequency response functions (FRFs), where parameter perturbations are replaced by FRF perturbations, see [14]

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Summary

Introduction

The continuously increasing demand for competitive, fast, high-quality and economical production forces the manufacturing industry to push the operational conditions of machines to their limit. The need for reliable predictions considering variations in machining and dynamical parameters was already recognized by the engineering community, and many attempts were made to construct such stability lobe diagrams that take the effect of modeling errors into account. A different robust method called Multi-frequency Solution with Structured Singular Value Analysis is based on the direct perturbation of the measured frequency response functions (FRFs), where parameter perturbations are replaced by FRF perturbations, see [14] In this latter case the computational effort is significantly reduced, but the prediction can be very conservative. This paper presents the application of a pseudospectral approach that considers uncertainties in the dynamical parameters of milling operations and provides robust stable machining domains to exploit the highest productivity.

Modeling of milling operations
Stability of time-periodic time-delay systems
Pseudospectral method for robust analysis
Extension to modal parameter uncertainties
Case study and experiment
Comparison with the MFS-SSV method
Conclusion
Calculation of the gradient

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