Fuzzy arithmetical stability analysis of uncertain machining systems

- Stability analysis of machining systems in the presence of uncertainty.
- Formulation and calculation of fuzzy stability lobe diagrams, providing a straightforward interpretability.
- Sensitivity analysis for the stability lobe diagrams, providing meaningful insight to the dynamics of machining systems.

The dynamical behavior of machining processes with parameter uncertainties is analyzed using the possibilistic approach of fuzzy arithmetic. The concept is used to simulate and analyze uncertain models of different complexity. Emphasis is put on the analysis of dynamic stability and the inclusion of the uncertain parameters therein. The stability limits, which are defined by an implicit equation, yield two-dimensional fuzzy-valued results, so that standard solution methods are not directly applicable. Therefore, a general method for the solution of implicit equations is presented that may be applied to the stability analysis of arbitrary time-delayed systems. The presented method as well as a fuzzy sensitivity analysis are then applied to the stability analysis of exemplary systems. The propagation characteristic as well as the fuzzy sensitivity analysis allow to see the effect of uncertainties on the system output and quantify the effect of given uncertain parameters.