High order vector numerical integration schemes applied in state space milling stability analysis

Third and fourth order vector numerical integration schemes were proposed in this work and applied in more accurate handling of difficult integration problem in milling stability analysis. Error vector analysis was carried out on a generalized discrete interval for each of the first and second order vector numerical integration methods (Known in literature 9) and also for the proposed third and fourth order vector numerical integration methods. The results from error vector analysis suggested that accuracy increases in the order; first, second, third and fourth order vector numerical integration methods. The suggestion was verified with both numerical rate of convergence and stability analysis of both 1 degree of freedom (1DOF) and 2 degree of freedom (2DOF) milling processes. The advantage of the proposed high-order vector numerical integration methods in terms of accuracy and their disadvantage in terms of computational time relative to recent methods are highlighted. Avenue for future work was identified as discussed in the conclusion.

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