Implicit subspace iteration as an efficient method to compute milling stability lobe diagrams

Zatarain, M. and Alvarez, J. and Bediaga, I. and Munoa J, J. and Dombóvári, Zoltán (2015) Implicit subspace iteration as an efficient method to compute milling stability lobe diagrams. INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY, 77 (1-4). pp. 597-607. ISSN 0268-3768

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Abstract

A new method for calculation of chip removal machining stability diagrams is proposed. The method can be considered as an application of the Floquet theorem by repeated time integrations and represents an alternative to the previously presented time domain stability methods (semi-discretisation, time finite elements and so on), without the requirement to build the transition matrix. In this way, the computation effort is very much reduced, especially when the required number of segments is large. As a result, the computing time depends on the number of segments with an exponent 1.5, instead of 2.8 that is the exponent for the optimised semi-discretisation. This results in that the presented method is the most efficient among the previous ones. As a further advantage, the memory requirements for the method are much lower, allowing computing very-high-order stability lobes. As a drawback, for the computation of high-order lobes, the method is not as efficient as could be expected, due to the slow convergence of the eigensystem resolution when many eigenvalues of similar magnitude exist. Even in that case, the method is five times faster than the optimised semi-discretisation, but a more efficient eigenvalue resolution method is sought for.

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