abstract
- © 2015, Springer-Verlag London.The demands for more precise tolerances in big industrial components has led to more versatile machine designs that allow a number of cutting operations to machine the part from the bulk to the final stage. This type of machine is usually oriented to the manufacture of a specific family of parts with large diameter where the operating conditions are known before the machine is built (work material, operations and tools). Therefore, obtaining the lobes diagram is a key issue at the design stage of the machine allowing to compare different architectures and define the best option. This paper presents three dynamic models that are combined with the multi-mode approach to consider various modes with non Cartesian orientations. The frequency method was first implemented to obtain stability maps of turning systems with very low rotational speeds (<100 rpm), as in the case of these machines. Alternatively, the formulation for the efficient Chebyshev method was also raised. The aim of this work is to present a technique based on the MATLAB dde23 routine for stability and time simulation purposes with a competitive computation time for large time delays. The models were verified each other with dynamic tests in a vertical turning lathe. The dde23 algorithm is more efficient than conventional numerical methods for low rotation speeds and can be used to reproduce the vibrational behaviour of turning systems with long delays together with complex cutting forces models.