A Dedicated Model Reduction Method for Turbo-Machines Using a Critical Speed Subspace

Finite element models representing industrial scale turbomachines have reached today a very large number of degrees of freedom. The large size of these models requires the use of reduced order modelling to make the simulations computationally affordable. However, the physical characteristics (i.e. modes shapes and natural frequencies) of a rotating machine depend on the rotating speed of the system and classical modal reduction approaches are not efficient in this case. A classical modal basis does not allow to decompose the unbalance response of a rotating system into independent components because the normal modes are evaluated for a constant rotating speed. They are thus invariant and insensitive to the rotating speed variation. In this work a method is proposed to evaluate a reduction basis composed only by the modes excited when the system runs through its own critical speeds. This method produces an essential basis of modes which is optimal for the identification of the main components of the unbalance response of a rotating system. The development of this reduction basis is firstly formulated mathematically. Then, the 'critical speed basis' is employed to reduce a real finite element model of about 100 DOFs and it is compared with a classical modal basis. Finally, the efficiency of the proposed reduction method is tested in a non-linear framework.