ABSTRACT
Reduction of model size reduces cost of calculation, processing and simulation. This paper attempts reducing size of equations of motion for a general rotor-dynamic system. A rotor-dynamic system comprises the shaft, disc or discs and support or supports. The former is a continuum with distributed inertia, dissipation and restoring properties. Discs, bearings, and supports, add locally, inertia, gyroscopic effects, restoring and stationary and rotary dissipative effects, unlike the shaft. Therefore, the shaft requires many more coordinates than the discs, bearings and supports to express its effects in the equations of motion, causing inflation of model size. Literature reports that the technique ‘System Equivalent Reduction Expansion Process’ (SEREP) and its modification to reduce the rotor-dynamic systems as a whole at each speed of rotation. The system matrix is generally non-symmetric, varies with spin speed, and a change in local effect, e.g. its location, properties, therefore, calls for a fresh reduction. In contrast, this paper reports reducing dynamic behaviour of only the shaft continuum and then adds the local effects subsequently, avoiding a fresh reduction. Thus, this paper proposes appropriate transformation matrices, which act upon the original system matrix to achieve the model of reduced size, that may be suitably augmented with local effects, e.g. inertia, restoring, gyroscopic effects, and dissipation properties, wherever desired, and very importantly the information of spin speed, without inflating the reduced size. A close match exists between the modal matrices of proposed reduced model and earlier published model based on Pseudo-Orthogonality Check (POC). A close match between relevant eigenvalues and response, between those predicted by Finite element method simulation and those predicted by the present methodology. This proves correctness of the reduction proposed.
Industrial Applications
Adjusting the rotor-shaft system characteristics at the design stage will be extremely simple and easy to use by following this process. Change of system properties may be easily tracked by revaluating the system. Applying control measures on a rotor-shaft system may be applied better with the help of a short model.
