Abstract
KEYWORDS
modal analysis, rotor, optimization, finite element.
ABSTRACT
The reliability and efficiency of every rotating machine depends on the designer’s ability to predict correctly a range of its dynamic characteristics, including stability, vibration response levels and fatigue. For these tasks, reliable structural dynamics models are essential. In general, the properties of the rotating elements (rotors, disc etc) are time varying as seen by a stationary observer, and in principle to obtain the complete set of left and right hand eigenvectors needed to describe the structure completely. It is well known that most vibrations in rotating machinery are induced by rotating related sources. For example, rotating unbalance is the major source of vibration synchronous to the rotational speed Ω; misalignment and cracks in shafts cause the vibration iΩ (i is an integer); ball bearings defects cause the vibration nΩ (n is a real number); and so forth. As a consequence, forced vibration analysis of a rotating equipment subject to synchronous or asynchronous harmonic excitation becomes essential to identify the vibration source or to ensure the proper design in considering vibration problems. Due to rotation-related factors such as gyroscopic effects and fluid dynamic forces in bearings and seals, the resulting eigenvalue problems of most rotor systems are expressed by nonself-adjoint differential operators. For the modal analysis of nonself-adjoint eigenvalue problems not only are classical modal parameters required but also adjoint modal parameters such as left eigenvectors. In paper has developed a set of analytical techniques for predicting the dynamic behaviour of rotating structures. Hear using the modal analysis procedure of rotor systems is proposed a new method for external optimisation of the rotor-bearings systems Based on the modal analysis of the rotor-bearing systems, we introduce several objective functions, which are a measure of the dynamic stiffness. The goal is to diminish the vibrations and is implemented by maximizing the dynamic stiffness, i.e., minimizing the receptance function. Therefore, the code computer optimisation program is obtained by the coupling of the FEM with the non-linear optimisation methods with constrains.