The new concept of the rotors and supporting structure transformation for non-linear vibrations analysis

In this paper we will discuss the problem of mathematical description of two basic sub-systems composing a rotating machine, which are the line of rotors with bearings and the supporting structure. If we want to obtain non-elliptic trajectories, with various types of defects in system's operation and complicated vibration spectra coded in their shapes - which makes the basis for technical diagnostics - we must turn to the non-linear analysis and solve the equations of motion in another reference system. The subsystems that frequently reveal non-linear characteristics include the line of rotors with constructional and operational imperfections (misalignment, shaft cracks), and, undoubtedly, the slide bearings and labyrinth seals. At the same time the supporting structure can be treated with satisfactory accuracy as a subsystem having the linear characteristics. In this situation a key question is how to unite in one system the supporting structure, with its linear characteristics, and the line of rotors and bearings, resting on the supporting structure and definitely representing the non-linear characteristics. Here, such an elegant notation in the form of a complex matrix for the entire machine is not possible any longer. From the mathematical point of view the situation is becoming dramatically more complicated. In this paper we will propose solutions to this problem in the form of so-called adequacy intervals of the supporting structure dynamic characteristics, with relevant transformation of those characteristics, and will present a novel concept how to incorporate those characteristics to the rotor line dynamics, based on a so-called weight functions proportional to the vibration spectrum of the supports. The proposed concept can be of extreme value for defining defect-symptom relations, to be used in a new and rapidly developing discipline of science bearing the name of the model based diagnostics.