Representing Flexible Supports by Polynomial Transfer Functions

Flexible bearing supports may have a great influence in the calculation of forced response and stability of rotor systems. However, this effect is not always included in rotor analyses since an accurate model of the foundation and pedestals may be difficult and costly to obtain. It is common practice to use either a one degree of freedom model or a full modal analysis to represent the bearing supports. While the one degree of freedom model is easy to set up for computer calculations, it often requires experience to determine values for the stiffness, mass and damping of the model that will accurately represent the support under study. This model, however, fails to capture the dynamics of the system for stability analyses when more than one mode of the support structure is in the range of interest. On the other hand, modal representation provides much more information and can be measured experimentally, but requires measurement of the mode shapes. Even though modal representation can include all the dynamics of the system in the frequency range of interest, it provides much more information than is required for calculation of the rotor response and it is more difficult to use in calculation programs. This paper presents a procedure to include the support characteristics using transfer functions. Transfer functions permit modeling of multi-degree of freedom systems while maintaining the size of a one degree of freedom system (2×2 matrix if rotation at the bearing is not considered). Another advantage of transfer functions is that they can be obtained from existing discrete models, from modal information or can be measured directly. The fixed size of the transfer function matrix permits the method to be easily incorporated into rotor dynamic stability and forced response programs. The method is applied to stability calculations of models of typical industrial machines.