Rotordynamic Parameters of Bearings, Seals, and Dampers

In Chapter 2 , rotor systems were analyzed for simple cases by considering the shaft to be flexible and the bearing to be rigid. However, in the real world, bearings do provide flexibility to the rotor system. Depending upon the type of bearing or other similar machine elements (e.g., dampers, seals, etc.), these provide the stiffness and/or the damping to the rotor system (or sometimes added-mass or inertia terms). In the present chapter, the procedure to theoretically/numerically obtain these dynamic properties of the support system will be explained. First, rolling element bearings are introduced and classified and the relationship between the load and the deformation is derived from the basic Hertzian contact theory. From the load–deformation relation, then, stiffness of the rolling element bearing is obtained. Hydrodynamic radial bearings are introduced and classified according to the shape of the bore and lubricant groove positions. To obtain the stiffness and damping coefficients of the hydrodynamic radial bearing, a procedure is described using the basic Reynolds equation. For a simple case based on the short bearing assumption, closed-form analytical rotordynamic parameter expressions are presented. Next, dynamic seals are introduced and classified based on various categories. Based on bulk-flow models, governing equations are presented, and for a simple case, the dynamic parameters are obtained and analyzed for various operating parameters. The basics of squeeze-film dampers (SFDs) are introduced and relevant rotordynamic parameters are presented. Finally the foil bearing is introduced regarding its various configurations in use and rotordynamic parameter calculation. Active magnetic bearings are covered in Chapter 8 of Volume II. The main aim of the present chapter is not to provide exhaustive coverage of bearings, seals, and dampers, because each of them is a subject in itself. The basic premise of this chapter is to acquaint readers with the rotordynamic parameters of these machine elements so that, if needed, a detailed analysis could be performed through the available textbooks on these topics. Hydrostatic bearings, gas bearings, etc., have not been dealt with here; however, these do impart similar rotordynamic characteristics to the rotor systems. Chapter 4 of Volume II describes the experimental procedures to obtain rotor dynamic coefficients for all such elements, which are often more reliable and preferred in industries.