Abstract
Tilting-pad journal bearings are widely used to promote stability in modern rotating machinery. However, the dynamics associated with pad motion alters this stabilizing capacity depending on the operating speed of the machine and the bearing geometric parameters, particularly the bearing preload. In modeling the dynamics of the entire rotor-bearing system, the rotor is augmented with a model of the bearings. This model may explicitly include the pad degrees of freedom or may implicitly include them by using dynamic matrix reduction methods. The dynamic reduction models may be represented as a set of polynomials in the eigenvalues of the system used to determine stability. All tilting-pad bearings can then be represented by a fixed size matrix with polynomial elements interacting with the rotor. This paper presents a procedure to calculate the coefficients of polynomials for implicit bearing models. The order of the polynomials changes to reflect the number of pads in the bearings. This results in a very compact and computationally efficient method for fully including the dynamics of tilting-pad bearings or other multiple degrees of freedom components that interact with rotors. The fixed size of the dynamic reduction matrices permits the method to be easily incorporated into rotor dynamic stability codes. A recursive algorithm is developed and presented for calculating the coefficients of the polynomials. The method is applied to stability calculations for a model of a typical industrial compressor.