Abstract: An analytic model as well as mathematical method is presented for calculating the dynamical characteristics of tilting-pad bearings. This model gives very concise expressions of the full dynamical coefficient matrix of tilting-pad bearings. Based upon the moving relationship between pads and the shaft, the local coordinate systems can be chosen. The global generalized coordinates, which associated with degrees of freedom including all pads and journal, are exactly transformed to the journal coordinates relative to the local moving system. In the local pad system, the oil-film forces and the Jacobians are computed through the algorithm used in fixed pad bearings. Then, those film forces are transformed to the global generalized forces exactly. Derivatives of the generalized forces give the Jacobians with respect to displacements and velocities of all generalized coordinates. Once the equilibrium position is found the negative of the global Jacobians are just the complete dynamic coefficient matrices. By making assumptions on pad motion, reduced characteristics can be obtained. This analytic method could be used in analyzing dynamic behavior of the tilting-pad bearing-rotor systems.

Key words: Analytic geometry model, Dynamic coefficients, Jacobian matrix, Tilting-pad journal bearing