Journal Asymmetric Heating—Part II: Alteration of Rotor Dynamic Properties

An approximation of heat conduction dynamics in a rotating shaft is presented for use in the rotor dynamic analysis of multiple hydrodynamic bearings to predict alteration of vibrations due to shaft bows. The interactions form a closed-loop system. Initial unbalance gives a vibration, which results in an asymmetrical temperature distribution on the surface of the journal. Heat conduction in the shaft results in a bow. The new bow changes the unbalance and thus the vibration of the rotor. The loop is thus closed. The approximation of heat conduction is in the form of an ordinary differential equation. The coefficients in this equation result from a curve-fitting to the solution of a nonstationary partial differential equation. The result opens the way for stability analysis, transient analysis, and evaluation of actual mass unbalance response (including fully developed bows).