A New, Iterative, Synchronous-Response Algorithm for Analyzing the Morton Effect

Abstract

Morton Effect problems involve the steady increase in rotor synchronous-response amplitudes due to differential heating across a fluid-film bearing that is induced by synchronous response. The present work presents a new computational algorithm for analyzing the Morton Effect. Previous approaches were based on Eigen or Nyquist analyses for stability studies and predicted an onset speed of instability. The present algorithm starts with a steady state elliptical orbit produced by the initial imbalance distribution, which is decomposed into a forward-precessing circular orbit and a backwards-precessing circular orbit. A separate (and numerically intensive) calculation based on the Reynolds equation plus the energy equation gives predictions for the temperature distributions induced by these separate orbits for a range of orbit radius-to-clearance ratios. Temperature distributions for the forward and backward orbits are calculated and added to produce the net temperature distribution due to the initial elliptic orbit. The temperature distribution is assumed to vary linearly across the bearing and produces a bent-shaft angle across the bearing following an analytical result due to Dimoragonas. This bent-shaft angle produces a synchronous rotor excitation in the form of equal and opposite moments acting at the bearing’s ends. For a rotor with an overhung section, the bend also produces a thermally induced imbalance. The response is due to: (1) the initial mechanical imbalance, (2) the bent-shaft excitation, and (3) the thermally-induced imbalance are added to produce a new elliptic orbit, and the process is repeated until a converged orbit is produced. For the work reported, no formal stability analysis is carried out on the converged orbit. The algorithm predicts synchronous response across the rotor’s speed range plus the speed where the response amplitudes becomes divergent by approaching the clearance. Predictions are presented for one example from the published literature, and elevated vibration levels are predicted well before the motion diverges. Synchronous-response amplitudes due to Morton Effect can be orders of magnitude greater than the response due only to mechanical imbalance, particularly near rotor critical speeds. For the example considered, bent-shaft-moment excitation produces significantly higher response levels than the mechanical imbalance induced by thermal bow. The impact of changes in: (1) bearing length-to-diameter ratio, (2) reduced lubricant viscosity, (3) bearing radius-to-clearance ratio and (4) overhung mass magnitude are investigated. Reducing lubricant viscosity and/or reducing the overhung mass are predicted to be the best remedies for Morton Effect problems.