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Gas Turbines: Structures and Dynamics

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

[+] Author and Article Information
Dara W. Childs1

 Turbomachinery Laboratory, Texas A&M University, College Station, TX 77843dchilds@tamu.edu

Rohit Saha

 Engineer - Machine Integration Tools, Cummins, Inc., 500 Jackson Street, MC: 60412, Columbus, IN 47201rohit.saha@cummins.com

1

Corresponding author.

J. Eng. Gas Turbines Power 134(7), 072501 (May 23, 2012) (9 pages) doi:10.1115/1.4005973 History: Received August 01, 2011; Revised August 26, 2011; Published May 23, 2012; Online May 23, 2012

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.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Shaft with a thermally-induced bend at the right-hand bearing

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Figure 2

Synchronous elliptic orbit for motion about an equilibrium position

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Figure 3

Decomposing an elliptic orbit into forward and backward circular orbits

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Figure 4

Rotor fixed x,y,z coordinate system

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Figure 5

Relative positions of the rotor fixed x,y,z and xT ,yT ,z coordinate systems

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Figure 6

Measured in-rotor temperature [12]

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Figure 7

Overhang model by De Jongh and Morton [11]

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Figure 8

Scheme of instability phenomenon after [11]

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Figure 9

Maximum differential temperature and phase lag angles for forward and backward orbits

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Figure 10

(a) Calculated ΔTf ,ΔTb and (b) ϕTf , ϕTb versus orbit amplitude at 7500 RPM at ɛ0  = 0.667 from Table 1

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Figure 11

Rotordynamic model of Keogh and Morton [9], symmetric rotor

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Figure 12

Morton Effect response ρmax versus ω of original model

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Figure 13

a/Cr versus ω with for various combinations of Morton Effect

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Figure 14

Morton Effect synchronous response with centered imbalances of 50 gm-cm and 100 gm-cm

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Figure 15

Morton Effect response-ρmax versus ω for different L/D ratios

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Figure 16

ΔTf versus F/Cr for L/D=0.35 and 0.5 at 7500 rpm

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Figure 17

ΔTf versus F/Cr for Cr/R = 0.001 and 0.002 at 7500 rpm

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Figure 18

Morton Effect response ρmax versus ω for different Cr/R ratios

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Figure 19

Morton Effect response ρmax versus ω for different overhang masses

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Figure 20

Morton Effect response ρmax versus ω for different viscosities

Tables

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