1. CASE STUDY OF MORTON EFFECT SHAFT DIFFERENTIAL HEATING IN A VARIABLE-SPEED ROTATING ELECTRIC MACHINE (GT2011-45228) by Brian Murphy Austin, Texas (presenter) Joshua Lorenz Mankato, Minn.

2. Subject Machine of this Paper Horizontal and vertical shaft displacement probes and housing velocity sensors Bearing locations 800 kg overhung mass

3. Shaft Differential Heating

4. Unit 1 - Quick Balancing Run Early Hint Something Unusual is Happening

5. Unit 2 - Long Slow Divergence at 4150 rpm First Incidence of a Trip on High Vibration

6. Unit 1 - Faster Divergence at 4200 rpm

7. Unit 1 - Rapid Divergence at 4200 rpm

8. Unit 1 - Progressive Thermal Transients at Progressively Higher Speed

9. Unit 4 - Divergence at 3950 rpm First unit to show instability below 4100 rpm This led to hardware fix based on analytical predictions

10. “ Simplified” Mathematical Treatment 1. Vibration V proportional to imbalance U 2. Shaft Temperature T proportional to vibration V (this one is Morton effect) 3. Imbalance U proportional to temperature T 4. Transient drift of hot spot T around shaft trying to attain steady state (  is thermal time constant) 5. Combine these 4 expressions 6. Solution for T is an exponential 7. Solve for complex eigenvalue s 8. Morton effect is unstable when real part of s is positive 9. A , B and C depend on speed. So plot s as a function of speed and look for unstable speeds A completely linear analysis. This simple model does replicate observed machine behavior. 4 Linear eqn’s form the model Solution is a simple exponential

12. Analysis Results Match Tests Partial Arc 4 Lobe Original Partial Arc Replacement 4 Lobe The model replicates the stable, borderline unstable, and outright divergent behavior with the partial arc bearing, and predicts complete stability with the 4 Lobe bearing. Plot of ABC (i.e.  s +1)

14. Questions?