CASE STUDY OF MORTON EFFECT SHAFT CASE STUDY OF MORTON EFFECT SHAFT DIFFERENTIAL HEATING IN A VARIABLE-DIFFERENTIAL HEATING IN A VARIABLE-SPEED ROTATING ELECTRIC MACHINESPEED ROTATING ELECTRIC MACHINE

(GT2011-45228)(GT2011-45228)

by

Brian MurphyAustin, Texas

(presenter)

Joshua LorenzMankato, Minn.

Subject Machine of this PaperSubject Machine of this Paper

Horizontal and verticalshaft displacement probes and

housing velocity sensors

Bearing locations800 kg overhung mass

-1.3

-0.8

-0.3

0.2

0.7

1.2

-1.3 -0.8 -0.3 0.2 0.7 1.2

-1.3

-0.8

-0.3

0.2

0.7

1.2

-1.3 -0.8 -0.3 0.2 0.7 1.2

High spotLow spot

Shaft Differential HeatingShaft Differential Heating

Unit 1 - Quick Balancing RunUnit 1 - Quick Balancing RunEarly Hint Something Unusual is HappeningEarly Hint Something Unusual is Happening

Unit 2 - Long Slow Divergence at 4150 rpmUnit 2 - Long Slow Divergence at 4150 rpmFirst Incidence of a Trip on High VibrationFirst Incidence of a Trip on High Vibration

0

50

100

150

200

9:30 AM 10:30 AM 11:30 AM

mic

ron

s p

-p

-300

200

700

1200

1700

2200

2700

3200

3700

4200

rpm

TE BN X

TE BN Y

NT BN X

NT BN Y

Speed

Unit 1 - Faster Divergence at 4200 rpmUnit 1 - Faster Divergence at 4200 rpm

Unit 1 - Rapid Divergence at 4200 rpmUnit 1 - Rapid Divergence at 4200 rpm

Unit 1 - Progressive Thermal Transients at Progressively Higher Unit 1 - Progressive Thermal Transients at Progressively Higher SpeedSpeed

Unit 4 - Divergence at 3950 rpmUnit 4 - Divergence at 3950 rpmFirst unit to show instability below 4100 rpmFirst unit to show instability below 4100 rpm

This led to hardware fix based on analytical predictionsThis led to hardware fix based on analytical predictions

““Simplified” Mathematical TreatmentSimplified” Mathematical Treatment

VUA

1. Vibration V proportional to imbalance U

TVB

2. Shaft Temperature T proportional to

vibration V (this one is Morton effect)

UTC

3. Imbalance U proportional to temperature T

ssTTT

4. Transient drift of hot spot T around shaft trying to attain steady state( is thermal time constant)

01 TCBAT

steTtT

)(

5. Combine these 4 expressions

6. Solution for T is an exponential

7. Solve for complex eigenvalue s

1

CBA

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

A Tough Nut to CrackA Tough Nut to Crack

A A Comes from the rotordynamic model (mils/oz-in)Comes from the rotordynamic model (mils/oz-in) C C Can be estimated with a simple formula (oz-in/Can be estimated with a simple formula (oz-in/°F)°F) Is not required to check stabilityIs not required to check stability BB Is the tough one (Is the tough one (°F/mil), requires computing °F/mil), requires computing

shaft delta T as a function of orbit sizeshaft delta T as a function of orbit size Our method for estimating Our method for estimating B B is detailed in paperis detailed in paper

-1.3

-0.8

-0.3

0.2

0.7

1.2

-1.3 -0.8 -0.3 0.2 0.7 1.2

155165

175185

195205

215225

235245

-180 -90 0 90 180Circumferential location, degrees

Fa

hre

nh

eit

68737883889398103108113118

Ce

lciu

s

Location of min film thickness

155165175185195205215225235245

-60 30 120 210 300

Circumferential location, degrees

Fa

hre

nh

eit

68737883889398103108113118

Ce

lciu

s

Location of min film thickness

170

175

180

185

190

195

200

205

-100 -50 0 50 100 150 200 250 300 350

Circumferential location, degreesF

ah

ren

he

it

77798183858789919395

Ce

lciu

s

P Arc

4 Lobe

Location of min film thickness

24 points around orbit, compute 24 bearing temperature profiles

Partial Arc

4 Lobe

4100

3900

4000

3900

4000

4100

4200

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

UnstableStable

Partial Arc

4 Lobe

Analysis Results Match TestsAnalysis Results Match Tests

3.0

2.5

2.0

1.5

1.0

0.5

0.0

mils

p-p

10:00 AM2/23/2009

12:00 PM 2:00 PM

dat

NTXamp NTYamp TEXamp TEYamp

4000

3000

2000

1000

0

rpm

10:00 AM2/23/2009

12:00 PM 2:00 PM

4000

3000

2000

1000

0

rpm

8:00 AM3/12/2009

10:00 AM 12:00 PM 2:00 PM

2.0

1.5

1.0

0.5

0.0

mils

p-p

8:00 AM3/12/2009

10:00 AM 12:00 PM 2:00 PM

NTXamp NTYamp TEXamp TEYamp

Partial Arc

4 Lobe

Original Partial Arc Replacement 4 LobeThe 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)

SummarySummary

The Morton Effect is a form of Shaft Differential Heating which The Morton Effect is a form of Shaft Differential Heating which occurs in occurs in allall oil film bearings oil film bearings

Can lead to thermal runaway by bowing a rotor Can lead to thermal runaway by bowing a rotor unstable unstable synchronous vibration (i.e. divergent spiral)synchronous vibration (i.e. divergent spiral)

Number of documented cases has increased markedly in past 10-15 Number of documented cases has increased markedly in past 10-15 yearsyears

Fully rigorous analytical treatment is extremely difficult, and not Fully rigorous analytical treatment is extremely difficult, and not practical with current tools practical with current tools (3D transient CFD with a full rotor-bearing system model)(3D transient CFD with a full rotor-bearing system model)

Approximate analysis method utilized here worked extremely well Approximate analysis method utilized here worked extremely well for this case history – but needs extensive experimental validation to for this case history – but needs extensive experimental validation to prove its general applicabilityprove its general applicability

In this case history, unstable Morton Effect was observed in multiple In this case history, unstable Morton Effect was observed in multiple builds of a high speed generatorbuilds of a high speed generator

A bearing change from partial arc to 4 lobe was predicted to A bearing change from partial arc to 4 lobe was predicted to eliminate the instability, and was confirmed in testingeliminate the instability, and was confirmed in testing

Questions?