ON THE MORTON EFFECT: SIMPLIFIED PREDICTIVE MODEL FOR A THERMALLY - - PowerPoint PPT Presentation

ON THE MORTON EFFECT:

SIMPLIFIED PREDICTIVE MODEL FOR A THERMALLY INSTABILITY INDUCED BY DIFFERENTIAL HEATING IN A JOURNAL BEARING

Lili Gu and Luis San Andres

TRC Project 40012400028

Justification

• The Morton Effect (ME) refers to a phenomenon of

thermal imbalance induced instability of rotors supported by fluid film bearings.

“They keep happening…” “Morton Effect instabilities were like a widely-spread but undiagnosed disease.” ----D. Childs (2015)

• Rotor thermal instability (ME) was added into

the rotordynamics tutorial in API 684 2015

Justification

1.Eccentricity is inevitable due to manufacturing, wear during operation, etc  eccentricity whirl yields differential heating (Fig. a)  temperature difference at the journal (Fig. b) thermal bending  levitating vibration level.

• Fig. a Differential Heating [de Jongh, 2008]

x

y

• ,2

H

P

,1 H

P

C,2

P

,1 C

P

, 1 H

P

,2 H

P

C,2

P

,1 C

P

• Fig. b Temperature Gradient

Justification

• However, ME only attracts a limited attrntion in

recent years.

Stats from “Web of Science” "Morton Effect" & "Newkirk Effect" & "Spiral Vibration" &"Thermal"

Publication Number Citation Number

Justification

• A major reason for the lack of research is that the

ME is less likely to cause catastrophe if under proper monitoring.

• However, “it did not appear immediately and did not

disappear once initiated (Berot & Dourlens 2009)”.

• Lack of theoretical guidance could cause failure to

eliminate ME-induced instability.

• A simplified predictive tools can guarantee a

continuous running and avoid a major change of rotor systems.

Objective and Executive Summary

Objective: Develop a simplified & general model for the ME-induced vibrations with required accuracy. Executive Summary: 1.General excitation mechanisms for ME-alike vibrational problems. 2.Modeling of thermal evolution in ME-alike problems. 3.Develop the simplified analytical model for Morton Effect. 4.Validation of the new Morton Effect model.

ME Mechanism

Thermal bow can be determined by solving heat transfer equation

,1 ,2 ,

( ) [ ( ) ( ) ... ( )]T

T T T n

t v t v t v t 

T

v

• Thermal bow (geometric imbalance)

Thermal boundaries along rotor shaft

Q

• Temperature distribution

Thermal bending Asymmetric temperature

ME Mechanism

1,2,..., 1,2,..., 1,2,. , , , ..,

• f thermal bow

betwee n and vibration vector magnitude phase

i n i n i T T T n

v v e v 

  

• Mechanism 2:Equivalent mass unbalance

   

2 i t

e

  

     

R b R R b R T

M v C +G v K K M e v F

𝒇𝑼 &𝜸 are products of the thermal bow

   

( ) t     

R b R R b R T

M v C +G v K K v F K v

• Mechanism 1: rotor bow theory

excitation due to thermal bow rotor stifness, mass and gyroscopic matrices bearing damping and stiffness mat ( ), , , , , , ri ces external forces t

R T R R R b b

K v K M G C K F

ሻ 𝐋𝐒𝐰𝐔(𝑢 ari arising from as asymmetric hea heating eff effect, , is is nat naturally a a fun unction of

• f

the the fac actors tha that ca can ca cause th the ME ME-induced ins instability

ME Mechanism

ሻ 𝐋𝐒𝐰𝐔(𝑢 ≠ 𝐍𝐒𝐟𝐔𝛻2𝑓𝑗𝛻𝑢+𝛾

“The mass unbalances will produce only small vibrations as the unbalance forces are small. However, geometric unbalances can give large vibrations even at low speed.”

• - B. Larsson (1999)

Mechanism 1 is chosen for a direct coupling

Thermal bow theory Equivalent mass unbalance theory

T

e

um

e

total

e g g y x v

T

v

um

e g v x y

Development of Thermal Bow

 

T

q i p      

n T

v ω I v v

• Schmied’s Model (S) [Schmied, 1987]

p, heat generation factor (𝑅+) q, heat dissipation factor (𝑅−) v, vibration vector 𝛛𝐨, natural frequency

1



x

y

• 
• T

v

e

v

v

2



Q Q

• Kellenberger Model (K) [1980]

   

, p i p q       

T 1 n T

v η ω I v Q

𝜽𝟐, coefficient determined by friction/shearing coefficient, dynamic properties of the system, and rotation speed. 𝐑, normalized heat generation Lack of coupling with vibration 𝐰 Simple, but lack of reflection of dynamic properties determined by the system

Development of Thermal Bow

• Schmied and Kellenberger Model (SK)

p q i                                                     

T T n T

v v ω v c I a b f(t) I I v v I v

𝐛′,𝐜′, 𝐝′, coefficients determined by friction/shearing coefficient and the dynamic properties of heating source ሻ 𝐠(𝐮 , external excitation vector Introduce equivalent dynamic coefficients to the rotor’s EOM

Development of Thermal Bow

• Improved Model 1 (IK model)

mf

f

c

f

k

x

y

• v



Q



 

, , , , ,

f f f

k m Q f c v 

 



Introduce a coefficient for heat generation to reflect dynamic properties of the system, and, normalized heat generation. Introduce a coefficient for heat generation to reflect dynamic properties

• f the system, and, the dynamic force induced by journal whirl.
• Improved Model 2 (ISK model)

Heat Generation , lubricant , , dynamic coe friction coeffic fficients of the fluid film ient

f f f

k c m 

Fluid Film Journal

Development of Thermal Bow

Positive Damping

Reference (Most time consuming) K model is better than S model. IK has the best prediction S model is better than K model when p is small Eigenvalues

Indicate Instability Under significant mf

Sensitive Study of Thermal Factors

• p – heating factor; q – dissipation factor

Frequency Damping factor Frequency Damping factor

• Thermal bending frequency is mainly influenced by heating factor p
• Thermal damping factor is mainly influenced by dissipation factor q
• ISK model can predict the nonlinear model because it models the heating generated

in the Newkirk Effect more accurately. However, the nonlinear trend is very small.

ME-Induced Thermal Bow

,

3

p j

kA q mC 

2 2 ,

3 2 1

J J p J eff

R p C c       

• Identifying the heating factor and the dissipation factor

𝑆𝐾

Journal radius

𝜸

Thermal bending coefficient

𝜁

Journal eccentricity ratio

𝐷𝑄,𝑘

Journal specific heat capacity

k

Shaft stiffness

𝜑𝑓𝑔𝑔

Effective viscosity

Model Features: Critical factors such as operational speed, bearing eccentricity, thermal and elastic properties are considered.

𝐉𝐨𝐮𝐟𝐡𝐬𝐛𝐮𝐟 𝐪 & 𝐫 𝐣𝐨𝐮𝐩 𝐮𝐢𝐟 𝐟𝐫𝐯𝐛𝐮𝐣𝐩𝐨 𝐩𝐠 𝐮𝐢𝐟𝐬𝐧𝐛𝐦 𝐜𝐩𝐱

Rotor System Residual Imbalance

1

I

 

2

I 

Thermo - Fluid Rotor Vibration

1

O

Thermo - Elastic Journal/Shaft Differential Temperature

2

O Thermal Bow



• Coupled Dynamics

ME-Induced Vibration

r

p                                                

ext vib vib vib T T T

F v v v M v v v D Q K I K I

• 𝐰𝐰𝐣𝐜 , lateral vibrations .
• M, D, K, mass, damping & stiffness matrices.
• 𝐰𝐔, thermal deformations (thermal bow). Using geometric constraints,

this vector’s dimension can be decreased to half the dimension in 𝐰𝐰𝐣𝐜

• 𝐋𝑠, shaft stiffness matrix. Its row dimension is the same as 𝐰𝐰𝐣𝐜 and its

column size corresponds to 𝐰𝐔. (4X2 for the Jeffcott rotor model)

The coupled dynamics forms a feedback loop 

A critical task is to find the evolution of thermal bending 𝐰𝐔.

Const-visc Therm-visc

ME-Induced Vibration

Effective Temperature VS Speeds

Lubricant effective temperature increases with speed (almost linearly). Whirl frequencies are independent of temperature rise.

Journal Whirl Frequency VS Speeds

ME-Induced Vibration

Influence of Temperature-Dependent Viscosity on Dynamic Coefficients

Constant Speed Varying Speed

   

       

   

       

More dramatic change is found at varying speeds than at a constant speed for both stiffness and damping coefficients  The rotational speed is more dominant than pure temperature rise in the determination of dynamic coefficients.

ME-Induced Vibration

• Model Validation

Results Based on the Proposed Models Results from Reference Referenc e data

ME-Induced Vibration

• Model Validation

Results Based on the Proposed Models Results from Reference

≅

Important Findings: The simplified model proves reliable in predicting the Morton Effect

ME-Induced Vibration

• Model Validation

Disk lateral vibrations

Spiral vibrations are found at the speeds over 7000 [rpm], of good agreement with the reference.

System Eigenvalues for speed between 6600-7400 [RPM]

According to the reference, instability was predicted to occur after 7000 rpm.

Conclusion

• The critical task for analyzing the ME-alike problems is to

embed rotor-stator-heating into the rotordynamics properly.

• The simplified heating factor and dissipation factor can be used

to model the thermal influence on the ME analysis.

• Rotating speed is more dominant than pure temperature rise in

the determination of dynamic coefficients.

• The simplified model developed in this work is verified via

comparisons with reference. The simplicity lying in the proposed model makes it efficient in assessing the ME.

Acknowledgement

• Texas A&M University Turbomachinery Research Consortium for its financial

support.

• Dr. Dara Childs for many fruitful discussions and sharing his perspectives on

the Morton Effect.

Outcome

• L. Gu, “ A Review of Morton Effect: from Theory to Industrial Practice,” STLE

Tribology Transactions, in press.

References

[1] de Jongh, F., 2008, The synchronous rotor instability phenomenon – ME, Proc. of the Thirty-Seventh Turbomachinery Symposium. [2] Childs, D., 2015, "The Remarkable Turbomachinery-Rotordynamics Developments During the Last Quarter of the 20th Century," SAE Technical Paper 2015-01-2487, doi:10.4271/2015-01-2487. [3] Schmied, J., 1987, “Spiral Vibrations of Rotors, Rotating Machinery Dynamics,” Vol. 2, ASME Design Technology Conference, Boston, September. [4] Berot, F., and Dourlens, H., (1999), “On Instability of Overhung Centrifugal Compressors,” ASME Proc. International Gas Turbine & Aeroengine Congress & Exhibition, Indiana, June 1999, PAPER No. 99-GT-202. [5] Kellenberger, W., 1980, “Spiral Vibrations Due to the Seal Rings in Turbogenerators Thermally Induced Interaction Between Rotor and Stator,” ASME J. Mech. Des., 102(1), pp 177-184, DOI:10.1115/1.3254710. [6] Guo ZL and Kirk G. 2010, Morton Effect induced synchronous instability in mid-span rotor– bearing systems, part 2: models and simulations. ASME: Proc. International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Aug. 2010, Montreal, Canada. Paper ID: DETC2010-28342