on the morton effect - tribgroup tamurotorlab.tamu.edu/tribgroup/2017 san andres trc/8 morton...

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

Justification1.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

o

,2HP,1HP

C,2P,1CP

(a) Forward Orbit

,1HP

,2HP

C,2P

,1CP

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"

Public

ation N

um

ber

Citation N

um

ber

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 nt v t v t v tTv

• Thermal bow (geometric imbalance)

Thermal boundaries along

rotor shaftQ

• Temperature distribution

Thermal bending

Asymmetric temperature

ME Mechanism

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

1,2,.

, ,

, ..,

of 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 te R b R R b R TM v C + G v K K M ev F 𝒆𝑻 &𝜷 are products of

the thermal bow

( )t R b R R b R TM 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

tR T

R R R

b b

K v

K M G

C K

F

ሻ𝐊𝐑𝐯𝐓(𝑡 arising from asymmetric heating effect, is naturally a function of the factors that can cause the ME-induced instability

ME Mechanism

ሻ𝐊𝐑𝐯𝐓(𝑡 ≠ 𝐌𝐑𝐞𝐓𝛺2𝑒𝑖𝛺𝑡+𝛽

“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

Te

umetotale

g gy

xv

Tv

ume

g

vx

y

Development of Thermal Bow

0T q ip n Tv ω I vv

• Schmied’s Model (S) [Schmied, 1987]

p, heat generation factor (𝑄+)

q, heat dissipation factor (𝑄−)

v, vibration vector

𝛚𝐧, natural frequency

1

x

yo

o

Tv

ev v

2

Q

Q

• Kellenberger Model (K) [1980]

,p i pq T 1 n Tv η ω I v Q

𝜼𝟏, coefficient determined by friction/shearing coefficient, dynamic

properties of the system, and rotation speed.

𝐐, normalized heat generation

Lack of coupling

with vibration 𝐯

Simple, but lack of

reflection of

dynamic properties

determined by the

system


• Schmied and Kellenberger Model (SK)

0p q i

T T n Tv v ω v

c Ia 0 b 0 f(t)

I I0 0 0

v v

I

v

𝐚′,𝐛′, 𝐜′, coefficients determined by friction/shearing coefficient and

the dynamic properties of heating sourceሻ𝐟(𝐭 , external excitation vector

Introduce equivalent dynamic coefficients to the rotor’s EOM


• Improved Model 1 (IK model)

mf

fc

fk

x

y

o

v

Q Q , , , ,, f f fk mQ 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

of 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 fk c m

Fluid Film

Journal


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

kAq

mC

2 2,

3

2 1

J

J p J

effRp

C c

• Identifying the heating factor and the dissipation factor

𝑅𝐽 Journal radius

𝜷 Thermal bending coefficient

𝜀 Journal eccentricity ratio

𝐶𝑃,𝑗 Journal specific heat capacity

k Shaft stiffness

𝜐𝑒𝑓𝑓 Effective viscosity

Model Features: Critical factors such as operational speed, bearing

eccentricity, thermal and elastic properties are considered.

𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐞 𝐩 & 𝐪 𝐢𝐧𝐭𝐨 𝐭𝐡𝐞 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞𝐫𝐦𝐚𝐥 𝐛𝐨𝐰

Rotor SystemResidual

Imbalance

1I

2I Thermo - Fluid

Rotor

Vibration 1O

Thermo - Elastic

Journal/Shaft

Differential Temperature

2O

Thermal

Bow

• Coupled Dynamics

ME-Induced Vibration

0

r

p

extvib vib vib

T T T

Fv v vM 0 0

v v v0 0 0

D

Q

K

I

K

I

• 𝐯𝐯𝐢𝐛 , lateral vibrations .

• M, D, K, mass, damping & stiffness matrices.

• 𝐯𝐓, thermal deformations (thermal bow). Using geometric constraints,

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

• 𝐊𝑟, shaft stiffness matrix. Its row dimension is the same as 𝐯𝐯𝐢𝐛 and its

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

The coupled dynamics forms a

feedback loop

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

Const-visc

Therm-visc

ME-Induced VibrationEffective 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 VibrationInfluence of Temperature-Dependent Viscosity on Dynamic Coefficients

Constant Speed Varying Speed

(a) At varying Speed, [0-1047] [rad/s] (b) At constant Speed, 754 [rad/s]






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


Results Based on the Proposed Models Results from Reference

≅

Important Findings:

The simplified model proves

reliable in predicting the

Morton Effect


(a) Disk, with Morton Effect (b) Journal, with Morton Effect 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

on the morton effect - tribgroup tamurotorlab.tamu.edu/tribgroup/2017 san andres trc/8 morton...

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