on the morton effect - tribgroup tamurotorlab.tamu.edu/tribgroup/2017 san andres trc/8 morton...
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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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
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Development of Thermal Bow
• 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
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Development of Thermal Bow
• 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
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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
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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.
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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
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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.
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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
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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]
(a) At varying Speed, [0-1047] [rad/s] (b) At constant Speed, 754 [rad/s]
(a) At varying Speed, [0-1047] [rad/s] (b) At constant Speed, 754 [rad/s]
(a) At varying Speed, [0-1047] [rad/s] (b) At constant Speed, 754 [rad/s]
(a) At varying Speed, [0-1047] [rad/s] (b) At constant Speed, 754 [rad/s]
(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.
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ME-Induced Vibration• Model Validation
Results Based on the Proposed Models Results from Reference
Referenc
e data
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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
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ME-Induced Vibration• Model Validation
(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.
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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.
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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.
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Outcome• L. Gu, “ A Review of Morton Effect: from Theory to Industrial Practice,” STLE
Tribology Transactions, in press.
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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