ON THE MORTON EFFECT - TRIBGROUP TAMUrotorlab.tamu.edu/tribgroup/2017 San Andres TRC/8 Morton...
Transcript of 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
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
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
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
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]
(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.
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
(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