1

ON THE PREDICTED EFFECT OF ANGULAR

MISALIGNMENT ON THE PERFORMANCE OF

OIL LUBRICATED THRUST COLLARS IN

INTEGRALLY GEARED COMPRESSORS

Supported by Hanhwa (formerly Samsung) Techwin

Proceedings of ASME Turbo Expo 2016: Turbine Technical Conference

and Exposition, June 13-17, 2016, Seoul, South Korea

Paper GT2016-57888

Travis A. CableResearch Assistant

Luis San AndrésMast-Childs Chair Professor, Fellow ASME

Mechanical Engineering

Texas A&M University

Karl WygantDirector of Engineering

Hanhwa Techwin

Houston, TX 77079,USA

Integrally Geared Compressors

Compared to single

shaft multistage

compressors, industry

selects IGCs for their:

• increased thermal

efficiency,

• decreased footprint,

&

• ease of access for

maintenance and

overhaul.

All pictures & components are a courtesy of Hanhwa (formerly Samsung) Techwin

2

3

The Thrust Collar (TC)

Lubricated zone in thrust collar

transmits axial load from pinion

shaft & gear to bull gear shaft.

Load is from gas pressure acting on the front and back sides of an

impeller plus the axial component of the transmission contact force in a

helical gear.

Thrust Collars in the Literature

1968

Sadykov, V.A. and Shneerson, L.M, “Helical

Gear Transmissions with Thrust Collars,”

Russian Engineering Journal.

1984

Simon, V., “Thermal Elastohydrodynamic

Lubrication of Rider Rings,” ASME J.

Tribology.

1991

Barragan de Ling, F., Evans, H.P. and

Snidle, R.W., “Thrust Cone Lubrication

Part 1: Elastohydrodynamic Analysis of

Conical Rims,” IMech J. Eng. Trib.

2006,

2009

Thoden, D., “Elasto-hydrodynamic

Lubrication of Pressure Ridges,”

Clausthal University of Technology.

2014

San Andrès, L., Cable, T.A., Wygant, K.D.

and Morton, A., “On the Predicted

Performance of Oil Lubricated Thrust

Collars in Integrally Geared

Compressors,” ASME J. Eng. Gas

Turbines Power.

2016

Wygant, K., Bygrave, J., Bosen, W. and

Pelton, R., 2016, “Tutorial on the

Application and Design of Integrally

Geared Compressors,” Proc. of Asia

Turbomachinery and Pump Symposium,

Feb. 22-26, Singapore.

empirical formula for selection of taper angles

and diametral interference fit. Table for selection of

thrust collars given operating speed and load.

Hydrodynamic analysis of rider rings (thrust

collars) with identical taper angles.

Hydrodynamic analysis of thrust cones (thrust

collars) for heavily loaded, low speed, marine gear

boxes. Only one taper angle.

Complete EHD analysis of TCs to optimize

geometry for largest load at design speed. Only

one taper angle.

Predictions of thrust collar performance

(mechanical power loss, film thickness, etc.) for

various thrust collar and bull gear taper angles.

Design considerations for IGCs. One section

addresses to thrust collars for balancing thrust

loads on IGC pinion shafts.

5

Kinematics of thrust collar

Film thickness

(exaggerated)

wB : BG speedwB : BG speed

wTC : TC speed

f : taper angle

6

Static Misalignment of Thrust Collar

Thrust Collar:

(a) No

misalignment

(b) αx

misalignment

(c) αy

misalignment

y

x

zθ

r

ωTC

ωB

TC

BG

y

x

z

ωTC

αx

αxTC

Angular

Misalignment

θr

ωB

BG

y

x

z

αy

ωTC

αy

TC

Angular

Misalignment

θr

ωB

BG

7

Static Misalignment of Bull Gear

Bull gear:

(a) No

misalignment

(b) βx

misalignment

(c) βy

misalignment

y

x

zθ

r

ωTC

ωB

TC

BG

y

x

zθ

r

βx

ωTC

ωB

βx

BG

TCAngular

Misalignment

y

x

zθ

r

ωTC

ωB

βy

βy

BG

TC

Angular

Misalignment

8

Generation of Hydrodynamic Pressure

AssumptionsLaminar thin film flow.

Incompressible lubricant.

Rigid surfaces. Steady state.

3 31 1

12 12

1 1sin cos

2 2B B TC

h p h pr

r r r r θ r

h hr b b r

r r r θ

w w w

wB : BG speed

wTC : TC speed

: oil viscosity

h : film thickness

11 1, tan tan cos

sin

R B TC y y y

x x

rh r θ h R d b φ R φ r θ β d β

r θ β

f : taper angles

9

Lubricant Temperature Rise

Assumptions Bulk-temperature ~ T(r,θ). Steady state.

TB, TTC: Bull gear and thrust collar temperatures

cp: Lubricant specific heat at constant pressure

: Energy dissipation

function

1 1

B TCP r θ B TCρc rq T q T h T T h T Tr r r θ

q: Lubricant flow rate (per unit length)

:h Heat convection coefficient

2 2

sin cos2

2 cos

B TC B TC B

B B TC TC

h p pbω ε rω bω ε

r r θ

b b r rωh

w w w

Convection + diffusion of lubricant thermal energy = Mechanical power loss.

10

Forces and Moments on a Thrust Collar

Equilibrium and first-order pressure fields cause an axial force and

moments on the Thrust Collar (and BG):

Equilibrium

force & moments

Gives:

max 1

max

,

, 0

,

x x yX x x y y

left

Y

TC z zθ R

i t

TC x a z y

θ r

TC y

z β β

F

M p p p p p p p e r dr dθ

M

w

First order force and

moments

0

0

0

,,

, ,

, ,

x

x

y

x x y y

x x x x x x y x y

y y x y x y y y y

zz z z z zTC zTC z

i t

TC x TC x z

yTC y TC y z

z

β

β

H H H H HFF

M M H H H H H e

M M H H H H H

w

H = K + i ωC defines the fluid film stiffness and damping coefficients

11

Validation of the Predictive Tool

Operating Conditions

Load W 5 kN

Speed Ratio R1ωTC / R2ωBG 1.5

Geometry R1 33.5 mm

R2 318.5 mm

d 336 mm

φTC = φBG 5°Material Young

modulusETC = EBG 210 GPa

LubricantSupply

TemperatureTs 60 °C

Dynamic Viscosity μ 0.135 Pa.s

Ambient Pressure pa 100 kPa

Max. angle θmax 56°Width at θ = 0 l 16 mm

Area Alub 6.23 cm2

Simon

[1984]

12

Validation of the Predictive Tool

• Results show good agreement with data from Simon [1984]

• Differences due to elastic deformation of the TC and BG surfaces

Simon [1984]

13

Parametric Study on

Effect of Static

Angular

Misalignments on TC

Performance

14

W/A=55 bar

Average axial load and speed selected from existing

machines

TC

BG

ww

w

*

WW

W

Operating Conditions

Load W 1.0

Speed (BG/TC) w 10

Geometry R2/R1 7.14

d/R1 7.78

Lubricant ISO VG 32

Supply Temperature Ts 49 °C

Dynamic Viscosity (49°C) μ 0.0204 Pa.s

Ambient Pressure pa 100 kPa

Max. angle θmax 47.3°

Length c/R1 1.47

Width at θ = 0 l/R1 0.36

Area 0.12

2

lub 1A R

15

Operating Conditions & Normalized Parameters

*

3

2

, , , , , * * * *

1

TCW p h TW P h f T Q Q

RW p h W R TTC

w

w

Normalized thrust load, pressure, film thickness, friction factor,

temperature rise and lubricant flow rate:

Constant load, speed and

surface taper angles

16

Contour Plots for Misalignments About x Axis

φB =φTC

• Location and magnitude of min. film shift with increasing TC

misalignment αx.

17

Contour Plots for Misalignments About x Axis

φB =φTC

• Location and magnitude of peak pressure (and min film) shift

with increasing TC misalignment αx.

18

Contour Plots for Misalignment About y Axis

φB =φTC

• Location and magnitude of min. film shift with increasing TC

misalignment αy.

19

Contour Plots for Misalignment About y Axis

φB =φTC

• Location and magnitude of peak pressure (and min film) shift

with increasing TC misalignment αy.

20

Minimum film thickness W = 1.0/h h h

0.2 0.2, 0x y x y

0.2 0.2, 0y x x y

• Only one misalignment

angle varies (either αx

or αy)

• Misalignment of the TC about

horizontal (x) axis produces

different film thickness for

positive and negative rotations.

• Minimum film thickness is nearly

symmetric for misalignments of

the TC about vertical (y) axis.

cavitation

area

reduces

21

Peak Pressure

Pmax ~ 40 Mpa ~ 7 W/Alub

• Pmax is nearly symmetric about the aligned condition for TC

misalignments about vertical (y) axis

maxmax *

PP

P

• Pmax decreases with increasing αx, indicating a larger load carrying area

(less lubricant cavitation)

W/Alub

22

Friction Factor f

f ~ 0.0014 Drag power ~ a few kW.

• f not + affected by TC misalignments about vertical (y) axis

1

*

TC

fω W R

• f decreases with αx, driven by an increase in oil cavitation area

23

Lubricant Temperature Rise ΔT

ΔTmax ~ 15 °C little temperature rise

• TC misalignments about vertical (y) axis has little effect on

lubricant temperature rise.

• Temperature rise drops with misalignment angle αx, driven by

increased lubricant flow and less power loss.

*

TT

T

24

Axial Stiffness Kzz and Damping Czz

W = 1.0

• Kzz and Czz decrease with increase

in misalignment αx about

horizontal (x) axis.

• Kzz is nearly symmetric about

aligned condition, while Czz

increases slightly with αy.

*

*zz zz

hK K

W

*

*TC

zz zz

hC C

W

w

25

Moment-Angle and Force-Angle Stiffness Coefficients

W = 1.0

• |Kαxαx| < |Kαyαy

| due to differences

in moment arms.

• When TC is misaligned about (x)

axis, symmetry in the lubricated

zone vanishes |Kαxαy| ≠ |Kαyαx

|

• Axial and angular motions are

coupled for the lubricated thrust

collar and bull gear pair

First subscript denotes the

direction of force or moment

while the second is the

direction motion or rotation

26

Hydrodynamic Coupling for a Lubricated TC

Rotor tilts around (x,y) axes produce an axial force and viceversa.

ForceFz= Kzx x

y

x

z

y

x

z

Kzαx≠ 0 Kzαy

≠ 0

ForceFz= Kzy y

Including TC moment coefficients in a lateral rotordynamics analysis

could change the system natural frequencies (and mode shapes) as well

as the system onset speed of instability.

x

y

27

Conclusion

For an aligned TC/BG, some cross coupled coefficients are nonzero,

indicating a hydrodynamic coupling between axial and angular tilt

motions.

Coupling (axial/lateral tilts) effect not yet studied.

For the TC/BG pair analyzed herein:

Static angular misalignments of the TC about the horizontal (x) axis affect

the hydrodynamic pressure field and extent of the lubricant cavitation

region, altering the static performance of the TC.

Misalignments of the TC/BG about the vertical axes do little to the static

performance (mechanical power loss, lubricant temperature rise, etc.), but

do alter the dynamic performance (stiffness and damping).

28

Acknowledgments

Thanks to Hanwha (formerly Samsung)

Techwin

Questions (?)

Learn more at http://rotorlab.tamu.edu

Paper GT2016-57888

29

Mechanical Power Loss

~ rz r θz θV V t V

Dissipation function =

Traction vector . velocity vector

2 2

sin cos2

2 cos

B TC B TC B

B B TC TC

h p pbω ε rω bω ε

r r θ

b b r rωh

w w w

TC and BG surfaces:

Integration of the dissipation over the lubricated area yields the

mechanical power loss:

dA

30

Equilibrium and Perturbed Pressures

Dynamic displacements introduce perturbations to the pressure field:

Substitution of the total (static plus dynamic) film thickness and pressure

field into the Reynolds equation determines zeroth and first order

pressure fields:

Zeroth order (equilibrium)

pressure field:

First order (perturbed)

pressure field:

0 eiωtp p p

3

0 10 02

12

hp s h

μ

3 2

0 00

3;

12 2 12 x x y yz β β

h hp iω s p

μ μ

Where the shear flow vector (s) is:

sin cosBG r BG TCs b e b r ew w w

31

Perturbation Analysis - Dynamic Displacements

Unsteady Reynolds equation includes squeeze film term:

3

012 2

h h h hp s q

t μ t

Introduce dynamic axial and tilt or angular displacements of the BG and

TC with frequency (ω) :

eiωtzAxial:

Trust Collar Angular:0 0

e , eiωt iωt

x x x y y y

0 0e , eiωt iωt

x x x y y y Bull Gear Angular:

Film thickness is: 0,

eiωt

r θ,th h where

x x y yz β β

1 sin sin cos cosr θ r θ r θ d r θ

ηκ is a set of geometric functions related to each displacement

Δκ denotes the direction of the small amplitude displacements

32

Numerical method of solution

An isoparametric FE formulation solves for the zeroth

and first order pressure fields.

Coarse

mesh

A control volume method solves a simplified thermal

energy transport equation.

33

Finite Element Formulation

0 0

1 1

;pe pen n

j j j j

j j

p P p P

Pressure approximations:

Discretized Equations (zeroth and first order):

0 0 0

0

j i i

e e e e

ij j i i

e e

ij ij j

k P q f

k P q f S P

Fluidity matrices contributions:

3

0

2

0

12

4

j je i iij

j je i iij

hk d

μ r r r θ r θ

hS d

μ r r r θ r θ

Shear flow contributions:

0 0

1

2

1

2

i

i

e i ir

i ii r

f h s s dr r

f iω d s s dr r

where d rdrdθ sin cosB r B TCs bω ε e bω ε rω e and

34

Thermal Energy Transport Equation

Discretized equation:

where the coefficients are:

1 1

H Hne nee e

p Top Top Bottom Bottom Left Left Right Right i B TC B B TC TC ii

i i

ρc T Q T Q T Q T Q h h T h T h T A

T Top P T Bottoma T S b T Simplified:

1

1

1 1

1

2 2

1

2 2

H

H

H H

nee

B TC iii

T Top Right

p

nee

B TC iii

T Bottom Right

p

ne nee e

i B B TC TC iii i

P s Left

p

h h A

a Q Qc

h h A

b Q Qc

h T h T A

S T Qρc

35

Heat Convection Coefficient

Heat convection coefficient extracted from Nusselt number:

Empirical (Hausen) model for Nusselt number:

Nu hDh

2

3

0.0668 Re Pr

Nu 3.66

1 0.04 Re Pr

h

h

D

L

D

L

Hydraulic diameter for a lubricated thrust collar:

2avg

h

avg

h lD

h l