INTEGRALLY GEARED COMPRESSORS Travis A. Cable Karl Wygant Research - - PowerPoint PPT Presentation

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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. Cable

Research Assistant

Luis San Andrés

Mast-Childs Chair Professor, Fellow ASME Mechanical Engineering Texas A&M University

Karl Wygant

Director 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

• verhaul.

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

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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

• ne 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.

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Kinematics of thrust collar

Film thickness (exaggerated)

wB : BG speed wB : BG speed wTC : TC speed f : taper angle

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Static Misalignment of Thrust Collar

Thrust Collar: (a) No misalignment (b) αx misalignment (c) αy misalignment y x z

θ r ωTC

ωB TC BG y x z ωTC αx αx

TC

Angular Misalignment

θ r

ωB BG y x z αy ωTC αy

TC

Angular Misalignment

θ r

ωB BG

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Static Misalignment of Bull Gear

Bull gear: (a) No misalignment (b) βx misalignment (c) βy misalignment y x z

θ r

ωTC ωB TC BG y x z

θ r

βx ωTC ωB βx BG TC

Angular Misalignment

y x

z

θ r

ωTC ωB βy βy BG

TC

Angular Misalignment

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Generation of Hydrodynamic Pressure

Assumptions

Laminar thin film flow. Incompressible lubricant. Rigid surfaces. Steady state.

   

3 3

1 1 12 12 1 1 sin cos 2 2

B B TC

h p h p r r r r r θ r h h r b b r r r r θ    w  w  w                                                            

wB : BG speed wTC : TC speed : oil viscosity h : film thickness

           



  

1 1

1

, tan tan cos sin

R B TC y y y x x

r

h r θ h R d b φ R φ r θ β d β r θ β  



         

f : taper angles

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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 TC P r θ B TC

ρc rq T q T h T T h T T r r r θ                 

q: Lubricant flow rate (per unit length)

: h

Heat convection coefficient

 

 

 

 

   

  



2 2

sin cos 2 2 cos

B TC B TC B B B TC TC

h p p bω ε rω bω ε r r θ b b r rω h  w w  w                         

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

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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

, , ,

x x y X x x y y left Y

TC z z θ 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 rdrdθ M

w      



   



   

                                

 

First order force and moments

, , , , , ,

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 z TC z TC z i t TC x TC x z y TC y TC y z

z β β

H H H H H F F 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

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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 modulus ETC = EBG 210 GPa

Lubricant

Supply Temperature Ts 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]

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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]

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Parametric Study on Effect of Static Angular Misalignments on TC Performance

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W/A=55 bar

Average axial load and speed selected from existing machines

TC BG

w w w 

*

W W 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 1

A R 

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Operating Conditions & Normalized Parameters

* 3 2

, , , , , * * * * 1

TC

W p h T W P h f T Q Q R W p h W R T TC w w                 

Normalized thrust load, pressure, film thickness, friction factor, temperature rise and lubricant flow rate: Constant load, speed and surface taper angles

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Contour Plots for Misalignments About x Axis

φB =φTC

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

misalignment αx.

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Contour Plots for Misalignments About x Axis

φB =φTC

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

with increasing TC misalignment αx.

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Contour Plots for Misalignment About y Axis

φB =φTC

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

misalignment αy.

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Contour Plots for Misalignment About y Axis

φB =φTC

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

with increasing TC misalignment αy.

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Minimum film thickness W = 1.0

/ h h h





0.2 0.2,

x y x y

          0.2 0.2,

y x x y

         

• Only one misalignment

angle varies (either αx

• r αy)
• Misalignment
• f

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

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Peak Pressure

Pmax ~ 40 Mpa ~ 7 W/Alub

• Pmax

is nearly symmetric about the aligned condition for TC misalignments about vertical (y) axis

max max *

P P P



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

(less lubricant cavitation)

W/Alub

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Friction Factor f

f ~ 0.0014  Drag power ~ a few kW.

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

1

*

TC

f ω W R  

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

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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.

* T T T    

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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

h K K W

     



* *

TC

zz zz

h C C W w

     



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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

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Hydrodynamic Coupling for a Lubricated TC

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

Fz= Kzx x y x z y x z

Kzαx≠ 0 Kzαy≠ 0

Force

Fz= Kzy 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

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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).

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Acknowledgments Thanks to Hanwha (formerly Samsung) Techwin Questions (?)

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

Paper GT2016-57888

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Mechanical Power Loss

 

~

rz r θz θ

V V       t V

Dissipation function =

Traction vector . velocity vector

 

 

 

 

   

  



2 2

sin cos 2 2 cos

B TC B TC B B B TC TC

h p p bω ε rω bω ε r r θ b b r rω h  w w  w                         

TC and BG surfaces: Integration of the dissipation over the lubricated area yields the mechanical power loss:

dA  



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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:

 

eiωt p p p    



 

3 1 2

12 h p s h μ          

3 2

3 ; 12 2 12

x x y y

z β β

h h p iω s p μ μ

      

  

   

                 

Where the shear flow vector (s) is:

 

 

 

 

sin cos

BG r BG TC

s b e b r e w  w  w   

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Perturbation Analysis - Dynamic Displacements

Unsteady Reynolds equation includes squeeze film term:

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12 2 h h h h p s q t μ t                 

Introduce dynamic axial and tilt or angular displacements of the BG and TC with frequency (ω) :

eiωt z 

Axial: Trust Collar Angular:

e , e

iωt iωt x x x y y y

            e , e

iωt iωt x x x y y y

            Bull Gear Angular: Film thickness is:

 

 

,

eiωt

r θ,t

h h



    



where

x x y y

z β β              

       

1 sin sin cos cos r 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

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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

1 1

;

pe pe

n n j j j j j j

p P p P

   

   

 

Pressure approximations: Discretized Equations (zeroth and first order):

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 2

12 4

j j e i i ij j j e i i ij

h k d μ r r r θ r θ h S d μ r r r θ r θ

 

                                            

 

Shear flow contributions:

         

1 2 1 2

i i

e i i r i i i r

f h s s d r r f iω d s s d r r

    

                                     

  

where

d rdrdθ  

 

 

 

 

sin cos

B r B TC

s bω ε e bω ε rω e



  

and

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Thermal Energy Transport Equation

Discretized equation: where the coefficients are:

   

 

1 1

H H

ne ne e e p Top Top Bottom Bottom Left Left Right Right i B TC B B TC TC i i i i

ρc T Q T Q T Q T Q h h T h T h T A

 

             



T Top P T Bottom

a T S b T  

Simplified:

     

1 1 1 1

1 2 2 1 2 2

H H H H

ne e B TC i i i T Top Right p ne e B TC i i i T Bottom Right p ne ne e e i B B TC TC i i i i P s Left p

h h A a Q Q c h h A b Q Q c h T h T A S T Q ρc  

   

                                    

   

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Heat Convection Coefficient

Heat convection coefficient extracted from Nusselt number: Empirical (Hausen) model for Nusselt number:

Nu

h

D h  

2 3

0.0668 RePr Nu 3.66 1 0.04 RePr

h h

D L D L               

Hydraulic diameter for a lubricated thrust collar:

2

avg h avg

h l D h l          