Current Techniques and Challenges in the Design of Vacuum ... · Current Techniques and Challenges...

Current Techniques and ChallengesCurrent Techniques and ChallengesCurrent Techniques and ChallengesCurrent Techniques and Challengesin the Design of Vacuum Pumpsin the Design of Vacuum Pumpsin the Design of Vacuum Pumpsin the Design of Vacuum Pumps

LeinsweilerLeinsweilerLeinsweilerLeinsweiler, 2011, 2011, 2011, 2011----05050505----17171717

Magnus Magnus Magnus Magnus JanickiJanickiJanickiJanicki

Oerlikon Leybold Vacuum, CologneOerlikon Leybold Vacuum, CologneOerlikon Leybold Vacuum, CologneOerlikon Leybold Vacuum, Cologne

64th IUVSTA Workshop 2Leinsweiler, 17.05.2011

Agenda

Introduction

Screw Vacuum Pumps

� Functional principle

� Design Problems

� Simulation with a Cell Model

� Challenges

Turbo Molecular Pump

� Function

� Design Problems

� Solutions via Simulation

� Monte Carlo Test Particle Method

� Laminar Flow Calculation

(Hagen-Poiseuille)

� 3D Monte Carlo Test Particle for stationary parts

� Challenges


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Production

Dresden, GermanyValence, France Cologne, Germany Tianjin, China

Office

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4 Production Sites

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>50 Agents / Distributors

1,477 Employees

Oerlikon Leybold Vacuum


Vacuum Pumps


Screw Vacuum Pump

Screw vacuum pumps are used since the 80s

� Fore vacuum pump � compressing against

atmosphere

� High pumping capacity

� Inlet pressure from 10-3 mbar to 1000 mbar

� Two rotating screw without contact

� Dry pump � no contamination of gas or oil

� High energy efficiency due to inner

compression ratio


Screw Vacuum Pump - Functional Principal

� Gas enters the pump on the suction side

� Tooth cavities form chambers that transport

the gas volume to the exhaust

� Volume of cavities may decrease �

volumetric compression

� Backward gas flow through clearances �

isochoric compression

� Gas leaves pump on discharge side

Vacuum performance of a screw pump is

mainly defined by

� Forward transport volume flow

� Backward clearance flow

Gas flow from molecular over transient to

viscous flow regime


Screw Vacuum Pump - Design Goals

Technical goals in the design of screw vacuum pumps

� Vacuum performance

� Pumping speed

� Ultimate pressure

� Energy efficiency

� Low maximum power consumption

� Low average power consumption

� Safe operation in different applications

� Controlled thermal behavior

0,00

0,50

1,00

1,50

2,00

2,50

3,00

0,01 0,1 1 10 100 1000

pin [mbar]

spe

cific

com

pre

ssio

n p

ow

er

[kW

/ 1

00

m³/

h]

volume ratio vi = 1,7




0

100

200

300

400

500

600

700

0,001 0,01 0,1 1 10 100 1000

pin [mbar]

Seff

[m

³/h

]

DRYVAC Sprinter 650S pumping speed [m³/h]

DRYVAC Champion 650S pumping speed [m³/h]


Cell Model for screw pumps

Simulation of the thermodynamic process of displacement machines with many cells

Approach:

trapped volumes are cells with homogenous gas conditions regarding

pressure

temperature

mixture

clearances are connections between cells

calculation of mass flow by time step model

transport

leakage through clearances


Cell Model for screw pumps

Input data:

rotor geometry

clearance height

inlet and exhaust pressure and

temperature

rotor speed

cell temperature

gas ballast or

purge gas flow

Simulation results:

pumping speed

power consumption

cell pressure

bearing load

clearance leakage flow

gas ballast flow

0

50

100

150

200

250

300

350

400

0,01 0,1 1 10 100 1000

inlet pressure p_IN [mbar]

pu

mp

ing

sp

ee

d S

EF

[m

3/h

]


Cell volume and volume curve

0

50

100

150

200

250

300

350

400

450

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

volume curve

closed cells AR

closed cells NR

Cell

vo

lum

e[c

m3]

rotor rotation [-]

inlet exhaustcell 1

2345678

910

11

12

13

14


CTHCTHCTHCTH clearance tip to housing and CTR CTR CTR CTR clearance tip to root

y

x

CTH CTR


CFPCFPCFPCFP clearance flank pitch and CFT CFT CFT CFT clearance flank tip

CFT_IN

CFT_EX and CFP

current cell


CBH CBH CBH CBH clearance blow hole

CBH_IN

CBH_EX

current cell

CFT_IN

CFT_EX and CFP


CBT CBT CBT CBT clearance blow hole tail

CBH_IN CBH_EX

current cell

intersection edge

CBT_IN CBT_EX


Clearance area for constant clearance height

0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10 12 14

cell number n_WCE [-]

cle

ara

nce a

rea

A [

mm

2]

total area

CTH

CFT_IN

CTR

CFT_EX

CBH_IN

CBT_IN

CFP

CBH_EX

CBT_EX

cell 1cell 14


Connection between cells (NOS=1)

CTH tip to housing

CTR tip to root

CFT_IN flank to tip,

inlet

CFT_EX flank to tip,

exhaust

CBH_IN blow hole,

inlet

CBT_IN blow hole

tail, inlet

CFP flank to

pitch

CBH_EX blow hole,

exhaust

CBT_EX blow hole

tail, exhaust

same rotor

sidealternating

rotor side

Cell 6Cell 5inlet

Cell -1 Cell 0exhaust

Cell 1

Cell 3

Cell 2

Cell 4


Calculation of leakage flow through clearances

0

0,2

0,4

0,6

0,8

1

0,1 1 10 100 1000

Source: Wenderott, D. “Spaltströmungen im Vakuum“ inlet pressure pin [mbar]

[-]

δδδδ0 =m

mth,max

Molecular Flow Viscous FlowTransition Flow

flow direction

pinpout � 0

test clearance contours


exhaust

inlet

1 V1 T1 p*1 m*

1

-1

4

T2

T4

T3

p*2

p*4

p*3

m*2

m*4

m*3

0

Tex

Tex

pex

pex

m-1

m0

6

2

3

5

V-1

V2

V4

V3

V0

V6

V5

Tin pin

Tin pin

m6

m5

Iterative solution of thermodynamic cell network

min = mout

mCS = const

mCS = S •ϱin

cells:

cross sections:


Simulated pumping speed of SP250 @ 60Hz, cold start

Variation of discharge side housing gap heights +- 0,02 mm

0

50

100

150

200

250

300

350

400

0,01 0,1 1 10 100 1000

pin [mbar]

Seff [

m³/

h]

60 Hz, h_CTH,DS = 0,14 mm




Simulated pumping speed of SP250 @ 60Hz, cold start

Variation of suction side housing gap heights +- 0,02 mm

0

50

100

150

200

250

300

350

400

0,01 0,1 1 10 100 1000

pin [mbar]

Seff [

m³/

h]

60 Hz, h_CTH,SS = 0.14 mm




Validation of the simulation tool

Validation of the simulation tools by experiments

� Measurement of the operating behaviour of a SP250

� in cold state � with cold clearances (known)

� pumping speed

� pressure measurement at 8 different stages

� rotor speed: 50 Hz, 60 Hz

(40 Hz, 30 Hz)

� pin = 0,001 .. 1000 mbar

� automated

Aim is the comparison of

� pumping speed curves

� compression curves

in simulation and measurement


Position of sensor bores in pump housing

Lage der Druckmessstellen

0

50

100

150

200

250

300

350

400

450

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

Rotorumdrehungen [-]

Kam

me

rvo

lum

en

[c

m3

]

position of pressure sensor

volume of cells in model

volumencurve


Cell movement during SP250 compression measurement (10°)


Pressure distribution SP250, 30 Hz

Simulation vs. Measurement 20s after cold start

0

200

400

600

800

1000

1200

-8 -7 -6 -5 -4 -3 -2 -1 0 1


Dru

ck [

mb

ar]

30 Hz, 775 mbar, Messung (20s)

30 Hz, 775 mbar, Simulation










0

200

400

600

800

1000

1200

1400

-8 -7 -6 -5 -4 -3 -2 -1 0 1


Dru

ck

[m

ba

r]

40 Hz, 783 mbar, Messung (20s) 40 Hz, 783 mbar, Simulation









0

1

10

100

1000

10000

-8 -7 -6 -5 -4 -3 -2 -1 0 1


Dru

ck

[m

ba

r]





50 Hz, 1,24 mbar, Messung (20s) 50 Hz, 1,24 mbar, Simulation






0,01

0,1

1

10

100

1000

10000

-8 -7 -6 -5 -4 -3 -2 -1 0 1


Dru

ck

[m

bar]








SeffSim / Mess

260 / 221258 / 220

299 / 292

332 / 346

322 / 343

228 / 255


Simulation of screw vacuum pumps with a cell model

The simulation my means of cell model

� allows the calculation of the compression cycle in the pump

� by calculation of leakage through clearances

� and making up the balance between forward transport and backward leakage

� gives a good accuracy regarding

� pumping speed,

� pressure distribution and

� compression power.

� can be used for the variational design of screw pumps


Opportunities in the simulation of screw pumps

The following parts of the simulation can be improved:

� Thermal simulation of the process and the pump parts

� Heat Transfer between the gas and the surrounding surfaces

� Calculation of gas temperature during compression

� FEM simulation for the pump parts

� Recalculation of clearance heights on the basis of simulated pump deformation

� Simulation of mixed gas flows in the clearances

� Empirical flow models limit the simulation capability to certain gases

� Theoratical / physical models would increase simulation capabilities

� Instationary simulation of inlet and exhaust flow


Thermal behaviour of screw pump housing

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350 400 450 500 550

z [mm]

tem

pe

ratu

re [

°C]

cusp @ pult cusp @ 20 mbar cusp @ 200 mbar

alpha12.1

alpha12.1

mean cusp temperature (top/bottom) of alpha4.6


DRYVAC Sprinter 650 S

Rotor temperature distribution 200 – 975 mbar @ 120 Hz

0

50

100

150

200

250

0 50 100 150 200 250 300 350 400 450 500 550

z [mm]

tem

pe

ratu

re [

°C]

rotor @ 200 mbar rotor @ 500 mbar rotor @ 975 mbar

Reduced rotor temperature due to

increased mass throughput


Vacuum Pumps


Turbo Molecular Pump (TMP)

� Molecular pumping principals were

described 1913 by W. Gaede

� Turbo molecular pump was invented

1958 by W. Becker

� Inlet pressure normally < 0.01 mbar

� Exhaust pressure normally < 0.5 mbar

� Higher exhaust pressures possible with

Holweck or Siegbahn stages

� Fore vacuum pump necessary to

compress to atmosphere, e.g.

� Rotary vane pump

� Diaphragm pump

� Screw pump

� Gas flow is mainly molecular but may

reach also the transient flow regime


Turbo Molecular Pump – Design Goals

Technical goals in the design of TMP:

� Optimization of Vacuum Performance� Pumping speed� Kompression� For different gases

� High Lifetime� Thermal Household� Mechanical stress

� Flexible solutions for the customer


Test Particle Method – TMP Modelling

Step 1: Generating Boundary Conditions

� The blade geometry is generated in,

� 2 dimensions only, therefore particle movement

down the blade is not considered

� At the RMS radius only. Initial models were

calculated at multiple radii along the blade, but

it was discovered that using RMS obtains

similar results.

� Both machined and pressed blade profiles can be

modelled with variable angle, height and thickness.

Gas outlet side

Gas Inlet side

Gas inlet side

Gas outlet side



Knudsen Cosine Law

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

Angle (Degrees)

Pro

bab

ilit

y (

%)

Step 2: Tracking Particle Movement

� For each particle traveling off a surface or

starting at the inlet or outlet,

� The initial velocity is randomly generated

using the Maxwell-Boltzmann molecular

speed distribution.

� The initial vector angle is randomly

generated using the Knudsen Cosine Law.

� If a particle contacts a moving blade the

blade velocity and vector is added.

� The particle is tracked as it travels through

the turbo pump until it exits either at the

top or bottom of the pump.



Step 3: Calculating Transmission Probability� The overall gas transmission probability is

calculated for the turbo mechanism and defined as,� Gas transmission probability

from inlet to outlet (M12)� Gas transmission probability

from outlet to inlet (M21)

Step 4: Calculating Speed & Compression� From the gas transmission probability the

pump performance can be calculated,� Smax – Maximum pumping speed (at K = 1)� Kmax – Maximum compression (at S = 0)

M

TRV

VnJ

o

⋅

⋅⋅=

⋅⋅=

π

8

4

1

Average Thermal Velocity

Gas Arrival Rate(per unit area)

n is the number density

21

12max

M

M

A

AK

outlet

inlet •=

)2112(4

max MAMAV

S outletinlet ⋅−⋅⋅=

Inlet

Outlet

M12

M21

ReferenceEmpirical and numerical calculations in two dimensions for predicting the

performance of a single stage turbomolecular pump

Schneider, T. N. Katsimichas, S. de Oliveira, C. R. E. Goddard, A. J. H.


2E35E2800l/s911l/sHydrogen

945l/s

750l/s

Model

Pumping Speed

990l/s

730l/s

Test Data

1E41E4Helium

3E67E10Nitrogen

Test DataModel

CompressionClass 1000 Class 1000 Class 1000 Class 1000

ISO160ISO160ISO160ISO160

Accuracy

~3 to 13%


37l/s

49l/s

Model

Pumping Speed

36l/s

48l/s

Test Data

3E24E2Helium

1E51E7Nitrogen

Test DataModel

CompressionClass 50Class 50Class 50Class 50

ISO 63ISO 63ISO 63ISO 63

Accuracy

~2 to 10%


227l/s

252l/s

Model

Pumping Speed

261l/s

225l/s

Test Data

6E36E3Helium

4E83E10Nitrogen

Test DataModel

CompressionClass 300Class 300Class 300Class 300

ISO 100ISO 100ISO 100ISO 100

Accuracy

~7 to13%

Modelling Validation


Pumping Speed Comparison Model vs Actual

0

200

400

600

800

1000

1200

1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00

Inlet Pressure (mbar)

Pu

mp

ing

Sp

ee

d (

l/s

)

Hydrogen (Actual)

Hydrogen (Model)

Compression Comparison Model vs Actual

1

10

100

1000

0.001 0.01 0.1 1

Outlet Pressure (mbar)

Co

mp

res

sio

n

Helium (Actual)

Helium (Model)

Modelling Results

� The model assumes molecular flow in all pressure regions hence the values of pumping

speed and compression do no decrease as inlet pressure increases.

� Model is only suitable in the molecular flow region!!!


Performance Simulation of TMPsViscous Flow Model

Simulation of TMP Performance with a

viscous flow model

� 2 dimensional geometry (RMS)

� Stationary flow

� Velocity profile depending on pressure

difference (Hagen-Poiseuille)

� Pressure dependent viscosity

� Forward flow reduced by clearance

flows in reverse direction

x

p

y

cx

∂

∂

η∂

∂⋅=

12

2

lh

hlc

′+⋅′⋅′⋅=

2

ρηwith

( )∫

⋅⋅⋅=

2

0 0

0V=Sh

y

x

xxF d

c

cchl&


Performance Simulation with viscous flow model

Simulation of the vacuum performance

� Shows generally good accuracy

� Allows a fast simulation of multiple design

variations


Validation of TMP Performance Simulation

Experimental Validation

� Measurement of single / double stages

� Pressure measurement directly before and

behind stages

� Variation of clearances and blade parameters


Molecular gas flow simulation through stationary parts

Simulation tool MCFlow for molecular

gas flow through stationary parts

� Test particle Monte Carlo method (3D)

� Part geometry from CAD system (ProE)

� Grouping of surfaces in CAD system

� Export of surface geometry to MCFlow

� Specification of inlet and outlet

� Calculation of throughput probabilities

� Gas type independent

� 10.000 particle take ~5s

� Result: Throughput probabilities

� Visualization of flow paths

� Implementation in C++


Performance Simulation of Turbo Molecular Pumps

A turbo molecular pumping (TMP) mechanism performance can be modelled

� in the molecular flow region by using a Test Particle Monte Carlo method to compute the gas transmission probabilities through the mechanism.

� In the viscous to transient flow regime by using a viscous flow model (Hagen-Poisseuille) with adopted viscosity.

Modelling accuracy is acceptable for all gas types.


Challenges in the simulation of Turbo Molecular Pumps

The following parts of the simulation can be improved:

� One (combined) flow model to simulate all flow regimesmolecular � transient � viscous

� Thermal simulation of the process and the pump parts

� Heat Transfer between the gas and the surrounding surfaces

- Housing

- Rotor Blades

- Holweck stage

� Calculation of gas temperature during compression

� FEM simulation for the pump parts

� 3D – model including the influences of complex flow channels inside the pump

� Simulation of mixed gas flows

Current Techniques and Challenges in the Design of Vacuum ... · Current Techniques and Challenges...

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