practical rotordynamics for centrifugal pumps 52pp sulzer

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Sulzer Pumps

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Practical Lateral Rotordynamics forCentrifugal Pumps

Pump SymposiumCalgary November 2007

Brian GermaineSulzer Pumps UK Ltd.

[email protected]

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Practical Rotordynamics for Centrifugal Pumps

This workshop will present a practical view of Lateral Rotordynamics for Centrifugal Pumps. The procedures for undertaking such investigations will be explained along with the important rotordynamic features that exist within multistage pumps.

API 610 Appendix I will be presented and compared to procedures adopted for centrifugal compressors. "Stiff-shaft" and "flexible-shaft" systems will be discussed along with practical examples.

This workshop will be of benefit for any Engineer involved in the specification, design or operation of Centrifugal Pumps who wants to gain a good understanding of rotordynamics and many of the myths that surround this subject.

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Agenda

Introduction to the World of Rotordynamics

API 610 Requirements: "Old" & "New"

Definition of "Stiff Shaft" and "Flexible Shaft"

The Process – Damped Lateral Calculations

Rotordynamic Development & Testing

Instability & Unbalance Response

Swirl Brake Design & Rotor Damping

Practical Examples & Parameter Changes

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Introduction

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"Rotordynamics is the science of predicting the vibrational

behaviour of rotors of any kind"

Rankine 1869 was the first person to perform ananalysis of a spinning shaft

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cm

k

x

F(t)

m)xx(k static+ xc&

)t(F mg

Single Degree of Freedom System

kxxc)t(Fxm −−= &&&

Equation of motion about the static equilibrium position does not contain weight and weight balancing force. Force is assumed to be linear to their driving parameters

Unforced System

Second-order homogenous ordinary differential equation

Eigenvalue problem (damping neglected)

Imaginary part of complex solution is the undamped natural frequency or Eigenfrequency

0=++ kxxcxm &&&

02 =++ kcm λλ

mkj

mk

±=−±= 02,1λ

mk

=Ω0

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Laval (Jeffcott) Rotor

m)ee(k static+

2Ωme mg

e

Mass-less shaft with bearing stiffness (k)Disc-like mass (m) at mid-span, supported on rigid bearings, perfectly balancedUnforced & un-damped system with circular orbit

Dynamic equilibrium i.e. centrifugal force = shaft force

Ω is called the critical speed and in this case is also the natural frequency

ω=Ω

02 =−Ω keme

0)( 2 =−Ωmkme

02 =−Ωmk

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Practical Rotordynamics for Centrifugal PumpsJournal Bearings

ω⋅η⋅⋅ψ⋅

=DB

FSo2

StaticSommerfeld Number,

2

StaticFnDBS

ψ⋅⋅η⋅⋅

=Sommerfeld Number US,

Cylindrical bearings have good static properties. Where dynamic behaviour is critical, lobed or tilting pad bearings are better

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OutletInlet

p

Fy

resulting force proportional to area

Annular Seals The main difference between bearing and annular seal is the axial pressure differential axial flowAxial flow in pump annular seals is normally turbulent.

"Lomakin" effect: Bearing capability due to axial through flow, without any contribution from rotor or fluid rotation, leads to restoring radial forces if the rotor is laterally displaced.

Stiffness (k) is proportional to the pressure differential

Stiffness (k) decreases with increasing clearance h0

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Annular Seals Circulatory De-stabilizing Force:The rotor as well as the fluid flowing through the annular seal are rotating i.e. have circumferential velocity. Distortion of the pressure profile due to this rotation yields forces perpendicular to the displacement.These forces are non-conservative

Fluid rotation in annular seals has two origins: 1) fluid pre-rotation at entrance u1 and 2) shear forces at the surface of the rotating part.

For short seals with L/D << 1, the destabilizing force is proportional to u1and is expressed by the cross-coupled stiffness

asymmetric pressureprofile due to rotation

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Annular Seals Coefficients

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As a pump rotor is subject to vibrations by nature, reaction forces always occur at the impeller due to the lateral movement relative to the pump casing or diffuser The flow around the impeller becomes asymmetric and this causes unsteady fluid forces on the impeller. Impeller-diffuser-interaction develops as well as the side room effects.

Impellers Interaction – Rotordynamic Coefficients

These forces are de-stabilising forces and counteract the available modal damping

If they are not included in a damped lateral rotordynamic analysis, modal damping will be higher than actual.

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Investigation of dynamic system behaviorFor pump rotors, Eigenfrequencies are a function of shaft speedCritical speeds are the intersection points of natural frequency curves with 1x n lineNatural frequencies depend on shaft speed, critical speeds do notDamping is "modal" damping

Campbell & Damping Diagrams

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API 610 10th Edition Appendix ISpecification for Performing Lateral

Rotordynamics for Pumps

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Practical Rotordynamics for Centrifugal PumpsAnalysis of 1st, 2nd and 3rd dry critical speedsClassically stiff first dry critical speed > 1.2x max. continuous shaft speed if wet running onlyAnalysis for new and worn (2x new) clearance conditionsAnalysis at expected temperature for water (new) and pumped liquid (new and worn)Analysis for operational speed range from 25% to 125% of rated shaft speedIncludes stiffness and damping at labyrinth type shaft seals, including bearingsConsiders stiffness of bearing support structureFor both new and worn clearances the damping factor vs. separation margin to be calculated

1) Acceptable Region

2) Improvement Desired

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API 610 7th Edition Appendix IA Specification for Compressors

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API 610 7th Edition; defined the analysis process completely differentlyAnalysis focused on unbalance response analysis onlyPosition of critical speed and damping level importantProcedure identical to API 617 – Turbo CompressorsDamping calculated from curve shape at first critical speed positionProcedure not sensible for centrifugal pumpsAmplification factor defines damping level, log decrement etc.

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Definition of "Stiff" vs. "Flexible" Rotors

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ISO 13709 (API 610) requires all 1 and 2 stage (OH, BB1 and BB2) pumps to have their first critical speed in air to be at least 20% above operating speed.

"Stiff Shaft" or "Large Shaft" machines have lower static deflection under no rotation than the radial clearance (statically stiff)

Duncan & Hood 1976, define "stiff shaft" pumps when the first Eigenfrequency in air is higher than the running frequency i.e. fe/fn > 1 (dynamically stiff)

Definition of "Stiff Shaft" Design

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"Flexible" or "slender" rotors have their first lateral critical speed in air, below the operating speed."Flexible" rotors typically will have contact between stationaryand rotating wear parts at start-up and shut-down.During operating the center and throttle bushings act as productlubricated bearings and add significant stiffening and damping – making for a very "stiff" rotor in operation.

Definition of "Flexible" Design

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Often the feeling is "The thicker the shaft the better" and pumps are praised (or cursed) based on the shaft thickness.

Concerning hydraulic behaviour, it is undisputed that thinner shafts tend to increase efficiency, head coefficient and improve suction performance.

In general, multistage centrifugal pumps are dynamically flexible.

Duncan & Hood Guidance Chart

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The Process – Damped Lateral Rotordynamic Calculations

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SULZER LATERAL-PU

Finite Element Core: MADYN

Pre-processor:Rotor geometryPump data: Bearings

LubricantSealsImpellersOperating data

BITER • Shaft Deflec. • Bearing load

PROGRAMS „SEAL“

„HSEALM“

DATA BASE

ROTOR GEOMETRY

PUMP DATA

• Bearings • Seals • Impellers • Oper. Data

• Seal Coeff. • Bearing

Coefficient • Impeller

Interaction

• Static Beahaviour • Eigenvalues • Forced Response

Damped Eigenvalues

Forced Response

Static Deflection and Stresses

Campbell Plot Runup

Stress Evaluation

• Yielding • Fatigue

Forces

A

n

ϕ

A, ϕ

MADYN

n

f

2

1

D2

D1

D=0

FAx

T

Mb

ms ms

Bearing

Bearing housing Support

kB cB

kS cS

kB cB

kS cS

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Standstill

Running

Radial clearances

Journal bearing

Journal bearing

at Standstill

Running

ee = Offset

Rotor Setting

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LATERAL DAMPED NATURAL FREQUENCIES ANALYSIS DATE: 12.Apr.2003LATERAL Rev. 4.5A

HPcp 350-425-8s/27m,NEWSulzer Pumps UK Ltd

Analysis.... 304122026, HPcp 350-425-8s/27m,NEWPump State: NewMode Shape No. 1

orbit with max. major axis, t = 0, t = /2

Y

X

Z

Speed = 1200 rpmF= 35.02 HzD= 26.9 %

Speed = 2400 rpmF= 57.21 HzD= 28.2 %

Speed = 3600 rpmF= 80.42 HzD= 25.6 %

Speed = 4800 rpmF= 105.53 HzD= 23.1 %

Speed = 6000 rpmF= 125.53 HzD= 20.4 %

EIGVC: CAMPBELL AND DAMPING DIAGRAM DATE: 12.Apr.2003LATERAL Rev. 4.5A


Analysis.... 304122026, HPcp 350-425-8s/27m,NEWPump State: New

Mode 2: Mode 1:List of Symbols:

1200 2160 3120 4080 5040 6000Rotor Speed [rpm]

030

60

90

120

150

Frequency [Hz]

Synchronous Excitation

nn

nmin

nmax

1200 2160 3120 4080 5040 6000Rotor Speed [rpm]

010

20

30

40

50

Damping [%]

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RotordynamicDevelopment & Testing

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Late 80's, early 90's Sulzer received a order from EPRI to investigate a number of specific areas of pump design with an aim of improving BFP reliability

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EPRI Tasks included; full dynamic testing of annular seals and development of new computer code

Impeller/diffuser interaction coefficients

Full verification testing of a 3-stage pump

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Instability & Unbalance Response

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Forced response is the dynamic shaft amplitude given in absolute terms due to excitation forces (mechanical or hydraulic unbalance)Results are presented in two ways: forced bending shape and orbits for a given shaft speed or vibration vectors and phase angles for discrete locations along the rotor as function of shaft speedIn centrifugal pumps, the typical damped response to unbalance does not show a peak in displacement at resonance large enough to assess the amplification factor, therefore it is restricted to comparing rotordisplacement to available clearancesThe peak-to-peak displacement of the unbalanced rotor at the points of max. displacement shall not exceeda defined percentage of the diametral running clearance (API 610 states 35%)

n=const.

Bode Plot

Forced Response

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Practical Rotordynamics for Centrifugal PumpsForced Response

50

[mm]

550

2275

344.4Mass [kg]

StationNumber

U1

20

U1

175

U1

200

U1

220

U1

255

U1

315

U1

350

U1

370

U1

395

U1

600

Mechanical Unbalance G = 2.5 x 4

Coupling Sensitivity Factor:SF = 4.988E+0

Y

X

Z

t = /2t = 0

Maximum Vibration Orbit

Load case... 2, WORN

ROTOR DEFORMATION LINE AT 6.000E+3 [rpm]

The dynamic behavior of shaft overhangs, notably the coupling overhang is very important.An overhang assessment should be made utilizing forced response techniques.Good rotordynamic reliability can be reached only if the coupling end of the shaft has a low sensitivity to unbalance forces.

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Swirl Brake Design & Rotor Damping Benefits

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Swirl Brakes Applied at Annular Seals

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Swirl Brakes Applied to Balance Drum Liner

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Application of Swirl Brakes – Swirl Brakes in Action!

Radial slot Swirl Brakes were applied to a 5-stage BFP to reduce shaft vibration at full speed, leak-off flow condition. Shaft vibration and response was considerably "damped"

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Damped Lateral Rotordynamic Calculations – Practical Examples

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Back to back

DesignConcept

81210Number of stage

8494 RPM6000 RPM8494 RPMSpeed

In lineBack to backImpeller arrangement

58s

46s+6s

25s+5s

Option

Back to back

DesignConcept

81210Number of stage

8494 RPM6000 RPM8494 RPMSpeed

In lineBack to backImpeller arrangement

58s

46s+6s

25s+5s

Option

Case StudiesLATERAL Analysis, Ultra High Pressure Seawater Injection Pump

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Evolution of First Eigenmodes from NEW- to WORN-Condition (2x Design Clearances)*

HPcp 220-5s+5s (Option 2) HPcp 285-6s+6s (Option 4) HPcp 250-8s (Option 5)

Speed = 8494 rpmF= 156.26 HzD= 22.9 %

Speed = 6000 rpmF= 142.76 HzD= 32.2 %

Speed = 8494 rpmF= 156.56 HzD= 22.1 %

Speed = 8494 rpmF= 153.21 HzD= 14.3 %

Speed = 6000 rpmF= 122.67 HzD= 12.5 %

Speed = 8494 rpmF= 139.21 HzD= -1.3 %

fe,1/fn = 1.10 --> 1.08 1.43 --> 1.23 1.11 --> 0.98

* without swirl breaks at impeller suction side annular seals

NEW

WORN

Case StudiesLATERAL Analysis, Ultra High Seawater Injection Pump

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Practical Rotordynamics for Centrifugal PumpsCase StudiesFFT Free Vibration in Air: Verification of Analysis 100Hz Operation

Rotor Tap Test in Vee Blocks

EIGENVECTOR Nr. 7F= 9.0750E+01 HzD= -1.7742E-05

EIGENVECTOR Nr. 11F= 2.0144E+02 HzD= -1.9899E-05

90.75 Hz

201.44 Hz

EIGENVECTOR Nr. 3F= 2.2254E+01 HzD= 3.8533E-06

22.25 Hz

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Practical Rotordynamics for Centrifugal PumpsCase StudiesFFT Frequency Spectra: Slave Tested Machine back-to-back design

2x Clearance TestsSpeed 6000 rpmFlow 250 m3/h (50%)

Pump DE (x-Direction)

Pump NDE (x-Direction)

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In-Line Shaft on Rigid Bearings

0

20

40

60

80

100

120

140

160

0 1200 2400 3600 4800 6000

Speed [rpm]

Nat

ural

Fre

quen

cy [H

z] NewWorn

The diagram above shows how the Natural Frequencies of the rotor change with speed for both New & Worn conditions.From Dry to Operating, frequencies can change by a factor of 4

EigenfrequencyShift withChanging Speed

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Related Seal Stiffness In-Line Pump

0

100

200

300

400

500

600

700

800

900

1000

0 1200 2400 3600 4800 6000

Speed [rpm]

rela

ted

seal

stif

fnes

sto

sha

ft s

tiffn

ess

[%]

new suction sealnew eye sealnew interstage sealnew pistonworn suction sealworn eye sealworn interstage sealworn piston

operating speed

Stiffness ofAnnular Seals

The diagram above plots "annular seal" stiffness with increasing speed.The piston stiffness is more than 6x that of annular eye or hub side labyrinths. For back-to-back pumps, this means that the centre bush acts as an additional hydrodynamic bearing, not so heavily influenced by worn clearances.

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Static Deflection and Mass vs. Shaft Diameter Increase

0

50

100

150

200

250

300

0 10 20 30 40 50

Diameter Increase [%]D

efle

ctio

n re

late

d to

cle

aran

ce

[%] a

nd M

ass

incr

ease

[%]

Deflection change in-line pump Deflection change back-to-back pumpMass change in-line pump Mass change back-to-back pump

The above diagram shows the shaft deflection related to the seal clearance. With an increase of 50mm (+27%), the static deflection is reduced by a factor of 2 for inline pump.For back-to-back this increases by a factor of 3, with a diameter increase of about 45%.This shows that the inline machine remains statically stiff but back-to-back design would have to see a 40% increase to make the rotor statically stiff.

Static Deflection and Increasing ShaftDiameter

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1st Critical Speed vs. Diameter Increase

0

0.5

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50

Diameter Increase [%]

1st C

ritic

al s

peed

rela

ted

to ru

nnin

g sp

eed

In-line pump, dry Back-to-back pump, dryIn-line pump, wet new Back-to-back pump, wet newIn-line pump, wet worn Back-to-back pump, wet worn

Change in Critical Speedwith Increasing ShaftDiameter

The above diagram shows the change in the first critical speed with increasing shaft diameter. Dry critical speeds do not change that much and according to the "old" criteria remain dynamically flexible.Shaft size has an effect on the wet critical speed but even at the original diameter they are well above running speed frequency.Notice large difference between wet and dry critical speeds for back-to-back pumps. The secret is the centre bush!!

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LATERAL DAMPED NATURAL FREQUENCIES ANALYSIS DATE: 12.Apr.2003LATERAL Rev. 4.5A


Analysis.... 304122026, HPcp 350-425-8s/27m,NEWDamping Criterion: API 610 8th EditionSpeed Range from 1800 to 5184 rpmNominal Speed = 4800 rpmPump State: New

Mode 2Mode 1List of Symbols:

0.0 0.5 1.0 1.5fe/fn

010

20

30

40

50

Damping %

Diagram ADamping of the Individual Modes

LATERAL DAMPED NATURAL FREQUENCIES ANALYSIS DATE: 15.Nov.2006LATERAL Rev. 4.6


Analysis.... 611151331, HPcp 350-425-8s/27m,NEWDamping Criterion: API 610 8th EditionSpeed Range from 1800 to 5184 rpmNominal Speed = 4800 rpmPump State: New

Mode 2Mode 1List of Symbols:

0.0 0.5 1.0 1.5fe/fn

010

20

30

40

50

Damping %

Diagram ADamping of the Individual Modes

Lateral Analysis – 8-stage inlineAPI Damping Diagram -Original Design

Lateral Analysis – 8-stage inlineAPI Damping Diagram – 10mm Increase on Shaft Diameter

No change to pump rotordynamics

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1-1

2-1

2-2

2-31-2

Pump Selection Chart

Region 1-1: In-line pumps that do not require any swirl brakesRegion 1-2: In-line pumps that require radial holes at balance drum entranceRegion 2-1: Back-to-back pumps that do not require any swirl brakesRegion 2-2: Back-to-back pumps that require radial slots at centre bushRegion 2-3: Back-to-back pumps that require swirl brakes at all annular seals and throttle bushes.

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Shrunk on coupling,oil press fit, parallel stepped or taper fit

Shrunk on balance drum,oil press fit

Shrunk on thrust collar,oil press fit

Shrink disk for mechanical seal sleeve

Impellers are shrunk on, have keys for torque transmission and use split ring for thrust loading

Advantageshrunk on parts allow for high rotor balancing qualityshrunk on parts avoid fretting corrosion and minimize stress concentrationsshrunk on parts avoid loose parts on shaft during operation and result in lower vibration

Rotor Design

For high speed pumps shrunk on components is key for good rotordynamic performance, balance and repeated build quality (>4000rpm)

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K-Factor Guideline Chart - Duncan & Hood

0

100

200

300

400

500

600

700

800

900

1000

2000 3000 4000 5000 6000 7000

Max Operating Speed N

Rot

or D

ynam

ic F

acto

r (k)

back to back

225,290 5s

225,290 6s

225,290 8s

225,290 9s

300,355 4s

300,355 5s

300,355 6s

300,355 7s

300,355 8s

395,405 4s

395,405 5s

395,405 7s

395,405 8s

515

455

430

Too slender difficult to achieve rub-fre initial build

Too slender difficulty maintaining rotor straightness& balance. Rotor sensitive to unbalance possibilty of premature wear at internal clearances

U p p er l imit s f o r slend er wet running p ump s

R eco mmend ed design line f o r slend er shaf t wet running p ump s

R eco mmend ed d esign l ine f o r larg e shaf t wet running

R eco mmend ed up p er l imit s f o r p ump wit h d ry running cap ab ili t y

Bragr plb

Brage plbAlba plb

ALBA SWI plb

Chirag 8 stage

Mars

SleipnerYibal 4 stage

Halfdan

TrollELF Angola

Nimar 2,3Hutton SWI

Buckland

Milne Point

Karang

Laminaria

Thunder Horse

Holstein

Eldf iskArmada

El Furrial

HuttonDorood

GormM aersk GormT ot al dun bar

Cusiana White TigerM iller Dev

Zakum

Girassol Fulmar

SchiehallionEr skin e

K = (W^0.5 x L^1.5 ) / D^2

Bonga

AIOC

C GY

A Last Look at the 30 Year Old Chart

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Typical "Flexible" Back-to-Back Pump Designs

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Conclusions

Pump shafts must be primarily sized for adequate stress levels, nominal torsional stress at coupling.

Shaft stiffness criteria "old school" methods, are completely inadequate as these are all based on rotor frequency in air

Making the shaft larger beyond the values determined for stress levels, will not generally improve the dynamic behaviour or reliability of the pump.

For high speed, multi-stage pumps, labyrinth and impeller interaction forces dominate. Full damped lateral analysis using modern toolsand knowledge is the only way to judge the rotordynamic design.

Special care must be given to pumps operating on fluids with lowdensity products but there are design options available such as swirl brakes to ensure these pumps remain rotordynamically stable.

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Thank You for Your Attention

For further details, contact:

Brian GermaineEngineering Director

Sulzer Pumps UK Ltd.Manor Mill Lane

LeedsLS11 8BR

Tel. +44 113 272 4528E-Mail: [email protected]

practical rotordynamics for centrifugal pumps 52pp sulzer

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