ANSYS V11 Rotor Dynamics Web Seminar

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© 2007 ANSYS, Inc. All rights reserved.

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ANSYS, Inc. Proprietary

ANSYS Structural Dynamics Aline BELEY Pierre THIEFFRY ANSYS, Inc.


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Rotordynamics

outline outline

Outline 1 2 3 4 5 6 7

Why / what is rotordynamics Equations for rotating structures Rotating and stationary frame of reference Elements that support Coriolis and/or gyroscopic matrices CORIOLIS command Campbell diagram - PLCAMP, PRCAMP, CAMP Backward / forward whirl & instability


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Rotordynamics

outline outline…

Outline … 8 9 10 11

Multi-spool rotors Whirl orbit plots – PLORB, PRORB Bearing element – COMBIN214 Unbalance response – SYNCHRO

12 Examples - 3D beam - 3D thin disk (solid) - Nelson (beam) - Multi-spool with unbalance (beam) - Transient orbits - Industrial rotor models


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Rotordynamics

1) 1) why why // what what is is rotordynamics rotordynamics ??

Why rotordynamics ?

• High speed machinery such as Turbine Engine Rotors, Computer Disk Drives, etc. • Very small rotor-stator clearances • Flexible bearing supports – rotor instability


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Rotordynamics


What is rotordynamics ?

• • • •

Finding critical speeds Unbalance response calculation Response to Base Excitation Rotor whirl and system stability predictions • Transient start-up and stop


6


Rotordynamics


What analysis features are needed ?

• Model gyroscopic moments generated by rotating parts. • Account for bearing flexibility (oil film bearings) • Model rotor imbalance and other excitation forces (synchronous and asynchronous excitation).


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Rotordynamics

2) 2) theory theory

Typical Rotor – Bearing System

Bearing support coefficients

C xx C  yx

C xy  u& x  K xx &  +   C yy  u y  K yx

K xy  u x  Fx   =   K yy  u y  Fy 

Bearing coefficients may be function of rotational speed:

C (ω )


K (ω )

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Rotordynamics

2) theory

Dynamic equation in stationary reference frame

[M ]{u&&} + ([C] + [Cgyr ]){u&} + [K ]{u} = {F}


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Rotordynamics

3) reference frames

Dynamic equation in rotating reference frame

[M ]{&u& r } + ([C] + [Ccor ]){u& r } + ([K ] − [K spin ]){u r } = {F} Coriolis matrix in dynamic analyses:

[Ccor ] = 2∫ ρ Φ T ω Φ dv

 0  ω =  ωz  − ωy

− ωz 0 ωx

ωy   − ωx   0  

By extension, the Coriolis force in a static analysis:

{f c } = [Ccor ]{u& r } © 2007 ANSYS, Inc. All rights reserved.

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Rotordynamics

3) reference frames

Stationary Reference Frame

Ref: Advanced Analysis Guide – Section 8.4 Choosing the Appropriate Reference Frame Option


Rotating Reference Frame

Not applicable in static analysis (ANTYPE, STATIC).

In static analysis, Coriolis force vector can be applied via the IC command

Can generate Campbell plots for computing rotor critical speeds.

Campbell plots are not applicable for computing rotor critical speeds.

Structure must be axi-symmetric about spin axis.

Structure need not be axi-symmetric about spin axis.

Rotating structure can be part of a stationary structure (ex: Gas Turbine Engine rotor-stator assembly).

Rotating structure must be the only part of an analysis model (ex: Gas Turbine Engine Rotor).

Supports more than one rotating structure spinning at different rotational speeds about different axes of rotation (ex: a multi-spool Gas Turbine Engine).

Supports only a single rotating structure (ex: a single-spool Gas Turbine Engine).

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Rotordynamics

4) ANSYS elements

Applicable ANSYS element types Stationary Reference Frame

Rel. 10.0

BEAM4, PIPE16, MASS21 BEAM188, BEAM189

Rel. 11.0

SOLID185, SOLID186, SOLID187, SOLID45, SOLID95

Rel. 12.0 (planned)


Rotating Reference Frame SHELL181, PLANE182, PLANE183, SOLID185 SOLID186, SOLID187, BEAM188, BEAM189, SOLSH190, MASS21

SHELL181, SHELL63, SHELL93, SOLSH190

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Rotordynamics

5) commands

Coriolis / Gyroscopic effect CORIOLIS, Option, --, --, RefFrame Specifies Coriolis effects flag for a rotating structure. SOLUTION: inertia

Option 1 (ON or YES) – Activate Coriolis effects (default). 0 (OFF or NO) -- Deactivate. RefFrame 1 (ON or YES) – Activate stationary reference frame. 0 (OFF or NO) – Deactivate (default).


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Rotordynamics

5) commands

Specify rotational velocity:

ω

OMEGA, OMEGX, OMEGY, OMEGZ, KSPIN Rotational velocity of the structure. SOLUTION: inertia

activate KSPIN for gyroscopic effect in rotating reference frame (by default for dynamic analyses)

CMOMEGA, CM_NAME, OMEGAX, OMEGAY, OMEGAZ, X1, Y1, Z1, X2, Y2, Z2, KSPIN

Rotational velocity -element component about a user-defined rotational axis. SOLUTION: inertia


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Rotordynamics – 6) 6) Campbell Campbell diagram diagram

Campbell diagram

•

Variation of the rotor natural frequency with respect to rotor speed ω

•

In modal analysis perform multiple load steps at different angular velocities ω

•

In post processor (POST1), use Campbell commands

– PLCAMP: display Campbell diagram – PRCAMP: print frequencies and critical speeds – CAMPB: support Campbell for prestressed structures


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Rotordynamics – 6) 6) Campbell Campbell diagram diagram

Campbell diagram PLCAMP, Option, SLOPE, UNIT, FREQB, Cname, STABVAL Option Flag to activate or deactivate sorting SLOPE The slope of the line which represents the number of excitations per revolution of the rotor. UNIT Specifies the unit of measurement for rotational angular velocities FREQB The beginning, or lower end, of the frequency range of interest. Cname The rotating component name STABVAL Plot the real part of the eigenvalue (Hz) © 2007 ANSYS, Inc. All rights reserved.

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Rotordynamics – 7) rotor whirl and instability

Rotor whirl motion

y

ω

whirl motion

x Elliptical whirl orbit


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Rotordynamics – 7) rotor whirl and instability

Rotor whirl motion

As frequencies split with increasing spin velocity, ANSYS identifies: • forward (FW) and backward (BW) whirl • stable / unstable operation • critical speeds (PRCAMP)


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Rotordynamics – 8) 8) multi-spool multi-spool rotors rotors

Multi-spool rotors

More than 1 spool and / or non-rotating parts, use components (CM) and component rotational velocities (CMOMEGA).

PLCAMP, Option, SLOPE, UNIT, FREQB, Cname

component name SPOOL1 © 2007 ANSYS, Inc. All rights reserved.

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Rotordynamics – 8) 8) multi-spool multi-spool rotor rotor

Multi-spool rotors


Whirl animation (ANHARM command)

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Rotordynamics – 9) 9) whirl whirl orbit orbit plot plot // print print

Whirl orbit plot •

In a plane perpendicular to the spin axis, the orbit of a node is an ellipse

•

It is defined by 3 characteristics: semi axes A , B and phase ψ in a local coordinate system (x, y, z) where x is the rotation axis

•

Angle ϕ is the initial position of the node with respect to the major semi-axis A.


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Rotordynamics –– 9) 9) whirl whirl orbit orbit plot plot // print print Whirl orbit plot / print Plot orbit: PLORB

Print orbit: PRORB PRINT ORBITS FROM NODAL SOLUTION LOCAL y AXIS OF ORBITS IN GLOBAL COORDINATES 0.0000E+00 0.1000E+01 0.0000E+00 LOAD STEP= 1 RFRQ= 0.0000 ORBIT NODE 1 2 3 4 5

A 0.0000 0.0000 0.38232 0.70711 0.92301

SUBSTEP= IFRQ=

B 0.0000 0.0000 0.38232 0.70711 0.92301


4 2.5606

PSI 0.0000 0.0000 0.0000 0.0000 0.0000

LOAD CASE=

PHI 0.0000 0.0000 0.0000 0.0000 0.0000

0

ymax 0.0000 0.0000 0.38232 0.70711 0.92301

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zmax 0.0000 0.0000 0.38232 0.70711 0.92301


Rotordynamics – 10) 10) bearing bearing element element

Bearing element COMBI214 • 2D spring/damper with cross-coupling terms • REAL constants are stiffness and damping coefficients • REAL constants can be table parameters varying with spin velocity


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Rotordynamics – 10) 10) bearing bearing element element

Bearing element

! Example of table parameters input omega1 = 0. KYY1 = 1.e+4 KZZ1 = 1.e+7 omega2 = 250. KYY2 = 1.e+5 KZZ2 = 1.e+7 omega3 = 500. KYY3 = 1.e+6 KZZ3= 1.e+7

REAL constant

/com, Tabular data definition *DIM,KYY,table,3,1,1,omegs KYY(1,0) = omega1 , omega2 , omega3 KYY(1,1) = KYY1 , KYY2 , KYY3 *DIM,KZZ,table,3,1,1,omegs KZZ(1,0) = omega1 , omega2 , omega3 KZZ(1,1) = KZZ1 , KZZ2 , KZZ3 et, 3, 214 keyopt, 3, 2, 1 ! YZ plane r,1, %KYY%, %KZZ%

k = k (ω) c = c (ω) © 2007 ANSYS, Inc. All rights reserved.

Tabular input for

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Rotordynamics – 11) 11) unbalance unbalance response response

Unbalance response Possible excitations caused by rotation velocity ω are: – Unbalance (ω) – Coupling misalignment (2* ω) – Blade, vane, nozzle, diffusers (s* ω) – Aerodynamic excitations as in centrifugal compressors (0.5* ω)


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Rotordynamics – 11) 11) unbalance unbalance response response

Unbalance response Ansys command for SYNCHRO, ratio, – ratio •

–

synchronous and asynchronous forces

cname

The ratio between the frequency of excitation, f, and the frequency of the rotational velocity of the structure.

Cname •

The name of the rotating component on which to apply the harmonic excitation.

Note: The SYNCHRO command is valid only for full harmonic analysis (HROPT,Method = FULL)

ω= 2πf / ratio

where, f = excitation frequency (defined in HARFRQ)

The rotational velocity, ω, is applied along the direction cosines of the rotation axis (specified via an OMEGA or CMOMEGA command) © 2007 ANSYS, Inc. All rights reserved.

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Rotordynamics – 11) unbalance response

Unbalance response How to input unbalance forces?

Fy = Fb cos ω t = Fb e j ω t

Fz = Fb sin ω t = Fb cos (ω t - π / 2 ) => Fz = − jF b e j ω t

Fz

! Example of input file

z

/prep7 … F0=m*r F, node, fy, F0 F, node, fz, , - F0


Fb = mrω 2 = F0 ω 2

m r

ωt

y

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Fy ANSYS, Inc. Proprietary

Rotordynamics – 12) examples

Ex: 1a

Modal analysis of a 3D beam (SOLID185 – SOLID45)

Stationary reference frame

CORIO, on, , , on

r

ω ω = 30,000 rpm © 2007 ANSYS, Inc. All rights reserved.

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Analytical solution from beam theory

Ex: 1a Frequencies at 30,000 rpm using

1

0 0

Finite element solution (SOLID185)

0.00000000 j - 0.00000000 j

QRDAMP eigensolver

1 -0.62751987E-08

0.27924146E-03j

-0.62751987E-08

-0.27924146E-03j

2 2

0 0

4.64000956 j - 4.64000956 j 3

3

Ref: Gerhard Sauer & Michael Wolf, ‘FEA of Gyroscopic effects‘, Finite Elements in Analysis & Design, 5, (1989), 131-140

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0 0 0 0

8.32109166 j - 8.32109166 j 18.5600383 - 18.5600383

5

0 0

33.2843666 j - 33.2843666 j

6

0 0

41.7600861 j 41.7600861 j

less than 0.5% error

4

5

6

7 7

0 0

74.889824 j - 74.889824 j 8

8 © 2007 ANSYS, Inc. All rights reserved.

0 0

74.2401530 j -74.2401530 j 29

0.0000000

4.6316102 j

0.0000000

-4.6316102 j

0.0000000

8.2842343 j

0.0000000

-8.2842343 j

0.0000000

18.515548 j

0.0000000

-18.515548 j

0.0000000

33.062286 j

0.0000000

-33.062286 j

0.0000000

41.619417 j

0.0000000

-41.619417 j

0.0000000

73.890203 j

0.0000000

-73.890203 j

0.0000000

74.113637 j

0.0000000

-74.113637 j ANSYS, Inc. Proprietary


Ex: 1a

Animation of the whirl using ANHARM command

Mode 1 - Backward whirl Mode 2 - Forward whirl


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Ex: 1b

Clamped-free beam in rotating reference frame /com, SOLID185 coriolis, on omega, 2*62.832, 0, 0

! (20 Hz)

Comparison of frequencies SOLID185 / BEAM188 SOLID185 196.42 236.28 658.52 698.06 782.58 1340.9 1380.0

First Bending Second Bending torsion Third Bending


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BEAM188 195.61 235.34 666.36 705.42 782.79 1385.3 1423.5



Ex: 2

Campbell diagram of spinning disk


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Ex: 2

Spinning disk modeled with solid elements (SOLID45)

/com animation of the whirl set,1,5 plnsol,u,sum

anharm ! >>>>>>>> © 2007 ANSYS, Inc. All rights reserved.

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Rotordynamics – 12) examples Ex: 3

Nelson rotor modeled with BEAM188 Damped Natural Frequencies (Hz) Whirl

0 rpm

70,000 rpm [1] Ansys

F (Hz)

Ansys

[1]

Ansys

[1]

1

BW

BW

271.2

271.1

214.5

213.6

2

FW

FW

271.2

271.1

329.8

330.6

3

BW

BW

808.8

806.4

762.4

760.0

4

FW

FW

808.8

806.4

844.9

842.6

5

BW

BW

1272.0

1273.0

1068.7

1066.5

6

FW

FW

1272.0

1273.0

1516.2

1522.0

Critical speeds (rpm) Ansys

[1]

15,494

15,470

17,146

17,159

46,729

46,612

50,114

49,983

64,924

64,752

95,747

96,457


Ref. [1]: ‘Dynamics of rotorbearing systems using finite elements’, J. of Eng. for Ind., May 1976

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Ex: 3

Animation of the whirl (Nelson rotor using BEAM188)

/com, animation of the whirl set,1,5 plnsol,u,sum anharm !>>>>>>>>


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Ex: 4

Unbalance response of a twin spool rotor

Twin spool rotor model - 2 spools (BEAM188) - 4 bearings (COMBI214) - 4 disks (MASS21)

Disks are not visible (MASS21) © 2007 ANSYS, Inc. All rights reserved.

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Ex: 4

Unbalance response of a twin spool rotor (Harmonic Analysis)

! Campbell plot of inner spool plcamp, ,1.0, rpm, , innSpool


! Input unbalance forces f0 = 70e-6 F, 7, FY, f0 F, 7, FZ, , -f0

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! Solve /SOLU antype, harmic synchro, , innSpool



Ex: 4

Unbalance response of a twin spool rotor (Harmonic analysis)

/POST1 set,1, 262 /view, , 1, 1, 1

plorb

! >>>>>


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Ex: 5 Transient orbital motion – rotor instability

unsymmetric bearings

Stable at 30,000 rpm

Unstable at 60,000 rpm

(3141.6 rad/sec)


(6283.2 rad/sec)

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Ex: 5

Modal analysis – rotor instability Damped frequencies from QRDAMP eigensolver

Stable at 30,000 rpm

Unstable at 60,000 rpm

(3141.6 rad/sec)

(6283.2 rad/sec) LOAD STEP OPTIONS

LOAD STEP OPTIONS LOAD STEP NUMBER. . . . . . . . . . . . . . . . 2 INERTIA LOADS X Y OMEGA. . . . . . . . . . . . 3141.6 0.0000

LOAD STEP NUMBER. . . . . . . . . . . . . . . . 3 INERTIA LOADS X Y OMEGA. . . . . . . . . . . . 6283.2 0.0000

Z 0.0000

Z 0.0000

***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGENSOLVER *****

***** DAMPED FREQUENCIES FROM REDUCED DAMPED EIGENSOLVER *****

MODE

MODE

1 2

COMPLEX FREQUENCY (HERTZ) -27.142724 -27.142724 -0.18391233 -0.18391233

203.90118 j -203.90118 j 272.56561 j -272.56561 j

MODAL DAMPING RATIO

1

0.13195307 0.13195307 0.67474502E-03 0.67474502E-03

2

All complex frequencies real parts are negative


COMPLEX FREQUENCY (HERTZ) -30.277781 -30.277781 6.0020412 6.0020412

186.52468 j -186.52468 j 289.58296 j -289.58296 j

MODAL DAMPING RATIO 0.16022861 0.16022861 0.20722049E-01 0.20722049E-01

One complex frequency has a positive real part

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Rotordynamics – 12) applications

1

Hard Disk Drive (I.Y. Shen and C.-P. Roger Ku “A non-Classical Vibration Analysis of Multiple Rotating Disks/Shaft Assembly” ASME 1997)

2

1 Model 2 Campbell analysis 3 Mode shapes analysis Blower Shaft 1 Model 2 Modal analysis 3 Unbalance synchronous response 4 Transient start-up 5 Campbell with thermal prestress


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Hard Disk Drive - model 3 disks HDD sketch

ANSYS 4 disks model Disks thickness = 0.8mm Total mass = 87.5g Spin = 755 rd/s 7855 elements


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Hard Disk Drive - Campbell

Balanced and Unbalanced modes in Stationary Reference Frame ***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) ***** Spin(rd/s) 3 4 5 6 7 8 9 10 11 12

BW FW BW BW BW BW FW FW FW BW

0.000 577.879 578.196 654.745 668.441 668.441 668.441 668.759 668.759 668.759 668.834

376.992 521.296 640.950 654.745 611.326 611.326 611.326 731.224 731.224 731.224 668.834

753.984 470.631 709.918 654.744 559.352 559.352 559.352 799.040 799.040 799.040 668.833

(0,1)u (0,0)u (0,1)b (0,0)b

(i,j)x where i is the number of nodal circles j is the number of nodal diameters x is b for balanced or u for unbalanced © 2007 ANSYS, Inc. All rights reserved.

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Hard Disk Drive – mode shapes

2 modes (0,1) unbalanced : FW and BW

Disks are vibrating in phase © 2007 ANSYS, Inc. All rights reserved.

Hub is titlting 44



Animation of (0,1)u

Hub looks still because its displacements are small compared to the disks displacements © 2007 ANSYS, Inc. All rights reserved.

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6 modes (0,1) balanced : 3 FW and 3 BW

1

2


Disks are not vibrating in phase

3

46



Animation of first (0,1)b

Hub is still while disks are vibrating © 2007 ANSYS, Inc. All rights reserved.

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1 modes (0,0) unbalanced

Disks are vibrating in phase © 2007 ANSYS, Inc. All rights reserved.

Hub is moving axially 48



Animation of (0,0)u

Hub looks still because its displacements are small compared to the disks displacements © 2007 ANSYS, Inc. All rights reserved.

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3 modes (0,0) balanced

1

2


Disks are not vibrating in phase

3

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Blower Shaft - model

Impeller to pump hot hydrogen rich mix of gas and liquid into Solid Oxyde Fluid Cell. Spin 10,000 rpm

ANSYS Model of rotating part 99 beam elements 2 bearing elements © 2007 ANSYS, Inc. All rights reserved.

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Blower Shaft - modal analysis Frequencies and corresponding mode shapes orbits ***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) ***** Spin(rpm)

0.000

1.00xSpin 1 BW 2 FW 3 BW 4 FW

0.000 115.552 115.552 490.534 490.534


5000.000

10000.000

83.333 105.999 124.949 448.773 537.184

166.667 96.640 133.875 413.217 586.075

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Blower Shaft – modal analysis Campbell diagram Stability values

Frequency values


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Blower Shaft – critical speed

First FW critical speed ***** CRITICAL SPEEDS (rpm) FROM CAMPBELL (sorting on) ***** Slope of line : 1 2 3 4

1.000

6222.614 7796.469 none none

Bearings are symmetric so FW critical speeds will be the only excited ones © 2007 ANSYS, Inc. All rights reserved.

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Blower Shaft – unbalance response

Harmonic response to disk unbalance - Disk eccentricity is .002” - Disk mass is .0276 lbf-s2/in. - Sweep frequencies 0-10000 rpm

Amplitude of displacement at disk © 2007 ANSYS, Inc. All rights reserved.

Orbits at critical speed 55


Blower Shaft – unbalance response

Bearings reactions

Forward bearing is more loaded than rear one as first mode is a disk mode.


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Blower Shaft – start up Transient analysis 10000

- Ramped rotational velocity over 4 seconds

8000

7000 Rotational velocity (rpm)

- Unbalance transient forces FY and FZ at disk

9000

6000

5000

4000

3000

2000

1000

0

0

0.5

1

1.5

2 Time (s)

2.5

3

3.5

4

Zoom of transient force © 2007 ANSYS, Inc. All rights reserved.

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Blower Shaft – start up

Displacement UY and UZ at disk zoom on critical speed passage

Amplitude of displacement at disk

Ampl = U y2 + U z2


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Blower Shaft – start up

Transient orbits 0 to 4 seconds

3 to 4 seconds

As bearings are symmetric, orbits are circular © 2007 ANSYS, Inc. All rights reserved.

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Blower Shaft – prestress

Include prestress due to thermal loading: Thermal body load up to 1500 deg F

Resulting static displacements


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Blower Shaft - prestress

Cambpell diagram comparison No prestress


With thermal prestress

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Compressor: Compressor: Free-Free Free-Free Testing Testing Apparatus Apparatus used used for for Initial Initial Model Model Calibration Calibration

+Z

Courtesy of Trane, a business of American Standard, Inc.


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Compressor: Compressor: Location Location of of Lumped Lumped Representation Representation of of Impellers Impellers and and Bearings Bearings

Courtesy of Trane, a business of American Standard, Inc. © 2007 ANSYS, Inc. All rights reserved.

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Compressor: Compressor: SOLID185 SOLID185 Mesh Mesh of of Shaft Shaft

Very stiff symmetric contact between axial segments


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Compressor: Compressor: Forward Forward Whirl Whirl Mode Mode


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Compressor: Compressor: Backward Backward Whirl Whirl Mode Mode


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Compressor: Compressor: Campbell Campbell Diagram Diagram with with Variable Variable Bearings Bearings


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Solid Solid Model Model of of Rotor Rotor with with Chiller Chiller Assembly Assembly


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Meshed Meshed Rotor Rotor and and Chiller Chiller Assembly Assembly


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Analysis Analysis model model –– Supporting Supporting Structure Structure Represented Represented by by CMS CMS Super Super Element Element

Finite Element Model of Rotor and Impellers

Housing and Entire Chiller Assembly Represented by a CMS Superelement Courtesy of Trane, a business of American Standard, Inc. © 2007 ANSYS, Inc. All rights reserved.

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Analysis Analysis Model Model

Bearing Locations

Impellers

Outline of CMS Superelement


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Typical Typical Mode Mode Animation Animation


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Additional v11 Web Events • • • • • • • • • • • •

ANSYS v11 Update v11 Enhancements to Elements, Materials and Solvers ANSYS CFX v11 Update Pressure Vessel Module Rotordynamics with ANSYS v11 ANSYS CFX TurboSystem Fluid Structure Interaction - ANSYS and CFX CFD Analysis with ANSYS CFX ANSYS AUTODYN in Workbench Design Modifications without CAD Up-Front CFD using ANSYS CFX Random Vibration Solutions in Workbench

http://www.ansys.com/special/ansys11/email1.htm © 2007 ANSYS, Inc. All rights reserved.

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ANSYS V11 Rotor Dynamics Web Seminar

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