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Step

Description

ANSYS Command(s)

 

 

 

 

 

MODOPT,QR-

 

 

DAMP,20

6.

Define the angular rotation velocity and the number of modes

OMEGA,…

 

expanded.

 

 

 

MXPAND,…

5.

Include the Coriolis effect in a rotating reference frame.

CORIOLIS,ON

7.

Solve.

SOLVE

The non-zero complex frequencies should match the following:

With Coriolis

Without Coriolis

Effect Applied

Effect Applied

----------------------------------------------------------

0.0000000

2661.9384

2700.8924

j

0.0000000

2740.4150

2700.8924

j

0.0000000

3043.0948

3078.1392

j

0.0000000

3113.5872

3078.1392

j

0.0000000

6342.7190

6362.7716

j

0.0000000

6365.8292

6362.7716

j

0.0000000

6382.8876

6366.7082

j

0.0000000

6593.8155

6626.0560

j

0.0000000

6658.4573

6626.0560

j

0.0000000

7183.0372

7216.0329

j

8.7. Example Unbalance Harmonic Analysis

Following is an example harmonic analysis with unbalance force. It illustrates the use of the SYNCHRO command and the following postprocessing capabilities:

Orbits plotting (PLORB)

Whirl animation (ANHARM)

8.7.1. Problem Description

The structure is a two-spool rotor on symmetric bearings. Both spools have two rigid disks. The inner spool rotates at up to 14,000 RPM and the outer spool rotates 1.5 times faster.

Disks are not visible in the plot because they are MASS21 elements.

 

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Example Unbalance Harmonic Analysis

8.7.2. Problem Specifications

The unbalance is located on the second disk of the inner spool and harmonic response is calculated. Outputs are as follows:

Amplitude at nodes 7 and 12 as a function of the frequency

Orbit plot at a given frequency

Animation of the whirl at a given frequency

8.7.3. Input for the Analysis

Use this input file to perform the example unbalance harmonic analysis of rotating structure using a stationary reference frame.

/batch,list

/title, twin spools - unbalance (inner spool) response /PREP7

mp,EX ,1,2.1e+11 mp,DENS,1,7800 mp,PRXY,1,0.3

!shaft et,1,188,,,2

sectype,1,beam,csolid

secdata,0.01524,32

sectype,2,beam,ctube

secdata,0.0254,0.03048,32

!disks

et,2,21 r,3,10.51,10.51,10.51,8.59e-2,4.295e-2,4.295e-2 r,4,7.01 ,7.01 ,7.01 ,4.29e-2,2.145e-2,2.145e-2 r,5,3.5 ,3.5 ,3.5 ,2.71e-2,1.355e-2,1.355e-2 r,6,7.01 ,7.01 ,7.01 ,6.78e-2,3.390e-2,3.390e-2

!bearings et,3,214,,1

r,7 ,2.63e+7 ,2.63e+7

r,8 ,1.75e+7 ,1.75e+7

r,9 ,0.875e+7,0.875e+7 r,10,1.75e+7 ,1.75e+7

!nodes

n,1

n,2 ,0.0762

n,3 ,0.1524

n,4 ,0.2413

n,5 ,0.32385

n,6 ,0.4064

n,7 ,0.4572

n,8 ,0.508

n,9 ,0.1524

n,10,0.2032

n,11,0.2794

n,12,0.3556

n,13,0.4064

!bearings second nodes n,101, ,0.05 n,108,0.508 ,0.05 n,109,0.1524,0.05

!components elements type,1

secn,1

e,1,2

egen,7,1,1

type,2

real,3

e,2

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real,6

e,7

cm,inSpool,elem

type,1

secn,2

e,9,10

egen,4,1,10

type,2

real,4

e,10

real,5

e,12

esel,u,,,inSpool

cm,outSpool,elem allsel

!bearings type,3 real,7 e,1,101 real,8 e,9,109 real,9 e,6,13 real,10 e,8,108

!boundary conditions d,all,ux,,,,,rotx d,101,all

d,108,all

d,109,all

!unbalance forces (eccentric mass * radius) f0 = 70e-6

f,7,fy,f0 f,7,fz,,-f0 fini

/SOLU

antype,harmic

synchro,,inSpool

nsubst,500

harfrq,,14000/60 ! implicitly defines OMEGA for Coriolis calculation kbc,1

dmpstr,0.01

cmomega,inSpool,100.

cmomega,outSpool,150.

coriolis,on,,,on solve

fini

!output: amplitude at nodes 7 and 12 as a function of the frequency /POST26

nsol,2,7,U,Y,UY

nsol,3,7,U,Z,UZ

realvar,4,2,,,UYR

realvar,5,3,,,UZR prod,6,4,4,,UYR_2 prod,7,5,5,,UZR_2 add,8,6,7,,UYR_2+UZR_2 sqrt,9,8,,,AMPL7

nsol,2,12,U,Y,UY

nsol,3,12,U,Z,UZ

realvar,4,2,,,UYR

realvar,5,3,,,UZR prod,6,4,4,,UYR_2 prod,7,5,5,,UZR_2 add,8,6,7,,UYR_2+UZR_2 sqrt,10,8,,,AMPL12

/gropt,logy,1 /yrange,1.e-7,1.e-3 plvar,9,10

fini

!output: orbit plot at the given frequency

 

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Example Unbalance Harmonic Analysis

/POST1

set,1,262

/view,,1,1,1 plorb

! output: animation of the whirl at the given frequency SET,1,500

!reset for subsequent post processing /eshape,1

/gline,,-1 plnsol,u,sum anharm

8.7.4. Analysis Steps

The following table describes the input listing and the general process involved in the example analysis in more detail.

Step

Description

ANSYS Command(s)

 

 

 

1.

Define material properties.

MP,EX,1,2.1e+11

 

 

MP,DENS,1,7800

 

 

MP,PRXY,1,0.3

2.

Define element types, sections, real and nodes.

ET,…

 

 

SECTYPE,…

 

 

SECDATA,…

 

 

R,…

 

 

N,…

3.

Define first component named inSpool.

TYPE,1

 

 

SECNUM,1

 

 

E,1,2

 

 

EGEN,7,1,1

 

 

TYPE,2

 

 

REAL,3

 

 

E,2

 

 

REAL,6

 

 

E,7

 

 

CM,inSpool,ELEM

4.

Define second component named outSpool.

TYPE,1

 

 

SECNUM,2

 

 

E,9,10

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Step

Description

ANSYS Command(s)

 

 

 

 

 

 

 

EGEN,4,1,10

 

 

 

TYPE,2

 

 

 

REAL,4

 

 

 

E,10

 

 

 

REAL,5

 

 

 

E,12

 

 

 

ESEL,u,,,inSpool

 

 

 

CM,outSpool,ELEM

 

 

 

ALLSEL

6.

Define bearing elements.

TYPE,3

 

 

 

REAL,7

 

 

 

E,1,101

 

 

 

REAL,8

 

 

 

E,9,109

 

 

 

REAL,9

 

 

 

E,6,13

 

 

 

REAL,10

 

 

 

E,8,108

5.

Set boundary conditions.

D,...

7.

Define the unbalance forces (eccentric mass * radius)

f0 = 70e-6

 

at node 7.

 

 

 

 

F,7,FY,f0

 

 

 

F,7,FZ,,-f0

8.

Set the solution options.

ANTYPE,HARMIC

 

Harmonic analysis

SYNCHRO,,inSpool

 

Unbalance on component inSpool

NSUBST,500

 

500 substeps

HARFRQ,,14000/60

 

• Frequency at end of range is 14000/60 Hz

KBC,1

 

Step loading

DMPSTR,0.01

 

• Damping ratio is 1%

CMOMEGA,inSpool,100.

 

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Example Unbalance Harmonic Analysis

Step

Description

ANSYS Command(s)

 

 

 

 

 

 

• Rotational velocity of component inSpool

CMOMEGA,out-

 

• Rotational velocity of component outSpool

Spool,150.

 

 

 

 

 

 

CORIOLIS,ON,,,ON

 

• Coriolis force in stationary reference frame

 

 

 

 

 

SOLVE

Note

The rotational velocities (CMOMEGA) are not applied in the usual way. Rather, ANSYS considers only their direction cosines and the velocity ratio between spools. For more information, see the documentation for the SYNCHRO command.

9.First output (in POST26).

The maximum amplitude of the displacement of nodes 7 (AMPL7) is calculated in variable 9.

The maximum amplitude of the displacement of nodes 12 (AMPL12) is calculated in variable 10.

Set logY scale.

Set a specific scale range in Y.

Plot variables 9 and 10.

/POST26

NSOL,2,7,U,Y,UY

NSOL,3,7,U,Z,UZ

REALVAR,4,2,,,UYR

REALVAR,5,3,,,UZR

PROD,6,4,4,,UYR_2

PROD,7,5,5,,UZR_2

ADD,8,6,7,,UYR_2+UZR_2

SQRT,9,8,,,AMPL7

!

NSOL,2,12,U,Y,UY

NSOL,3,12,U,Z,UZ

REALVAR,4,2,,,UYR

REALVAR,5,3,,,UZR

PROD,6,4,4,,UYR_2

PROD,7,5,5,,UZR_2

ADD,8,6,7,,UYR_2+UZR_2

SQRT,10,8,,,AMPL12

!

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Step

Description

ANSYS Command(s)

 

 

 

 

 

/GROPT,LOGY,1

 

 

/YRANGE,1.e-7,1.e-3

 

 

PLVAR,9,10

10.

Second output (in POST1).

/POST1

 

• Read load step 1 and substep 262 from results file.

SET,1,262

 

• Change the view.

/VIEW,,1,1,1

 

• Plot the orbits at each rotating node.

PLORB

11.

Third output.

/ESHAPE,1

 

• Display takes dimensions into account.

/GLINE,,-1

 

• No element outline.

PLNSOL,U,SUM

 

• Display the displacements as contours.

ANHARM

 

• Animate the displays (defined by the last set command

 

 

and last display command).

 

The outputs of your analysis should match those shown here:

You can obtain the two critical frequencies (at which the amplitudes are largest) via PRCAMP with SLOPE = 1.0.

 

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Example Unbalance Harmonic Analysis

Orbits are represented in different colors. Orbits from the inner spool appear in sky blue, and from the outer spool in purple. Spool lines appear in dark blue.

The following demo is presented as an animated GIF. Please view online if you are reading the PDF version of the help. Interface names and other components shown in the demo may differ from those in the released product.

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The animation of the whirls shown here is the third output resulting from the example harmonic analysis with unbalance.

 

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