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Example Campbell Diagram Analysis

Reference Frame Considerations

 

Stationary Reference Frame

Rotating structure can be part of a stationary structure in an analysis model (such as a gas turbine engine rotor-stator assembly). The stationary structure and supports (such as bearings) need not be axisymmetric.

Rotating Reference Frame

Rotating structure must be the only part of an analysis model (such as a gas turbine engine rotor).

Supports more than one rotating structure spinning at different rotational speeds about different axes of rotation (such as a multi-spool gas turbine engine).

Supports only a single rotating structure (such as a single-spool gas turbine engine).

See the CORIOLIS command for the list of elements supported in the Stationary Reference Frame.

See the CORIOLIS command for the list of elements supported in the Rotating Reference Frame.

Natural Frequencies

Natural frequencies differ according to the reference frame type. In most cases, natural frequencies are known in a stationary reference frame through analytical expressions or experiment, for example. ANSYS therefore recommends using the stationary reference frame for modal analyses.

8.5. Example Campbell Diagram Analysis

Following is a modal analysis of a rotating structure using a stationary reference frame. The analysis generates a Campbell diagram (PLCAMP).

8.5.1. Problem Description

The model is a simply supported beam spinning at up to 30,000 rd/s.

8.5.2. Problem Specifications

The geometric properties for this analysis are as follows:

Length: 8m

Diameter: 0.2m

The material properties for this analysis are as follows:

Young's modulus (E) = 2e+11 N/m2

Poisson's ratio (υ) = 0.3

Density = 7800 kg/m3

8.5.3. Input for the Analysis

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

/batch,list

 

 

/title, Spinning Simply

Supported Beam

!* Parameters

 

 

lx=8

!

length

dia=0.2

!

diameter

/PREP7

!

-----

ET,1,16

 

 

R,1, dia, dia/2

 

 

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MP,EX,1,2e+11

 

MP,DENS,1,7800

 

MP,PRXY,1,0.3

 

n,1

 

n,9,lx

 

fill,1,9

 

e,1,2

 

egen,8,1,-1

 

d,1,uy,,, ,,uz

! simply supported left end

d,9,uy,,, ,,uz

! simply supported right end

d,all,ux

! supress axial motion

d,all,rotx

! supress torsion

finish

 

/SOLU

! -----

antype,modal

 

!Use the QRDAMP eigensolver, request 8 modes,

!get complex eigensolutions modopt,qrdamp,8,,,on

!Reuse the block Lanczos eigenvectors from the first loadstep qrdopt,on

!Write 8 modes to the result file, calculate

!element results

mxpand,8,,,yes

!Apply Coriolis effect and specify

!stationary reference frame coriolis,on,,,on

!Solve 2 loadsteps with rotational velocity omega,0.

solve omega,30000. solve

finish

/POST1

! -----

!Plot Campbell Diagram plcamp

!Print Campbell Diagram prcamp

finish

8.5.4. 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.

Set parameters.

lx=8

 

 

dia=0.2

2.

Define nodes, elements, and material properties.

ET,…

 

 

R,…

 

 

MP,...

 

 

N,…

 

 

E,…

3.

Set boundary conditions.

D,...

4.

Set the analysis type (modal in this case). Use the QRDAMP ei-

ANTYPE,MODAL

 

gensolver, request 8 modes, and specify complex ei-

 

 

gensolutions.

MODOPT,QR-

 

 

DAMP,8,,,ON

 

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Example Campbell Diagram Analysis

Step

Description

ANSYS Command(s)

 

 

 

 

 

MXPAND,...

5.

Include the Coriolis effect in a stationary reference frame.

CORIOL-

 

 

IS,ON,,,ON

6.For each load step, define the rotation velocity, and then solve. OMEGA,…

 

SOLVE

7. Plot and print the Campbell diagram.

PLCAMP

 

PRCAMP

The results of your analysis should be similar to those shown here:

The printout (PRCAMP) should yield the following data:

PRINT CAMPBELL DIAGRAM

Sorting : ON

X axis unit : rd/s

***** FREQUENCIES (Hz) FROM CAMPBELL (sorting on) *****

Spin(rd/s)

0.000

30000.000

1

BW

6.207

4.639

2

FW

6.207

8.305

3

BW

24.750

18.547

4

FW

24.750

33.027

5

BW

55.461

41.735

6

FW

55.461

73.701

7

BW

98.248

74.337

8

FW

98.248

129.852

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of ANSYS, Inc. and its subsidiaries and affiliates.

233