ANSYS v7.1 Modal C li S t Cyclic Symmetry - CAE Associates

74 Pages·2003·1.57 MB·English

ANSYS v7.1 Modal
CCyclliic SSymmettry:
Answers to
Common
QQuueessttiioonnss
© 2003 CAE Associates
ANSYS V7.1 Modal Cyclic
Symmetry:
Answers to Common Questions
Presented by:
Computer Aided Engineering Associates, Inc.
October 10, 2003
Presentation Goals
Present a Brief Overview of ANSYS Modal Cyclic Symmetry.
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Address Common Questions Regarding the Procedures and the Related
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Commands.
Discuss Potential Ways to Check for Proper Execution of the Procedures.
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Outline Potential Approaches for Modeling of Shroud Connections Using
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Cyclic Symmetry.
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Presentation Topics
Overview of ANSYS Modal Cyclic Symmetry
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Basic Assumptions/Restrictions
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Preprocessing Notes
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Sector Definition
—
CYCLIC Command
—
Recommended Checks
—
Solution Notes
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CYCOPT Command
—
Recommended Checks
—
Postprocessing Notes
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Unexpanded Results
—
/CYCEXPAND Command
—
CYCPHASE Command
—
Working with Part of the Model
—
Recommended Checks
—
Modeling Approaches for Shroud Interfaces
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Overview
Many structural components possess geometric characteristics which are
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repeated about an axis of symmetry (e.g. disks, gears, impellers). We can
define the structure in terms of a primary segment which is repeated at
equally spaced intervals about the symmetry axis. If the displacement
BC’s of all segments are identical with respect to the axis of symmetry, we
can analyze the entire structure in terms of the mass and stiffness
characteristics of a single segment.
This technique is called cyclic symmetry.
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Its primary advantage is large savings in CPU/elapsed time and computer
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resources.
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Overview
A proper sector represents a pattern that, if repeated n times in a
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cylindrical coordinate system, would yield the complete structure.
Single sector modeled
Display full model results
Low Edge
High Edge
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Overview
By using the ANSYS Modal Cyclic Symmetry capability we can obtain
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the natural frequencies and mode shapes of the entire structure for a
user-prescribed range of nodal diameters using the model of a single
sector. We can also perform Linear Buckling analysis using this
technique.
Cyclic symmetry is implemented in
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ANSYS by defining constraint
relationships between the high and
low edges of the basic sector.
The basic sector is used twice to
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satisfy the required constraint
relationship.
The definition of the constraint
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equations depends on the
"harmonic index" specified.
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Overview
The relationship between harmonic index, k, and nodal diameter, d,
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for a model consisting of n sectors is given by the following
equation:
= ⋅ ± =
d m n k; m 0,1,2,3
K
For example, if there are 7 sectors (n = 7) and we specify k = 2,
ANSYS will obtain the solution for nodal diameters 2, 5, 9, 12, 16,
19, 23, . . .
The harmonic index range is from 0 to n/2 ([n -1]/2 if n is odd).
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Overview
The equation relating nodal diameter, harmonic index, and
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number of sectors is shown in table form below:

Harmonic
Index Nodal Diameter
k d

0 0 n n 2n 2n . .

1 1 n-1 n+1 2n-1 2n+1 . .

2 2 n-2 n+2 2n-2 2n+2 . .

3 3 n-3 n+3 2n-3 2n+3 . .

4 4 n-4 n+4 2n-4 2n+4 . .

. . . . . . . .

. . . . . . . .

n/2 n/2 n/2 3n/2 3n/2 5n/2 . .
(n even)

(n-1)/2 (n-1)/2 (n+1)/2 (3n-1)/2 (3n+1)/2 (5n-1)/2 . .
(n odd)

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Overview
D
I
H
N/2
18
2N
N/2 N 3N/2
18 22 40 58 62
ND
A graphical representation of the table on the previous page is shown by this sawtooth,from which the harmonic index,
required as input to ANSYS, can be determined by specifying the nodal diameter of interest.
For example, a 58E driver exciting a rotor with 40 blades will elicit responses of 18, 22, 58, and 62, … nodal diameters,
which will all be found in the ANSYS solution for harmonic index 18
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