cyclic symmetry topics

ANSYS V7.1 Modal Cyclic Symmetry:

Answers to Common Questions

Presented by:Computer Aided Engineering Associates, Inc.

October 10, 2003

Computer Aided Engineering Associates, Inc. 2Copyright 2003

Computer Aided Engineering Associates, Inc.

Presentation Goals

Present a Brief Overview of ANSYS Modal Cyclic Symmetry.

Address Common Questions Regarding the Procedures and the Related Commands.

Discuss Potential Ways to Check for Proper Execution of the Procedures.

Outline Potential Approaches for Modeling of Shroud Connections Using Cyclic Symmetry.



Presentation Topics

Overview of ANSYS Modal Cyclic Symmetry Basic Assumptions/RestrictionsPreprocessing Notes

— Sector Definition— CYCLIC Command— Recommended Checks

Solution Notes— CYCOPT Command— Recommended Checks

Postprocessing Notes— Unexpanded Results— /CYCEXPAND Command— CYCPHASE Command— Working with Part of the Model— Recommended Checks

Modeling Approaches for Shroud Interfaces



Overview

Many structural components possess geometric characteristics which are 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.

Its primary advantage is large savings in CPU/elapsed time and computer resources.



Overview

A proper sector represents a pattern that, if repeated n times in a cylindrical coordinate system, would yield the complete structure.

Single sector modeled Display full model results

High Edge

Low Edge



Overview

By using the ANSYS Modal Cyclic Symmetry capability we can obtain 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 ANSYS by defining constraint relationships between the high and low edges of the basic sector. The basic sector is used twice to satisfy the required constraint relationship. The definition of the constraint equations depends on the "harmonic index" specified.



Overview

The relationship between harmonic index, k, and nodal diameter, d, for a model consisting of n sectors is given by the following equation:

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).

K3,2,1,0; =±⋅= mknmd



Overview

The equation relating nodal diameter, harmonic index, and number of sectors is shown in table form below:

Harmonic

Index k

Nodal Diameter 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 even)

n/2

n/2

3n/2

3n/2

5n/2

.

.

(n-1)/2 (n odd)

(n-1)/2

(n+1)/2

(3n-1)/2

(3n+1)/2

(5n-1)/2

.

.



Overview

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

HID

ND

NN/2

N/2

3N/2 2N

4022 62

18

5818



Overview

There is no way to select results by nodal diameter – only harmonic index.

Actual nodal diameter (and ring) must be determined via postprocessing of results.

Normally, except for the first few nodal diameters, higher nodaldiameters occur at higher frequencies.



Basic ANSYS Assumptions/Restrictions

Cyclic symmetry is supported for static, modal, and linear buckling analyses.

Sector model must be cyclically symmetric in any defined cylindrical system.

The angle, ∆θ spanned by the basic sector should be such that n = 360°/∆θ , where n is an integer.

Contact (Node-to-node and surface-surface), constraint equations and couples are permitted. They are automatically copied to the duplicate sector.



Basic ANSYS Assumptions/Restrictions

It is recommended that the basic sector should have matching right and left node patterns, i.e. for each node with position (r, θ, z) on the right edge, there is a corresponding node with position (r, θ +∆θ, z) on the left edge.

If patterns do not match, ANSYS employs an unmatched-node algorithm (similar to that of the CEINTF command) to connect dissimilar meshes.

The edges may be of arbitrary shape.

The edge components are defined using the CYCLICcommand in either automaticor manual mode.



Procedure for Cyclic Symmetry Modal Analysis

Modal Analysis:— Define the basic sector.— Specify cyclic symmetry (CYCLIC),

then mesh or vice-versa.— Apply boundary conditions, couples,

constraint equations etc.— Specify MODAL analysis type and

mode extraction options.— Define cyclic symmetry options,

including harmonic index range (CYCOPT).

— Solve modal analysis— Save database – now have 2 sectors— Review results using CYCPHASE and

/CYCEXPAND tools.



Procedure for Large-Deflection Prestressed Modal

Static Analysis:— Define the basic sector.— Specify cyclic symmetry (CYCLIC),

then mesh or vice-versa.— Apply boundary conditions, couples,

constraint equations etc.— Include large deformation effects, load

step options, etc.— Turn prestress on manually if

SOLCON,OFF— Define cyclic symmetry options

(CYCOPT).— Solve static analysis— Save database – now have 2 sectors— Finish out of SOLUTION mode



Procedure for Large-Deflection Prestressed Modal

Modal Analysis:— Re-enter SOLUTION mode.— Specify MODAL analysis type and

mode extraction options.— Modify boundary conditions, as

required. (Do not modify internalCP’s or CE’s).

— Turn prestress effects on (PSTRES,ON).

— Define harmonic index range (CYCOPT).

— Solve the modal analysis.— Review results using CYCPHASE and

/CYCEXPAND tools.



General Procedure Notes

Use release 7.1 documentation, as the procedure has changed significantly from release 5.7.

— Advanced Guide > Chapter 6. Cyclic Symmetry Analysis.

Make sure to save the database after the modal cyclic symmetry solution.

— Results need not be stored in database— Do not require one database for each harmonic index— Undocumented procedure can be used if database is not available*

*Discussed later



Preprocessing Notes – Sector Definition

Two options exist for identifying cyclic symmetry planes:Automatic Procedure:

— Issue the CYCLIC command to detect:• the number of sectors• the sector angle• cyclic coordinate system• cyclic boundaries

Manual Procedure:— Select nodes along the lowest θ angle.— Create a component of nodes: Utility Menu > Select >

Comp/Assembly > Create Component…— Select nodes along the highest θ angle.— Create a component of nodes: Utility Menu > Select >

Comp/Assembly > Create Component…— Issue CYCLIC command specifying all fields— Be sure to select everything when done!

DISC_M01L

DISC_M01H




Manual procedure is generally the most reliable. Edge componentsare usually readily available, since they were likely used to ensure matching mesh on boundaries.

If manual mode is used, make sure components are named properly and that “low” and “high” edges are not reversed. Note that only one pair is required unless different DOF behavior is required in various regions (shrouds).

Automatic mode can be used in the event that edge components aredifficult to define manually. In this case, it is usually best to input as much information as is readily available:

— number of sectors (NSECTOR)— the cyclic coordinate system (KCN)



Preprocessing Notes – CYCLIC Command

Automatically detects the number of sectors (NSECTOR), the sector angle (ANGLE), the cyclic coordinate system (KCN) and the cyclic boundaries based upon the solid or finite element model. KCN argument can be any defined cylindrical coordinate system number (global or local).Sector Pairing is accomplished by defining edge components

— The naming convention for each low and high edge component pair is:

NAME_MxxL and NAME_MxxH where NAME is the root component name (default = ‘CYCLIC’) and xx is the component pair number (sequential, starting at 01)

USRCOMP is the number of pairs of user-defined low and high edge components (default = 0, auto detection of sector edges).

CYCLIC, NSECTOR, ANGLE, KCN, NAME, USRCOMP




Auto detection tries to use solid geometry if it is present. If user wants auto-detection to use nodes they should delete all solid model data, or manually specify edge components

During CYCLIC’s matching up of AREA GROUPS from low to high (volume model),it checks:

— surface area matches within length tolerance squared— extreme keypoint locations correspond within length tolerance in R and Z— extreme keypoint locations correspond within angle tolerance in THETA




During CYCLIC’s matching up of LINE GROUPS from low to high (area model), it checks:

— length matches within length tolerance— extreme keypoint locations correspond within length tolerance in R and Z— extreme keypoint locations correspond within angle tolerance in THETA

During CYCLIC’s matching up of ELEMENT FACE GROUPS from low to high (non-solid model), it checks:

— surface area matches within length tolerance squared— extreme node locations correspond within length tolerance in R and Z— extreme node locations correspond within angle tolerance in THETA




As of Version 7.1 ANSYS now correctly auto-detects mixed solid-shell models

************************************************************ COMPUTED QUANTITIES ********************************************************************************** NUMBER OF SECTORS = 10 ** SECTOR ANGLE = 36.000 ** CYCLIC COORDINATE SYSTEM = 1 ** EDGE COMPONENTS CONTAIN AREAS ** LOW EDGE COMPONENT = CYCLIC_M01L MATCHED ** HIGH EDGE COMPONENT = CYCLIC_M01H ** LOW EDGE COMPONENT = CYCLIC_M02L MATCHED ** HIGH EDGE COMPONENT = CYCLIC_M02H ** EDGE COMPONENTS CONTAIN LINES ** LOW EDGE COMPONENT = CYCLIC_M03L MATCHED ** HIGH EDGE COMPONENT = CYCLIC_M03H *******************************************************




If the CYCLIC command is issued prior to meshing:— Subsequent mesh (VMESH or AMESH only) will have matching nodes at the high

and low edges. — If line divisions are to be specified, they must be defined on the “high”

component.— Currently, volume sweep meshing (VSWEEP) is not supported for CYCLIC

generated meshes.



Preprocessing Notes – Recommended Checks

Most errors in cyclic symmetry analysis are caused by improper definition of Low and High components or by conflicting CE’s or CP’s involving these components.

— Is number of nodes identical on each boundary component?— Is number of nodes in each boundary component consistent with what is

expected?— Is number of components > 99?— Is cyclic coordinate system consistent with what is expected?— Is number of sectors consistent with what is expected? — Nodes involved in coupling and/or constraint equations should generally not be

in the sector boundary components. If this occurs,check thoroughly.



Solution Notes - CYCOPT Command

Cyclic symmetry options specified using CYCOPTMenu Path isSolution > Cyclic Options…

— CYCOPT, OPTION, Value1, Value2,…, Value7




If OPTION = HINDEX:— Harmonic index range of Value1 through Value2 in steps of Value3.— Value4 = blank adds this range to the set to solve.— Value4 = -1 removes this range from the set to solve.— Repeat CYCOPT to add/remove other harmonic indexes.

If OPTION = DOF:— Value1 is the component pair ID number.— Value2 – Value7 are the constraint equation/coupling degrees of freedom

(DOF) for this pair.— Repeat CYCOPT to specify additional DOF’s.

Other valid inputs for OPTION are STATUS and DEFAULT.— Remaining fields are ignored.

CYCOPT, OPTION, Value1, Value2, Value3, Value4, Value5, Value6, Value7




If OPTION = NONR:— Value1 = 1 do not rotate nodes on sector boundaries into cyclic coordinate

system.— This is commonly used in conjunction with CYCOPT,DOF,… to apply cyclic

symmetric boundary conditions for specified directions across the sector boundaries.

— Note this option suppresses ALL nodal rotations on sector boundaries therefore, any sector edge nodes which need to be rotated into the cyclic coordinate system must be rotated manually before solution.




If OPTION = TOLER:— The tolerance used to determine whether a node on the low edge is

paired with a node on the high edge.— Value1 > 0 = The absolute distance tolerance for automatic sector-

boundary detection and low/high edge component node pairing.— Value1 < 0 = The relative tolerance for automatic sector boundary

detection and low/high edge component node pairing. The tolerance is Value1*Length where Length is the length of the diagonal of an imaginary box enclosing the model.

— The default tolerance is –1.0E-04 (also represented by Value1 = 0)




If OPTION = MOVE:— Flag specifying whether ANSYS should move the high or low edge

component nodes paired within the specified tolerance (TOLER) to create precisely matched pairs.

— Value1 = 0 do not move edge component nodes. This is the default.— Value1 = 1 or HIGH to move the high edge component nodes to

precisely match the low edge component nodes.— Value1 = -1 or LOW to move the low edge component nodes to

precisely match the high edge component nodes.

A typical command sequence to ensure node compatibility between the high and low sector edges would be to issue the CYCOPT,TOLER,TOL command followed be a CYCOPT,MOVE,1 or CYCOPT,MOVE,-1 command.



Solution Notes

Solve the modal analysis using SOLVE command.

After clicking OK, ANSYS generates the duplicate sector and the proper constraint equations and solves the eigenvalue problem for each harmonic index, k, specified by the user.

Note that a separate modal analysis will be performed at this time for each harmonic index using the modal analysis and cyclic symmetryoptions defined previously.

The results file will contain the results for each harmonic index as a separate load step.



Solution Notes

Will generally need to extract twice the number of modes expected in a frequency range, since modes will occur in pairs. Exceptions are harmonic index 0 and N/2.

When looking for nodal diameters higher than the harmonic index, make sure to extract more modes or modify frequency range for search, as these modes will generally appear at higher frequencies.

Currently ANSYS does not automatically select the corresponding part of the duplicate sector when operating on only a portion of the model.

— OUTRES,,,COMP will not be useful unless components contain corresponding duplicate sector entities. Need to run dummy static run to generate duplicate sector and then create components.



Solution Notes – Recommended Checks

Check constraint equation summary in output file:

NUMBER OF CONSTRAINT EQUATIONS GENERATED= 124 (USING THE MATCHED NODES ALGORITHM -- MAX NODE LOCATION ERROR NEAR ZERO)

Meaning: 124 constraint equations are created, used, and then deleted to enforce cyclic symmetry conditions between the low- and high-edge nodes. Every node on the low edge is precisely matched to a corresponding node on the high edge, representing the best possible situation.

NUMBER OF CONSTRAINT EQUATIONS GENERATED= 124 (USING THE MATCHED NODES ALGORITHM -- MAX NODE LOCATION ERROR = 0.73906E-02)

Meaning: 124 constraint equations are created, used, and then deleted to enforce cyclic symmetry conditions between the low- and high-edge nodes. Every node on the low edge is matched to a corresponding node on the high edge within the current tolerance setting, but not all matches are precise. The largest position mismatch is 0.0073906.



Solution Notes – Recommended Checks

Check constraint equation summary in output file:

NUMBER OF CONSTRAINT EQUATIONS GENERATED= 504 (USING THE UNMATCHED NODES ALGORITHM)

Meaning: 504 constraint equations are created, used, and then deleted toenforce cyclic symmetry conditions between the low- and high-edge nodes. At least one node on the low edge does not match any node on the high edge within the current tolerance setting, so

Carefully check errors and warnings about CE’s or CP’s

Use /DEBUG,,,,,,,,,,,,,,,1 (15 commas) to have ANSYS print the CE’s that are generated to the output file if you think there is a problem.



Postprocessing Notes

Use the General Postprocessor (/POST1)Four main steps:

— List frequencies and read in results set (SET command)— Display results on full 360° model (/CYCEXPAND).— Perform a phase sweep of repeated mode shapes to determine the possible

min/max displacements/stresses/strains values and phase angle at which they occur (CYCPHASE).

— Animate the traveling mode shape (ANCYC).



Postprocessing Notes

List frequencies:— General Postproc > Results Summary— Each harmonic index is stored as a

separate load step.

Harmonic index 0, modes 1-5







Postprocessing Notes – Unexpanded Results

Prior to expansion, the results for each mode consist of results for both the original sector, often referred to as the real or cosine part of the solution, and the duplicate sector, often referred to as the imaginary or sine part of the solution.

The results for the duplicate sector are zeroed out for harmonic indices 0 and N/2.




Real Part

Imaginary Part




When reviewing unexpanded results ANSYS displays the warning:

— The mode shapes are normalized to the mass of the 2 sectors (not the full 360° mass). Divide by SQRT(N/2) to make it consistent with full 360.



Postprocessing Notes - /CYCEXPAND Command

To turn expansion on, type the command /CYCEXPAND,,ON. ( General Postproc > Cyclic Analysis > Cyc Expansion )

All displays will now be graphically expanded to a full 360º image, by default.

No new underlying nodes or elements will be defined for the model. Use of the /CYCEXPAND command does not change the database. The command does not modify the geometry, nodal displacements or element stresses.




For /CYCEXPAND to work properly, the database must be saved subsequent to the modal analysis.An undocumented option in ANSYS 7.1 allows the user to read results directly from results file. Database is not required.

— Issue a SET command with out a RESUME will pull geometry (base and duplicate sector) from RST file.

— /CYCEXPAND, and other cyclic symmetry commands are not displayed in the menu when using this method

— Issue /CYCEXPAND,,ON manually— Gives warning

— Refreshing the menu will now display cyclic commands.— /CYCEXPAND,,EDGE has no effect




The /CYCEXPAND verifies a cyclically symmetric model by graphically expanding it partially or through the full 360°.

For nodal or element solution plots (PLNSOL, PLESOL), the command graphically expands displacements, stresses and strains of a cyclically symmetric model partially or through the full 360° degrees by combining the real or cosine (original nodes and elements) and imaginary or sine (duplicate nodes and elements) parts of the solution.

For the print nodal solution operation (PRNSOL), expands the printed output of displacements or stresses on a sector-by-sector basis.

The command affects element and result plots only. It has no effect on operations other than plot element solution (PLESOL), plot nodal solution (PLNSOL) and print nodal solution (PRNSOL). All other operations, such as NSEL and NSORT continue to operate on the unprocessed real and imaginary parts of a cyclic symmetry solution.



Postprocessing Notes – Plotting and Printing

Plotting (PLNS, PLES) and Listing (PRNS) results with /CYCEXPAND on:

— Use PowerGraphics procedures

— Show results for as many sectors as specified on /CYCEXP

— Use current RSYS— Averaging at sector

boundaries based on /CYCEXP,EDGE key

— PRNS lists complete results repeated for N sectors

— Normalizes to full 360°mass.

THE FOLLOWING X,Y,Z VALUES ARE IN COORDINATE SYSTEM 1 ***** POST1 NODAL STRESS LISTING ***** NODAL RESULTS ARE FOR CYCLIC SECTOR 4 - PHASE ANGLE = 0.000

LOAD STEP= 2 SUBSTEP= 1 FREQ= 771.19 LOAD CASE= 0 NODAL RESULTS ARE FOR MATERIAL 1

NODE SX SY SZ SXY SYZ SXZ 281 0.85797 -0.83585 0.36382E-01 -2.3238 0.26121E+06-0.28349E+07284 0.15515E+06 0.12275E+08 1.2438 -0.10750E+07-0.25008E+06-0.47413E+06285 -0.80528 -4.3039 1.2439 -0.68689 -0.25007E+06-0.47413E+06

With CYCEXPAND,EDGE,1 RSYS,1

284 0.16096E+06 0.12104E+08 2.5915 -0.71828E+06-0.11392E+07-0.41714E+06

THE FOLLOWING X,Y,Z VALUES ARE IN GLOBAL COORDINATES ***** POST1 NODAL STRESS LISTING ***** NODAL RESULTS ARE FOR CYCLIC SECTOR 4 - PHASE ANGLE = 0.000

LOAD STEP= 2 SUBSTEP= 1 FREQ= 771.19 LOAD CASE= 0 NODAL RESULTS ARE FOR MATERIAL 1

NODE SX SY SZ SXY SYZ SXZ 281 -2.2731 2.2952 0.36382E-01 0.94864 -0.27006E+07 0.90078E+06284 0.33201E+07 0.91101E+07 1.2438 0.54312E+07 -76371. 0.53057E+06285 -2.6673 -2.4419 1.2439 -1.8760 -76371. 0.53057E+06




If OPTION = ON:— Activates cyclic expansion using the previous settings (if any). If no

previous settings exist, this option activates the default settings.If OPTION = DEFAULT:

— Reset options to default settings.If OPTION = OFF:

— Deactivates cyclic expansion. (Default)If OPTION = STATUS:

— Lists the current cyclic expansion settings.

/CYCEXPAND, -- , OPTION, Value1, Value2




If OPTION = AMOUNT:— Specify the number of repetitions (Value1 = NREPEAT)

• Value2 = number of repetitions (default is total number of sectors in 360° model)— or the total angle (VALUE1 = ANGLE)

• Value2 = total angle in degrees. The default is 360°.

If OPTION = WHAT:— Expand a specified portion or subset of the model where Value1 is the

component name of elements to expand. Default is all selected components.If OPTION = PHASEANG:

— Value1 = the phase angle shift which is typically obtained via the CYCPHASEcommand.



Postprocessing Notes - CYCPHASE Command

Non-unique repeated modes are a consequence of the cyclically symmetric geometry.

A linear combination of the repeated modes is also a valid mode shape.

To determine the peak values of stress, strain or displacement in the full structure, it is necessary to calculate the mode shape at all possible orientations using the CYCPHASE command.




Used to determine peak values of displacement/stresses/strains at all possible angular orientations. (CYCPHASE):

— General Postproc > Cyclic Analysis > Cyclic Phase > Phase Sweep…

— Note that the cyclic phase sweep is only valid for harmonic index, h, solutions in the range of

where n is the number of sectors.

−=

<<

odd ,2/)1(even ,2/

0

nnnn

N

Nh

1

2

3




If TYPE = DISP, STRESS, STRAIN or ALL:— Maximum and minimum result quantities at each node in the basic sector model are

calculated by performing a phase angle sweep.— Opt1 controls the sweep angle increment to use in the search

• Default is 1 degree.• Maximum permitted value is 10 degrees.• Minimum permitted value is 0.1 degrees.

If TYPE = PUT:— Puts the resulting sweep values over the results for the original sector model. This

allows the display of MAX or MIN values on the original sector without performing an expansion.

— Opt1 controls which values are placed onto the model for results viewing• Valid input for Opt1 is MAX or MIN.

CYCPHASE, TYPE, Opt1




Other valid inputs for TYPE are LIST, STATUS and CLEAR.— Opt1 is ignored for these values of TYPE.— LIST will display a listing of the results from the previous phase sweep.— STATUS will give a summary of the results from the previous phase sweep

indicating the MAX and MIN values for each quantity in the phase sweep.

CYCPHASE, TYPE, Opt1




CYCPHASE,ALL (or DISP,STRESS,STRAIN)— Calculates the maximum value of quantities that the sector will see as

the cyclic traveling wave passes through it.• This is important and is the reason for the statement that the maximum

component value in a Cartesian direction may not be correct unless it falls in the base sector.

• ANSYS is not listing the maximum value for the full 360º, it is listing the maximum value for the base sector as the wave passes through it.




Summary of Modal Cyclic Symmetry Phase Angle Sweep

Load Step = 1 Sub Step = 1

MINIMUM MAXIMUM

Node Value Phase Ang (DEG) Node Value Phase Ang (Deg)

UX: 10 -11.6257063 180.0000 10 11.6257063 0.0000

UY: 25 -2.51814374 180.0000 25 2.51814374 0.0000

UZ: 25 -2.09678143 0.0000 25 2.09678143 180.0000

USUM: 761 0 0.0000 10 11.9554596 0.0000

Max UY in RSYS,0 = 11.771

Basic Sector




CYCPHASE,ALL (or DISP,STRESS,STRAIN)— Loops through phase angles from 0 – 360 in user specified increment

(default = 1º ) and stores maximum value.— Uses the following equation:

— Normalizes to full 360° mass.— The SectA and SectB values are extracted in the currently active RSYS,

which allows for review of peak component values in a system other than Global Cartesian.

)(*)(* Φ−Φ SINSectBCOSSectA






MINIMUM MAXIMUM

Node Value Phase Ang (DEG) Node Value Phase Ang(Deg)

UX: 25 -0.88103405 259.0000 25 0.881034052 79.0000

UY: 10 -2.30264039 65.0000 10 2.30264036 245.0000

UZ: 25 -5.67450146 76.0000 25 5.67450154 256.0000

USUM: 1396 0.030109599 334.0000 25 6.15796647 258.0000



MINIMUM MAXIMUM

Node Value Phase Ang (DEG) Node Value Phase Ang(Deg)

UX: 10 -2.30264036 245.0000 10 2.30264039 65.0000

UY: 25 -1.00769854 260.0000 25 1.00769856 80.0000

UZ: 25 -5.67450146 76.0000 25 5.67450154 256.0000

USUM: 1396 0.030109599 334.0000 25 6.15796647 258.0000

CYCPHASE Performed in RSYS,1

CYCPHASE Performed in RSYS,0




CYCPHASE,LIST— Lists the calculated maximum and minimum values and the phase angle

at which they occur• List maximum and minimum value at each node in the basic sector.• Mid-side node values are not available

— Mid-side node values are set to zero, and are not listed by CYCPHASE,LIST• Once values are stored, RSYS has no effect on CYCPHASE,LIST

CYCPHASE,STAT— Lists the max and min for each component/invariant, the phase angle

and the nodes at which they occur.




CYCPHASE,PUT,(Max or Min)— “Puts” the CYCPHASE results back onto the basic sector for visualization

purposes.— For plotting, ANSYS automatically:

• Unselects the duplicate sector• Removes the /CYCEXPAND from plots• Sets EFACET,1 (no mid-side node data available)• Issues warning

— Plots or listings (using PRNS - not recommended) should only be viewed in RSYS,0 regardless of what RSYS was used to generate the CYCPHASEvalues. Any other RSYS will display invalid results.




Maximum Displacement and Phase Ang (Deg):

UX Phase UY Phase UZ Phase USUM Phase

Node (Deg) (Deg) (Deg) (Deg)

25 0.88103 79.000 2.2874 270.000 5.6745 256.000 6.158 258.000

PRINT U NODAL SOLUTION PER NODE

***** POST1 NODAL DEGREE OF FREEDOM LISTING *****

THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN COORDINATE SYSTEM 1

NODE UX UY UZ USUM

25 -1.1355 -2.1723 5.6745 6.1813

PRINT U NODAL SOLUTION PER NODE

***** POST1 NODAL DEGREE OF FREEDOM LISTING *****

THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN GLOBAL COORDINATES

25 0.88103 2.2874 5.6745 6.1813

CYCPHASE,DISP Performed in RSYS,1

Results of CYCPHASE,LIST at Node 25

Results of PRNS in RSYS,1 after CYCPHASE,PUT

Results of PRNS in RSYS,0 after CYCPHASE,PUT




CYCPHASE,PUT.. Continued— When plotting (PLNS) or listing (PRNS) results, the vector sum

displacement (USUM) and the stress intensity (SINT) quantities are notvalid.

• These quantities are recalculated from the components upon plotting or listing. Thus, they may be combining components from different phase angles.

• Use CYCPHASE,LIST to obtain the correct values for these quantities.

— When listing results (PRNS) the /CYCEXPAND information is notautomatically removed. The user should issue /CYCEXPAND,OFF before using PRNS.

— Note: It is recommend to use CYCPHASE,LIST rather than PRNS to obtain a listing of the CYCPHASE maximum or minimum quantities.




CYCPHASE,PUT.. Continued— No additional post-processing should be done on a model that has been

updated with CYCPHASE,PUT without re-reading the results.• Avoid: /CYCEXPAND, Additional CYCPHASE commands, etc.• ANSYS displays a warning on each subsequent plot or list

• Issue a new SET command to re-read results into the database before continuing to post-process.

• Make sure to issue ALLSEL to activate duplicate sector.



Working with Part of a Model

Note that both CYCPHASE and /CYCEXPAND work on only the currently selected parts of the model. ANSYS does not automatically select the corresponding part of the duplicate sector when operating on only a portion of the model. This is the user’s responsibility.

— CYCPHASE results will be incorrect unless the corresponding part of the duplicate model is selected.

— CYCPHASE,PUT automatically unselects duplicate sector, so users should issue ALLSEL before subsequent operations.

— Take special care if partial data has been written to the results file using OUTRES,,,COMP.



Poatprocessing Notes – Recommended Checks

Verify rotation of low and high components into cyclic CS by checking nodal rotation angles.

Do modes come in pairs, except harmonic index 0 and N/2?

Are harmonic index 0 results identical for low and high components in cyclic CS?

Do harmonic index 0 results exactly match CPCYC results?

Does expanded shape look correct?

Nonzero nodal forces should generally appear on low and high components.



Modeling of Shroud Interfaces

Modeling of shroud interfaces with non-axial cuts requires special care.Different approaches exist for dealing with these interfaces in a modal analysis:

1. Shrouds are completely locked.2. Shroud interfaces are completely free.3. Shrouds are assumed locked in the normal direction and free to slide

tangentially along their entire surface.4. Shroud contact status determined by static analysis using contact elements

with friction. Subsequent modal analysis is conducted using conditions at the end of the modal analysis.




Case 1 requires no special considerations for cyclic symmetry – shrouds can be treated as integral and standard procedures apply.

Case 2 requires no special considerations for cyclic symmetry – shroud faces are not considered as part of edge components and left free.

Cases 3 and 4 require special treatment if shroud contact surfaces are also defined as edge components.




Approach A— Edge of sector consists of

shroud face nodes.— Nodes on “low” edge manually

rotated into a CS with axes aligned normal and tangential to shroud face.

— Nodes on “high” edge manually rotated into a CS identical to that of “low” edge, but rotated by the sector angle about the axis of symmetry.

Case 3 - Shrouds are assumed locked in the normal direction and free to slide tangentially along their entire surface (no gap).

LOW

HIGH




LOWHIGH

CS 21

CS 22

Local Z (CS 21, 22) is normal to the shroud surface




SYSTEM TYPE CENTER

21 0 (CARTESIAN) 1.759 14.897 2.000

22 0 (CARTESIAN) -3.442 14.600 2.000

SYSTEM ORIENTATION VECTORS (X,Y,Z)

21 0.39 -0.06 -0.92 0.12 0.99 -0.01 0.91 -0.11 0.39

22 0.38 0.08 -0.92 -0.23 0.97 -0.01 0.90 0.21 0.39

CSYS TYPE XC YC ZC THXY THYZ THZX

21 0 1.7590 14.897 2.0000 -6.987 -0.590 66.865

22 0 -3.4420 14.600 2.0000 13.013 -0.590 66.865

LIST CYCLIC SYMMETRY STATUS

******************************************************

****** CYCLIC SYMMETRY STORED QUANTITIES *************

******************************************************

* NUMBER OF SECTORS = 18 *

* SECTOR ANGLE = 20.000 *

* CYCLIC COORDINATE SYSTEM = 1 *

* COMPONENT NAME ROOT = CYCLIC *

* LOW EDGE COMPONENT = CYCLIC_M01L MATCHED *

* HIGH EDGE COMPONENT = CYCLIC_M01H *

* DUPLICATE SECTOR DEFINED *

******************************************************




Approach A (continued)— CYCOPT,NONR,… used to override

automatic rotation of edge nodes into cyclic CS. NOTE: This will require manual rotation of alledge nodes into the proper CS, not only the shroud nodes.

— CYCOPT,DOF,… used to specify which DOF are to be connected. In this case, only UZ and ROTX DOF (normal to shroud face) will be tied together using cyclic CE’s. All other DOF are not considered as part of the edge, allowing the faces to slide relative to one another.

LIST CYCLIC SYMMETRY SOLUTION OPTION STATUS

LIST OF CYCLIC SYMMETRY HARMONIC INDICES TO BE SOLVED

0 THROUGH 2

CYCLIC SYMMETRY EDGE COMPONENT PAIR 1

TO USE DEGREES OF FREEDOM UZ ROTX

CYCLIC SYMMETRY SPECIFIED DISTANCE TOLERANCE (RELATIVE) = 0.10000E-03

USER WILL APPLY NODAL ROTATIONS TO ALL EDGE COMPONENT NODES

(ALL AUTOMATIC ROTATIONS SUPPRESSED)




Approach A (continued)— Solution and

postprocessingproceed as usual.




Approach B— Cut through shroud in a way

which assures shroud faces DO NOT lie on the sector edges. Sector angle must be maintained, but edges need not be straight.

— Nodes on shroud faces manually rotated into a CS with axes aligned normal and tangential to shroud face.

— Nodes on “high” and “low” edges require no special treatment.

Case 3 - Shrouds are assumed locked in the normal direction and free to slide tangentially along their entire surface (no gap).

LOW

HIGH

Shroud Face




LOWHIGH

CS 21

Local Z (CS 21) is normal to the shroud surface




SYSTEM TYPE CENTER

21 0 (CARTESIAN) 1.759 14.897 2.000

SYSTEM ORIENTATION VECTORS (X,Y,Z)

21 0.39 -0.06 -0.92 0.12 0.99 -0.01 0.91 -0.11 0.39

CSYS TYPE XC YC ZC THXY THYZ THZX

21 0 1.7590 14.897 2.0000 -6.987 -0.590 66.865

LIST CYCLIC SYMMETRY STATUS

******************************************************

****** CYCLIC SYMMETRY STORED QUANTITIES *************

******************************************************

* NUMBER OF SECTORS = 18 *

* SECTOR ANGLE = 20.000 *

* CYCLIC COORDINATE SYSTEM = 1 *

* COMPONENT NAME ROOT = CYCLIC *

* LOW EDGE COMPONENT = CYCLIC_M01L MATCHED *

* HIGH EDGE COMPONENT = CYCLIC_M01H *

* DUPLICATE SECTOR NOT DEFINED *

******************************************************




Approach B (continued)— Couple appropriate DOF on

shroud interface. In this case, only UZ and ROTX DOF (normal to shroud face) are coupled. All other DOF are not coupled, allowing the faces to slide relative to one another.

— Use of CYCOPT,NONR and CYCOPT,DOF is not required.

LIST CYCLIC SYMMETRY SOLUTION OPTION STATUS

LIST OF CYCLIC SYMMETRY HARMONIC INDICES TO BE SOLVED

0 THROUGH 2

ALL CYCLIC SYMMETRY EDGE COMPONENT PAIRS

TO USE ALL ACTIVE DEGREES OF FREEDOM

CYCLIC SYMMETRY SPECIFIED DISTANCE TOLERANCE (RELATIVE) = 0.10000E-03

MOST RECENTLY COMPUTED ABSOLUTE TOLERANCE = 0.68236E-03, BASED UPON MODEL SIZE = 6.8236

EDGE COMPONENT NODES WILL BE AUTOMATICALLY ROTATED

INTO THE CYCLIC COORDINATE SYSTEM




Approach B (continued)— Solution and

postprocessingproceed as usual.

— Results are identical to Approach A




Although both approaches give the same results, Approach B has some distinct advantages:

— Use of local CS for cyclic edges is not required.

— Approach A will become more complicated if there is a gap between the shroud faces, since the sector angle from face to face may not result in a repeatable sector. Approach B will have the gap internal to the sector and does not suffer from this complication.

— Approach B can be easily extended for the situation where a static analysis with contact is required to determine the shroud contact status for the modal analysis (Case 4). Coupling equations are simply replaced by contact elements interior to the sector. Trying to do this with Approach A will often be much more difficult.

cyclic symmetry topics

Documents

separate load

apply boundary

cyclic coordinate

general postproc

deflection

mode extraction

current tolerance

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