7.1. HBM Cyclic Analysis: Single Stage Generation Pass

  1. Create a single stage cyclic model (applies to all cases, prestress and non-prestress)

    • Define the mesh (base and duplicate sectors).

    • Define the generation pass boundary conditions.

    • Define the spatial harmonic index 0 cyclic constraint equations using the MSOPT,NEW procedure.

  2. Run the static prestress analysis (if necessary).

  3. Determine the necessary spatial harmonic indices that contribute to the response as a function of the number of cyclic sectors, the fundamental engine order of excitation, and the number of time harmonics. For theoretical details, see Harmonic Balance Method Cyclic Equations.

  4. Run a CMS substructuring (or prestressed CMS substructuring if static prestress was performed) analysis for each contributing harmonic index. In each of these analyses, select the harmonic index of interest by modifying the stage harmonic index using MSOPT,MODIFY. These analyses will generate superelements that correspond to various time harmonics of the HBM analysis in the use pass and must have the following characteristics:

    • A spatial harmonic index 0 stage without a duplicate sector must be generated for time harmonic 0 (primary stage).

    • All other stages must have a duplicate sector: even spatial harmonic index stage 0 or N/2 (N even) that corresponds to non-zero time harmonics.

    • If surface pressure or inertial loads need to be applied in the use pass, define those loads in the generation pass to create CMS load vectors.

    • The number of CMS modes for each substructure is related to the number of modes NMODE (NMODE on the CMSOPT command) requested for the primary stage. For all other stages, the number of modes requested should be 2*NMODE. The primary stage has only a base sector while all other stages have both base and duplicate sectors.

    • The name of each superelement defined as Sename on SEOPT command must be Sname_HIx where x is the spatial harmonic index of the cyclic stage.

Macros are available on the Ansys installation media to simplify the generation of the single stage superelements for an HBM use pass. See the example below.

  • Use the HBMCYCHIGET macro to perform step 3.

  • Use the HBMCYCSEGEN macro to perform step 4 (except the load vector generation, which must be done manually).

Example

The following example snippet and selected output demonstrate the HBM cyclic generation using macros. The cyclic model has 24 sectors, 11 time harmonics, and fundamental engine order 3 loading.

!!! MODEL DEFINITION – step 1.

Nsec = 24 ! number of sectors
NH   = 11 ! number of time harmonics
EO   = 3  ! fundamental engine order of excitation

/prep7

! geometry creation (base sector mesh)
[...]

! multistage components
cm,_stage_base_nod,node
cm,_stage_base_elm,elem

! master nodes component
[...]
cm,master_node,node

! generation pass boundary conditions
[...]

! stage duplication
MSDUPL,'stage'

! multistage constraint equations definition - HI=0
[...]
msopt,new,stage,Nsec,0
cecycms

! master nodes creation
cmsel,s,master_node
m,all,all
allsel

finish

!!! HBM CYCLIC GENERATION PASS

Sname  = 'stage'         ! stage name
Nmode  = 3               ! number of CMS modes for primary stage 
			    !(twice will be computed for h>>>0 stages)

HBMCYCHIGET,Nsec,EO,NH,'GEN' ! step 3.
HBMCYCSEGEN,Sname,Nmode      ! step 4.

The necessary spatial harmonics computed in step 3 by the HBMCYCHIGET macro are:

________________________ HBMCYCHIGET MACRO _______________________
 *
 * CYCLIC HARMONIC INDICES REQUIRED FOR AN HBM ANALYSIS GEN PASS
 * WITH ENGINE ORDER 3 AND 11 TIME HARMONICS ARE WRITTEN
 * IN VECTOR ARRAY 'HBMCYCHIarray'
 *
 * LIST OF HARMONIC INDICES/ALIASED ENGINE ORDERS (IF EXPA)
 *            0
 *            3
 *            6
 *            9
 *            12
 *            0
 *