Cyclic Symmetry Considerations in ANSYS® Workbench Mechanical
Figure 1: One Sector in a Cyclic Symmetry Analysis, Showing Low and High Boundary Selections
ANSYS Workbench Mechanical supports cyclic symmetry analysis, and makes it easy to simulate with a Symmetry branch in the Outline at the Model level. A user indicates the Low Boundary and the High Boundary for the Cyclic Region of interest. Analyses such as static structural and modal analysis can follow, with both of them performing the analysis as if an entire circular structure was present.
In the simplest cases, the Low Boundary and High Boundary for a Cyclic Region are selected on opposite side faces on one body. They can also be applied to opposite side faces on a multibody part as in the half-cylinders in Figure 1 above. In DesignModeler, parts that do not touch can be declared to form a multibody part, with the result that they will aid in creating Symmetry branches for cyclic symmetry. This article explores some of the details.
Details that Aid Cyclic Symmetry Analysis
Inside Workbench DesignModeler, in the Outline, bodies can be grouped with “Form New Part” into multibody parts. If solid bodies grouped into a multibody part have shared faces between them, the materials become continuous between them, and when meshed in Mechanical, there are nodes on the common interface between them. Bodies that do not touch can also be formed into multibody parts, as seen below in Figure 2:
Figure 2: Multibody Parts in a Sector of a Wheel
Creation of Symmetry Cyclic Regions is aided by multibody parts, because a Low Boundary and High Boundary cannot both be chosen on completely independent bodies, even though face topologies and sizes on the Low and High Boundaries are identical. With multibody parts, as above, selections of Low and High Boundaries will work.
Figure 3: Low and High Boundary Choices in a Cyclic Symmetry Sector
Because of the Cyclic Region, the mesh appearance on the Low Boundary and High Boundary faces will match, so that cyclic symmetry node degree of freedom coupling will work. In Figure 3 above, a Cylindrical Coordinate System was created with its Z axis on the axis of the wheel in this model. Note independent meshing in the parts below.
Figure 4: Meshed for Cyclic Symmetry Analysis
Sufficient boundary conditions should be applied to prevent free motion along the Z axis of the cylindrical coordinate system, and to prevent free rotation movement Y direction (theta) of the cylindrical coordinate system, in a static structural analysis. In a modal analysis, a user should consider what is suitable for constraint.
Figure 5: Cyclic Symmetry Static Result, Expanded from One Sector
In a modal analysis, both Cyclic Mode and Harmonic Index have to be examined by a user. A sufficient number of modes and harmonic indices should be considered to completely fill a range of frequencies of interest. Workbench Mechanical expands the view of the results to suggest the presence of all sectors.
Figure 6: Cyclic Symmetry Mode Shape, Cyclic Mode 3, Harmonic Index 0, Frequency = 739.79 Hz.
Animation of results makes it considerably easier to understand the deformations that are calculated.
Workbench Mechanical can apply Symmetry Cyclic Region High and Low Boundaries to a sector made of many bodies, as long as bodies with faces on the low and high boundary sides are declared to be members of a multibody part. This works for bodies that do not share a common boundary. Once enough multibody parts have been created, matching faces on the low and high boundary sides can be selected for Cyclic Region definition.
The remaining challenge for a user is suitable definition of boundary conditions, and the usual challenges of meshing, contact definition, loading, and other considerations.
Plots of results are automatically expanded to show a complete circle of sector images, permitting reviews that are easier to understand, and that confirm that parts are connecting properly. Recent versions of ANSYS Workbench permit control of the number of sectors expanded, and offer some tolerance for imperfect matching of Low and High Boundary face shapes.