Periodic media analysis

Quite often industrial processes that need to be analyzed involve sections that repeat in a simple pattern and move through a process zone. A prominent example is a conveyor belt with regularly spaced packages, as illustrated schematically in Figure 1 and exemplified with a finite element mesh in Figure 2. Continuous forming operations such as metal rolling are also good examples because the deforming material can be broken up into an arbitrary number of identical sections.

Figure 1. Schematic representation of periodic media.

Figure 2. Conveyor belt with packages on top.

For the sake of clarity we will use the conveyor belt example throughout this discussion to illustrate many of the concepts associated with the periodic media analysis technique. Figure 1 shows a conceptual decomposition of the conveyor belt; in reality, the belt is a continuous entity.

Conceptually, the overall model can be decomposed into blocks (topologically identical meshed structures) that are connected together and span the process zone. You create a part that defines a “building block” (the meshed structure that is repeated to model the entire periodic media) and then construct the whole model via a chain of appropriately positioned instances. The periodic media analysis technique provides a simple way to automatically connect these instances together at the front and back ends of adjacent blocks. This technique also provides a convenient way to define loads and boundary conditions that represent the physical system at the unconnected ends of the first and last blocks in the chain. The first block of the chain is referred to as the inlet, and the last block is referred to as the outlet. Finally, when the periodic media moves through the process zone, blocks from the outlet are automatically shuffled to the inlet. The blocks (meshed structures) defined with this technique can interact via contact with other modeling features that are not periodic in nature, such as the rollers depicted in Figure 1.

At the core of the periodic media analysis technique lies the concept of shuffling blocks from the outlet back to the inlet. A dedicated algorithm is used to detect when the inlet has moved too far into the process zone and to shuffle a block from the outlet directly to the inlet. The dashed arrow in Figure 1 illustrates the shuffling process. To ensure a smooth transition, the necessary nodal and element state data from the inlet block are stored at the beginning of the current step. When shuffling occurs, the stored nodal and element state data are mapped to the new inlet block and any inlet/outlet loads or boundary conditions are transferred to the newly exposed block ends.

Thus, the periodic media analysis technique offers a convenient way for an Eulerian-like view into the moving repetitive structure. For example, you may be interested in assessing the package dynamics on the belt at a location somewhere between the rollers in both transient and steady-state conditions. You define several blocks around that location, you define contact with the rollers as necessary, and you provide appropriate inlet and outlet loading conditions. The periodic media analysis technique provides a convenient and economical way to create and analyze this system. By re-using elements that have left the process zone via this shuffling process, you can avoid the large meshes at the inlet end required for purely Lagrangian simulations.

The first step in constructing a periodic media model is to identify the portion of the model that constitutes the building block of the repetitive structure. In Figure 2 one square belt patch together with one asymmetrically shaped package on top constitute such a building block. If you string together several blocks, the entire belt with packages can be modeled as shown.

The shuffling process can be activated on a step-by-step basis. By default, the shuffling process is inactive. In many cases the configuration of the periodic media in the operating condition can be determined only via simulation. This allows any number of analysis steps to be carried out prior to activating the shuffling process.

The example illustrated in Figure 2 and in Media transport shows a conveyor belt transporting asymmetrical packages placed initially at regular intervals. In its operating condition the belt will be tensioned. You can pre-stretch the belt assembly in either Abaqus/Standard or Abaqus/Explicit. If the pre-stretch analysis is conducted in Abaqus/Standard, all ties between adjacent blocks as well as boundary conditions at the inlet and outlet ends nodes need to be defined explicitly as the periodic media analysis technique is available only in Abaqus/Explicit. If the pre-stretching step is conducted in Abaqus/Explicit, the shuffling process should remain inactive during the pre-stretching step. A boundary condition should be applied at the front end of the inlet block to keep the inlet block aligned with the direction of the movement in the pre-stretching step, and this boundary condition should be removed after the shuffling process is activated in the following step.

MEDIA TRANSPORT
periodic_media_name1, ACTIVE
periodic_media_name2, INACTIVE
...

The periodic media analysis technique is a powerful feature; however, you must exercise good engineering judgement when using it. The following comments and recommendations will help you avoid common pitfalls when using this technique:

• The block shuffling process is inherently noisy as chunks of elements are detached at one end and reattached at the other. Although the process uses appropriate material and kinematic states, small shocks are inherent to the process. A small amount of mass proportional damping is recommended to dampen out this excitation.

• The combination of boundary conditions at the inlet control node and any loads applied in the process zone should ensure that the inlet block moves across the trigger plane without a change in direction. In the conveyor belt example, a good modeling practice would be to place a fixed guide roller at least two blocks away from the trigger plane.

• For more complex geometries (such as belts that change direction between rollers or package wrapping analyses when the belt is the wrapping material itself), it may be necessary to start with a straight sequence of blocks and move the belt rollers (which are not part of the periodic media definition) into the desired locations. Contact interaction between the belt and the rollers would deform the belt in the desired configuration. This additional analysis step can greatly simplify the definition of the initial mesh.

• Sometimes it may be necessary to model the process of threading a belt wrapping through rollers, just as in physical reality at the start of a manufacturing process. If this leading segment is followed by periodic blocks that include actual packages, you can attach the periodic media mesh to a regular mesh to execute the threading. The periodic media part of the mesh can then be imported into a separate model without the leading mesh, and the analysis of the periodic media consisting only of the wrapper and packages can be executed.