For incremental forming process simulations, the Dual-Mesh technique implemented in Transvalor’s FORGE® simulation software offers the result quality obtained with a very fine mesh at the computing calculation cost of a coarser one.
From a simulation viewpoint, incremental forming is an interesting challenge. First, it requires the capability to manage more complex die kinematics, including the use of manipulators that maintain the part during one blow and move it for the next. Second, the number of time increments needed to accurately describe the die path and part deformation increases dramatically with obvious consequences to computational time. In a situation like this, a typical solution would be to use a coarser mesh and/or an explicit solver, but both these options compromise the high level of precision expected and desired.
An alternative is to turn one of the incremental forming process specifics – namely, the localized deformation – into a simulation advantage by adapting the mesh to this situation. But since the fine-mesh area needs to correspond to the area of deformation, the result is a de-refinement and loss of precision in the simulation.
The Dual-Mesh technique, available with Transvalor’s FORGE® software package, combines the efficiency of an adapted mesh with the precision of a uniformly fine mesh.
How does this all work?
Simply stated, the main idea behind the Dual-Mesh technique is to separate the mesh dedicated to computation from the mesh devoted to storing the results. The user inputs a homogeneous fine mesh, and the software will automatically derive an adapted mesh by de-refining the mesh out of the deformation area. The mesh remains the same in the deformation area.
The solution is computed on the adapted mesh and interpolated onto the fine mesh. The adapted mesh, having fewer nodes and elements, requires less computational time. In the deformation area with identical meshes, interpolation is error-free. Elsewhere, since there are only rigid body movements, interpolation is nearly error-free.
From this solution, a regularly updating marching-scheme algorithm may be applied to update both meshes and associated results (strain, stress, etc.). The thermal equation is solved on the fine mesh. The gain is a function of the de-refinement efficiency. De-refinement efficiency is often constrained by the necessity to keep a good description of geometry details. When the deformation area moves, a new adapted mesh is regenerated automatically. If the fine mesh needs to be re-meshed, a new adapted mesh is rebuilt as well.
In the comparisons presented in this article, the Dual-Mesh computation was done using traditional computation mesh as the fine mesh. All other parameters were kept identical.
To demonstrate the Dual-Mesh technique computational efficiency, two very different forming situations are examined.
Example 1 – Cogging
This is a typical forging-machine example. The equipment is comprised of four hydraulic hammers moving up and down. Between each blow, the bar is rotated and moved along the machine axis (Figures 1a and 1b).
The primary objective of this modeling example was to predict the metallurgical situation at the end of the forging process. Achieving the desired precision requires a fine enough mesh for thermal computations. The computing platform was a 12-core server. The Dual-Mesh computation was 7.4 times faster than the traditional single-mesh method.
Example 1 uses a relatively bulky part, and, as such, de-refinement is effective. To test the method in a less favorable situation, a “deep-drawing process” was selected.
Example 2 – Deep Drawing
In this instance, the forming tool is a kind of finger with a rotational movement combined with linear displacement. Figure 2a displays initial, intermediate and final forming steps. Figure 2b shows the adapted mesh at the beginning and at an intermediate stage. To get computational results along the thickness of the part, we used a mesh with three to four elements in the thickness. To accommodate the part shape factor, an anisotropy meshing factor of 2 was used, which resulted in a 500,000-element fine mesh (Figure 2c). The adapted mesh ranges from 60,000-120,000 elements toward the end of simulation (Figure 2b). The shape becomes increasingly complex as forming progresses. Consequently, the adapted mesh requires more elements to keep good geometric control.
Quality of Results
The cogging and deep-drawing examples illustrate the advantages of quick computational times. Obtaining computation time seven to 10 times faster (Figure 3) than with traditional mesh modeling is good, but not if it is obtained at the expense of accuracy. The section that follows compares a number of results (force, strain and temperature distribution) obtained with traditional mesh and Dual-Mesh computations. The same cogging and deep drawing (examples 1 and 2, respectively) are used throughout the following sections.
In Figures 4a and 4b the vertical axis represents force. The horizontal axis in Figure 4a represents time and represents computational steps in Figure 4b. In both cases, red corresponds to Dual-Mesh and blue is traditional fine mesh.
For Example 1, forces are so close that both curves almost overlap. For Example 2, Dual-Mesh shows some small oscillations created by the rebuild of the adapted mesh linked with the forming-die displacement. Even if oscillations are visible, they remain within engineering tolerance.
Strain and Temperature Distribution
Local distribution is usually trickier. Figure 5a displays the strain distribution in both traditional fine-mesh and Dual-Mesh computations and at the end of the cogging operation (Example 1). The very typical helical pattern created by the combined rotation and displacement of the bar is the same. Figure 5b displays temperature distribution in cross section with identical results.
For Example 2, Figures 6a and 6b display thickness distribution and first principal stress in a section using Dual-Mesh and traditional fine-mesh techniques, respectively. Once again, as intended, results from both techniques are identical.
A More Complex Application – Becking Example
The objective here is to increase the inner diameter of a large tube. It is done by incrementally reducing the wall thickness (Figures 7a and 7b). Upper dies move up and down to reduce thickness against a continually rotating mandrel. When the upper die is no longer in contact with the workpiece, friction by the mandrel is strong enough to rotate the part to the area where thickness is to be further reduced.
This example combines a number of technical modeling challenges. These include a long process time (with the associated large number of time increments – about 10,000 in this case), a free surface, poor contact and almost rigid body movement during the rotational phases together with the associated possible convergence difficulties.
In this situation, the shape ratio is not very favorable and limits the use of a coarser mesh. Despite this difficulty, using the Dual-Mesh technique speeds computational time by a factor of three over traditional mesh techniques, making it possible to complete computation in 20 hours. In this case, again, results with and without the Dual-Mesh technique are very similar. Force evolution and strain distribution comparisons can be seen on Figures 8a, 8b and 8c.
Until recently, simulating incremental forming processes was, in most cases, very costly in terms of computational time. Some work-around or “tricks” were experimented with over the years, but all had their drawbacks. Mostly, the desire to shorten computation cycles was almost always achieved only at the expense of the simulation’s quality. Now, with the introduction of the Dual-Mesh technique, Transvalor FORGE® is lifting this barrier. Incremental forming process simulations are now affordable without trading off the accuracy of their results.
Authors R. Ducloux and E. Perchat are employed at Transvalor’s operations in France. Author B. Castejon heads TransvalorAmericas in Chicago, Ill. He may be reached at email@example.com