Mesh morphing in mechanical design.

Pupaza, Cristina

Abstract: Mesh morphing is an advanced CAE modeling technique used to modify the shape of mechanical parts and assemblies without returning in the CAD system, which is time consuming and generates unexpected modeling preparation stages. The paper deals with mesh morphing examples for mechanical components. The procedure is simple and fast, keeps the desired mesh pattern unchanged and allows meshed model parametrization. The benefits of this CAE modeling technique are enforced by the link with the optimization procedures in order to shorten the product development time. The procedure is a promising step for future implementation of virtual reality in mechanical engineering design. Key words: mesh, morphing, CAD, CAE, optimization.

1. INTRODUCTION

Morphing is a procedure that modifies the shape of model into another one through gradual transition changes. This technique was primary used in the music video and film industry in the early '90s, but rapidly evolved to technical applications, such as modeling algorithms applied in automotive industry, biomechanics, computer integrated manufacturing and re-engineering. Mesh morphing enables the analyst to create different variants of mechanical components or assemblies and to rapidly obtain an improved solution without returning in the CAD system for slight changes. Morphing capabilities were introduced in powerful CAE preprocessing systems such as HyperMorph (Altair Engineering), ANSA (BETA CAE System), ANSYS ParaMesh (ANSYS Inc.), where specialized modules are now tested and enhanced, pointing out the importance of this modeling technique for the industry. Advances on mesh morphing algorithms have been reported in recent literature (Alexa, 2002). Multiresolution mesh morphing of arbitrary topology were discussed and presented (Lee et al., 2006). The possibility of using the morphing tool in biomechanical applications was studied and remarks were done regarding the integration of this procedure in reverse engineering attempts (Chalkidis & Karatsis, 2005). Automated shape variation procedures were also developed, but they work with simulation procedures used in the automotive industry (Lehnhauser et al., 2006). Although the technique is already applied in other domains, few information refers to possible application on machine components or assemblies. The paper deals with mesh morphing examples and the benefits for structural analysis of machine elements are emphasized. The procedure is simple, efficient, acts both on parts and assemblies and keeps a desired mesh pattern unchanged. The return in the CAD system is avoided. Remarks regarding links with optimization procedures integrated in solvers are also included.

2. MESH MORPHING

The general objective of the procedure is to change the shape of the meshed model for improving the design solution. Mesh morphing is based on special entities, such as morphing boxes, which represent shape functions and allow user's control on model shape changes.

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Morphing boxes are hexahedral volumes (Fig. 1) (ANSA, 2005) including FE-model with lines, shell or solid elements, which belong to volume entities, connection points, elements placed in the neighborhood, called nested elements or any combination of them. By changing the shape of this box, the included elements will change their shape and position accordingly. Control points reside at morphing box corners and on the edges of morphing boxes and support free or controlled movements in the 3D space. The morphing box edges are splines, so they conserve their tangency continuity. Tangency is a constraint that can be defined between two successive morphing box edges. Hatches are symbols and center points reside in the middle of a box and allow the box selection. Nested elements are constraints, frozen or rigid restrictions for the nodes or elements that are used in the morphing procedure.

3. MORPHING MACHINE COMPONENTS

3.1 Shape changes

Shape morphing preserves model integrity and connectivity. Fig. 2 shows a machine tool main spindle before and after the morphing attempt. The initial mapped mesh is preserved, even the length of the right end changes. Mapped mesh gives coherence under model geometry variation, but is difficult to obtain for 3D complex geometries without user interaction. In this case no distorted elements appear after morphing, no initial parametrization is needed and the changes are done interactively or using numerical input values.

Mesh morphing is efficient especially for molded parts, sheet metal or components with complex geometry (Fig. 3).

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3.2 Stress reduction due to shape changes

Morphing allows rapidly scaling and reshaping existing design solutions, using templates or libraries for complex geometry parts. Several mechanical components were used for test cases of stress reduction capabilities, comparing the initial meshed models with the morphed ones. The morphing process was completed using ANSA preprocessing system and solved with ANSYS. Free point movement and automatically smoothed meshed options were chosen. Shape tests revealed a good quality of the morphed mesh. The maximum von Misses stress was easily decreased with 1015% and the processes took few minutes on a Pentium PC under Windows Operating System.

3.3. Meshed model parametrization

Handling and maintaining the parameters definition in CADCAE attempts is not easy, mainly because the same assembly presumes multiple simulations for which different solvers are used (Pupaza, 2004). Usually when transferring data between CAD-CAE systems parameter definition in a text format is not available. Meshed model parametrization allows the definition of geometrical parameters in a late stage of the design without returning in the CAD system, which is an important advantage because parametrical optimization procedures can be accessed. Another advantage is that the parameters definition refers exactly to the design variables. The parameters of the morphing box are (ANSA, 2005): * length of selected edges; * angle between two edges; * offset of the selected box faces; * translational and rotational movements of the selected control points.

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Fig. 4 shows an example of model parametrization for a roller bearing support. All the parameters were defined once and then the morphing actions were done by changing numerical values. Running an application through a script and performing morphing in batch mode are also available. Morphing parameters were used to efficiently handle the Finite Element model in a parametric way.

4. MORPHING OPTIMIZATION PROCEDURES

Optimization became a chain of optimization procedures accessed several times at different product development stages. Mesh morphing optimization is a parametric procedure.

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The movement of the control points is output in a text file as the definition of the design variables. This text file can be adapted for different solvers with optimization capabilities, such as ANSYS, ABAQUS, NASTRAN, LS-DYNA etc. Fig. 5 shows a block scheme for mesh morphing optimization. Because during mesh morphing the pattern is unchanged, problems may arise for large definitions of the design variables, when reconstruction stages have to be included for mesh quality improvement. Morphing means in fact shape variation using 3D movement of control points. As such, statistical data are useful to reduce the computation time.

5. CONCLUSION

Appling mesh morphing in mechanical design has the following advantages: it is simple and fast; no CAD-CAE reverse data transfers are needed, so important time savings can be obtained in model preparation; mesh quality improvement is possible after shape changes, if needed; model parametrization is realized directly on the meshed structure; shape improvements can be further enhanced by coupling morphing techniques with optimization procedures; including adaptive mesh algorithms can allow procedure extension for large shape changes. The procedure is a promising step for future implementation of virtual reality techniques and an innovating tool in mechanical engineering design.

6. REFERENCES

Alexa, M. (2002). Recent advances in mesh morphing, Computer graphics forum 2002, Fraunhofer IGD (Ed.), Vol. 21 Issue 2, pp. 173-198, ISSN 0167-7055, June 2002, Germany

ANSA User's Guide v. 12.0.3 (2005). BETA CAE Systems S.A., Kato Scholari, Thessaloniki, GR-57500, Epanomi, Greece, pp. 786-833

Chalkidis, I. & Karatsis, E. (2005). Applications of ANSA Morphing Tool in Biomechanics modeling, ANSA & iETA International Congress, BETA CAE Systems, June 2-3 2005, Halkidiki, Greece, Available from: http://www.betacae. gr/congress.htm. Accessed: 2007-04-06

Lee, A.W.F.; Dobkin, D.; Sweldens, W. & Schroder, P. (2006). Multiresolution Mesh Morphing, Available from: http: cm.bell-labs.com/who/wim/papers/morphing/morphing_ lowres.pdf. Accessed: 2006-10-05

Lehnhauser, Th.; Ratzel, M.; Braun J. & Marie, L. (2006). Automatic Shape-Optimization of a Close Coupled Catalytic Converter. NAFEMS Seminar: "Virtual Testing Simulation Methods as Integrated Part of an Efficient Product Development", May 10-11, 2006, Wiesbaden, Germany. Available from: http://www.altair.de/pdf. software/NAFEMS_2006.pdf. Accessed: 2007-02-07

Pupaza, C. (2004). Topology Optimization of Machine Elements, Proceedings of the 15th International Conference on Manufacturing Systems, Ispas, C., Ghionea, A., Constantin, G. (Ed.), 26-27 October 2004, pp. 477-480, ISSN 1942-3183, Editura Academiei, Bucharest, Romania