fem modelling of a bellows and a bellows- based micromanipulator

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FEM modelling of a bellows and a bellows-based micromanipulatorI. Introductionmodels the meshing would also be finer than this, because such an assemblage would be weakand unrepresentative.In figure 4, the difference between a mathematical model (4b) composed by those elementsand nodes, and the solid model (4a), that has the exact geometry can be seen. Nearly all finiteelement analysis models today are built using a solid model. This CAD-type mathematicalrepresentation of the structure defines the geometry to be filled with nodes and elements, andcan also be used to facilitate applying loads or other analysis data. However, the solid modeldoes not participate in the finite element solution! All analysis information must ultimatelybe transferred to the FE model for solution. The process of creating a finite element modelfrom a solid model is called meshing.(a)meshing(b)Figure 4.Figure (b) shows the mathematical modelof the solid model (a). It is important tonote that they are not equal.1.2.4 MODELLINGModelling is the simulation of a physical structure or physical process by means of asubstitute analytical or numerical construct. It is not simply preparing a mesh of nodes andelements. Modelling requires that the physical action of the problem be understood wellenough to choose suitable kinds of elements, and enough of them, to represent the physicalaction adequately.Badly shaped elements and elements too large to represent important variations of the fieldquantity should be avoided. At the other extreme, we should avoid the waste of analysis timeand computer resources associated with over-refinement, that is, using many more elementsthan needed to adequately represent the field and its gradients. Later, when the computer hasdone the calculations, the results must be checked to see if they are reasonable. Checking isvery important because it is very easy to make mistakes in describing the problem to thesoftware.The FE method calculates nodal displacements, then – in present ANSYS ® software too –uses the displacement information of the field to calculate strains and finally stresses. Ifdisplacements are incorrect, stresses will of course also be erroneous. Accordingly, we shouldexamine the computed displaced shape first. If it is substantially different from what isexpected, an error in the model is suspected. The software will permit the display of thedisplaced shape superposed on the original shape, with displacement scaled up if necessary,so that they are easily visible. Additionally, the displacement shape can be animated, so thatthe model appears to be vibrating slowly between its deformed and unreformed positions.Thus, it can easily be seen if it coincides with the real motion or not.As for stresses, the software will plot them as bands of different colours. ANSYS ® allowsusers to select an option that calls for averaging of stresses. This means that stresses fromindividual elements are averaged at nodes before plotting, so that stress contours have nodiscontinuities between elements. This is poor practice, because it removes information usefulto analyse. A stress plot that displays significant interelement discontinuities warns that afiner mesh is needed.1.2.5 DISCRETIZATION AND APPROXIMATIONWhatever the analysis method, the actual physical problem is not analysed, but themathematical model of it. Thus, we introduce modelling errors. For example, it is regularly5
I. Introduction FEM modelling of a bellows and a bellows-based micromanipulatornecessary to make some simplifications. A problem cannot be modelled taking into accountevery kind of geometrical incertitude – the geometrical model always differs from the truth,since the real model has constantly imperfections, as small as they can be – or all true materialproperties. The model is invariably only an approximation of the real problem. When meshingthe solid model, a discretization is introduced, as small as the elements can be.Finally, it must be admitted that software almost certainly contains errors. Commercialsoftware packages, like ANSYS ® , are large, versatile and under continual revision. It ispractically impossible to get everything right. Many errors either make a software featureinoperable or cause the program to crash, but some can lead to erroneous results. It istempting to blame all strange results on the software, but it is far more often the case that wehave blundered in modelling or in describing the model to the software. Strange results areobtained so often, that it is vital that, once more, the analyst be able to recognise that resultsare strange.1.3 ANSYS ®1.3.1 WHAT ANSYS ® ISThe finite element analysis (FEA) program that will be used in this project is ANSYS ® . Thissoftware is well-known and used by a lot of design-companies around the world. Ansys Incheadquarters is based in Canonsburg, south of Pittsburgh. It has 250 employees, of whichsixteen are developers. Over seventy-five offices are based world-wide.The father of ANSYS ® is Dr. John Swanson, very eminent in the FEA-field. He wrote thefirst code-lines of that program. The first release came out in the early seventies, giving proofthat in more than twenty-five years of being used by several companies, this software shouldbe quite reliable.The current release of ANSYS ® is 5.5 and came out in the beginning of November, butrelease 5.4 is used in this study, because of the minor differences in importing solid modelfiles from other CAD-packages. ANSYS ® capabilities are: structural, thermal, electromagneticand fluid analysis. It can also make coupled-field analysis. All these differentabilities are contained in different products. ANSYS ® Faculty Research is going to be used,which contains the same package as ANSYS ® Multiphysics, aside from some little restrictionson the element amount. But it will be largely enough for the simulations.ANSYS ® offers also a very large panel of about 150 different element types. It providesstructural beam elements, shell elements, pipe elements, for plastic or elastic materialproperties, linear or non-linear behaviour, and all that either for two or three dimensionalanalysis. It has also a comprehensive graphical user interface (GUI) that gives usersinteractive access to program functions, commands, documentation and reference material.An intuitive menu system helps users to navigate through the program. Users can input datausing the GUI, or by producing an input file that the software can thereafter read, so that hecan re-run his simulation very easily by changing just some parameters, without having torestart from the beginning.6
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