fem modelling of a bellows and a bellows- based micromanipulator

FEM modelling of a bellows and a bellows-based micromanipulatorV. Completion5. COMPLETION5.1 Project conclusions5.1.1 RELIABILITYIn this work, the most observed principle has been mistake forethought. At each phase, stepafter step, any result was carefully checked before proceeding through the next phase. Indeed,a non-negligible part of the allowed task duration was devoted to understand the FE methods,in order to select the most fitting elements for each case. Different models were experimentedfor a same problem, so that the results given by different methods compare could becompared.After having chosen the elements, they were checked by setting up three models. Thosevery unlike models were built with completely distinct elements. One was constructed in twodimensioned space with plane element accepting axial symmetry. Another was made of 3Dsolid elements, and the third composed by shell elements. The theory on which these elementsare based differ radically. Hence, if all three results for one corresponding concur, theoutcome is very likely reliable.If two different models are based on too similar elements, the way to construct them may beso identical that the same error can be committed in both cases, and lead to the identical butfalse answer. On the contrary, if the models are completely unlike, the way to establish themmay also be utterly in contrast, and ensure that the same mistake cannot occur in both models.This is actually exactly our case. The way to construct a 2D-model absolutely differs from a3D one. Moreover, solid elements fill a volume-based model, but a shell-based model can befabricated with areas exclusively. These changed building methods ensure that it is nearlyimpossible that one identical mistake appears in two models, and make an accordant resultbeing even more reliable.It is finally to note, that there have been no previous studies of this sort of microcomponent,which made the simulations and modelling much harder.5.1.2 BELLOWS' PERFORMANCESThis project showed that the bellows has very linear characteristics. Its bending varies in aperfectly proportional fashion to the applied load. Moreover, some parameters are quasiconstantover the full work range of the micromanipulator. The bellows' stiffness varies nomore than 0,002% for bending forces varying from 10 [mN] to 50 [mN].The spring ratio varies a few percentages when applying varying compressing or elongatingloads. But even then, it varies in a very linear way, and can easily be taken into account forthe open-loop control, if necessary.The axial expansion of the bellows when applying interior pressure also varies less than0,3% over the full pressure range, and in an entirely linear way.Finally, it can be concluded that the high linearity of the bellows' motion constitute anexcellent connection between the piezoactuators and the end-effector, and that it can improvea new type of accurate join-free parallel structure, where the joints are integrated into theactuation links.Furthermore, once the geometrical parameters exactly checked for each bellows through anelementary calibration method, and the kinematic precisely adapted, the open-loop control of43