fem modelling of a bellows and a bellows- based micromanipulator

FEM modelling of a bellows and a bellows-based micromanipulatorIII. ModellingQ parameter [mN mm 2 ]82762.1082762.0582762.0082761.9582761.9082761.85Bending parameter Q for the whole bellowsConstant pressure p = 20 [mN/mm 2 ]82761.8010 15 20 25 30 35 40 45 50Force [mN]The Q value doesn't vary more than 0,002% in the full range of bending force. It means thatthe bellows' inclination depends in a very linear way on the applied force. The mean value ofthose results – which is 82,77·10 3 [mN·mm 2 ] – differs less than 0,6% of the value determinedearlier.3.4 Pressure vs axial displacementThe previous parameters acquired were so called passive parameters, since they don't reallyact on the bellows, but are just some kind of response when applying external loads – asbending force, or as a mass. They are necessary to settle the correct behaviour of the bellowsacting together, and to build the whole micromanipulator beam-based model.From the viewpoint of the command, there are also other important elements that have to bedetermined. Since the micromanipulator is only controlled by the voltage applied on the threepiezoelectric actuators, it is important to get now the different parameters entering at stakethrough the whole motion-process of one bellows:y cControly c ë VvoltagePiezosV ë ppressureBellowsp ë yyFigure 22Motion-process of themicromanipulator: y c is the desiredposition of the bellows' top, and yits reached position.In this project, the point of interest is of course only the bellows. Therefore, the lastparameter to be found now is the conversion constant Z between the pressure applied by thepiezoactuator and the axial motion of the bellows.Hence, the next simulation will be the same as the one used for the comparison between thethree different models (figure 18). For a more accurate answer, the 3D model with SOLID45-elements is used. But this time, a time-varying internal pressure is applied into the ring, sothat it can also be checked if Z is really constant over the entire pressure range. It can also beseen if the radial displacement is truly negligible, as the manufacturer suggests.Inasmuch as only a lone ring simulation was considered, care has to be taken about whichnode should be observed during the measurements. The upper-part of the ring can movefreely, and that's actually not exactly the case of each ring constituting the bellows. It meansthat when applying an internal pressure, the top surface can have very little twist, as shown infigure 23.31