fem modelling of a bellows and a bellows- based micromanipulator

FEM modelling of a bellows and a bellows-based micromanipulatorIV. OutlookIn order to examine if the selected element, and its inputs are valid, it is first wanted to builda simple beam-based model of only one bellows. Comparative load is applied, to get resultsthat are known from previous simulations. Hence, all degrees of freedom of one beam's leftborder are fixed, and a force F = 50 [mN] is applied to its free edge, as shown below:Bending at the free-edge of the beam in this model equals 1.337 [µm], which is quite closeto the result obtained with the antecedent ring-based model, 1.335 [µm]. But this does notprove that the foregoing results were exact 'till now, since the parameter Q was calculated sothat it will be valid for the beams. It can only be inferred that, according to previoussimulations, the correct beam parameters have been found for the beam-based model of theentire micromanipulator.4.2 Beam-based model of the entire micromanipulator4.2.1 MODELThe micromanipulator model can now be constructed. It might be quite simple, only threebeams, and a platform binding them together are needed. But one has to be very careful in theway the geometry is erected.Considering that software can only compute numbers with limited decimals, rounding offerrors can generate misbehaving of the model. Therefore, it is better to put parameters in thelisting, and let the program make the calculations. For example in the case studied, thegeometry is "120º axi-symmetrical". So, instead of calculating the location of keypoints "byhand", it is preferable to copy one bellows three times, to guarantee a perfectly"axisymmetric" model.In a previous study [Lind98] the whole micromanipulator just collapsed when a load wasapplied on it, because the model was not perfectly symmetric. It took a long time to discoverthat this strange bearing came from numerical errors occurring because of such round offerror.39