fem modelling of a bellows and a bellows- based micromanipulator

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FEM modelling of a bellows and a bellows-based micromanipulatorIII. ModellingAccordingly to notation of figure 25, the controller may calculate the individual y c,i positionof each constituting bellows, throughout the inverse kinematic model (IKM), to attain adesired position y of the micromanipulator's end-effector. This IKM will be constructedespecially with data obtained from the simulations performed during this project, butassuming a nominal 25 bellows.However, mismatches between different bellows cannot be taken into account in the IKM.As calculated, one bellows' bending δx and axial growth δy can consequently vary up to 30%,depending on its effective geometry. This would of course affect the reached position y i of thevarious bellows, and surely, the resulting y of the end-effector.Consequently, the bellows' should be selected in a more accurate way, in order to avoidlarge mismatches. Servometer proposes for instance bellows with smaller tolerances. Anotherpossibility could be to enable a calibration in the control system.Figure 26Photography of a prototype of themicromanipulator built inUniversity of Technology ofTampere.25 I.e. a bellows which geometrical parameters have their nominal value.37
IV. OutlookFEM modelling of a bellows and a bellows-based micromanipulator4. OUTLOOK4.1 Expansion of the bellows' model to the entire micromanipulator4.1.1 PRELIMINARIESThe main point of this project was modelling of one bellows, in order to be able to buildafterwards the model of the whole micromanipulator. Therefore, the time allowed for thischapter was very short. The aim of it was only to build the beam-based model, but all thesimulations that have to be performed in order to build the kinematic model are to becontinued in an upcoming project.Consequently, the following paragraphs are only a starting point and a short overview of theprospective work, and have no pretension to cover all.4.1.2 CHOOSING RIGHT 3D-BEAM ELEMENTThe very next step is now the expansion of the bellows' model, in order to build a model ofthe entire micromanipulator. ANSYS ® proposes various beam-like elements and pipeelement.The first idea would be to choose a pipe element, since the bellows behaves mostlyas a pipe with very thin walls and small axial stiffness filled with water. But the completecomportment of those elements is quite complicated, and all the needed parameters are notavailable. The simulations have been oriented in a way to replace the bellows in future modelby a beam, and our artificial bending parameter Q for instance can only be used with beams 26 .BEAM44-element is proposed to be used for this model. It is a tapered uniaxial elementwith tension, compression, torsion and bending capabilities. The element has six degrees offreedom at each node: translations in the nodal x, y and z directions and rotations about thoseaxes. Stress stiffening and large deflection 27 capabilities are also included (figure 27).zziyiIyxixjyjJzjFigure 27Representation of the three-dimensional elementBEAM44, that has two principal nodes, I and J.This element is tapered, on the contrary of otherusual beam-elements, which are not axisymmetric.xThis element requires additional parameters, such as the momentum of inertia I and beam'sthickness t x and t y in y and x-direction. Since the Q parameter is known, this permits to choosethe inertial momentum I and Young's modulus E as desired. It is proposed to keep the originalmaterial's Young's modulus, and to compute I with formula Q = E·I.QI = = 5,11·10 -7 [mm 4 ] (4.1)EAs the corresponding beam's cross-section is not known, the bellows' wall thickness t is firsttried as input for the beam's widths t x and t y .26 ANSYS ® 's pipe are beam-like elements with modified parameter, to take into account the internal cavity.But our parameters are made for non-hole beams.27 What allows non-linear analysis.38
Page 1: Helsinki University of Technology C
Page 4: PrefaceThe author wishes to thank t
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