fem modelling of a bellows and a bellows- based micromanipulator

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FEM modelling of a bellows and a bellows-based micromanipulatorII. Bellows' dimensionspixels of the pictures. Hence, a factor converting dimensions measured by numbering pixelsin millimetres is determined. One example is exhibited in figure 6. The conversion factorfrom pixels into millimetres is 49 – but not in this figure, that has been re-sized – and thepicture is orthogonal, i.e. the same factor suits for both x- and y-directions.2.3 Solid model2.3.1 CONSISTENT UNITSANSYS ® is an unitless program. This means that it does not take into account any units forthe parameters it calculates with. It is up to the operator to be consistent with the units heutilises. Therefore, one basis has to be chosen, and all units have to be adapted to it. TheI.U.S. 2 involves meters for length, kilograms for weight, seconds for time, amperes forcurrent, Kelvins for temperature, moles for substance quantity and candelas for luminousintensity. With those seven units, it is possible to build all other, accordingly to theirdefinitions.2.3.2 UNITS CONVERSIONBecause of the bellows’ dimensions, millimetres are used for the geometrical description.Consequently, the unit basis will be the following (only these are needed):Length = [mm] Mass = [kg] Time = [s]Let’s now deduce from the I.U.S., the units of different parameters to be applied in thissimulation, such as velocity, acceleration, force, pressure, and density. The followingcalculations are shown, to make the reader attentive of the unit-problem:• 1 [m] = 1 [m] · [m/m] = 1 [m] · (10 3 [mm/m]) = 10 3 [m·mm/m] = 10 3 [mm] (3)• 1 [m/s] = 1 [m/s] · (10 3 [mm/m]) = 10 3 [mm/s]• 1 [m/s 2 ] = 1 [m/s 2 ] · (10 3 [mm/m]) = 10 3 [mm/s 2 ]• 1 [N] = 1 [m·kg/s 2 ] = 1 [m·kg/s 2 ] · (10 3 [mm/m]) = 10 3 [mm·kg/s 2 ] = 10 3 [mN]• 1 [N/m 2 ] = 1 [N/m 2 ] · (10 -3 [m/mm]) 2 = 10 -6 [N·m 2 /m 2·mm 2 ] = 10 -3 [mN/mm 2 ]• 1 [kg/m 3 ] = 1 [kg/m 3 ] · (10 -3 [m/mm]) 3 = 10 -9 [kg·m 3 /m 3·mm 3 ] = 10 -9 [kg/mm 3 ]The following conversion table can be given:{ [m] ; [kg] ; [s] } { [mm] ; [kg] ; [s] }Length 1 [m] = 10 3 [mm]Velocity 1 [m/s] = 10 3 [mm/s]Acceleration 1 [m/s 2 ] = 10 3 [mm/s 2 ]Force 1 [N] = 10 3 [mN]Pressure 1 [Pa] = [N/m 2 ] = 10 -3 [kPa] = 10 -3 [mN/mm 2 ]Density 1 [kg/m 3 ] = 10 -9 [kg/mm 3 ]2 International Units System3 This result is evident, but shows the correct method which should be applied for all other units.9
II. Bellow's' dimensionFEM modelling of a bellows and a bellows-based micromanipulatorIt is very important to consider these units definitions when settling values in ANSYS ® .Otherwise, it can induce misinterpretation of the results given by the software – because whenshowing results, the postprocessor doesn’t furnish any unit – or inject wrong data to its solver.Now that the units are known as being consistent, the results of the measurements 4performed on the pictures taken under the microscope, as well as the data furnished by themanufacturer, can be resumed in the subsequent table, accordingly to figure 7.For the inner and outer radii r 1 and r 2 , 6 measures were took each time, and the mean ofthem was put as value in that table. For the straight part m, it was needed to take themeasurements between one reference point on two different pictures, since that dimension isto big to fit entirely under one microscope photo. The tolerances are the minimum andmaximum values measured.PartValue in US systemValue in I.U.S.Outer diameter A 0.250 - [in] 6.3500 - [mm]Inner diameter B 0.150 ± 0.005 [in] 3.8100 ± 0.13 [mm]Mating part C 0.246 - [in] 6.2484 - [mm]Convolution pitch D 0.032 ± 0.010 [in] 0.8128 ± 0.254 [mm]Total convolution l 0 0.740 - [in] 18.7960 - [mm]Thickness of wall t 0.0015 - [in] 0.0381 - [mm]Inner radius r 1 75.375 ± 3.25 [pixels] 0.151 ± 0.007 [mm]Outer radius r 2 90.000 ± 7.00 [pixels] 0.1800 ± 0.014 [mm]Straight part m 402.625 ± 6.00 [pixels] 0.8053 ± 0.012 [mm]Number of pitches N 24 - - 24 - -Max. compression stroke 0.15 - [in] 3.7846 - [mm]Max. c. stroke per conv. 0.0067 - [in] 0.1702 - [mm]Effective area S 0.03 - [in 2 ] 18.7096 - [mm 2 ]Spring ratio k 5.9 ± 1.77 [lb./in] 1033 ± 310 [N/m]Spring ratio k per conv. 141 ± 42.3 [lb./in] 24'693 ± 7407 [N/m]Density of Ni/Co 0.03197 - [lb./in 3 ] 8.85 10 -7 - [kg/mm 3 ]Young's modulus E 23.35 10 6 - [psi] 162 10 6 - [mN/mm 2 ]Yield strength 110 10 3 - [psi] 760 10 3 - [mN/mm 2 ]Tensile strength 125 10 3 - [psi] 862 10 3 - [mN/mm 2 ]Hardness 270 - [Vickers] 270 - [Vickers]DBAl 0LDr 1r 2tB/2Figure 7Drawings that provideparameter location, andfurthermore, parametersdefinitions.mCA/24 The measured values are shown in the table with darker background colour.10
Page 1: Helsinki University of Technology C
Page 4: PrefaceThe author wishes to thank t
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