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' dimensions2. BELLOWS' DIMENSIONS AND PROPERTIES2.1 PreliminariesThe bellows are manufactured by SERVOMETER ® Electroforms. They guarantee thefollowing tolerances accordingly to their data sheets:• Inner diameter B : ±0,13 [mm]• Wall thickness t is only the average metal thickness of the entire bellows.• Outer diameter A varies with wall thickness and size of the bellows.• Length of convolutions length D : ±0,25 [mm]• Spring rate k : ±30%The standard metal is nickel. Normally, the bellows have a 0.0025 [mm] lamination ofcopper between equal thickness' of nickel. Servometer ® bellows have about the samechemical analysis as commercial “A” nickel with the exclusion of the copper lamina.The composition of the metal is:• Ni + Co 99.80%• Sulphur < 0.05%• Interstitially deposited impurities 0.05% (Oxygen and carbon)The bellows normally have a bright corrosion resistant surface and are leak tested 100% ona helium mass spectrometer leak detector. No bellows is shipped if its leak rate exceeds1·10 -9 [cc/sec]. This rate amounts to one cubic centimetre of helium in 32 years.The following properties are given for this nickel :• Young’s modulus23'350'000 [psi]• Yield strength125'000 [psi]• Tensile strength110'000 [psi]• Hardness270 [Vickers]2.2 Geometrical data2.2.1 SERVOMETER ® DATA-SHEETSBecause the details of the way to manufacture these bellows are maintained secret, the onlygeometrical parameters available are the following:• Outer diameter A 0.250 [in.]• Wall thickness0.0015 [in.]• Inner diameter B 0.150 [in.]• Spring ratio k 5.9 [lb./in.]• Convolution length l o 0.740 [in.]• Number of convolution 24• Effective area S 0.0292 [in. 2 ]• Maximum pressure for ½ stroke 290 [psi]Of course, this information does not give all the basics, to create the entire solid model. Theradius of the convolution curves is missing, for example, as well as the length between thetwo curves. Servometer ® didn’t want to give any further informations. Hence this had to bemeasured in this project.7
II. Bellow's' dimensionFEM modelling of a bellows and a bellows-based micromanipulator2.2.2 MEASUREMENTSThe parameters to be determined are (figure 7) : the inner and outer radii, respectively r 1 andr 2 , of the convolutions, and the straight length m between the inner and outer curves. Theycan be deducted from the given parameters, but only if symmetricity assumption is made, i.e.r 1 = r 2 . These measurements have to be made to be on the safe side.The first step was to cut carefully the bellows axially into two equal parts, in a way asprecise as possible. If the FE analysis is made with inexact geometrical basis, the results willbe erroneous, and it is useless to proceed.bellowsPower drillwooden maintaining-toolCircular cuttingplatezxFigure 5Overview of the cutting system.The power-drill is fixed andguarantees a non-displacementin Z-direction. The X- and Y-direction movements areperformed by moving thewooden piece, which lays onthe table.Consequently, a small oblong hole was built in a wooden cube, so that the bellows has justenough place to be put in, without moving it too much. A thin circular cutting-tool was fixedon a power drill, and adjusted the elevation so that it will cut the bellows just in its axis, asshowed in figure 5.To study at the imprecision ratio, two bellows are cut in order to compare if similardimensions are obtained, and so that an average value for each needed measurement can beselected. is more accurate in this manner, because there are four different parts to measure.Figure 6Photo taken under a microscope,showing a part of onehalf-bellows. The ruler on theleft side is in millimetres. Itmeans that the picture heightrepresents about 0.9 [mm].The dimensions of the bellows are so tiny, that some photographs had to be taken under amicroscope. A ruler is set on the bottom of the bellows, so that it can be compared it with the8
Page 1: Helsinki University of Technology C
Page 4: PrefaceThe author wishes to thank t
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