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4.1.6 Technological

4.1.6 Technological Limitations 4 – FUNDAMENTALS When estimating the parameters in (4.2) for the MSTS design, it becomes obvious, that especially the thickness h of the FH blades can achieve very small dimensions. Therefore, it is reasonable to check the technological limitations of the applied manu- facturing methode. Wire-cut EDM is a swarf-free machining method, because the electric discharges melt and vaporize the metal for cutting. Nevertheless, vibrations occur due to electrical arcs and busts, electrostatic forces and due to the jet of the dielectric fluid for rinsing. This limits the aspect ratio of machined blades and therefore affects the MSTS FH structure design. A maximum aspect ratio of aF H= l/h ≈ 60 was defined for steel based on manufacturing experiments [4]. Figure 4.4 sketches occuring blade deflections during the wire-cut EDM process due to the above mentioned disturbances. The minimum notch thickness depends on the material and the EDM quality. Circular notch hinges can reach values of a few microns. For blades as in leaf spring hinges, a minimum thickness of at least 50 µm is reasonable. In this dimension range no violation of the three basic assumptions noted in subsection 4.1.2 shall occur. 4.1.7 Linear Stage with Necked Down Flexures To avoid the technological limitations for extending the dimensioning range of the FH structure shown in figure 4.3 (left), an improved variant called linear stage with necked down flexures is presented in [4]. As sketched in figure 4.3 (right), both blades carry a segment considered as infinitely rigid. A parameter ξ defines the ratio between the flexible and rigid parts to ξ = 2lc l with 0 < ξ ≤ 1. (4.5) A multidimensional optimization including the rigidity, the blade thickness and the critical load yields an ideal ratio for the necked down flexure of ξopt ≈ 0.3 [4]. An adequate aspect ratio shall be optained for the MSTS FH stucture design using ξopt. The required force in this setup will be higher due to the augmented translational rigidity, but increases as well the eigenfrequencies, what is highly desired for the control as discussed in section 4.5. The formula for the deflection can be deduced to f = P l3 ξ(3 − 3ξ + ξ 2 ) 2Ebh 3 . (4.6) 18

Analogously follows for the rigidity and the buckling load 4.2 Dynamics 4.2.1 Introduction c = 2bh 3 E ξ(3 − 3ξ + ξ 2 )l 3 4 – FUNDAMENTALS (4.7) Nc = 8π2 EI ξ 2 l 2 . (4.8) The design of the MSTS FH structure shall be optimized in terms of dimensions and weight to achieve the requirements listed in table 2.1. To fulfill the shutting frequency and especially the maximum open/close time, an optimization in consideration of the MSTS dynamics is essential. 4.2.2 Theory A mathematical model for the MSTS FH structure design as proposed in figure 4.3 is required to optimize the mentioned parameters. The sketch 4.10 (left) allows to deduce the mathematical description for a driven damped spring-mass system satisfying the equation m d2x dx + k + cx = F (x, t), (4.9) dt2 dt whereas m is the mass, k the attenuation constant, c the spring constant and F the applied dynamic force. The mass and the spring constant are coupled with the system’s first eigenfrequency f (1) eig 1 c = . (4.10) 2π m The parameters in (4.10) can be determined by means of FEM calculations. How- ever, determing the attenuation constant is virtually impossible with simple calcula- tion methods. Measurements at a manufactured FH structure must be performed for disclosing the attenuation constant. The required open/close time is in the range of a few milliseconds. A relatively high first eigenfrequency of the FH structure shall therefore be achieved to guarantee fast 19

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