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4 – FUNDAMENTALS

4 – FUNDAMENTALS containing carbon fiber show good performances for FH structures. However, a com- parison of the above listed properties with the requirements (tab. 2.1) obviate their usage, what reduces the range of applicable materials for the MSTS FH. For a further confinement, the endurance strength is regarded as most important cri- terion due to the high required number of cycles of the MSTS. Some metals have an endurance strength limit, what means that the number of cycles until a loaded FH breaks, tends to infinity, when a certain stress limit will never be exceeded. The en- durance strength of a metal depends on its crystal system. Metals with body-centered cubic systems have an endurance strength limit, whereas metals with face-centered cu- bic systems do not. The S-N curve 4 characterizes the magnitude of an applied cyclical stress against the logarithmic scale of cycles until failure [8]. This fatigue test with structural damage divides the applicable metals for the MSTS in two groups, which are listed in table 4.1. Beryllium copper, titanium alloys and cobalt alloys have been classified as best candi- dates for the MSTS FH structure. Beryllium copper (CuBe) is an excellent alloy for springs and is space qualified. However, the high density and the missing endurance strength limit exclude its applicability. Furthermore, the toxicity of Beryllium is a problem during the wire-cut EDM due to emerging vapours. NIVAFLEX R○ 45/18, basically used in the watch industry, is designed especially for long term cyclical stressed springs 5 . Thus, it has an endurance strength limit. A high elastic force is required according to the high Young’s modulus, which possibly cannot be generated with the VCA. Missing space qualification and minimum deliv- ery quantities of several 100 kg avoid the usage of NIVAFLEX R○ for the MSTS FH structure. As most commonly used titanium alloy for space applications, Ti-6Al-4V shows ideal properties like an existing endurance strength limit [3], a low density and a low Young’s modulus. The influence of these properties for the MSTS FH structure design will be discussed in chapter 5.4. Figure 4.2 shows a collection of S-N curves of Ti-6Al-4V samples with different milling axes and surface finishes respectively. Obviously the endurance limit depends on the surface finish. Thus, it is crucial for the MSTS FH design, that the maximum stress which occurs in the flexible hinges never exceeds the endurance strength limit. 4 Also known as Wöhler curve. 5 http://www.vacuumschmelze.de accessed on June 4, 2008. 14

4 – FUNDAMENTALS Otherwise, a nondestructive operation cannot be guaranteed over several billion cycles. For the most demanding applications e.g. aerospace, lifetime and fatigue tests must be perforemd at any rate [2]. Alloy ρ / kg m 3 E / GPa S ′ e / MPa λT / W Km Ti-6Al-4V 4420 114 ≈ 350 7.2 NIVAFLEX R○ 45/5 8500 220 n/a n/a Beryllium Copper (CuBe) 8260 131 - 106 Table 4.1: Properties of the investigated materials for the MSTS FH structure. Listed are the mass density ρ, the Youngs’s modulus E, the endurance strength S ′ e and the coefficient of thermal conductivity λT . The table is separated in two parts characterized by the endurance strength limit. 4.1.4 Wire-Cut EDM EDM allows very high precision and arbitrary shaped machining of electrical conduc- tive materials. There are two main types of EDM called sinker EDM and wire-cut EDM. Flexible hinges with one degree of freedom will be ideally machined by wire-cut EDM. Reasons for selecting this method are the simpler machine setup, because no special matrices must be prepared, and the lower costs. A maximum precision of 5 µm and an average roughness height of Ra ≈ 0.18 µm are obtainable by wire-cut EDM [4]. The average roughness height has an influence on the endurance strength limit as shown in figure 4.2. Thus, a roughness measurement on the surface of the manufactured MSTS FH structure should be performed before the flight model will be constructed. The wire diameters are generally in the range of a few hundred microns. The MSTS FH design must be optimized for the applied wire diameter. For example, with a diameter of 0.2 mm no radii smaller than 0.3 mm can be cut. Repeated passages with reduced cutting velocities improve the surface finish, but increase the machining costs [4]. 4.1.5 Stage with two Parallel Blades Since the movement of the shutter blade will be performed just in one direction, a FH structre variant called stage with two parallel blades presented in [4] should be discussed in detail. 15

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