Avoidance of brake squeal by a separation of the brake ... - tuprints

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3 Efficient modeling of brake discs positive material parameters. The clearance is modeled as material with a very low density ˜ρ and elastic modulus Ẽ, all other modeling assumptions and basic parameters and dimensions are the same as for the disc with radial holes. The angular and radial position of the cooling ribs will be varied in the optimization. Two angles ϕ 1 and ϕ 2 and two radii r 1 and r 2 are shown in Fig. 3.10, b), respectively. Each friction ring has a thickness of h f , a modulus of elasticity E and a density ρ as well as the cooling ribs, which have a thickness ofh c , the lengthl c and the widthb c . The cooling ribs are all assumed to be of the same, constant shape. It would be possible to vary the shape of the cooling ribs also, but as will be shown in section 4.3, the optimization goal can be reached and even exceeded without this additional variation of the design parameters. The rotor is assumed to be simply-supported 1 at the inner lower ring, therefore, the hat of the brake rotor is not modeled explicitly, as was also the case for the disc with radial holes. Not only automotive brake discs will be studied and optimized, but also bicycle brake discs. The design of bicycle brake discs is completely different from automotive ones as can be seen in Fig. 3.11, a), where a state-of-theart bicycle brake disc of a major German manufacturer is shown. These brake discs are far smaller, thinner and lighter than automotive ones and normally manufactured of stainless, martensitic steel instead of cast iron. In the first optimization step, a simplified brake disc without the bars connecting the hub and the friction ring will be optimized by variation of the radial and angular position of axial holes drilled into the friction ring. For bicycle applications, these holes are intended to decrease the weight of the disc and can be found in all state-of-the-art brake discs with varying compositions. The friction ring is assumed to have free-free boundary conditions allowing to optimize the bending modes of the disc. A top view on the friction ring is shown in Fig. 3.11, b), where two holes with radial positions r 1 and r 2 and angular positions ϕ 1 and ϕ 2 are shown. Linear-elastic material with E, ρ and ν is assumed and the holes are inserted using the EMM with negative material parameters E = −E and ρ = −ρ. The thickness is denoted as 1 In this thesis, the term simply-supported refers to fixed displacement DOF and rotational DOF that are not limited. 60
3.4 Application to brake discs a) b) y r 2 ϕ r 1 2 ϕ 1 x r i r a Figure 3.11: a) Steel bicycle brake disc of a major German brand. b) Top view on the friction ring of a bicycle brake disc, two axial holes are shown exemplarily. h as in the case for the automotive brake discs and each hole is assumed to have a fixed radius r h . A more realistic model of a bicycle brake disc is then introduced in paragraph 4.5.2. In the next chapter, the structural optimization of automotive as well as bicycle brake discs will be introduced and discussed in detail based on the modeling presented in this section. 61
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MECHANIK FORSCHUNGSBERICHT Avoidanc
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Wagner, Andreas Avoidance of brake
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Meinem ehemaligen Kollegen Gottfrie
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Kurzfassung Bremsenquietschen stell
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Contents 1 Introduction 1 1.1 Excit
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1 Introduction The technical progre
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1.1 Excitation mechanism of brake s
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1.2 Modeling and analysis of squeal
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1.3 Brake squeal countermeasures be
Page 21: 1.4 Outline of the thesis concept a
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Page 51 and 52: 3 Efficient modeling of brake discs
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Page 59 and 60: 3.2 Longitudinal vibrations of an i
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Page 63 and 64: 3.3 Free vibrations of a rectangula
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4 Structural optimization of automo
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5 Conclusions After a short introdu
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Bibliography [10] Barthold, F.J.; S
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Bibliography [33] Grandhi, R.: Stru
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Bibliography and negative penalty p
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Bibliography [74] Massi, F.; Gianni
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Bibliography [96] Schumacher, A.: O
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Bibliography [117] Takahashi, S.: V
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Bisher sind in dieser Reihe erschie
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Band 20 Finite-Element-Modelle zur
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Brake squeal is a high-pitched nois
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