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

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3 Efficient modeling of brake discs a) b) Figure 3.8: Convergence of the first and sixth eigenfrequency of case 4. a) 54009 DOF in the plate mesh, varying DOF in the hole mesh. b) 12609 DOF in the hole mesh, varying DOF in the plate mesh. The reference eigenfrequencies are 32,17 Hz and 144,03 Hz, respectively. in their paper. The comparison is shown in Tab. 3.6. The results of the ICCM C1 ref. sol. C1 EMM C1 ICCM C3 ref. sol. C3 EMM C3 ICCM 31.10 31.12 32 31.63 31.68 31 44.67 44.67 45 45.57 45.55 44 54.78 54.83 57 55.87 55.86 56 84.58 84.61 85 84.78 85.03 82 84.58 84.61 85 84.78 85.03 82 140.15 140.07 149 145.34 145.34 137 Table 3.6: Comparison between the first six non-zero eigenfrequencies (Hz) calculated using the EMM and the ICCM presented in [63]. Also, a reference solution calculated in Abaqus is given. Case 1 (C1) and case 3 (C3) are considered. have been taken from Figs. 10 and 14 presented in [63] in the highest possible observational accuracy, while the results of the EMM have been calculated using 20-node brick elements and 54009 degrees of freedom in the basis structure and 12609 degrees of freedom in the hole’s mesh. The results are in good agreement, however, it should be kept in mind that the results in [63] were 56
3.3 Free vibrations of a rectangular plate with a rectangular or circular hole obtained based on Kirchhoff plate theory while the results presented here were obtained using FE meshes with solid isoparametric elements. On the one hand, the four discussed settings have been chosen to demonstrate that the EMM can not only be applied when meshes for basis structure and modification are similar, as in the rectangular plate with rectangular hole cases, but also when they differ in shape. On the other hand, it is shown that it is not necessary that nodes of the modification’s mesh directly overlap the basis structure’s nodes, which allows for the usage of non-matching meshes. It can also be seen that the eigenfrequencies calculated with the EMM do not represent upper bounds for the real eigenfrequencies, as would be the case using the well known standard Ritz method. This has been expected, since it has also been observed in the case of the inhomogeneous bar studied previously. Two interesting observations can additionally be made. The first remarkable point is that the rapid convergence of the method is partially caused by the fact that the allocation of the coordinate coupling matrix S is exact, since the mesh of the rectangular plate solely consists of regular bricks with edge angles of 90 o making the transformation between global node coordinates of the hole to local coordinates of the plate element errorless. Consequently, this means that for a mesh with more distorted elements a slower convergence might be expected. The second observation is that most of the CPU time necessary to compute the eigenfrequencies with the EMM is needed for the solution of the eigenvalue problem and not for the allocation of the mass and stiffness matrices of the assembled rectangular plate with a hole. For the computation of the results presented here, the Matlab function ’eigs’ has been used to solve the eigenvalue problem and this took at least 80 % of the CPU time. Concluding, the assembly of the mass and stiffness matrices of the system can be considered as very efficient with the EMM. This strongly encourages the use of this approach in structural optimization problems regarding global properties like frequencies, where the modifications are not too complex. In the next section, the application of the method to the modelling of automotive and bicycle brake discs is discussed. 57
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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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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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