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

3 Efficient modeling of brake discs
the number of DOF either in the hole’s or in the plate’s mesh. The calculated
reference values are given in the captions. The number of DOF in the
a)
b)
Figure 3.5: Convergence of the first and sixth eigenfrequency of case 1. a) 54009
DOF in the plate mesh, varying DOF in the hole mesh. b) 19809 DOF in the
hole mesh, varying DOF in the plate mesh. The reference eigenfrequencies are
31,10 Hz and 140,15 Hz, respectively.
plate’s mesh is kept constant in parts a), while in parts b) the number of
DOF in the hole’s mesh is constant. The minimal number of DOF in the base
mesh corresponds to 5 elements in each direction and the maximum number
to 50 elements. The characteristic side length of the plate’s elements therefore
varies between 0.2·a and 0.02·a. It lies in the same range for the holes. The
error for the first eigenfrequency is shown as a (red) dashed line, while the
error for the sixth one is shown as (blue) solid line. As can be seen, the
eigenfrequencies calculated with the EMM rapidly converge to the reference
values for both the varying number of plate DOF and the hole DOF for all
considered cases. The calculated results for the other four eigenfrequencies
are not presented, but show exactly the same convergence behavior. It can be
concluded that it is not necessary to use a high number of DOF in the hole’s
mesh for a certain required precision, but for the plate a much finer grid has to
be used. The reason for this is that first the convergence of the plate without
a hole has to be ensured by a proper choice of DOF before the hole can be
inserted. This can be seen as a rather general guideline. Still, before using the
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