1. Reference problem#

1.1. Geometry#

A simple rotor model supported by 2 bearings (first and last rotor nodes respectively), is composed of 3 disks, the shaft section is \(0.05m\) in radius. It measures \(1.3m\) (see figure below). The rotor is rotating along the Z axis.

_images/Object_1.svg

Figure 1.1-a-a: Rotor model with 3 discs from [bib1]

The respective lengths are:

\({L}_{1}=0.2m\) \({L}_{2}=0.3m\) \({L}_{3}=0.5m\) \({L}_{4}=0.3m\)

1.2. Material properties#

The characteristics of the material of the shaft and the discs are:

  • Young’s module \(E={2.10}^{11}\)

  • Density \(\rho =7800\mathrm{kg}/{m}^{3}\)

  • Poisson’s ratio \(\nu =0.3\)

The characteristics of the discs are:

Disc

\({D}_{1}\)

\({D}_{2}\)

\({D}_{3}\)

Thickness (\(m\))

0.05

0.05

0.06

Inner radius (\(m\))

0.05

0.05

0.05

Outside radius (\(m\))

0.12

0.12

0.20

0.20

The characteristics of the bearings are:

\({K}_{\mathit{xx}}\mathrm{=}{7.10}^{7}N\mathrm{/}m\)

\({K}_{y}\mathrm{=}{5.10}^{7}N\mathrm{/}m\)

\({K}_{\mathit{yx}}\mathrm{=}{K}_{\mathit{xy}}\mathrm{=}0\)

\({C}_{\mathit{xx}}\mathrm{=}{7.10}^{2}\mathit{Ns}\mathrm{/}m\)

\({C}_{\mathit{yy}}\mathrm{=}{5.10}^{2}\mathit{Ns}\mathrm{/}m\)

\({C}_{\mathit{yx}}\mathrm{=}{C}_{\mathit{xy}}\mathrm{=}0\)

1.3. Boundary conditions#

To block rigid body movements in the \(z\) direction, we block the degree of freedom \(\mathit{DZ}\) at the node of the first level (first node of the tree).