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.
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 |
\({D}_{1}\) |
|
|
|
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:
\({K}_{\mathit{xx}}\mathrm{=}{7.10}^{7}N\mathrm{/}m\) |
|
|
\({C}_{\mathit{xx}}\mathrm{=}{7.10}^{2}\mathit{Ns}\mathrm{/}m\) |
|
|
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).