3. Modeling A#
3.1. Characteristics of modeling#
The tree is modelled with POU_D_T beam elements with variable cross sections. In addition, discrete elements of the DIS_TR type are used for modeling the bearings.
3.2. Characteristics of the mesh#
Number and type of elements:
100 SEG2
2 POI1
Number of knots: 101
3.3. Tested sizes and results#
The values of the first 12 frequencies, when stopped and for rotation speed \(4000\mathrm{tr}/\mathrm{min}\), are shown in the table below.
Frequency Number |
Rotation speed ( \(\mathit{tr}/\mathit{mn}\) ) |
Cadyro calculation with a variable-section tree \(F\) ( \(\mathit{Hz}\) ) |
Tolerance (%) |
1 |
0 |
332.14 |
1.0 |
4000 |
331.51 |
1.0 |
|
2 |
0 |
332.14 |
1.0 |
4000 |
334.10 |
1.0 |
|
3 |
0 |
1193.81 |
1.0 |
4000 |
1196.30 |
1.0 |
|
4 |
0 |
1193.81 |
1.0 |
4000 |
1202.05 |
1.0 |
|
5 |
0 |
1607.19 |
1.0 |
4000 |
1607.19 |
1.0 |
|
6 |
0 |
2291.51 |
1.0 |
4000 |
2304.73 |
2.0 |
|
7 |
0 |
2291.51 |
1.0 |
4000 |
2312.08 |
2.0 |
|
8 |
0 |
2512.22 |
1.0 |
4000 |
2512.22 |
1.0 |
|
9 |
0 |
3160.39 |
1.0 |
4000 |
3160.39 |
1.0 |
|
10 |
0 |
3520.23 |
2.0 |
4000 |
3516.43 |
2.0 |
|
11 |
0 |
3520.23 |
2.0 |
4000 |
3524.02 |
2.0 |
|
12 |
0 |
4724.14 |
2.0 |
4000 |
4724.14 |
2.0 |
In addition, the calculation of the mass of the elements with homothetic variation of the section is also verified.
The mass calculation is accurate only when the ratio is \({R}_{1}/{R}_{2}={\mathit{Ep}}_{1}/{\mathit{Ep}}_{2}\). Otherwise, a sufficiently fine mesh is needed to mitigate the error made. See [R3.08.01].
The error is the most significant on the last element (M100). The mass of this element is 0.99549 kg.
The total mass of the rotor is 63.7115kg.