Modeling A ============== 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. Characteristics of the mesh ---------------------------- Number and type of elements: 100 SEG2 2 POI1 Number of knots: 101 Tested sizes and results ------------------------------ The values of the first 12 frequencies, when stopped and for rotation speed :math:`4000\mathrm{tr}/\mathrm{min}`, are shown in the table below. +--------------------+--------------------------------------------------------------+---------------------------------------------------------------------------------------------+-----------------+ |**Frequency Number**|**Rotation speed** **(** :math:`\mathit{tr}/\mathit{mn}` **)**|**Cadyro calculation with a variable-section tree** :math:`F` **(** :math:`\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 :math:`{R}_{1}/{R}_{2}={\mathit{Ep}}_{1}/{\mathit{Ep}}_{2}`. Otherwise, a sufficiently fine mesh is needed to mitigate the error made. See [:ref:`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.