SDLL133 - Calculation of the clean modes prestressed D [] · Responsable : BRIE Nicolas Clé : V2.02.133 Révision : 054678e2a3c0 SDLL133 - Calculation of the prestressed clean modes

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Titre : SDLL133 - Calcul des modes propres précontraints d[...] Date : 01/08/2011 Page : 1/9Responsable : BRIE Nicolas Clé : V2.02.133 Révision :

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SDLL133 - Calculation of the prestressed clean modes of a aubagée wheel

Summary:

The objective of this CAS-test is to calculate the prestressed clean modes of a aubagée wheel. Prestressing isobtained by applying a rotation to the wheel and by blocking one of the wings.

Two modelings are carried out:

• Modeling a: one models with elements 3D the whole of the wheel,• Modeling b: one models with elements 3D only one wing to which one applies conditions of cyclic

symmetry.

For each of two modelings, one carries out the first calculation in nonlinear statics to find the constraints, then amodal analysis to obtain the prestressed clean modes.

Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and isprovided as a convenience.Copyright 2020 EDF R&D - Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)



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1 Problem of reference

1.1 Geometry

Figure 1.1: Geometry of the wheel

Coordinates of the points m : C : 0.0 ,0.0 ,0.0

Geometry of the wheel m : • Diameter L : 7.75 • thickness (according to axis z ) : 0.09

1.2 Elastic properties of material

A linear model of work hardening is used.

• Young modulus, E=7.1×1010Pa• Poisson's ratio, =0.3• Voluminal density, =7820.0kg.m−3

• Slope of the traction diagram, ET=0• Yield stress, =1.×1015Pa


w

L

LC

B A S _ N Ox

y

w

L

LC

B A S _ N Ox

y



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1.3 Boundary conditions and loadings

Imposed rotation:

=157 rad.s−1 , rotation of center C (around the axis Z )

Imposed displacement:

BAS_NO : DX=DY=DZ=0

2 Reference solution

2.1 Size and result of reference

A reference of the type is used NON_REGRESSION to check the prestressed clean modes. The 5smaller clean modes are calculated. One compares the results by “direct” calculation and calculationon a sector with boundary conditions cyclic.

2.2 Reference variable

• FREQ : frequency

2.3 Size and result of reference

The results of reference presented below correspond to the results got with modeling 3D:

• Of the whole of the wheel.

Size N° modeReference

Hz

FREQ

1 31.4503

2 31.975

3 31.975

4 33.4833

5 33.4833

• Of a wing to which one applies conditions of cyclic symmetry.


Hz

FREQ

1 33.4833

2 33.4833

3 44.8997

4 44.8997

5 80.2363




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3 Modeling A

3.1 Characteristics of modeling A

One models the whole of the wheel with a Modeling 3D.

Many nodes 9024

Many meshs 5616 That is to say:

HEXA8 5616

Figure 3.1. Grid of modeling A

Group of meshs: BAS_NO

3.2 Sizes tested and results


Hz Tolerance

%

FREQ

1 31.4503 0.10

2 31.975 0.10

3 31.975 0.10

4 33.4833 0.10

5 33.4833 0.10




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Mode 1 :31.4503Hz

Mode 2 :31.975Hz

Mode 3 :31.975Hz

Mode 4 :33.4833Hz

Mode 5 :33.4833Hz

Figure 3.2. Modal deformations of the first 5 clean modes

It is observed that the first mode does not have a modal diameter, the two following has one and thefourth and fifth modes show two of them.




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4 Modeling B

4.1 Characteristics of modeling B

One models (Modeling 3D), only one wing to which one applies conditions of cyclic symmetry ofdouble diameter.

NB: one could have chosen another number of modal diameters (0, 1.3,…)

Many nodes 600

Many meshs 777 That is to say:

QUAD4 426

HEXA8 351

Figure 4.1. Grid of a wing for modeling B

4.2 Sizes tested and results


Hz Tolerance

%

FREQ

1 33.4833 0.10

2 33.4833 0.10

3 44.8997 0.10

4 44.8997 0.10

5 80.2363 0.10




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Mode 1 :33.4833Hz

Mode 2 :33.4833Hz

Mode 3:44.8997Hz

Mode 4 :44.8997Hz




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Mode 5 :80.2363Hz

Figure 4.2 modal deformations of the first 5 clean modes of diameter 2




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5 Summary of the results

The got results are satisfactory. One observes a good correspondence between “total” calculation andcalculation on a sector with cyclic condition of symmetry of double diameter.Of course one finds in modeling B neither the first clean mode, which does not have no modal diameter, northe two following clean modes, which correspond to modes with a modal diameter.

Modeling A(3D)

Modeling B(3D, cyclic symmetry)

N° modeFrequency

Hz N° modeFrequency

Hz

1 31.4503

2 31.975

3 31.975

4 33.4833 1 33.4833

5 33.4833 2 33.4833

3 44.8997

4 44.8997

5 80.2363


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SDLL133 - Calculation of the clean modes prestressed D [] · Responsable : BRIE Nicolas Clé : V2.02.133 Révision : 054678e2a3c0 SDLL133 - Calculation of the prestressed clean modes