Example56 Buckling Analysis of Bimetal Switch

General

  • A bimetal consisting of two warped materials with different thermal expansion coefficients is analyzed.
    When it is subjected to temperature change and thermal load, it deforms and warps in reverse direction suddenly at certain temperature.
     
  • In large displacement analysis, calculation stops where the buckling takes place as the stress is released.
    By converging the calculation forcibly, deformation analysis can be continued after the model warps in opposite direction.
     
  • Unless specified in the list below, the default conditions will be applied.

Analysis Space

Axisymmetric analysis is applied as we deal with a shape like curved saucer.

 

Item

Setting

Analysis Space

Axisymmetric

Model unit

mm

Analysis Conditions

It is necessary to take rotation of elements into account strictly to simulate the reverse warping of the bimetal. Therefore, select “Large displacement” in “Large deformation”.

 

Item

Setting

Solvers

Mechanical Stress Analysis [Galileo]

Analysis Type

Static Analysis

Large Deformation

Select Large displacement

Options

Select Thermal load.

The Step/Thermal Load tab is set as follows.

Select “Multiple steps” and set the reached temperature to keep history of temperature changes.

Tab

Setting Item

Setting

Step/Thermal Load

Step Setting

Multi-step thermal load analysis

Reference temperature

25[deg]

Step/Reached Temperature Setting

Step

Substeps

Reached temperature [deg]

1

100

150

2

100

25

3

100

-100

4

100

25

 

Options for the Multi-Step Analysis

Save the results of substeps : Select

 

Setting on the High-level setting tab is as follows.

Tab

Setting Item

Settings

High-level setting

Nonlinear analysis

Converge the steps forcibly and continue analysis
is selected

Graphical Objects

To form two models, create two arcs with diameter of 100[mm] and angle of 5°. Stretch them by 0.01 in Z direction.
As a combination of different thermal expansion coefficients, set material properties of copper and stainless steel (SUS410) for each body.

Set the boundary condition on the edge of lower body with displacement in Z direction fixed.

General mesh size is 0.1[mm]

Body Attributes and Materials

Body Number/Type

Body Attribute Name

Material Name

0/Solid

CU_PLATE

008_Cu (*)

1/Solid

SUS_PLATE

518_SUS410 (*)

(*) Available from the Material DB

Boundary Conditions

Boundary Condition Name/Topology

Tab

Boundary Condition Type

Setting

zFix/Face

Mechanical

Displacement

Select the Z component
UZ=0

 

Results

At the end of the analysis, a message will appear saying “Warning: Converged the nonconverged steps forcibly and continued analysis.” But the results can be shown.
In the list of modes below, [Forced convergence] is shown at the results of 80th (126.25℃) and 81st (127.50℃) steps since these did not converge.

 

 

The diagrams below show the deformation at 79th (125℃) and 82nd (128.75℃) steps before and after the forced convergence.

The contour is the displacement in Z direction.
[Full Model] is selected for viewing.

 

The deformation up to 125℃ is small and the shape is almost the same as the original shape. At 128.75℃, its central area is observed to bend in -Z direction.
Buckling is considered to be taking place between 125℃ and 128.75℃.

 

 

 

The displacement is plotted in the diagram below with temperature on horizontal axis.

When the temperature is rising, the displacement in -Z direction at temperature beyond 125℃ is rapid while it is gentle below 125℃.

When the temperature is falling, the displacement in +Z direction at temperature below -32.5℃ is rapid while it is gentle until -32.5℃.

Hysteresis of the different behaviors in the temperature rise and fall is analyzed.