Calculation bimetallic actuator
How much does a bimetal actuator bends at a certain temperature and how is this calculated?
Sketch of a deflected bimetallic actuator
![Bild "Bilder:MatheFormel053.gif"](/en/kategorien/Bilder/dateien/MatheFormel053.gif)
A bimetallic element is composed of two materials which are joined together and expand differently with changes in temperature. If the material 2 (shown in red) expands more than when heated material 1 (shown in blue), the material composite curves. The radius of curvature and thus the deflection at the end can be calculated.
Material 1 is blue Material 2 is red. The materials are firmly bonded together.
R: neutral fiber of the bimetallic actuator
R1: neutral fiber of the material 1
R2: neutral fiber of the material 2
f: Included angle in radians
A: Coefficient of Thermal Expansion
delta T: temperature difference for hibernation (bimetallic actuator straight)
l0: Length of the bimetallic actuator in the straight state
The length of a metal at a given temperature is:
![Bild "Bilder:MatheFormel047.gif"](/en/kategorien/Bilder/dateien/MatheFormel047.gif)
Furthermore, the following applies:
![Bild "Bilder:MatheFormel052.gif"](/en/kategorien/Bilder/dateien/MatheFormel052.gif)
Change in length of the materials to each other:
![Bild "Bilder:MatheFormel048.gif"](/en/kategorien/Bilder/dateien/MatheFormel048.gif)
Change in length due to the geometry:
![Bild "Bilder:MatheFormel007.gif"](/en/kategorien/Bilder/dateien/MatheFormel007.gif)
Equating the two above formulas gives:
![Bild "Bilder:MatheFormel022.gif"](/en/kategorien/Bilder/dateien/MatheFormel022.gif)
After canceling:
![Bild "Bilder:MatheFormel009.gif"](/en/kategorien/Bilder/dateien/MatheFormel009.gif)
Since bimetallic actuators are usually constructed from two materials with the same thickness d remains valid:
![Bild "Bilder:MatheFormel017.gif"](/en/kategorien/Bilder/dateien/MatheFormel017.gif)
it follows:
![Bild "Bilder:MatheFormel026.gif"](/en/kategorien/Bilder/dateien/MatheFormel026.gif)
Changing according to R.
The formula for the bimetallic actuator:
![Bild "Bilder:MatheFormel016_big.gif"](/en/kategorien/Bilder/dateien/MatheFormel016_big.gif)
Note: This is the minimum bending radius, since the modulus of elasticity of the materials was not taken into account. In reality, the radius of which is slightly larger.
Example iron-nickel bimetallic actuator:
![Bild "Bilder:MatheFormel008.gif"](/en/kategorien/Bilder/dateien/MatheFormel008.gif)
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