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"

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"

Furthermore, the following applies:
Bild "Bilder:MatheFormel052.gif"

Change in length of the materials to each other:
Bild "Bilder:MatheFormel048.gif"

Change in length due to the geometry:
Bild "Bilder:MatheFormel007.gif"

Equating the two above formulas gives:
Bild "Bilder:MatheFormel022.gif"

After canceling:
Bild "Bilder:MatheFormel009.gif"

Since bimetallic actuators are usually constructed from two materials with the same thickness d remains valid:
Bild "Bilder:MatheFormel017.gif"

it follows:
Bild "Bilder:MatheFormel026.gif"

Changing according to R.

The formula for the bimetallic actuator:

Bild "Bilder: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"

Talk to us