# 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

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:

Furthermore, the following applies:

Change in length of the materials to each other:

Change in length due to the geometry:

Equating the two above formulas gives:

After canceling:

Since bimetallic actuators are usually constructed from two materials with the same thickness d remains valid:

it follows:

Changing according to R.

## The formula for the bimetallic actuator:

*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:

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