## Bi-metallic Strip

### August 10, 2009

A bi-metallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand at different rates as they are heated, usually steel and copper, or in some cases brass instead of copper. The strips are joined together throughout their length either riveting, brazing or welding. The different expansions force the flat strip to bend one way if heated, and in the opposite direction if cooled below its normal temperature. The metal with the higher coefficient of thermal expansion is on the outer side of the curve when the strip is heated and on the inner side when cooled.

The sideways displacement of the strip is much larger than the small lengthways expansion in either of the two metals. This effect is used in a range of mechanical and electrical devices. In some applications the bi-metal strip is used in the flat form. In others, it is wrapped into a coil for compactness. The greater length of the coiled version gives improved sensitivity.

A bi-metallic coil from a thermometer reacts to the heat from a lighter, by uncoiling and then coiling back up when the lighter is removed.

Calculations
Curvature of a Bimetallic Beam:

$\kappa = \frac{6 E_1 E_2 (h_1 + h_2)h_1 h_2 \epsilon }{E_1^2 h_1^4 + 4 E_1 E_2 h_1^3 h_2 + 6 E_1 E_2 h_1^2 h_2^2 + 4 E_1 E_2 h_2^3 h_1 + E_2^2 h_2^4}$

Where E1 and h1 are the Young’s Modulus and height of Material One and E2 and h2 are the Young’s Modulus and height of Material Two. ε is the misfit strain, calculated by:

$\epsilon = (\alpha_1-\alpha_2) \Delta T \,$

Where α1 is the Coefficient of Thermal Expansion of Material One and α2 is the Coefficient of Thermal Expansion of Material Two. ΔT is the current temperature minus the reference temperature (the temperature where the beam has no flexure).

http://en.wikipedia.org/wiki/Bimetallic_strip