Bimetallic strip

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 steel and brass. The strips are joined together throughout their length by 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 initial 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.

In some applications, the bimetal 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.

The radius of curvature ${\displaystyle R}$ of a bimetallic strip depends on temperature ${\displaystyle T}$ according the formula derived by French physicist Yvon Villarceau in 1863 in his research for improving the precision of clocks:[2]

${\displaystyle {\frac {1}{R}}-{\frac {1}{R_{0}}}={\frac {3}{2a}}{\frac {(\alpha _{2}-\alpha _{1})(T-T_{0})}{h}}={\frac {3}{2a}}{\frac {\Delta \epsilon }{h}}}$,

where ${\displaystyle h=h_{1}+h_{2}}$ is the total thickness of the bimetal and ${\displaystyle a=1+(E_{1}h_{1}^{2}-E_{2}h_{2}^{2})^{2}/(4\ E_{1}h_{1}\ E_{2}h_{2}\ h^{2})}$ is a dimensionless coefficient. For each metallic strip: ${\displaystyle E_{i}}$ is the Young modulus, ${\displaystyle \alpha _{i}}$ is the coefficient of thermal expansion and ${\displaystyle h_{i}}$ is the thickness. The formula can also be rewritten as a function of the thermal misfit strain ${\displaystyle \Delta \epsilon =(\alpha _{2}-\alpha _{1})(T-T_{0})}$. And if the modulus and height are similar, we simply have ${\displaystyle a\simeq 1}$.

An equivalent formula can be derived from the beam theory.[3][4]

John Harrison's Memorial in Westminster Abbey, London

The earliest surviving bimetallic strip was made by the eighteenth-century clockmaker John Harrison who is generally credited with its invention. He made it for his third marine chronometer (H3) of 1759 to compensate for temperature-induced changes in the balance spring.[5] It should not be confused with the bimetallic mechanism for correcting for thermal expansion in his gridiron pendulum. His earliest examples had two individual metal strips joined by rivets but he also invented the later technique of directly fusing molten brass onto a steel substrate. A strip of this type was fitted to his last timekeeper, H5. Harrison's invention is recognized in the memorial to him in Westminster Abbey, England.

This effect is used in a range of mechanical and electrical devices.

Thermostats

Thermostat with bimetal coil at (2)

See also: Thermostat hysteresis

In the regulation of heating and cooling, thermostats that operate over a wide range of temperatures are used. In these, one end of the bimetallic strip is mechanically fixed and attached to an electrical power source, while the other (moving) end carries an electrical contact. In adjustable thermostats another contact is positioned with a regulating knob or lever. The position so set controls the regulated temperature, called the set point.

Some thermostats use a mercury switch connected to both electrical leads. The angle of the entire mechanism is adjustable to control the set point of the thermostat.

Depending upon the application, a higher temperature may open a contact (as in a heater control) or it may close a contact (as in a refrigerator or air conditioner).

The electrical contacts may control the power directly (as in a household iron) or indirectly, switching electrical power through a relay or the supply of natural gas or fuel oil through an electrically operated valve. In some natural gas heaters the power may be provided with a thermocouple that is heated by a pilot light (a small, continuously burning, flame). In devices without pilot lights for ignition (as in most modern gas clothes dryers and some natural gas heaters and decorative fireplaces) the power for the contacts is provided by reduced household electrical power that operates a relay controlling an electronic ignitor, either a resistance heater or an electrically powered spark generating device.

Thermometers

A mechanical outdoor thermometer.

A direct indicating dial thermometer, common in household devices (such as a patio thermometer or a meat thermometer), uses a bimetallic strip wrapped into a coil in its most common design. The coil changes the linear movement of the metal expansion into a circular movement thanks to the helicoidal shape it draws. One end of the coil is fixed to the housing of the device as a fix point and the other drives an indicating needle inside a circular indicator. A bimetallic strip is also used in a recording thermometer. Breguet's thermometer consists of a tri-metallic helix in order to have a more accurate result.

• Thermotime switch

• Video of a circular bimetallic wire powering a small motor with iced water. Accessed February 2011.
• Video of a bimetlic coil powering engine (among others like Curie, Stirling and Hero)