Balance wheel
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The balance wheel is the part of a mechanical watch that facilitates even passage of time, analogous to a pendulum in a pendulum clock. The balance wheel rotates in both directions, and its movement is controlled by the balance spring. As the wheel rotates back and forth, the impulse jewel strikes the pallet fork, which in turn allows the escape wheel to advance. Since the mass of the balance wheel and the spring coefficient of the balance spring are known, the amount of time between impacts of the impulse jewel and pallet fork is known. By advancing the rest of the wheel train at set intervals of time the watch is able to keep the hands on the face of the watch to the current time.
[edit] Self-compensating balance wheel
A crucial problem with mechanical watches, after Robert Hooke and Christiaan Huygens applied the balance spring to a watch in 1675, was that the spring was very sensitive to temperature changes. If the temperature rose for example, the metal spring would extend due to thermal expansion. However from the timekeeping point of view, what was worse was that the elasticity of the spring changed. Thus the spring would have a lower frequency and the clock would lose time. The key to solving this problem was to modify the construction of the balance wheel to vary the size of the wheel with temperature, employing conservation of angular momentum to speed up or slow down. As an example, think of an ice skater spinning. If she starts spinning with the arms close to her body and then extends her arms outwards, her spin rate will decrease. In other words the radius of gyration changes.
This is the fundamental regulation method of the self-compensating balance wheel. It changes shape with temperature. An increase in temperature will make the diameter of the balance wheel smaller and the clock will go faster. This is counter to the typical mechanics of thermal expansion. The trick was to make the balance wheel change shape in such a way that it would cancel out the effect of the spring increasing or decreasing its elasticity.
The solution to constructing a balance wheel that would change shape was to use two different metals that would increase differently in length with temperature (a bimetallic strip). If two flat bars of different metals are fixed together and heated, the bar will bend since one of the parts will increase more in length than the other. Instead of using a solid ring as a balance wheel, the wheel was constructed out of two metals, and cut open at two points, resembling an s-shape. The metals were chosen such that with an increase in temperature the arms would bend inwards, thus making the wheel spin faster.
Furthermore, small screws were mounted on the balance wheel in order to be able to fine tune how much the arms would bend.
Eventually, the spring and the wheel were manufactured from bi-metals which are not affected by temperature, thus removing the whole problem of self-compensation. An example of this is the Gyromax balance wheel by Patek Philippe.
