A balance wheel, or balance, is the timekeeping device used in mechanical watches and small clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, known as the balance spring or hairspring. It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel. Each swing of the wheel (called a "tick" or "beat") allows the gear train to advance a set amount, moving the hands forward. The balance wheel and hairspring together form a harmonic oscillator, which due to resonance oscillates preferentially at a certain rate, its resonant frequency or "beat", and resists oscillating at other rates. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or "tick" very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present. From its invention in the 14th century until tuning fork and quartz movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel.
Overview
Until the 1980s balance wheels were the timekeeping technology used in chronometers, bank vault time locks, time fuzes for munitions, alarm clocks, kitchen timers and stopwatches, but quartz technology has taken over these applications, and the main remaining use is in quality mechanical watches.
Modern (2007) watch balance wheels are usually made of Glucydur, a low thermal expansion alloy of beryllium, copper and iron, with springs of a low thermal coefficient of elasticity alloy such as Nivarox. The two alloys are matched so their residual temperature responses cancel out, resulting in even lower temperature error. The wheels are smooth, to reduce air friction, and the pivots are supported on precision jewel bearings. Older balance wheels used weight screws around the rim to adjust the poise (balance), but modern wheels are computer-poised at the factory, using a laser to burn a precise pit in the rim to make them balanced. Balance wheels rotate about 1½ turns with each swing, that is, about 270° to each side of their center equilibrium position. The rate of the balance wheel is adjusted with the regulator, a lever with a narrow slit on the end through which the balance spring passes. This holds the part of the spring behind the slit stationary. Moving the lever slides the slit up and down the balance spring, changing its effective length, and thus the resonant vibration rate of the balance. Since the regulator interferes with the spring's action, chronometers and some precision watches have ‘free sprung’ balances with no regulator, such as the Gyromax. Their rate is adjusted by weight screws on the balance rim.
A balance's vibration rate is traditionally measured in beats (ticks) per hour, or BPH, although beats per second and Hz are also used. The length of a beat is one swing of the balance wheel, between reversals of direction, so there are two beats in a complete cycle. Balances in precision watches are designed with faster beats, because they are less affected by motions of the wrist. Alarm clocks and kitchen timers often have a rate of 4 beats per second (14,400 BPH). Watches made prior to the 1970s usually had a rate of 5 beats per second (18,000 BPH). Current watches have rates of 6 (21,600 BPH), 8 (28,800 BPH) and a few have 10 beats per second (36,000 BPH). Audemars Piguet currently produces a watch with a very high balance vibration rate of 12 beats/s (43,200 BPH). During World War II, Elgin produced a very precise stopwatch that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug'.
The precision of the best balance wheel watches on the wrist is around a few seconds per day. The most accurate balance wheel timepieces made were marine chronometers, which were used on ships for celestial navigation, as a precise time source to determine longitude. By World War II they had achieved accuracies of 0.1 second per day.
Period of oscillation
A balance wheel's period of oscillation T in seconds, the time required for one complete cycle (two beats), is determined by the wheel's moment of inertia I in kilogram-meter2 and the stiffness (spring constant) of its balance spring κ in newton-meters per radian: