Balance wheel

foliotcompensation balanceauxiliary temperature compensationbalancetemperature compensation of balance wheelstemperature-compensated balance
A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock.wikipedia
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Mechanical watch

mechanicalmechanical watchesmanual winding
A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock.
Its force is transmitted through a series of gears to power the balance wheel, a weighted wheel which oscillates back and forth at a constant rate.

Clock

clockstimepiecemechanical clock
A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock.
A major advance occurred with the invention of the verge escapement, which made possible the first mechanical clocks around 1300 in Europe, which kept time with oscillating timekeepers like balance wheels.

Balance spring

hairspringisochronousbalance spring or "hair spring
It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, the balance spring or hairspring. 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-meter 2 and the stiffness (spring constant) of its balance spring κ in newton-meters per radian:
A balance spring, or hairspring, is a spring attached to the balance wheel in mechanical timepieces.

Escapement

detent escapementCross-beat escapementduplex escapements
It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel.
The impulse action transfers energy to the clock's timekeeping element (usually a pendulum or balance wheel) to replace the energy lost to friction during its cycle and keep the timekeeper oscillating.

Resonance

resonantresonant frequencyresonance frequency
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.
Timekeeping mechanisms of modern clocks and watches, e.g., the balance wheel in a mechanical watch and the quartz crystal in a quartz watch

Pendulum

pendulumssimple pendulumpendula
A balance wheel, or balance, is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock.
The timekeeping elements in all clocks, which include pendulums, balance wheels, the quartz crystals used in quartz watches, and even the vibrating atoms in atomic clocks, are in physics called harmonic oscillators.

Watch

wristwatchwatchesdigital watch
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.
During most of its history the watch was a mechanical device, driven by clockwork, powered by winding a mainspring, and keeping time with an oscillating balance wheel.

Timer

timerstiming devicesoftware timer
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.
They function similarly to a mechanical alarm clock; the energy in the mainspring causes a balance wheel to rotate back and forth.

Wheel train

going traingear trainkeyless winding
It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel.
It consists of the wheels that transmit the force of the timepiece's power source, the mainspring or weight, to the escapement to drive the pendulum or balance wheel.

Torsion spring

torsion balancetorsion pendulumtorsion
It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, the balance spring or hairspring.
The balance spring or hairspring in mechanical watches is a fine, spiral-shaped torsion spring that pushes the balance wheel back toward its center position as it rotates back and forth. The balance wheel and spring function similarly to the torsion pendulum above in keeping time for the watch.

Marine chronometer

chronometerchronometersmarine chronometers
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.
In 1675, Huygens, who was receiving a pension from Louis XIV, invented a chronometer that employed a balance wheel and a spiral spring for regulation, instead of a pendulum, opening the way to marine chronometers and modern pocket watches and wristwatches.

Glucydur

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.
Glucydur is the trade name of a metal alloy with a low coefficient of thermal expansion, used for making balance wheels and other parts of mechanical watches.

Nivarox

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.
Nivarox is most famous for producing hairsprings which are attached to the balance wheel inside a mechanical watch movement, as well as mainsprings which provide the motive power for the watch.

Gyromax

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.
The Gyromax is the trade name for an adjustable mass (or adjustable inertia) balance wheel used in Patek Philippe wristwatches.

Hooke's law

spring constantforce constantelasticity tensor
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-meter 2 and the stiffness (spring constant) of its balance spring κ in newton-meters per radian:
It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.

Verge escapement

verge and foliotfoliotcrown wheel and verge escapement
It is an improved version of the foliot, an early inertial timekeeper consisting of a straight bar pivoted in the center with weights on the ends, which oscillates back and forth.
They kept time by using the verge escapement to drive the foliot, a primitive type of balance wheel, causing it to oscillate back and forth.

Quartz clock

quartz watchquartzquartz movement
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. 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.
By the 1980s, quartz technology had taken over applications such as kitchen timers, alarm clocks, bank vault time locks, and time fuzes on munitions, from earlier mechanical balance wheel movements, an upheaval known in watchmaking as the quartz crisis.

Pierre Le Roy

PierreLe Roy
A simpler solution was devised around 1765 by Pierre Le Roy, and improved by John Arnold, and Thomas Earnshaw: the Earnshaw or compensating balance wheel.
He was the inventor of the detent escapement, the temperature-compensated balance and the isochronous balance spring.

Jewel bearing

jeweljewelsjeweled
The wheels are smooth, to reduce air friction, and the pivots are supported on precision jewel bearings.
A typical fully jeweled time-only watch has 17 jewels: two cap jewels, two pivot jewels, an impulse jewel for the balance wheel, two pivot jewels, two pallet jewels for the pallet fork, and two pivot jewels each for the escape, fourth, third, and center wheels.

John Arnold (watchmaker)

John ArnoldJohn Arnold (1736–1799)
A simpler solution was devised around 1765 by Pierre Le Roy, and improved by John Arnold, and Thomas Earnshaw: the Earnshaw or compensating balance wheel.
A detached escapement, which gave minimal interference with the vibrating balance and balance spring

John Harrison

H-4H4H4 and H5
John Harrison was first to apply temperature compensation to a balance wheel in 1753, using a bimetallic ‘compensation curb’ on the spring, in the first successful marine chronometers, H4 and H5.
In the 1720s, the English clockmaker Henry Sully invented a marine clock that was designed to determine longitude: this was in the form of a clock with a large balance wheel that was vertically mounted on friction rollers and impulsed by a frictional rest Debaufre type escapement.

Bimetallic strip

bi-metallic stripbimetallicbi-metallic
John Harrison was first to apply temperature compensation to a balance wheel in 1753, using a bimetallic ‘compensation curb’ on the spring, in the first successful marine chronometers, H4 and H5.
The most common method is to use a bimetallic construction for the circular rim of the balance wheel.

Stackfreed

In such an "inertial' wheel, the acceleration is proportional to the drive force. In a clock or watch without balance spring, the drive force provides both the force that accelerates the wheel and also the force that slows it down and reverses it. If the drive force is increased, both acceleration and deceleration are increased, this results in the wheel getting pushed back and forth faster. This made the timekeeping strongly dependent on the force applied by the escapement. In a watch the drive force provided by the mainspring, applied to the escapement through the timepiece's gear train, declined during the watch's running period as the mainspring unwound. Without some means of equalizing the drive force, the watch slowed down during the running period between windings as the spring lost force, making it useless as a timekeeper. This is why all pre-balance spring watches required fusees (or in a few cases stackfreeds) to equalize the force from the mainspring reaching the escapement, to achieve even minimal accuracy.
The force of the mainspring, transmitted through the clock's gears, gives pushes to the oscillating balance wheel which keeps time.

Lantern clock

As clocks were made smaller, first as bracket clocks and lantern clocks and then as the first large watches after 1500, balance wheels began to be used in place of foliots.
Before this invention, lantern clocks used a balance wheel lacking a balance spring for their timekeeping element, which limited their accuracy to perhaps 15 minutes per day.

Mainspring

springspring motorspring-wound
In such an "inertial' wheel, the acceleration is proportional to the drive force. In a clock or watch without balance spring, the drive force provides both the force that accelerates the wheel and also the force that slows it down and reverses it. If the drive force is increased, both acceleration and deceleration are increased, this results in the wheel getting pushed back and forth faster. This made the timekeeping strongly dependent on the force applied by the escapement. In a watch the drive force provided by the mainspring, applied to the escapement through the timepiece's gear train, declined during the watch's running period as the mainspring unwound. Without some means of equalizing the drive force, the watch slowed down during the running period between windings as the spring lost force, making it useless as a timekeeper. This is why all pre-balance spring watches required fusees (or in a few cases stackfreeds) to equalize the force from the mainspring reaching the escapement, to achieve even minimal accuracy.
If very little slack was left in the spring after winding ('overwinding"), the pressure of the last turn of the winding knob put the end of the spring under excessive tension, which was locked in by the last click of the ratchet. So the watch ran with excessive drive force for several hours, until the extra tension in the end of the spring was relieved. This made the balance wheel rotate too far in each direction, causing the impulse pin on the wheel to knock against the back of the fork horns. This caused the watch to gain time, and could break the impulse pin. In older watches this was prevented with 'stopwork'. In modern watches this is prevented by designing the 'click' with some 'recoil' (backlash), to allow the arbor to rotate backward after winding by about two ratchet teeth, enough to remove excess tension.