Balance spring
Encyclopedia
A balance spring, or hairspring, is a part used in mechanical timepieces. The balance spring, attached to the balance wheel
, controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands. A regulator lever on the balance spring is used to adjust the speed so that the timepiece keeps accurate time.
The balance spring is a fine spiral
or helical torsion spring
used in mechanical watch
es, marine chronometer
s, and other timekeeping mechanisms to control the rate of oscillation of the balance wheel
. A balance spring usually has a regulator lever to adjust the rate of the timepiece, but other designs use adjusting screws on the balance wheel instead. The balance spring is an integral part of the balance wheel, because it reverses the direction of the balance wheel causing it to oscillate back and forth. The balance spring and balance wheel together form a harmonic oscillator
, whose resonant
period is resistant to changes from perturbing forces, which is what makes it a good timekeeping device.
The invention of the balance spring around 1657 greatly increased the accuracy of portable timepieces, transforming early pocketwatches from expensive novelties to useful timekeepers. Improvements since then made timepieces even more accurate by reducing the effect of temperature, and also the effect of the driving force, which for a mainspring
decreases as the mainspring winds down.
or Dutch scientist Christian Huygens, with the likelihood being that Hooke first had the idea, but Huygens built the first functioning watch that used a balance spring. Before that time, balance wheel
s or foliot
s without springs were used in clocks and watches, but they were very sensitive to fluctuations in the driving force, causing the timepiece to slow down as the mainspring
unwound. The introduction of the balance spring effected an enormous increase in the accuracy of pocketwatches, from perhaps several hours per day to 10 minutes per day, making them useful timekeepers for the first time. The first balance springs had only a few turns.
A few early watches had a Barrow regulator, which used a worm drive
, but the first widely used regulator was invented by Thomas Tompion
around 1680. In the Tompion regulator the curb pins were mounted on a semicircular toothed rack, which was adjusted by fitting a key to a cog and turning it. The modern regulator, a lever pivoted concentrically with the balance wheel, was patented by Joseph Bosley in 1755, but it didn't replace the Tompion regulator until the early 19th century.
In older watches, the slit is the gap between two tiny pins, called the Curb Pins.
The regulator interferes slightly with the motion of the spring, causing inaccuracy, so precision timepieces like marine chronometer
s and some high end watches are free sprung, meaning they don't have a regulator. Instead, their rate is adjusted by timing screws on the balance wheel.
There are two principal types of Balance Spring Regulator.
There is also a "Hog's Hair" or "Pig's Bristle" regulator, in which stiff fibres are positioned at the extremities of the Balance's arc, and bring it to a gentle halt before throwing it back. The Watch is accelerated by shortening the arc. This is not a Balance Spring Regulator, being used in the earliest Watches before the Balance Spring was invented.
There is also a Barrow Regulator, but this is really the earlier of the two principal methods of giving the Mainspring "set-up tension"; that required to keep the Fusee chain in tension but not enough to actually drive the Watch. Verge Watches can be regulated by adjusting the set-up tension, but if any of the previously described Regulators is present then this is not usually done.
, used gold, which avoids the problem of corrosion, but retains the problem of gradual weakening. Hardened and tempered steel was first used by John Harrison
and subsequently remained the material of choice until the 20th century.
In 1833, E. J. Dent (maker of the Great Clock of the Houses of Parliament) experimented with a glass Balance Spring. This was much less affected by heat than steel, reducing the Compensation required, and also didn't rust. Other trials with glass revealed that they were difficult and expensive to make, and there was a widespread opinion that they must be fragile. This latter objection is proved false by glass-fibre loft insulation and fibre-optic cables.
and Christian Huygens observed this effect without finding a solution to it.
John Harrison
, in the course of his development of the marine chronometer
, solved the problem by a "compensation curb" – essentially a bimetallic thermometer which adjusted the effective length of the balance spring as a function of temperature. While this scheme worked well enough to allow Harrison to meet the standards set by the Longitude Act, it was not widely adopted.
Around 1765, Pierre Le Roy
(son of Julien Le Roy
) invented the compensation balance, which became the standard approach for temperature compensation in watches and chronometers. In this approach, the shape of the balance is altered, or adjusting weights are moved on the spokes or rim of the balance, by a temperature-sensitive mechanism. This changes the moment of inertia of the balance wheel, and the change is adjusted such that it compensates for the change in modulus of elasticity of the balance spring. The compensating balance design of Thomas Earnshaw
, which consists simply of a balance wheel with bimetallic rim, became the standard solution for temperature compensation.
Around 1900, a fundamentally different solution was created by Charles Édouard Guillaume
, inventor of elinvar
. This is a nickel-steel alloy with the property that the modulus of elasticity is essentially unaffected by temperature. A watch fitted with an elinvar balance spring requires either no temperature compensation at all, or very little. This simplifies the mechanism, and it also means that middle temperature error is eliminated as well, or at a minimum is drastically reduced.
: the restoring torque is proportional to the angular displacement. When this property is exactly satisfied, the balance spring is said to be isochronous, and the period of oscillation is independent of the amplitude of oscillation. This is an essential property for accurate timekeeping, because no mechanical drive train can provide absolutely constant driving force. This is particularly true in watches and portable clocks which are powered by a mainspring
, which provides a diminishing drive force as it unwinds. Another cause of varying driving force is friction, which varies as the lubricating oil ages.
Early watchmakers empirically found approaches to make their balance springs isochronous. For example, John Arnold
in 1776 patented a helical (cylindrical) form of the balance spring, in which the ends of the spring were coiled inwards. In 1861 M. Phillips published a theoretical treatment of the problem. He demonstrated that a balance spring whose center of gravity
coincides with the axis of the balance wheel is isochronous.
; together they form a harmonic oscillator
. The balance spring provides the linear restoring force
that reverses the motion of the wheel so it oscillates back and forth. The motion of the balance wheel is approximately simple harmonic motion
, i.e., a sinusoidal motion of constant period. Its resonant
period is resistant to changes from perturbing forces, which is what makes it a good timekeeping device. The stiffness of the spring, its spring coefficient,
in N-m/radian, along with the balance wheel's moment of inertia
,
in kg-m2, determines the wheel's oscillation
period
in seconds:
This period controls the rate of the timepiece.
Balance wheel
The balance wheel is the timekeeping device used in mechanical watches and some 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 spring, the balance spring or hairspring...
, controls the speed at which the wheels of the timepiece turn, and thus the rate of movement of the hands. A regulator lever on the balance spring is used to adjust the speed so that the timepiece keeps accurate time.
The balance spring is a fine spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...
or helical torsion spring
Torsion spring
A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force it exerts is proportional to the amount it is twisted. There are two types...
used in mechanical watch
Mechanical watch
A mechanical watch is a watch that uses a mechanical mechanism to measure the passage of time, as opposed to modern quartz watches which function electronically. It is driven by a spring which must be wound periodically...
es, marine chronometer
Marine chronometer
A marine chronometer is a clock that is precise and accurate enough to be used as a portable time standard; it can therefore be used to determine longitude by means of celestial navigation...
s, and other timekeeping mechanisms to control the rate of oscillation of the balance wheel
Balance wheel
The balance wheel is the timekeeping device used in mechanical watches and some 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 spring, the balance spring or hairspring...
. A balance spring usually has a regulator lever to adjust the rate of the timepiece, but other designs use adjusting screws on the balance wheel instead. The balance spring is an integral part of the balance wheel, because it reverses the direction of the balance wheel causing it to oscillate back and forth. The balance spring and balance wheel together form a harmonic oscillator
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
, whose resonant
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
period is resistant to changes from perturbing forces, which is what makes it a good timekeeping device.
The invention of the balance spring around 1657 greatly increased the accuracy of portable timepieces, transforming early pocketwatches from expensive novelties to useful timekeepers. Improvements since then made timepieces even more accurate by reducing the effect of temperature, and also the effect of the driving force, which for a mainspring
Mainspring
A mainspring is a spiral torsion spring of metal ribbon that is the power source in mechanical watches and some clocks. Winding the timepiece, by turning a knob or key, stores energy in the mainspring by twisting the spiral tighter. The force of the mainspring then turns the clock's wheels as it...
decreases as the mainspring winds down.
History
There is some dispute as to whether it was invented around 1660 by British physicist Robert HookeRobert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
or Dutch scientist Christian Huygens, with the likelihood being that Hooke first had the idea, but Huygens built the first functioning watch that used a balance spring. Before that time, balance wheel
Balance wheel
The balance wheel is the timekeeping device used in mechanical watches and some 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 spring, the balance spring or hairspring...
s or foliot
Foliot
A foliot may refer to:* Part of the verge escapement for early clocks* A creature of Italian folklore , as recorded by Gerolamo Cardano and Robert Burton...
s without springs were used in clocks and watches, but they were very sensitive to fluctuations in the driving force, causing the timepiece to slow down as the mainspring
Mainspring
A mainspring is a spiral torsion spring of metal ribbon that is the power source in mechanical watches and some clocks. Winding the timepiece, by turning a knob or key, stores energy in the mainspring by twisting the spiral tighter. The force of the mainspring then turns the clock's wheels as it...
unwound. The introduction of the balance spring effected an enormous increase in the accuracy of pocketwatches, from perhaps several hours per day to 10 minutes per day, making them useful timekeepers for the first time. The first balance springs had only a few turns.
A few early watches had a Barrow regulator, which used a worm drive
Worm drive
A worm drive is a gear arrangement in which a worm meshes with a worm gear...
, but the first widely used regulator was invented by Thomas Tompion
Thomas Tompion
Thomas Tompion was an English clock maker, watchmaker and mechanician who is still regarded to this day as the Father of English Clockmaking. Tompion's work includes some of the most historic and important clocks and watches in the world and can command very high prices whenever outstanding...
around 1680. In the Tompion regulator the curb pins were mounted on a semicircular toothed rack, which was adjusted by fitting a key to a cog and turning it. The modern regulator, a lever pivoted concentrically with the balance wheel, was patented by Joseph Bosley in 1755, but it didn't replace the Tompion regulator until the early 19th century.
Regulator
In order to adjust the rate, the balance spring usually has a regulator, a moveable lever with a narrow slit on the end through which the last turn of the spring passes. The portion of the spring after the slit is held stationary, so the slit controls the usable length of the spring. Moving the regulator slides the slit up or down the spring, changing its effective length. Moving it away from the spring's attachment point (stud) shortens the spring, making it stiffer, increasing the balance's oscillation rate, and making the timepiece gain time.In older watches, the slit is the gap between two tiny pins, called the Curb Pins.
The regulator interferes slightly with the motion of the spring, causing inaccuracy, so precision timepieces like marine chronometer
Marine chronometer
A marine chronometer is a clock that is precise and accurate enough to be used as a portable time standard; it can therefore be used to determine longitude by means of celestial navigation...
s and some high end watches are free sprung, meaning they don't have a regulator. Instead, their rate is adjusted by timing screws on the balance wheel.
There are two principal types of Balance Spring Regulator.
- The Tompion Regulator, in which the Curb Pins are mounted on a sector-rack, moved by a pinion. The pinion is usually fitted with a graduated silver or steel disc.
- The Bosley Regulator, as described above, in which the Pins are mounted on a lever pivoted coaxially with the Balance, the extremity of the lever being able to be moved over a graduated scale. There are several variants of this, including the "Snail" regulator, in which the lever is sprung against a cam of spiral profile which can be turned, and the Micrometer, in which the lever is moved by a worm gear.
There is also a "Hog's Hair" or "Pig's Bristle" regulator, in which stiff fibres are positioned at the extremities of the Balance's arc, and bring it to a gentle halt before throwing it back. The Watch is accelerated by shortening the arc. This is not a Balance Spring Regulator, being used in the earliest Watches before the Balance Spring was invented.
There is also a Barrow Regulator, but this is really the earlier of the two principal methods of giving the Mainspring "set-up tension"; that required to keep the Fusee chain in tension but not enough to actually drive the Watch. Verge Watches can be regulated by adjusting the set-up tension, but if any of the previously described Regulators is present then this is not usually done.
Material
A number of materials have been used for balance springs. Early on, steel was used, but without any hardening or tempering process applied; as a result, these springs would gradually weaken and the watch would start losing time. Some watchmakers, for example John ArnoldJohn Arnold
John Arnold was an English watchmaker and inventor.John Arnold was the first to design a watch that was both practical and accurate, and also brought the term "Chronometer" in to use in its modern sense, meaning a precision timekeeper...
, used gold, which avoids the problem of corrosion, but retains the problem of gradual weakening. Hardened and tempered steel was first used by John Harrison
John Harrison
John Harrison was a self-educated English clockmaker. He invented the marine chronometer, a long-sought device in solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionising and extending the possibility of safe long distance sea travel in the Age...
and subsequently remained the material of choice until the 20th century.
In 1833, E. J. Dent (maker of the Great Clock of the Houses of Parliament) experimented with a glass Balance Spring. This was much less affected by heat than steel, reducing the Compensation required, and also didn't rust. Other trials with glass revealed that they were difficult and expensive to make, and there was a widespread opinion that they must be fragile. This latter objection is proved false by glass-fibre loft insulation and fibre-optic cables.
Effect of temperature
The modulus of elasticity of materials is dependent on temperature. For most materials, this temperature coefficient is large enough that variations in temperature significantly affect the timekeeping of a balance wheel and balance spring. The earliest makers of watches with balance springs, such as Robert HookeRobert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
and Christian Huygens observed this effect without finding a solution to it.
John Harrison
John Harrison
John Harrison was a self-educated English clockmaker. He invented the marine chronometer, a long-sought device in solving the problem of establishing the East-West position or longitude of a ship at sea, thus revolutionising and extending the possibility of safe long distance sea travel in the Age...
, in the course of his development of the marine chronometer
Marine chronometer
A marine chronometer is a clock that is precise and accurate enough to be used as a portable time standard; it can therefore be used to determine longitude by means of celestial navigation...
, solved the problem by a "compensation curb" – essentially a bimetallic thermometer which adjusted the effective length of the balance spring as a function of temperature. While this scheme worked well enough to allow Harrison to meet the standards set by the Longitude Act, it was not widely adopted.
Around 1765, Pierre Le Roy
Pierre Le Roy
Pierre Le Roy was a French clockmaker. He was the inventor of the detent escapement, the temperature-compensated balance and the isochronous balance spring. His developments are considered as the foundation of the modern chronometer...
(son of Julien Le Roy
Julien Le Roy
Julien Le Roy was a major 18th-century Parisian clockmaker and watchmaker.He was born in Tours in 1686, and by the age of 13, had already made his first clock. In 1699, he moved to Paris for further training. He became maitre horloger in 1713 and later juré of his guild...
) invented the compensation balance, which became the standard approach for temperature compensation in watches and chronometers. In this approach, the shape of the balance is altered, or adjusting weights are moved on the spokes or rim of the balance, by a temperature-sensitive mechanism. This changes the moment of inertia of the balance wheel, and the change is adjusted such that it compensates for the change in modulus of elasticity of the balance spring. The compensating balance design of Thomas Earnshaw
Thomas Earnshaw
Thomas Earnshaw was an English watchmaker who following John Arnold's earlier work, further simplified the process of marine chronometer production, making them available to the general public...
, which consists simply of a balance wheel with bimetallic rim, became the standard solution for temperature compensation.
Elinvar
While the compensating balance was effective as a way to compensate for the effect of temperature on the balance spring, it could not provide a complete solution. The basic design suffers from "middle temperature error": if the compensation is adjusted to be exact at extremes of temperature, then it will be slightly off at temperatures between those extremes. Various "auxiliary compensation" mechanisms were designed to avoid this, but they all suffer from being complex and hard to adjust.Around 1900, a fundamentally different solution was created by Charles Édouard Guillaume
Charles Edouard Guillaume
Charles Édouard Guillaume was a Swiss physicist who received the Nobel Prize in Physics in 1920 in recognition of the service he had rendered to precision measurements in physics by his discovery of anomalies in nickel steel alloys.Guillaume is known for his discovery of nickel-steel alloys he...
, inventor of elinvar
Elinvar
Elinvar is a nickel steel alloy with a modulus of elasticity which does not change much with temperature changes. The name is a contraction of the French elasticité invariable. It was invented in the late 1890s by Charles Édouard Guillaume, a Swiss physicist who also invented Invar, another...
. This is a nickel-steel alloy with the property that the modulus of elasticity is essentially unaffected by temperature. A watch fitted with an elinvar balance spring requires either no temperature compensation at all, or very little. This simplifies the mechanism, and it also means that middle temperature error is eliminated as well, or at a minimum is drastically reduced.
Isochronism
A balance spring obeys Hooke's LawHooke's law
In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...
: the restoring torque is proportional to the angular displacement. When this property is exactly satisfied, the balance spring is said to be isochronous, and the period of oscillation is independent of the amplitude of oscillation. This is an essential property for accurate timekeeping, because no mechanical drive train can provide absolutely constant driving force. This is particularly true in watches and portable clocks which are powered by a mainspring
Mainspring
A mainspring is a spiral torsion spring of metal ribbon that is the power source in mechanical watches and some clocks. Winding the timepiece, by turning a knob or key, stores energy in the mainspring by twisting the spiral tighter. The force of the mainspring then turns the clock's wheels as it...
, which provides a diminishing drive force as it unwinds. Another cause of varying driving force is friction, which varies as the lubricating oil ages.
Early watchmakers empirically found approaches to make their balance springs isochronous. For example, John Arnold
John Arnold
John Arnold was an English watchmaker and inventor.John Arnold was the first to design a watch that was both practical and accurate, and also brought the term "Chronometer" in to use in its modern sense, meaning a precision timekeeper...
in 1776 patented a helical (cylindrical) form of the balance spring, in which the ends of the spring were coiled inwards. In 1861 M. Phillips published a theoretical treatment of the problem. He demonstrated that a balance spring whose center of gravity
Center of gravity
In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity...
coincides with the axis of the balance wheel is isochronous.
Period of oscillation
The balance spring is an essential part of the balance wheelBalance wheel
The balance wheel is the timekeeping device used in mechanical watches and some 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 spring, the balance spring or hairspring...
; together they form a harmonic oscillator
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
. The balance spring provides the linear restoring force
Restoring force
Restoring force, in a physics context, is a variable force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium....
that reverses the motion of the wheel so it oscillates back and forth. The motion of the balance wheel is approximately simple harmonic motion
Simple harmonic motion
Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration....
, i.e., a sinusoidal motion of constant period. Its resonant
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
period is resistant to changes from perturbing forces, which is what makes it a good timekeeping device. The stiffness of the spring, its spring coefficient,
in N-m/radian, along with the balance wheel's moment of inertiaMoment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
,
in kg-m2, determines the wheel's oscillationOscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
period
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
in seconds:This period controls the rate of the timepiece.