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The 'balance spring' is a device used in a mechanical watch or marine chronometer to control the vibrations of the balance wheel.

Contents

History

Purpose

Material

Effect of temperature

Elinvar

Isochronism

See also

References

History

There is some dispute as to whether it was invented around 1660 by Robert Hooke or Christian Huygens, with the likelihood being that Hooke first had the idea, but Huygens built the first functioning watch that used a balance spring. ^[1][2] Before that time, the balance wheel or foliot had been used for timekeeping, but such mechanisms are very sensitive to fluctuations in the driving force and are as a result incapable of keeping accurate time. In watches, the balance spring is generally a flat spiral, but other forms have been used; for example, in the marine chronometer the usual form is a cylindrical helix.

Purpose

The combination of balance wheel and balance spring forms a harmonic oscillator. In the absence of perturbations, the motion of the balance wheel is simple harmonic motion, i.e., a sinusoidal motion of constant period. It can therefore serve as the basis of a clock or watch. For this to be practical, the oscillating motion of the balance has to be converted to rotary motion of the gear train by the escapement, and the escapement also supplies energy to the balance wheel to compensate for friction and maintain the oscillation.

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 Arnold, 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.

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 Hooke 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 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.

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, 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.

Isochronism

A balance spring obeys 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 a mechanical drive train cannot provide absolutely constant driving force, even if the prime power is a weight, or a spring with compensation provided by a fusee. One of the causes ofr varying driving force is friction, including the variation in friction caused by aging of lubricating oil.
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. ^[3] He demonstrated that a balance spring whose center of gravity coincides with the axis of the balance wheel is isochronous.

See also

★ Balance wheel

★ Watch

★ Marine chronometer

References

1. A. R. Hall, "Horology and criticism: Robert Hooke", ''Studia Copernicana, XVI, Ossolineum, 1978, 261-81.
2. The Marine Chronometer. Its History and Development, Gould, Rupert T., , , J. D. Potter, 1923, ISBN 0-907462-05-7
3. M. Phillips, "Sur le spiral reglant", Paris, 1861.