balance wheel

Balance wheel in a cheap 1950s alarm clock, the Apollo, by Lux Mfg. Co. showing the balance spring (1) and regulator (2).

The balance wheel is the part of a mechanical watch that controls its rate, analogous to the pendulum in a pendulum clock. The balance wheel rotates back and forth, being returned toward its center position by a spiral spring, 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 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 near universal use as the timekeeper in mechanical watches and small clocks up to the present.

Perhaps the earliest existing drawing of a balance wheel, in Giovanni De Dondi's astronomical clock, built 1364, Padua, Italy. The balance wheel (crown shape, top) had a beat of 2 seconds. Tracing of an illustration from his 1364 clock treatise, Il Tractatus Astarii.

Origin

The balance wheel appeared with the first mechanical clocks, in 14th century Europe, but it seems unknown exactly when or where it was first used. It is an improved version of the foliot, a primitive inertial timekeeper consisting of a straight bar with weights on the ends. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels (White 1966, p. 124). As clocks were made smaller, first as table clocks and then as the first large watches after 1500, balance wheels began to be used in place of foliots (Milham 1923, p. 92). The wheel shape had less air resistance, and its geometry partly compensated for thermal expansion error due to temperature changes (Headrick 2002). Since more of its weight is located on the rim away from the axis, a balance could have a larger moment of inertia and keep better time.

Addition of balance spring

Early balance wheel with spring in an 18th century French watch.

These early balance wheels were crude timekeepers because they lacked the other essential element: the balance spring. Early balance wheels rotated freely in each direction until the escapement pushed it back the other way. This made the timekeeping strongly dependent on the driving force, so the watch slowed down as the mainspring unwound.

A way forward opened when it was noticed that springy hog bristle curbs, added to limit the rotation of the wheel, increased its accuracy (Britten 1898, p. 9). Robert Hooke first applied a metal spring to the balance in 1658 and John Hautefeuille and Christian Huygens improved it to its present spiral form in 1674 (Headrick 2002)(Milham 1923, p. 224). The addition of the spring made the balance wheel a harmonic oscillator, the basis of every modern clock, with a natural resonance frequency or ‘beat’ resistant to changes in the drive force or friction. This crucial innovation greatly increased the accuracy of watches, from several hours per day (Milham 1923, p. 226) to perhaps 10 minutes per day (NIST 2002, p. 3), changing them from expensive novelties into useful timekeepers.

Temperature error

After the spring was added, a major remaining source of inaccuracy was the effect of temperature changes. An increase in temperature made the spring and the balance get longer from thermal expansion, but a more important effect was that the elasticity of the spring decreased. The weaker spring would take longer to return the balance wheel back toward the center, so the frequency of oscillation or ‘beat’ would get slower and the watch would lose time. Ferdinand Berthoud found in 1773 that a brass balance, subjected to a 60° F. temperature increase, loses 6 minutes 33 seconds per day, of which 5 minutes 12 seconds is due to spring elasticity decrease (Britten 1898, p. 37).

Temperature compensated balance wheels

Need for an accurate clock to determine longitude during sea voyages drove many advances in balance technology in 18th century Britain. Even a 1 second per day error in a chronometer could result in a 17 mile error in ship's position after a 2 month voyage. 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. These achieved an accuracy of a fraction of a second per day (NIST 2002, p. 3).

Bimetallic temperature compensated balance wheel, from an early 1900s pocket watch. 17mm dia. (1) Moving opposing pairs of weights closer to the ends of the arms increases temperature compensation. (2) Unscrewing pairs of weights near the spokes slows the oscillation rate. Adjusting a single weight changes the poise, or balance.

A simpler solution was devised around 1765 by Pierre Le Roy, and improved by John Arnold, and Thomas Earnshaw: the compensating balance wheel (Milham 1923, p. 233). The key was to make the balance wheel change size with temperature. If the balance could be made to shrink in diameter as it got warmer, conservation of angular momentum would make it rotate faster, like a spinning ice skater that pulls in her arms. The faster balance would take less time to oscillate back and forth, compensating for the slowing caused by the weaker spring.

To accomplish this, the outer rim of the balance was made of a ‘sandwich’ of two metals; a layer of steel on the inside fused to a layer of brass on the outside. Strips of this bimetallic construction bend toward the steel side when they are heated, because the thermal expansion of brass is greater than steel. The rim was cut open at two points next to the spokes of the wheel, so it resembled an S-shape (see figure) with two circular bimetallic ‘arms’. A temperature increase makes the arms bend inward toward the center of the wheel, and the shift in mass inward makes the balance spin faster, cancelling out the slowing due to the spring. The amount of compensation is adjusted by moveable weights on the arms. Marine chronometers with this type of balance had errors of only 3 - 4 seconds per day over a wide temperature range. (Glasgow 1885). By the 1870s compensated balances began to be used in watches.

Middle temperature error

Marine chronometer balance wheels from the mid 1800s, with various 'auxiliary compensation' systems to reduce middle temperature error.

The standard Earnshaw compensation balance dramatically reduced error due to temperature variations, but it didn't eliminate it. As first described by J. G. Ulrich, a balance adjusted to keep correct time at a given low and high temperature will be a few seconds per day fast at intermediate temperatures (Gould 1923, p. 176-177). The reason is that the moment of inertia of the balance is a quadratic function of the radius of the compensation arms, and thus of the temperature. But the elasticity of the balance spring is a linear function of temperature.

Chronometer makers adopted 'auxiliary compensation' schemes, which reduced error below 1 second per day. Most of the chronometers that came in first in the annual Greenwich Observatory trials between 1850 and 1914 were auxiliary compensation designs(Gould 1923, p. 265-266). Auxiliary compensation was never used in watches because of its complexity.

Better materials

Low temperature coefficient alloy balance and spring, in an ETA 1280 movement from a Benrus Co. watch made in the 1950s.

The bimetallic compensated balance wheel was made obsolete in the early 1900s by advances in metallurgy. Charles Edouard Guillaume won a Nobel prize for the 1899 invention of Invar, a nickel steel alloy with very low thermal expansion, and Elinvar (from El asticité invar iable) an alloy whose elasticity is unchanged over a wide temperature range, for balance springs (Milham 1923, p. 234). This led to a series of improved low temperature coefficient alloys for balances and springs. A solid alloy balance with a spring of Elinvar was largely unaffected by temperature, so it replaced the difficult-to-adjust bimetallic balance.

Some chronometer designers, such as Paul Ditisheim (Gould 1923, p. 202) still used compensation on the balance to cancel out the small remaining temperature coefficient of the Elinvar balance spring. These have a solid balance wheel (not cut as in the conventional bimetallic balance) but with adjusting screws mounted along the rim to adjust the amount of compensation. In the design used by Paul Ditisheim, the balance wheel rim is of one material while the spokes are of another. In the chronometers built by the Hamilton Watch Company in the 1940s, the rim is bimetallic but not cut. In either case, the effect of temperature change is to change the wheel shape from circular to slightly oval. The amount of compensation is small, so no auxiliary compensation is used.

Modern balance wheels

Modern balance wheel (arrows), in a Chinese watch movement.

Until the 1980s balance wheels were used in chronometers, bank vault time locks, alarm clocks, kitchen timers, stopwatches, and time fuzes for bombs, but quartz technology has taken over these applications, and the main remaining use is in quality watches.

Modern (2007) watch balance wheels are usually made of Glucydur, an alloy of beryllium, copper and iron, with springs of alloys such as Nivarox (Odets 2007). They are smooth, to reduce air friction. Instead of weight screws to adjust the poise, they are computer-poised at the factory, using a laser to burn a precise pit in the rim to make them balanced (Odets 2005). Balances rotate about 1½ turns in each direction. The rate of the balance is adjusted with the regulator, a lever with a narrow slit on the end through which the balance spring passes. 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, some precision watches have ‘free sprung’ balances with no regulator, such as the Gyromax (Odets 2007).

A balance’s vibration rate is measured in beats (ticks) per hour, or BPH. 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 (Arnstein 2007). Watches made prior to the 1970s usually had a rate of 18,000 BPH (5 beats per second). Current watches have beats of 21,600, 28,800, and a few have 36,000 BPH (10 beats per second). During WW2, Elgin produced a very precise stopwatch that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug' (Schlitt 2002).

The precision of the best balance wheel watches on the wrist is around a few seconds per day.

References

• Arnstein, Walt (2007), Does faster mean more accurate?, TimeZone.com, <http://www.timezone.com/library/comarticles/comarticles0017>. Retrieved on June 15, 2007.
• Brittanica (2007), Marine Chronometers article, Encyclopedia Brittanica online, <http://www.britannica.com/ebc/article-9360740>. Retrieved on June 15, 2007.
• Britten, Frederick J. (1898), On the Springing and Adjusting of Watches, Spon & Chamberlain, <http://books.google.com/books?id=1SgJAAAAIAAJ&q=hog+bristle#search>. Has detailed account of development of balance spring.
• Glasgow, David (1885), Watch and Clock Making, Cassel & Co., <http://books.google.com/books?id=9wUFAAAAQAAJ>. Detailed section on balance temperature error and auxiliary compensation.
• Gould, Rupert T. (1923), The Marine Chronometer. Its History and Development, London: J. D. Potter, pp. 176-177, ISBN 0-907462-05-7
• Headrick, Michael (2002), "Origin and Evolution of the Anchor Clock Escapement", Control Systems magazine, Inst. of Electrical and Electronic Engineers 22 (2), <http://www.geocities.com/mvhw/anchor.html>. Retrieved on June 6, 2007. Good engineering overview of development of clock and watch escapements, focusing on sources of error.
• "Inventing the Clock". John H. Lienhard. The Engines of Our Ingenuity. NPR. KUHF-FM Houston. 2000. No. 1535. Transcript. Transcript page shows one of the earliest drawings of a balance wheel: the Di Dondi clock, 1379.
• Milham, Willis I. (1923), Time and Timekeepers, MacMillan, ISBN 0780800087. Comprehensive 616p. book by astronomy professor, good account of origin of clock parts, but historical research dated. Long bibliography.
• NIST (2002), A Walk Through Time, part 3: A Revolution in Timekeeping, <http://physics.nist.gov/GenInt/Time/revol.html>. Retrieved on June 6, 2007. Nontechnical history of clocks and watches, by National Institute of Standards and Technology.
• Odets, Walt (2005), Balance Wheel Assembly, Glossary of Watch Parts, TimeZone Watch School, <http://www.timezonewatchschool.com/WatchSchool/Glossary/Glossary%20-%20Balance%20Assembly/glossary%20-%20balance%20assembly.shtml>. Retrieved on June 15, 2007. Detailed illustrations of parts of a modern watch, on watch repair website
• Odets, Walt (2007), The Balance Wheel of a Watch, The Horologium,TimeZone.com, <http://www.timezone.com/library/horologium/horologium0013>. Retrieved on June 15, 2007. Technical article on construction of watch balance wheels, starting with compensation balances, by a professional watchmaker, on watch repair website
• Perez, Carlos (2001), TimeZone, Artifacts of the Golden Age, part 1, <http://www.timezone.com/library/cjrml/cjrml0006>. Retrieved on June 6, 2007. Narrative history of watches, by antique watch afficionado, on watch collector's website.
• Schlitt, Wayne (2002), The Elgin Collector's Site, <http://elginwatches.org/databases/watch_codes.html>. Retrieved on June 20, 2007.
• White, Lynn Jr. (1966), Medieval Technology and Social Change, Oxford Press, ISBN 978-0195002669. Has in-depth historical analysis of medieval clock development, copious references to original sources.

External links

• Video of antique mid-1800s watch showing the balance wheel turning
• Costa, Alan (1998), The History of Watches,, <http://www.atmos-man.com/historyo.html>. Retrieved on June 19, 2007 History of watches, on commercial website.
• The Watch Cabinet Pictures of an extensive private collection of antique watches from 1710 to 1908, showing many different varieties of balance wheel.

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