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Balance wheel
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Balance wheel
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{{Short description|Time measuring device}}{{stack|File:Floating Balance Escapement.gif|thumb|Balance wheel in mantel clock. The spiral balance springbalance springFile:Alarm Clock Balance Wheel.jpg|thumb|220px|Balance wheel in a 1950s alarm clock, the Apollo, by Lux Mfg. Co. showing the balance spring (1) and regulator (2)]]File:Chinese movement escapement and jewels.jpg|right|thumb|Modern balance wheel in a watch movementwatch movement}}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.- the content below is remote from Wikipedia
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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.WEB, Odets
, Walt
, 2007
, The Balance Wheel of a Watch
, The Horologium
, TimeZone.com
,weblink
, 2007-06-16
,weblink" title="web.archive.org/web/20070706233745weblink">weblink
, 6 July 2007
, dead
, 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.WEB, Odets, Walt, 2005, Balance Wheel Assembly, Glossary of Watch Parts, TimeZone Watch School,weblink , Walt
, 2007
, The Balance Wheel of a Watch
, The Horologium
, TimeZone.com
,weblink
, 2007-06-16
,weblink" title="web.archive.org/web/20070706233745weblink">weblink
, 6 July 2007
, dead
Balance spring#Regulator>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 âfree sprungâ balances with no regulator, such as the Gyromax. Their rate is adjusted by weight screws on the balance rim.
, Jules Audemars Watch with Audemars Piguet Escapement
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.ENCYCLOPEDIA, Encyclopædia Britannica online, 2007, Marine Chronometer, Encyclopædia Britannica Inc.,weblink 2007-06-15, , Audemars press release , Professional Watches magazine , 19 January 2009 ,weblink ,weblink" title="web.archive.org/web/20091228174548weblink">weblink 2009-12-28 , dead , 15 October 2020, During World War II, Elgin produced a very precise stopwatch for US Air Force bomber crews that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug'.WEB, Schlitt, Wayne, 2002, The Elgin Collector's Site,weblink 2007-06-20, Period of oscillationA 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:
T = 2 pi sqrt{ frac {I}{kappa} } ,
(File:Verge and foliot from De Vick's clock.svg|thumb|Foliot (horizontal bar with weights) from De Vick clock, built 1379, Paris)HistoryFile:Giovanni Di Dondi clock .png|thumb|left|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 Astrarii.)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, an early inertial timekeeper consisting of a straight bar pivoted in the center with weights on the ends, which oscillates back and forth. The foliot weights could be slid in or out on the bar, to adjust the rate of the clock. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels.BOOK, White, Lynn Jr., Medieval Technology and Social Change, 1966, Oxford Press, 978-0-19-500266-9, , p. 124 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.BOOK, Milham, Willis I., Time and Timekeepers, 1945, MacMillan, New York, 0-7808-0008-7, , p. 92 Since more of its weight is located on the rim away from the axis, a balance wheel could have a larger moment of inertia than a foliot of the same size, and keep better time. The wheel shape also had less air resistance, and its geometry partly compensated for thermal expansion error due to temperature changes.JOURNAL, Headrick, Michael, April 2002, Origin and Evolution of the Anchor Clock Escapement, IEEE Control Systems, 22, 2, 10.1109/37.993314, 41â52,weblink 2007-06-06,weblink" title="web.archive.org/web/20091025120920weblink">weblink 2009-10-25,Addition of balance spring(File:Balance Wheel in Early Watch Berthoud.png|thumb|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 were pushed in one direction by the escapement until the verge flag that was in contact with a tooth on the escape wheel slipped past the tip of the tooth ("escaped") and the action of the escapement reversed, pushing the wheel back the other way. 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, causing it to lose time. 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."Brittens Old Clocks & Watches" Edited by Cecil Clutton, G H Baillie & C A Ilbert, Ninth Edition Revised and Enlarged by Cecil Clutton. Bloomsbury Books London 1986 {{ISBN|0906223695}} page 16 Even with these devices, watches prior to the balance spring were very inaccurate.Temperature errorAfter the balance spring was added, a major remaining source of inaccuracy was the effect of temperature changes. Early watches had balance springs made of plain steel and balances of brass or steel, and the influence of temperature on these noticeably affected the rate.An increase in temperature increases the dimensions of the balance spring and the balance due to thermal expansion. The strength of a spring, the restoring force it produces in response to a deflection, is proportional to its breadth and the cube of its thickness, and inversely proportional to its length. An increase in temperature would actually make a spring stronger if it affected only its physical dimensions. However, a much larger effect in a balance spring made of plain steel is that the elasticity of the spring's metal decreases significantly as the temperature increases, the net effect being that a plain steel spring becomes weaker with increasing temperature. An increase in temperature also increases diameter of a steel or brass balance wheel, increasing its rotational inertia, its moment of inertia, making it harder for the balance spring to accelerate. The two effects of increasing temperature on physical dimensions of the spring and the balance, the strengthening of the balance spring and the increase in rotational inertia of the balance, have opposing effects and to an extent cancel each other.A.L. Rawlings, Timothy Treffry, The Science of Clocks and Watches, Publisher: BHI, {{ISBN|0 9509621 3 9}}, Edition: 1993, 3rd enlarged and revised edition. The major effect of temperature which affects the rate of a watch is the weakening of the balance spring with increasing temperature.In a watch that is not compensated for the effects of temperature, the weaker spring takes longer to return the balance wheel back toward the center, so the âbeatâ gets slower and the watch loses time. Ferdinand Berthoud found in 1773 that an ordinary brass balance and steel hairspring, subjected to a 60 °F (33 °C) temperature increase, loses 393 seconds ({{frac|6|1|2}} minutes) per day, of which 312 seconds is due to spring elasticity decrease.Britten 1898, p. 37Temperature-compensated balance wheel(File:Pocket Watch Balance Wheel.jpg|right|thumb|Bimetallic temperature-compensated balance wheel, from an early 1900s pocket watch. 17 mm 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.)The need for an accurate clock for celestial navigation during sea voyages drove many advances in balance technology in 18th century Britain and France. Even a 1-second per day error in a marine chronometer could result in a {{convert|17|mi|adj=on}} 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 âcompensation curbâ on the spring, in the first successful marine chronometers, H4 and H5. These achieved an accuracy of a fraction of a second per day, but the compensation curb was not further used because of its complexity.Middle temperature error(File:Early Chronometer Balance Wheels.png|thumb|right|500px|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 compensated balance adjusted to keep correct time at a given low and high temperature will be a few seconds per day fast at intermediate temperatures.BOOK, Gould, Rupert T., The Marine Chronometer. Its History and Development, London, J. D. Potter, 1923, 0-907462-05-7, pp. 176â177 The reason is that the moment of inertia of the balance varies as the square of the radius of the compensation arms, and thus of the temperature. But the elasticity of the spring varies linearly with temperature.To mitigate this problem, chronometer makers adopted various 'auxiliary compensation' schemes, which reduced error below 1 second per day. Such schemes consisted for example of small bimetallic arms attached to the inside of the balance wheel. Such compensators could only bend in one direction toward the center of the balance wheel, but bending outward would be blocked by the wheel itself. The blocked movement causes a non-linear temperature response that could slightly better compensate the elasticity changes in the spring. Most of the chronometers that came in first in the annual Greenwich Observatory trials between 1850 and 1914 were auxiliary compensation designs.Gould 1923, pp. 265â266 Auxiliary compensation was never used in watches because of its complexity.Better materialsFile:Benrus Watch Balance Wheel 2.jpg|thumb|Low-temperature-coefficient alloy balance and spring, in an ETA 1280 movement from a BenrusBenrusThe bimetallic compensated balance wheel was made obsolete in the early 20th century by advances in metallurgy. Charles Ãdouard Guillaume won a Nobel prize for the 1896 invention of Invar, a nickel steel alloy with very low thermal expansion, and Elinvar (from , 'invariable elasticity') an alloy whose elasticity is unchanged over a wide temperature range, for balance springs.Milham 1945, p. 234 A solid Invar balance with a spring of Elinvar was largely unaffected by temperature, so it replaced the difficult-to-adjust bimetallic balance. This led to a series of improved low temperature coefficient alloys for balances and springs.Before developing Elinvar, Guillaume also invented an alloy to compensate for middle temperature error in bimetallic balances by endowing it with a negative quadratic temperature coefficient. This alloy, named anibal, is a slight variation of invar. It almost completely negated the temperature effect of the steel hairspring, but still required a bimetal compensated balance wheel, known as a Guillaume balance wheel. This design was mostly fitted in high precision chronometers destined for competition in observatories. The quadratic coefficient is defined by its place in the equation of expansion of a material;Gould, p. 201.
ell_theta = ell_0 left(1 + alpha theta + beta theta^2right) ,
where:
scriptstyle ell_0 is the length of the sample at some reference temperature
scriptstyle theta is the temperature above the reference
scriptstyle ell_theta is the length of the sample at temperature scriptstyle theta
scriptstyle alpha is the linear coefficient of expansion
scriptstyle beta is the quadratic coefficient of expansion
Footnotes{{reflist}}References
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