cog-wheel

A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic principle behind the operation of gears is analogous to the basic principle of levers. A gear may also be known informally as a cog. Geared devices can change the speed, torque, and direction of a power source. Gears of different sizes produce a change in torque, creating a mechanical advantage, through their ''gear ratio'', and thus may be considered a simple machine. The rotational speeds, and the torques, of two meshing gears differ in proportion to their diameters. The teeth on the two meshing gears all have the same shape.

Two or more meshing gears, working in a sequence, are called a gear train or a '' transmission''. The gears in a transmission are analogous to the wheels in a crossed, belt pulley system. An advantage of gears is that the teeth of a gear prevent slippage. In transmissions with multiple gear ratios—such as bicycles, motorcycles, and cars—the term "gear" (e.g., "first gear") refers to a gear ratio rather than an actual physical gear. The term describes similar devices, even when the gear ratio is continuous rather than discrete, or when the device does not actually contain gears, as in a continuously variable transmission (CVT). Sometimes a CVT is referred to as an "infinitely variable transmission".

Furthermore, a gear can mesh with a linear toothed part, called a ''rack'', producing movement in a straight line instead of rotation (movement in a circle). See Rack and Pinion for an example.

History

Early examples of gears date from the 4th century BC in China Derek J. de Solla Price
On the Origin of Clockwork, Perpetual Motion Devices, and the Compass
p.84 (Zhan Guo times – Late East Zhou dynasty), which have been preserved at the Luoyang Museum of Henan Province, China. The earliest preserved gears in Europe were found in the Antikythera mechanism an example of a very early and intricate geared device, designed to calculate astronomical positions. Its time of construction is now estimated between 150 and 100 BC. Gears appear in works connected to Hero of Alexandria, in Roman Egypt circa AD 50, but can be traced back to the mechanics of the Alexandrian school in 3rd-century BC Ptolemaic Egypt, and were greatly developed by the Greek polymath Archimedes (287–212 BC).

A complex geared calendrical device showing the phase of the Moon, the day of the month and the places of the Sun and the Moon in the Zodiac was invented in the Byzantine empire in the early 6th century CE. The worm gear was invented in the Indian subcontinent, for use in roller cotton gins, some time during the 13th–14th centuries. Irfan Habib
''Economic History of Medieval India, 1200-1500'', page 53
Pearson Education Differential gears may have been used in some of the Chinese south-pointing chariots, but the first verifiable use of differential gears was by the British clock maker Joseph Williamson in 1720.

Examples of early gear applications include:
*1386 CE: The Salisbury Cathedral clock: it is the world's oldest still working geared mechanical clock.
*The Astrarium of Giovanni Dondi dell'Orologio was a complex astronomical clock built between 1348 and 1364 by Giovanni Dondi dell'Orologio. The Astrarium had seven faces and 107 moving parts; it showed the positions of the sun, the moon and the five planets then known, as well as religious feast days.
*c. 13th–14th centuries: The worm gear was invented as part of a roller cotton gin in the Indian subcontinent.
*c. 1221 CE The geared astrolabe was built in Isfahan showing the position of the moon in the zodiac and its phase, and the number of days since new moon.
*c. 6th century CE: A geared calendrical device showing the phase of the Moon, the day of the month and the Zodiac was invented in the Byzantine empire.
*725 CE: The first geared mechanical clocks were built in China.
*2nd century BC: The Antikythera mechanism, the world's oldest analog computer is built. It could predict the movement and position of the sun, moon and planets decades in advance and could solve different astronomical problems.
*c. 200–265 CE: Ma Jun used gears as part of a south-pointing chariot.
*In nature: in the hind legs of the nymphs of the planthopper insect '' Issus coleoptratus''.

Etymology

The word ''gear'' is probably from Old Norse ''gørvi'' (plural ''gørvar'') 'apparel, gear,' related to ''gøra'', ''gørva'' 'to make, construct, build; set in order, prepare,' a common verb in Old Norse, "used in a wide range of situations from writing a book to dressing meat". In this context, the meaning of 'toothed wheel in machinery' first attested 1520s; specific mechanical sense of 'parts by which a motor communicates motion' is from 1814; specifically of a vehicle (bicycle, automobile, etc.) by 1888.

A ''cog'' is a tooth on a wheel. From Middle English cogge, from Old Norse (compare Norwegian ''kugg'' ('cog'), Swedish ''kugg'', ''kugge'' ('cog, tooth')), from Proto-Germanic *''kuggō'' (compare Dutch ''kogge'' (' cogboat'), German ''Kock''), from Proto-Indo-European *''gugā'' ('hump, ball') (compare Lithuanian ''gugà'' ('pommel, hump, hill'), from PIE *''gēw-'' ('to bend, arch'). First used c. 1300 in the sense of 'a wheel having teeth or cogs; late 14c., 'tooth on a wheel'; cog-wheel, early 15c.

Historically, cogs were teeth made of wood rather than metal, and a cogwheel technically consisted of a series of wooden gear teeth located around a mortise wheel, each tooth forming a type of specialised 'through' mortise and tenon joint. The wheel can be made of wood, cast iron, or other material. Wooden cogs were formerly used when large metal gears could not be cut, when the cast tooth was not even approximately of the proper shape, or the size of the wheel made manufacture impractical.

The cogs were often made of maple wood. In 1967 the Thompson Manufacturing Company of Lancaster, New Hampshire still had a very active business in supplying tens of thousands of maple gear teeth per year, mostly for use in paper mills and grist mills, some dating back over 100 years. Since a wooden cog performs exactly the same function as a cast or machined metal tooth, the word was applied by extension to both, and the distinction has been generally lost.

Comparison with drive mechanisms

The definite ratio that teeth give gears provides an advantage over other drives (such as traction drives and V-belts) in precision machines such as watches that depend upon an exact velocity ratio. In cases where driver and follower are proximal, gears also have an advantage over other drives in the reduced number of parts required. The downside is that gears are more expensive to manufacture and their lubrication requirements may impose a higher operating cost per hour.

Types

External versus internal gears

An ''external gear'' is one with the teeth formed on the outer surface of a cylinder or cone. Conversely, an ''internal gear'' is one with the teeth formed on the inner surface of a cylinder or cone. For bevel gears, an internal gear is one with the pitch angle exceeding 90 degrees. Internal gears do not cause output shaft direction reversal.

Spur

''Spur gears'' or ''straight-cut gears'' are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Though the teeth are not straight-sided (but usually of special form to achieve a constant drive ratio, mainly involute but less commonly cycloidal), the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears mesh together correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.

Helical

''Helical'' or "dry fixed" gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling makes the tooth shape a segment of a helix. Helical gears can be meshed in ''parallel'' or ''crossed'' orientations. The former refers to when the shafts are parallel to each other; this is the most common orientation. In the latter, the shafts are non-parallel, and in this configuration the gears are sometimes known as "skew gears".

The angled teeth engage more gradually than do spur gear teeth, causing them to run more smoothly and quietly. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face to a maximum, then recedes until the teeth break contact at a single point on the opposite side. In spur gears, teeth suddenly meet at a line contact across their entire width, causing stress and noise. Spur gears make a characteristic whine at high speeds. For this reason spur gears are used in low-speed applications and in situations where noise control is not a problem, and helical gears are used in high-speed applications, large power transmission, or where noise abatement is important. The speed is considered high when the pitch line velocity exceeds 25 m/s.

A disadvantage of helical gears is a resultant thrust along the axis of the gear, which must be accommodated by appropriate thrust bearings. However, this issue can be turned into an advantage when using a herringbone gear or ''double helical gear'', which has no axial thrust - and also provides self-aligning of the gears. This results in less axial thrust than a comparable spur gear.

A second disadvantage of helical gears is also a greater degree of sliding friction between the meshing teeth, often addressed with additives in the lubricant.

Skew gears

For a "crossed" or "skew" configuration, the gears must have the same pressure angle and normal pitch; however, the helix angle and handedness can be different. The relationship between the two shafts is actually defined by the helix angle(s) of the two shafts and the handedness, as defined:
:$E = \beta_1 + \beta_2$ for gears of the same handedness,
:$E = \beta_1 - \beta_2$ for gears of opposite handedness,
where $\beta$ is the helix angle for the gear. The crossed configuration is less mechanically sound because there is only a point contact between the gears, whereas in the parallel configuration there is a line contact.

Quite commonly, helical gears are used with the helix angle of one having the negative of the helix angle of the other; such a pair might also be referred to as having a right-handed helix and a left-handed helix of equal angles. The two equal but opposite angles add to zero: the angle between shafts is zero—that is, the shafts are ''parallel''. Where the sum or the difference (as described in the equations above) is not zero, the shafts are ''crossed''. For shafts ''crossed'' at right angles, the helix angles are of the same hand because they must add to 90 degrees. (This is the case with the gears in the illustration above: they mesh correctly in the crossed configuration: for the parallel configuration, one of the helix angles should be reversed. The gears illustrated cannot mesh with the shafts parallel.)

3D animation of helical gears (parallel axis)

3D animation of helical gears (crossed axis)

Double helical

Double helical gears overcome the problem of axial thrust presented by single helical gears by using a double set of teeth, slanted in opposite directions. A double helical gear can be thought of as two mirrored helical gears mounted closely together on a common axle. This arrangement cancels out the net axial thrust, since each half of the gear thrusts in the opposite direction, resulting in a net axial force of zero. This arrangement can also remove the need for thrust bearings. However, double helical gears are more difficult to manufacture due to their more complicated shape.

Herringbone gears are a special type of helical gears. They do not have a groove in the middle like some other double helical gears do; the two mirrored helical gears are joined so that their teeth form a V shape. This can also be applied to bevel gears, as in the final drive of the Citroën Type A.

For both possible rotational directions, there exist two possible arrangements for the oppositely-oriented helical gears or gear faces. One arrangement is called stable, and the other unstable. In a stable arrangement, the helical gear faces are oriented so that each axial force is directed toward the center of the gear. In an unstable arrangement, both axial forces are directed away from the center of the gear. In either arrangement, the total (or ''net'') axial force on each gear is zero when the gears are aligned correctly. If the gears become misaligned in the axial direction, the unstable arrangement generates a net force that may lead to disassembly of the gear train, while the stable arrangement generates a net corrective force. If the direction of rotation is reversed, the direction of the axial thrusts is also reversed, so a stable configuration becomes unstable, and vice versa.

Stable double helical gears can be directly interchanged with spur gears without any need for different bearings.

Bevel

A bevel gear is shaped like a right circular cone with most of its tip cut off. When two bevel gears mesh, their imaginary vertices must occupy the same point. Their shaft axes also intersect at this point, forming an arbitrary non-straight angle between the shafts. The angle between the shafts can be anything except zero or 180 degrees. Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called miter (US) or mitre (UK) gears.

Spiral bevels

Spiral bevel gears can be manufactured as Gleason types (circular arc with non-constant tooth depth), Oerlikon and Curvex types (circular arc with constant tooth depth), Klingelnberg Cyclo-Palloid (Epicycloid with constant tooth depth) or Klingelnberg Palloid. Spiral bevel gears have the same advantages and disadvantages relative to their straight-cut cousins as helical gears do to spur gears. Straight bevel gears are generally used only at speeds below 5 m/s (1000 ft/min), or, for small gears, 1000 r.p.m..

The cylindrical gear tooth profile corresponds to an involute, but the bevel gear tooth profile to an octoid.
All traditional bevel gear generators (like Gleason, Klingelnberg, Heidenreich & Harbeck, WMW Modul) manufacture bevel gears with an octoidal tooth profile. For 5-axis milled bevel gear sets it is important to choose the same calculation / layout like the conventional manufacturing method.
Simplified calculated bevel gears on the basis of an equivalent cylindrical gear in normal section with an involute tooth form show a deviant tooth form with reduced tooth strength by 10-28% without offset and 45% with offset iss. Hünecke, TU Dresden
Furthermore, the "involute bevel gear sets" cause more noise.

Hypoid