Editing Gear (section)

==Tooth cut direction==
Gear teeth typically extend across the whole thickness of the gear.  Another criterion for classifying gears is the general direction of the teeth across that dimension.  This attribute is affected by the relative position and direction of the axes or rotation of the gears that are to be meshed together.

===Straight===
[[File:Spur Gear 12mm, 18t.svg|thumb|upright|Spur gear]]
In a cylindrical ''[[spur gear]]'' or ''straight-cut gear'', the tooth faces are straight along the direction parallel to the axis of rotation.  Any imaginary cylinder with the same axis will cut the teeth along parallel straight lines.  

The teeth can be either internal or external.  Two spur gears mesh together correctly only if fitted to parallel shafts.<ref>{{cite web|url=http://science.howstuffworks.com/transport/engines-equipment/gear2.htm|title=How Gears Work|date=16 November 2000|website=howstuffworks.com|access-date=20 September 2018}}</ref> No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds.<ref>{{Cite book|title=Machinery's Handbook|url=https://archive.org/details/machineryshandbo00ober_611|url-access=limited|publisher=Industrial Press|year=2012|isbn=978-0-8311-2900-2|location=New York|pages=[https://archive.org/details/machineryshandbo00ober_611/page/n2130 2125]}}</ref> 

For arrangements with crossed non-parallel axes, the faces in a straight-cut gear are parts of a [[conical surface|general conical surface]] whose generating lines (''generatrices'') go through the meeting point of the two axes, resulting in a [[bevel gear]].  Such gears are generally used only at speeds below {{cvt|5|m/s|ft/min|-1}}, or, for small gears, 1000 [[rpm]].<ref name="straightbevel">{{harvnb|McGraw-Hill|2007|p=742}}.</ref>
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===Helical===
[[File:Helical Gears.jpg|left|thumb|Helical gears<br/>Top: parallel configuration<br/>Bottom: crossed configuration]]

In a ''[[helical gear|helical]]'' or ''dry fixed'' gear the tooth walls are not parallel to the axis of rotation, but are set at an angle.  An imaginary pitch surface (cylinder, cone, or hyperboloid, depending on the relative axis positions) intersects  each tooth face along an arc of a [[helix]]. Helical gears can be meshed in either ''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".

[[File:Anim engrenages helicoidaux.gif|thumb|An external contact helical gear in action]]
The angled teeth engage more gradually than do spur gear teeth, causing them to run more smoothly and quietly.<ref>{{Citation|last=Khurmi|first=R. S.|title=Theory of Machines|publisher=S.CHAND}}</ref> 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.<ref>{{citation|chapter-url=https://kyotoo.org/|chapter=Minimizing gearbox noise inside and outside the box|first=Richard|last=Schunck|title=Motion System Design|postscript=.}}{{Dead link|date=May 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> The speed is considered high when the pitch line velocity exceeds 25&nbsp;m/s.<ref name="pitchlinespeed">{{harvnb|Vallance|Doughtie|1964|p=281|quote=Pitch-line speeds of 4,000 to 7,000 fpm [20 to 36 m/s] are common with automobile and turbine gears, and speeds of 12,000 fpm [61 m/s] have been successfully used.}}</ref>

A disadvantage of helical gears is a resultant [[thrust]] along the axis of the gear, which must be accommodated by appropriate [[thrust bearing]]s. However, this issue can be circumvented by 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 a greater degree of [[sliding friction]] between the meshing teeth, often addressed with additives in the lubricant.

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:<ref name="roymech">{{Citation |title=Helical gears |url=http://www.roymech.co.uk/Useful_Tables/Drive/Hellical_Gears.html |access-date=15 June 2009 |postscript=. |url-status=dead |archive-url=https://web.archive.org/web/20090626030945/http://www.roymech.co.uk/Useful_Tables/Drive/Hellical_Gears.html |archive-date=26 June 2009 }}</ref>
:<math>E = \beta_1 + \beta_2</math> for gears of the same handedness,
:<math>E = \beta_1 - \beta_2</math> for gears of opposite handedness,
where <math>\beta</math> 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.<ref name="roymech"/>

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.)

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* [https://www.youtube.com/watch?v=Qcgjsor1Q-Y 3D animation of helical gears (parallel axis)]
* [https://www.youtube.com/watch?v=ZpJuyK842RQ 3D animation of helical gears (crossed axis)]

===Double helical===
[[File:Herringbone gears (Bentley, Sketches of Engine and Machine Details).jpg|thumb|left|Herringbone gears]]

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 gear]]s 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 gear]]s, as in the [[final drive]] of the [[Citroën Type A]]. Another type of double helical gear is a [[Wuest type herringbone gear|Wüst]] gear.

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.
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===Worm===
[[File:Worm Gear and Pinion.jpg|thumb|left|Worm gear]]
[[File:Worm Gear.gif|thumb|left|4-start worm and wheel]]
{{Main|Worm drive|Slewing drive}}

''Worms'' resemble [[screw]]s. A worm is meshed with a ''worm wheel'', which looks similar to a [[spur gear]].

Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed gear ratio. For example, helical gears are normally limited to gear ratios of less than 10:1 while worm-and-gear sets vary from 10:1 to 500:1.<ref name="wormgears1">{{harvnb|Vallance|Doughtie|1964|p=287}}.</ref> A disadvantage is the potential for considerable sliding action, leading to low efficiency.<ref name="wormgears2">{{harvnb|Vallance|Doughtie|1964|pp=280, 296}}</ref>

A worm gear is a species of helical gear, but its helix angle is usually somewhat large (close to 90 degrees) and its body is usually fairly long in the axial direction. These attributes give it screw like qualities. The distinction between a worm and a helical gear is that at least one tooth persists for a full rotation around the helix. If this occurs, it is a 'worm'; if not, it is a 'helical gear'. A worm may have as few as one tooth. If that tooth persists for several turns around the helix, the worm appears, superficially, to have more than one tooth, but what one in fact sees is the same tooth reappearing at intervals along the length of the worm. The usual screw nomenclature applies: a one-toothed worm is called ''single thread'' or ''single start''; a worm with more than one tooth is called ''multiple thread'' or ''multiple start''. The helix angle of a worm is not usually specified. Instead, the lead angle, which is equal to 90 degrees minus the helix angle, is given.

In a worm-and-gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. In traditional [[music box]]es, however, the gear drives the worm, which has a large helix angle. This mesh drives the speed-limiter vanes which are mounted on the worm shaft.

Worm-and-gear sets that do lock are called '''self locking''', which can be used to advantage, as when it is desired to set the position of a mechanism by turning the worm and then have the mechanism hold that position. An example is the [[machine head]] found on some types of [[stringed instrument]]s.

If the gear in a worm-and-gear set is an ordinary helical gear only a single point of contact is achieved.<ref name="hypoidgears" /><ref name="wormgears4">{{harvnb|Vallance|Doughtie|1964|p=290}}.</ref> If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact by making both gears partially envelop each other. This is done by making both concave and joining them at a [[saddle point]]; this is called a '''cone-drive'''<ref name="wormgears5">{{harvnb|McGraw-Hill|2007|p=744}}</ref> or "Double enveloping".

Worm gears can be right or left-handed, following the long-established practice for screw threads.<ref name="ansiagma">{{Citation | last1 = American Gear Manufacturers Association | last2 = American National Standards Institute | title = Gear Nomenclature, Definitions of Terms with Symbols | publisher = American Gear Manufacturers Association | edition = ANSI/AGMA 1012-G05| author1-link = American Gear Manufacturers Association }}</ref>
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