Gear-Tooth ActionFundamental Law of Gear-Tooth ActionThe figure shows two mating gear teeth, in which Tooth profile 1 drives tooth profile 2 by acting at the instantaneous contact pointK. N1N2is the common normal of the two profiles. N1is the foot of the perpendicular fromO1toN1N2 N2is the foot of the perpendicular fromO2toN1N2.Two gearing tooth profiles

Although the two profiles have different velocitiesV1andV2at pointK, their velocities alongN1N2are equal in both magnitude and direction. Otherwise the two tooth profiles would separate from each other. Therefore, we have

(1)or

(2)We notice that the intersection of the tangencyN1N2and the line of centerO1O2is pointP, and

(3)Thus, the relationship between the angular velocities of the driving gear to the driven gear, orvelocity ratio, of a pair of mating teeth is

(4)PointPis very important to the velocity ratio, and it is called thepitch point. Pitch point divides the line between the line of centers and its position decides the velocity ratio of the two teeth. The above expression is thefundamental law of gear-tooth action.

Constant Velocity RatioFor a constant velocity ratio, the position ofPshould remain unchanged. In this case, the motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radiusR1andR2or diameterD1andD2. We can get two circles whose centers are atO1andO2, and through pitch pointP. These two circle are termedpitch circles. The velocity ratio is equal to the inverse ratio of the diameters of pitch circles. This is the fundamental law of gear-tooth action.Thefundamental law of gear-tooth actionmay now also be stated as follow (for gears with fixed center distance):The common normal to the tooth profiles at the point of contact must always pass through a fixed point (the pitch point) on the line of centers (to get a constant velocity ration).

Conjugate ProfilesTo obtain the expectedvelocity ratioof two tooth profiles, the normal line of their profiles must pass through the correspondingpitch point, which is decided by thevelocity ratio. The two profiles, which satisfy this requirement, are called conjugate profiles. Sometimes, we simply termed the tooth profiles which satisfy thefundamental law of gear-tooth action theconjugate profiles.Although many tooth shapes are possible for which a mating tooth could be designed to satisfy the fundamental law, only two are in general use: thecycloidalandinvoluteprofiles. The involute has important advantages -- it is easy to manufacture and the center distance between a pair of involute gears can be varied without changing thevelocity ratio. Thus close tolerances between shaft locations are not required when using the involute profile. The most commonly usedconjugate tooth curve is theinvolute curve.

Gear teeth could be manufactured with a wide variety of shapes and profiles. The involute profile is the most commonly used system for gearing today, and all Boston spur and helical gears are of involute form.An involute is a curve that is traced by a point on a taut cord unwinding from a circle, which is called a BASE CIRCLE. The involute is a form of spiral, the curvature of which becomes straighter as it is drawn from a base circle and eventually would become a straight line if drawn far enough.An involute drawn from a larger base circle will be less curved (straighter) than one drawn from a smaller base circle. Similarly, the involute tooth profile of smaller gears is considerably curved, on larger gears is less curved (straighter), and is straight on a rack, which is essentially an infinitely large gear.

On an involute profile gear tooth, the contact point starts closer to one gear, and as the gear spins, the contact point moves away from that gear and toward the other. If you were to follow the contact point, it would describe a straight line that starts near one gear and ends up near the other. This means that the radius of the contact point gets larger as the teeth engage.The pitch diameter is the effective contact diameter. Since the contact diameter is not constant, the pitch diameter is really the average contact distance. As the teeth first start to engage, the top gear tooth contacts the bottom gear tooth inside the pitch diameter. But notice that the part of the top gear tooth that contacts the bottom gear tooth is very skinny at this point. As the gears turn, the contact point slides up onto the thicker part of the top gear tooth. This pushes the top gear ahead, so it compensates for the slightly smaller contact diameter. As the teeth continue to rotate, the contact point moves even further away, going outside the pitch diameter -- but the profile of the bottom tooth compensates for this movement. The contact point starts to slide onto the skinny part of the bottom tooth, subtracting a little bit of velocity from the top gear to compensate for the increased diameter of contact. The end result is that even though the contact point diameter changes continually, the speed remains the same. So an involute profile gear tooth produces a constant ratio of rotational speed.A profile is one side of a tooth in a cross section between the outside circle and the root circle. Usually a profile is the curve of intersection of a tooth surface and a plane or surface normal to the pitch surface, such as the transverse, normal, or axial plane.The fillet curve (root fillet) is the concave portion of the tooth profile where it joins the bottom of the tooth space. As mentioned near the beginning of the article, the attainment of a nonfluctuating velocity ratio is dependent on the profile of the teeth.Frictionand wear between two gears is also dependent on the tooth profile. There are a great many tooth profiles that provides a constant velocity ratio. In many cases, given an arbitrary tooth shape, it is possible to develop a tooth profile for the mating gear that provides a constant velocity ratio. However, two constant velocity tooth profiles have been by far the most commonly used in modern times. They are thecycloidand theinvolute. The cycloid was more common until the late 1800s; since then the involute has largely superseded it, particularly in drive train applications. The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center to center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio. Cycloidal gears only work properly if the center spacing is exactly right. Cycloidal gears are still used in mechanical clocks.Anundercutis a condition in generated gear teeth when any part of the fillet curve lies inside of a line drawn tangent to the working profile at its point of juncture with the fillet. Undercut may be deliberately introduced to facilitate finishing operations. With undercut the fillet curve intersects the working profile. Without undercut the fillet curve and the working profile have a common tangent.

INVOLUTE GEARInvolute gear tooth forms and standard tooth proportions are specified in terms of a basic rack which has straight-sided teeth, for involute systems.

Theinvolute gearprofile, originally designed byLeonhard Euler,is the most commonly used system forgearingtoday, withcycloidal gearing still used for some specialties such as clocks. In an involute gear, the profiles of the teeth areinvolutesof a circle.(The involute of a circle is the spiraling curve traced by the end of an imaginary taut string unwinding itself from that stationary circle called the base circle.)Irrespective of whether a gear is spur or helical, in every plane of the involute gears the contact between a pair of gear teeth occurs at a single instantaneous point (see figure at right) where two involutes of the same spiral hand meet. Contact on the other side of the teeth is where both involutes are of the other spiral hand. Rotation of the gears causes the location of this contact point to move across the respective tooth surfaces. The tangent at any point of the curve is perpendicular to the generating line irrespective of the mounting distance of the gears. Thus the line of the force follows the generating line, and is thus tangent to the two base circles, and is known as theLine of Action(also called Pressure Line or Line of Contact). When this is true, the gears obey the Fundamental Law of Gearing:

The angular velocity ratio between two gears of a gear set must remain constant throughout the mesh.

This property is required for smooth transmission of power with minimal speed or torque variations as pairs of teeth go into or come out of mesh, but is not required for low-speed gearing.Where the line of action crosses the line between the two centres it is called thePitch Pointof the gears, where there is no sliding contact.ThePressure Angleis the acute angle between the line of action and a normal to the line connecting the gear centers. The pressure angle of the gear varies according to the position on the involute shape, but pairs of gears must have the same pressure angle for the teeth to mesh properly, so specific portions of the involute must be matched.While manufacturers can produce any pressure angle, the most common stock gears have a 20 pressure angle, with 14 and 25 pressure angle gears being much less common.Increasing the pressure angle increases the width of the base of the gear tooth, leading to greater strength and load carrying capacity. Decreasing the pressure angle provides lower backlash, smoother operation and less sensitivity to manufacturing errors.Only used in limited situations are helical involute gears, where the spirals of the two involutes are of different 'hand' and the Line of Action is the external tangents to the base circles (like a normal belt drive whereas normal gears are like a crossed-belt drive), and the gears rotate in the same direction,and there is sliding at the contact point which gives inefficiency and thus can be used in limited slip differentials. These cannot be spur gears unless they comprise multiple sectors of gears, and are otherwise helical, but the meshing gears are of the same helix angle rather than of opposite hand.

The Involute Curve of a CircleIt is known that involute gears are the most widely used in practice, being preferred over cycloidal and circular profile gears, because of the following favorable properties: the transmission ratio between two involute gears is not sensitive to the center distance modification; the same cutting tool can be used to manufacture gears with any number of teeth - the module (or diametral pitch) and whole depth of these gears will of course be the same; the cutting tools used to fabricate involute gears (in particular the rack and hob cutter), can be conveniently mass produced because of their cutting surfaces are straight and therefore easy to sharpen. As their name suggests, involute gears have the active flanks of their teeth shaped as involute curves of a common circle, called base circle. The involute of a circle is obtained by attaching a taut, inextensible string to this given circle, and tracing its free end as it is wound or unwound onto the base circle18. Fig. 1 illustrates this concept, where BC represents the string, while the involute curve is the locus generated by the end point C of the string.

Properties of Involute Curves1. The distanceBKis equal to the arcAB, because linkMNrolls without slipping on the circle.2. For any instant, theinstantaneous centerof the motion of the line is its point of tangent with the circle.Note: We have not defined the terminstantaneous centerpreviously. Theinstantaneous centerorinstant centeris defined in two ways(Bradford & Guillet 43):1. When two bodies have planar relative motion, the instant center is a point on one body about which the other rotates at the instant considered.2. When two bodies have planar relative motion, the instant center is the point at which the bodies are relatively at rest at the instant considered.3. The normal at any point of an involute is tangent to the base circle. Because of the property (2) of the involute curve, the motion of the point that is tracing the involute is perpendicular to the line at any instant, and hence the curve traced will also be perpendicular to the line at any instant.4. There is no involute curve within the base circle.

Pressure anglein relation togearteeth, also known as theangle of obliquity,is the angle between the tooth face and the gear wheel tangent. It is more precisely the angle at a pitch point between the line of pressure (which is normal to the tooth surface) and the plane tangent to the pitch surface. The pressure angle gives the direction normal to the tooth profile. The pressure angle is equal to theprofile angleat the standard pitch circle and can be termed the "standard" pressure angle at that point. Standard values are 14.5, 20 and 25 degrees. Earlier gears with pressure angle 14.5 were commonly used because the cosine is larger for a smaller angle, providing more power transmission and less pressure on the bearing; however, teeth with smaller pressure angles are weaker. To run gears together properly their pressure angles must be matched. The pressure angle is also the angle of the sides of the trapezoidal teeth on the corresponding rack.Just as there are three types ofprofile angle, there are three types of corresponding pressure angle: the transverse pressure angle, the normal pressure angle, and the axial pressure angle.

Condition for Correct MeshingFigure shows two meshing gears contacting at pointK1andK2.

Two meshing gearsTo get a correct meshing, the distance ofK1K2on gear 1 should be the same as the distance ofK1K2on gear 2. AsK1K2on both gears are equal to thebase pitchof their gears, respectively. Hence

Since

and

Thus

To satisfy the above equation, the pair of meshing gears must satisfy the following condition:

Ordinary Gear TrainsGear trainsconsist of two or more gears for the purpose of transmitting motion from one axis to another.Ordinary gear trainshave axes, relative to the frame, for all gears comprising the train.Figure 6ashows asimple ordinary trainin which there is only one gear for each axis. InFigure 6bacompound ordinary trainis seen to be one in which two or more gears may rotate about a single axis.

Figure 6 Ordinary gear trains

Epicyclic Gearing This planetary gear train consists of a sun gear (yellow), planet gears (blue) supported by the carrier (green) and an annular gear (pink). The red marks show the relative displacement of the sun gear and carrier, when the carrier is rotated 45 clockwise and the annular gear is held fixed.Anepicyclic gear trainconsists of twogearsmounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates to carry one gear, called theplanet gear, around the other, called the sun gear. The planet and sun gears mesh so that theirpitch circlesroll without slip. A point on the pitch circle of the planet gear traces anepicycloidcurve. In this simplified case, the sun gear is fixed and the planetary gear(s) roll around the sun gear.An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of a fixed, outer gear ring, which is called anannular gear. In this case, the curve traced by a point on the pitch circle of the planet is ahypocycloid.The combination of epicycle gear trains with a planet engaging both a sun gear and an annular gear is called aplanetary gear train.In this case, the annular gear is usually fixed and the sun gear is driven.Epicyclic gears get their name from their earliest application, which was the modeling of the movements of the planets in the heavens. Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion. At around 500 BC, the Greeks invented the idea of epicycles, of circles traveling on the circular orbits. With this theoryClaudius Ptolemyin theAlmagestin 148 AD was able to predict planetary orbital paths. TheAntikythera Mechanism, circa 80 BC, had gearing which was able to approximate the moon's elliptical path through the heavens, and even to correct for the nine-year precession of that path.

Epicyclic gearingorplanetary gearingis agearsystem consisting of one or more outer gears, orplanetgears, revolving about a central, orsungear. Typically, the planet gears are mounted on a movable arm orcarrierwhich itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate the use of an outer ring gear orannulus, which meshes with the planet gears. Planetary gears (or epicyclic gears) are typically classified as simple and compound planetary gears. Simple planetary gears have one sun, one ring, one carrier, and one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet (there are at least two more planets in mesh with each other in each planet train), stepped-planet (there exists a shaft connection between two planets in each planet train), and multi-stage structures (the system contains two or more planet sets). Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, and more exible congurations.The axes of all gears are usually parallel, but for special cases likepencil sharpenersanddifferentials, they can be placed at an angle, introducing elements ofbevel gear(see below). Further, the sun, planet carrier and annulus axes are usuallycoaxial. Epicyclic gearing is also available which consists of a sun, a carrier, and two planets which mesh with each other. One planet meshes with the sun gear, while the second planet meshes with the ring gear. For this case, when the carrier is fixed, the ring gear rotates in the same direction as the sun gear, thus providing a reversal in direction compared to standard epicyclic gearing.

HistoryIn the 2nd-century AD treatiseAlmagest,Ptolemyused rotatingdeferent and epicyclesthat form epicyclic gear trains to predict the motions of the planets. Accurate predictions of the movement of the Sun, Moon and the five planets, Mercury, Venus, Mars, Jupiter and Saturn, across the sky assumed that each followed a trajectory traced by a point on the planet gear of an epicyclic gear train. This curve is called anepitrochoid.Epicyclic gearing was used in theAntikythera Mechanism, circa 80 BCE, to adjust the displayed position of themoon for its ellipticity, and even for the precession of the ellipticity. Two facing gears were rotated around slightly different centers, and one drove the other not with meshed teeth but with a pin inserted into a slot on the second. As the slot drove the second gear, the radius of driving would change, thus invoking a speeding up and slowing down of the driven gear in each revolution.Richard of Wallingford, an English abbot of St Albans monastery is credited for reinventing epicyclic gearing for an astronomical clock in the 14th century. In 1588, Italian military engineerAgostino Ramelliinvented thebookwheel, a vertically-revolving bookstand containing epicyclic gearing with two levels of planetary gears to maintain proper orientation of the books.

Gear ratio of Standard Epicyclic Gearing In this example, the carrier (green) is held stationary while the sun gear (yellow) is used as input. The planet gears (blue) turn in a ratio determined by the number of teeth in each gear. Here, the ratio is 24/16, or 3/2; each planet gear turns at 3/2 the rate of the sun gear, in the opposite direction.Thegear ratioof an epicyclic gearing system is somewhat non-intuitive, particularly because there are several ways in which an input rotation can be converted into an output rotation. The three basic components of the epicyclic gear are: Sun: The central gear Planet carrier: Holds one or more peripheralplanetgears, all of the same size, meshed with the sun gear Annulus: An outer ring with inward-facing teeth that mesh with the planet gear or gears

The overall gear ratio of a simple planetary gearset can be reliably calculated using the following two equations,representing the sun-planet and planet-annulus interactions respectively:

From which we can deduce that:

OR

Considering

Where:

is theangular velocityof theAnnulus,Sun Gear,Planet GearsandPlanet Carrierrespectively.

is the Number of teeth of theAnnulus, theSun Gearand eachPlanet Gearrespectively.

Alternatively, if the number of teeth on each gear meets the relationship, this equation can be re-written as the following:, where

These relationships can be used to analyze any epicyclic system, including those, such as hybrid vehicle transmissions, where two of the components are used asinputswith the third providingoutputrelative to the two inputs. In many epicyclic gearing systems, one of these three basic components is held stationary; one of the two remaining components is aninput, providing power to the system, while the last component is anoutput, receiving power from the system. The ratio of input rotation to output rotation is dependent upon the number of teeth in each gear, and upon which component is held stationary.In one arrangement, the planetary carrier (green) is held stationary, and the sun gear (yellow) is used as input. In this case, the planetary gears simply rotate about their own axes (i.e., spin) at a rate determined by the number of teeth in each gear. If the sun gear hasNsteeth, and each planet gear hasNpteeth, then the ratio is equal to Ns/Np. For instance, if the sun gear has 24 teeth, and each planet has 16 teeth, then the ratio is 24/16, or 3/2; this means that oneclockwiseturn of the sun gear produces 1.5counterclockwiseturns of each of the planet gear(s) about its axis.This rotation of the planet gears can in turn drive the annulus (not depicted in diagram), in a corresponding ratio. If the annulus hasNateeth, then the annulus will rotate byNp/Naturns for each turn of the planet gears. For instance, if the annulus has 64 teeth, and the planets 16, one clockwise turn of a planet gear results in 16/64, or 1/4 clockwise turns of the annulus. Extending this case from the one above: One turn of the sun gear results inturns of the planets One turn of a planet gear results inturns of the annulusSo, with the planetary carrier locked, one turn of the sun gear results inturns of the annulus.The annulus may also be held fixed, with input provided to the planetary gear carrier; output rotation is then produced from the sun gear. This configuration will produce an increase in gear ratio, equal to 1+Na/Ns. If the annulus is held stationary and the sun gear is used as the input, the planet carrier will be the output. The gear ratio in this case will be 1/(1+Na/Ns). This is the lowest gear ratio attainable with an epicyclic gear train. This type of gearing is sometimes used intractorsand construction equipment to provide high torque to the drive wheels.In bicyclehub gears, the sun is usually stationary, being keyed to the axle or even machined directly onto it. The planetary gear carrier is used as input. In this case the gear ratio is simply given by (Ns+Na)/Na. The number of teeth in the planet gear is irrelevant. Compound planets of aSturmey-ArcherAM bicycle hub (gear ring removed)

Fixed Carrier Train RatioA convenient approach to determine the various speed ratios available in a planetary gear train begins by considering the speed ratio of the gear train when the carrier is held fixed. This is known as the fixed carrier train ratio. In the case of a simple planetary gear train formed by a carrier supporting a planet gear engaged with a sun and annular gear, the fixed carrier train ratio is computed as the speed ratio of thegear trainformed by the sun, planet and annular gears on the fixed carrier. This is given by,

In this calculation the planet gear is an idler gear.The fundamental formula of the planetary gear train with a rotating carrier is obtained by recognizing that this formula remains true if the angular velocities of the sun, planet and annular gears are computed relative to the carrier angular velocity. This becomes,

This formula provides a simple way to determine the speed ratios for the simple planetary gear train under different conditions:1. The carrier is held fixed, c=0,

2. The annular gear is held fixed, a=0,

3. The sun gear is held fixed, s=0,

Each of the speed ratios available to a simple planetary gear train can be obtained by using band brakes to hold and release the carrier, sun or annular gears as needed. This provides the basic structure for anautomatic transmission.

Spur Gear Differential

A spur gear differential constructed by engaging the planet gears of two co-axial epicyclic gear trains. The casing is the carrier for this planetary gear train.Aspur gear differentialis constructed from two identical coaxial epicyclic gear trains assembled with a single carrier such that their planet gears are engaged. This forms a planetary gear train with a fixed carrier train ratioR = -1.In this case, the fundamental formula for the planetary gear train yields,

or

Thus, the angular velocity of the carrier of a spur gear differential is the average of the angular velocities of the sun and annular gears.In discussing the spur gear differential, the use of the termannular gearis a convenient way to distinguish the sun gears of the two epicyclic gear trains. The second sun gear serves the same purpose as the annular gear of a simple planetary gear train, but clearly does not have the internal gear mate that is typical of an annular gear.

Gear ratio of Reversed Epicyclic GearingSome epicyclic gear trains employ two planetary gears which mesh with each other. One of these planets meshes with the sun gear, the other planet meshes with the annulus (or ring) gear. This results in different ratios being generated by the planetary. The fundamental equation becomes:

where

which results in:when the carrier is locked,when the sun is locked,when the annulus is locked.

Compound Planetary Gears

Stepped planet series of theRohloff Speedhubinternally geared bicycle hubwith the smaller planet series meshing with the sun wheel and the larger planet series meshing with the ring gear."Compound planetary gear" is a general concept and it refers to any planetary gears involving one or more of the following three types of structures:meshed-planet(there are at least two more planets in mesh with each other in each planet train),stepped-planet(there exists a shaft connection between two planets in each planet train), andmulti-stage structures(the system contains two or more planet sets).Some designs use "stepped-planet" which have two differently-sized gears on either end of a common casting. The large end engages the sun, while the small end engages the annulus. This may be necessary to achieve smaller step changes in gear ratio when the overall package size is limited. Compound planets have "timing marks" (or "relative gear mesh phase" in technical term). The assembly conditions of compound planetary gears are more restrictive than simple planetary gears, and they must be assembled in the correct initial orientation relative to each other, or their teeth will not simultaneously engage the sun and annulus at opposite ends of the planet, leading to very rough running and short life. Compound planetary gears can easily achieve larger transmission ratio with equal or smaller volume. For example, compound planets with teeth in a 2:1 ratio with a 50T annulus would give the same effect as a 100T annulus, but with half the actual diameter.More planet and sun gear units can be placed in series in the same annulus housing (where the output shaft of the first stage becomes the input shaft of the next stage) providing a larger (or smaller) gear ratio. This is the way someautomatic transmissionswork.DuringWorld War II, a special variation of epicyclic gearing was developed for portableradargear, where a very high reduction ratio in a small package was needed. This had two outer annular gears, each half the thickness of the other gears. One of these two annular gears was held fixed and had one tooth fewer than did the other. Therefore, several turns of the "sun" gear made the "planet" gears complete a single revolution, which in turn made the rotating annular gear rotate by a single tooth.

Benefits

The mechanism of apencil sharpenerwith stationary annulus and rotating planet carrier as input. Planet gears are extended into cylindrical cutters, rotating around the pencil that is placed on the sun axis. The axes of planetary gears join at the pencil sharpening angle.Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. They provide a reduction volume, multiple kinematic combinations, purely torsional reactions, and coaxial shafting. Disadvantages include high bearing loads, constant lubrication requirements, inaccessibility, and design complexity.The efficiency loss in a planetary gear train is 3% per stage. This type of efficiency ensures that a high proportion of the energy being input is transmitted through the gearbox, rather than being wasted on mechanical losses inside the gearbox.The load in a planetary gear train is shared among multiple planets, therefore torque capability is greatly increased. The more planets in the system, the greater the load ability and the higher the torque density.The planetary gear train also provides stability due to an even distribution of mass and increased rotational stiffness. Torque applied radially onto the gears of a planetary gear train is transferred radially by the gear, without lateral pressure on the gear teeth.

3D printingPlanetary Gears have become popular in 3D printing for a few different reasons. Some people use them for the gearing benefits and use them to get more accurate 3D prints, getting their layers of plastic down to just a few microns thick, this produces very quality 3D prints. But the largest use of them is as toys for kids. Since herring bone gears are easy to 3D print it has become very popular to 3D print a moving herring bone Planetary Gear system for teaching kids how gears work. Since they are herring bone they don't fall out of the ring and done need a mounting plate.

Transmission

Amachineconsists of a power source and a power transmission system, which provides controlled application of the power. Merriam-Webster definestransmissionas an assembly of parts including the speed-changing gears and the propeller shaft by which the power is transmitted from an engine to a live axle.Oftentransmissionrefers simply to thegearboxthat usesgearsandgear trainsto providespeedandtorqueconversions from a rotating power source to another device. In British English, the termtransmissionrefers to the wholedrivetrain, including clutch, gearbox, prop shaft (for rear-wheel drive), differential, and final drive shafts. In American English, however, the term refers more specifically to thegearboxalone, and the usage details are different. The most common use is inmotor vehicles, where the transmission adapts the output of theinternal combustion engineto the drive wheels. Such engines need to operate at a relatively highrotational speed, which is inappropriate for starting, stopping, and slower travel. The transmission reduces the higher engine speed to the slower wheel speed, increasingtorquein the process. Transmissions are also used on pedal bicycles, fixed machines, and where different rotational speeds and torques are adapted.Often, a transmission has multiple gear ratios (or simply "gears"), with the ability to switch between them as speed varies. This switching may be done manually (by the operator), or automatically. Directional (forward and reverse) control may also be provided. Single-ratio transmissions also exist, which simply change the speed and torque (and sometimes direction) of motor output.In motor vehicles, the transmission generally is connected to the enginecrankshaftvia a flywheel and/or clutch and/or fluid coupling, partly because internal combustion engines cannot run below a particular speed. The output of the transmission is transmitted viadriveshaftto one or moredifferentials, which in turn, drive the wheels. While a differential may also provide gear reduction, its primary purpose is to permit the wheels at either end of an axle to rotate at different speeds (essential to avoid wheel slippage on turns) as it changes the direction of rotation.Conventional gear/belt transmissions are not the only mechanism for speed/torque adaptation. Alternative mechanisms includetorque convertersand power transformation (for example,diesel-electric transmissionandhydraulic drive system). Hybrid configurations also exist.

Single stage gear reducer.Most modern gearboxes are used to increasetorquewhile reducing the speed of a prime mover output shaft (e.g. a motor crankshaft). This means that the output shaft of a gearbox rotates at a slower rate than the input shaft, and this reduction in speed produces amechanical advantage, increasing torque. A gearbox can be set up to do the opposite and provide an increase in shaft speed with a reduction of torque. Some of the simplest gearboxes merely change the physical rotational direction of power transmission.Many typicalautomobiletransmissions include the ability to select one of several differentgear ratios. In this case, most of the gear ratios (often simply called "gears") are used to slow down the output speed of the engine and increase torque. However, the highest gears may be "overdrive" types that increase the output speed.

UsesGearboxes have found use in a wide variety of differentoftenstationaryapplications, such aswind turbines.Transmissions are also used inagricultural,industrial,construction,miningandautomotiveequipment. In addition to ordinary transmission equipped with gears, such equipment makes extensive use of the hydrostatic drive and electricaladjustable-speed drives.

Simple

The main gearbox and rotor of aBristol SycamorehelicopterThe simplest transmissions, often called gearboxes to reflect their simplicity (although complex systems are also called gearboxes in the vernacular), provide gear reduction (or, more rarely, an increase in speed), sometimes in conjunction with a right-angle change in direction of the shaft (typically inhelicopters, see picture). These are often used onPTO-powered agricultural equipment, since the axial PTO shaft is at odds with the usual need for the driven shaft, which is either vertical (as with rotary mowers), or horizontally extending from one side of the implement to another (as withmanure spreaders,flail mowers, andforage wagons). More complex equipment, such assilagechoppers andsnowblowers, have drives with outputs in more than one direction.The gearbox in awind turbineconverts the slow, high-torque rotation of the turbine into much faster rotation of theelectrical generator. These are much larger and more complicated than the PTO gearboxes in farm equipment. They weigh several tons and typically contain three stages to achieve an overall gear ratio from 40:1 to over 100:1, depending on the size of the turbine. (Foraerodynamicand structural reasons, larger turbines have to turn more slowly, but the generators all have to rotate at similar speeds of several thousand rpm.) The first stage of the gearbox is usually a planetary gear, for compactness, and to distribute the enormous torque of the turbine over more teeth of the low-speed shaft.Durability of these gearboxes has been a serious problem for a long time. Regardless of where they are used, these simple transmissions all share an important feature: thegear ratiocannot be changed during use. It is fixed at the time the transmission is constructed.For transmission types that overcome this issue, seeContinuously Variable Transmission, also known as CVT.

Multi-ratio systems

Tractortransmission with 16 forward and 8 backward gears

Amphicar gearbox cutaway w/optional shift for water going propellersMany applications require the availability of multiplegear ratios. Often, this is to ease the starting and stopping of a mechanical system, though another important need is that of maintaining goodfuel efficiency.Automotive basicsThe need for a transmission in anautomobileis a consequence of the characteristics of theinternal combustion engine. Engines typically operate over a range of 600 to about 7000revolutions per minute(though this varies, and is typically less for diesel engines), while the car's wheels rotate between 0 rpm and around 1800 rpm.Furthermore, the engine provides its highest torque and power outputs unevenly across the rev range resulting in atorque bandand apower band. Often the greatest torque is required when the vehicle is moving from rest or traveling slowly, while maximum power is needed at high speed. Therefore, a system is required that transforms the engine's output so that it can supply high torque at low speeds, but also operate at highway speeds with the motor still operating within its limits. Transmissions perform this transformation.

A diagram comparing the power and torque bands of a "torquey" engine versus a "peaky" oneThe dynamics of a car vary with speed: at low speeds, acceleration is limited by the inertia of vehicular gross mass; while at cruising or maximum speeds wind resistance is the dominant barrier.Many transmissions andgearsused inautomotiveandtruckapplications are contained in acast ironcase, though more frequentlyaluminiumis used for lower weight especially in cars. There are usually three shafts: a mainshaft, a countershaft, and an idler shaft.The mainshaft extends outside the case in both directions: the input shaft towards the engine, and the output shaft towards the rear axle (on rear wheel drive cars. Front wheel drives generally have the engine and transmission mounted transversely, the differential being part of the transmission assembly.) The shaft is suspended by the mainbearings, and is split towards the input end. At the point of the split, a pilot bearing holds the shafts together. The gears andclutchesride on the mainshaft, the gears being free to turn relative to the mainshaft except when engaged by the clutches.Types of automobile transmissions includemanual,automaticorsemi-automatic transmission.

ManualManual transmissions come in two basic types: A simple but ruggedsliding-meshorunsynchronized/non-synchronoussystem, where straight-cut spur gear sets spin freely, and must be synchronized by the operator matching engine revs to road speed, to avoid noisy and damaging clashing of the gears The now commonconstant-meshgearboxes, which can include non-synchronised, orsynchronized/synchromeshsystems, where typically diagonal cut helical (or sometimes either straight-cut, ordouble-helical) gear sets are constantly "meshed" together, and adog clutchis used for changing gears. On synchromesh boxes, friction cones or "synchro-rings" are used in addition to the dog clutch to closely match the rotational speeds of the two sides of the (declutched) transmission before making a full mechanical engagement.The former type was standard in many vintage cars (alongside e.g. epicyclic and multi-clutch systems) before the development of constant-mesh manuals and hydraulic-epicyclic automatics, older heavy-dutytrucks, and can still be found in use in some agricultural equipment. The latter is the modern standard for on- and off-road transport manual and semi-automatic transmission, although it may be found in many forms; e.g., non-synchronised straight-cut in racetrack or super-heavy-duty applications, non-synchro helical in the majority of heavy trucks and motorcycles and in certain classic cars (e.g. the Fiat 500), and partly or fully synchronised helical in almost all modern manual-shift passenger cars and light trucks.Manual transmissions are the most common type outsideNorth AmericaandAustralia. They are cheaper, lighter, usually give better performance, but the newest automatic transmissions, and CVTs give better fuel economy.It is customary for new drivers to learn, and be tested, on a car with a manual gear change. InMalaysiaandDenmarkall cars used for testing (and because of that, virtually all those used for instruction as well) have a manual transmission. Manual transmissions can include both synchronized and unsynchronized gearing. For example, reverse gear is usually unsynchronised, as the driver is only expected to engage it when the vehicle is at a standstill. Many older (up to 1970s) cars also lacked synchronisation on first gear (for various reasonscost, typically "shorter" overall gearing, engines typically having more low-end torque, the extreme wear on a frequently used first gear synchroniser ...), meaning it also could only be used for moving away from a stop unless the driver became adept at double-declutching and had a particular need to regularly downshift into the lowest gear.Some manual transmissions have an extremely low ratio for first gear, called acreeper gearorgranny gear. Such gears are usually not synchronized. This feature is common on pick-up trucks tailored to trailer-towing, farming, or construction-site work. During normal on-road use, the truck is usually driven without using the creeper gear at all, and second gear is used from a standing start. Some off-road vehicles, most particularly the Willy's Jeep and its descendants, also had transmissions with "granny first"s either as standard or an option, but this function is now more often provided for by a low-range transfer gearbox attached to a normal fully synchronized transmission.

Non-synchronousSome commercial applications use non-synchronized manual transmissions that require a skilled operator. Depending on the country, many local, regional, and national laws govern operation of these types of vehicles (seeCommercial Driver's License). This class may includecommercial, military,agricultural, orengineering vehicles. Some of these may use combinations of types for multi-purpose functions. An example is apower take-off(PTO) gear. The non-synchronous transmission type requires an understanding of gear range, torque, engine power, and multi-functional clutch and shifter functions. Also seeDouble-clutching, andClutch-brakesections of the main article.

Automatic

Epicyclic gearingor planetary gearing as used in an automatic transmission.Most modern North American and Australian and some European and Japanese cars have anautomatic transmissionthat selects an appropriate gear ratio without any operator intervention. They primarily usehydraulicsto select gears, depending onpressureexerted by fluid within the transmission assembly. Rather than using aclutchto engage the transmission, a fluid flywheel, ortorque converteris placed in between the engine and transmission. It is possible for the driver to control the number of gears in use or select reverse, though precise control of which gear is in use may or may not be possible.Automatic transmissions are easy to use. However, in the past, automatic transmissions of this type have had a number of problems; they were complex and expensive, sometimes had reliability problems (which sometimes caused more expenses in repair), have often been less fuel-efficient than their manual counterparts (due to "slippage" in the torque converter), and theirshift timewas slower than a manual making them uncompetitive for racing. With the advancement of modern automatic transmissions this has changed. Attempts to improve fuel efficiency of automatic transmissions include the use oftorque convertersthat lock up beyond a certain speed or in higher gear ratios, eliminating power loss, and overdrive gears that automatically actuate above certain speeds. In older transmissions, both technologies could be intrusive, when conditions are such that they repeatedly cut in and out as speed and such load factors as grade or wind vary slightly. Current computerized transmissions possess complex programming that both maximizes fuel efficiency and eliminates intrusiveness. This is due mainly to electronic rather than mechanical advances, though improvements inCVTtechnology and the use of automatic clutches have also helped. A few cars, including the 2013 Subaru Imprezaand the 2012 model of the Honda Jazz sold in the UK, actually claim marginally better fuel consumption for the CVT version than the manual version.For certain applications, the slippage inherent in automatic transmissions can be advantageous. For instance, indrag racing, the automatic transmission allows the car to stop with the engine at a high rpm (the "stall speed") to allow for a very quick launch when the brakes are released. In fact, a common modification is to increase the stall speed of the transmission. This is even more advantageous forturbochargedengines, where the turbocharger must be kept spinning at high rpm by a large flow of exhaust to maintain theboost pressureand eliminate theturbo lagthat occurs when the throttle suddenly opens on an idling engine.

Semi-automatic A hybrid form of transmission where an integrated control system handles manipulation of theclutchautomatically, but the driver can stilland may be required totake manual control of gear selection. This is sometimes called a "clutchless manual", or "automated manual" transmission. Many of these transmissions allow the driver to fully delegate gear shifting choice to the control system, which then effectively acts as if it was a regular automatic transmission. They are generally designed using manual transmission "internals", and when used in passenger cars, have synchromesh operated helical constant mesh gear sets.Early semi-automatic systems used a variety of mechanical and hydraulic systemsincluding centrifugal clutches, torque converters, electro-mechanical (and even electrostatic) and servo/solenoid controlled clutchesand control schemesautomatic declutching when moving the gearstick, pre-selector controls, centrifugal clutches with drum-sequential shift requiring the driver to lift the throttle for a successful shift, etc.and some were little more than regular lock-up torque converter automatics with manual gear selection.Most modern implementations, however, are standard or slightly modified manual transmissions (and very occasionally modified automaticseven including a few cases of CVTs with "fake" fixed gear ratios), with servo-controlled clutching and shifting under command of the central engine computer. These are intended as a combined replacement option both for more expensive and less efficient "normal" automatic systems, and for drivers who prefer manual shift but are no longer able to operate a clutch, and users are encouraged to leave the shift lever in fully automatic "drive" most of the time, only engaging manual-sequential mode for sporty driving or when otherwise strictly necessary.Specific types of this transmission include:Easytronic,TiptronicandGeartronic, as well as the systems used as standard in all ICE-poweredSmart-MCCvehicles, and on geared step-through scooters such as theHonda Super CuborSuzuki Address.Adual-clutchtransmission alternately uses two sets of internals, each with its own clutch, so that a "gearchange" actually only consists of one clutch engaging as the other disengagesproviding a supposedly "seamless" shift with no break in (or jarring reuptake of) power transmission. Each clutch's attached shaft carries half of the total input gear complement (with a shared output shaft), including synchronised dog clutch systems that pre-select which of its set of ratios is most likely needed at the next shift, under command of a computerised control system. Specific types of this transmission include:Direct-Shift Gearbox.There are also sequential transmissions that use the rotation of a drum to switch gears, much like those of a typical fully manual motorcycle. These can be designed with a manual or automatic clutch system, and may be found both in automobiles (particularly track and rally racing cars), motorcycles (typically light "step-thru" type city utility bikes, e.g., the Honda Super Cub) and quadbikes (often with a separately engaged reversing gear), the latter two normally using a scooter-style centrifugal clutch.

Bicycle gearing

ShimanoXT rear derailleur on amountain bikeBicyclesusually have a system for selecting different gear ratios. There are two main types:derailleur gearsandhub gears. The derailleur type is the most common, and the most visible, usingsprocketgears. Typically there are several gears available on the rear sprocket assembly, attached to the rear wheel. A few more sprockets are usually added to the front assembly as well. Multiplying the number of sprocket gears in front by the number to the rear gives the number of gear ratios, often called "speeds".Hub gears useepicyclic gearingand are enclosed within theaxleof the rear wheel. Because of the small space, they typically offer fewer different speeds, although at least one has reached14 gear ratiosand Fallbrook Technologies manufactures atransmissionwith technically infinite ratios. Several attempts have been made to fit bicycles with an enclosed gearbox, giving obvious advantages for better lubrication, dirt-sealing and shifting. These have usually been in conjunction with a shaft drive, as a gearbox with a traditional chain would (like the hub gear) still have many of the derailleur's disadvantages for an exposed chain. Bicycle gearboxes are enclosed in a box replacing the traditionalbottom bracket. The requirement for a modified frame has been a serious drawback to their adoption. One of the most recent attempts to provide a gearbox for bicycles is the 18 speed Pinion P1.18.This gives an enclosed gearbox, but still a traditional chain. When fitted to a rear suspension bike, it also retains a derailleur-like jockey cage chain tensioner, although without the derailleur's low ground clearance.Causes for failure of bicycle gearing include: worn teeth, damage caused by a faulty chain, damage due to thermal expansion, broken teeth due to excessive pedaling force, interference by foreign objects, and loss of lubrication due to negligence.

Uncommon typesDual clutch transmissionThis arrangement is also sometimes known as a direct shift gearbox or powershift gearbox. It seeks to combine the advantages of a conventional manual shift with the qualities of a modern automatic transmission by providing different clutches for odd and even speed selector gears. When changing gear, the engine torque is transferred from one gear to the other continuously, so providing gentle, smooth gear changes without either losing power or jerking the vehicle. Gear selection may be manual, automatic (depending on throttle/speed sensors), or a 'sports' version combining both options.Continuously variableThe continuously variable transmission (CVT) is a transmission in which the ratio of the rotational speeds of two shafts, as the input shaft and output shaft of a vehicle or other machine, can be varied continuously within a given range, providing an infinite number of possible ratios. The CVT allows the driver or a computer to select the relationship between the speed of the engine and the speed of the wheels within a continuous range. This can provide even better fuel economy if the engine constantly runs at a single speed. The transmission is, in theory, capable of a better user experience, without the rise and fall in speed of an engine, and the jerk felt when changing gears poorly.CVTs are increasingly found on small cars, and especially high-gas-mileage orhybridvehicles. On these platforms, the torque is limited because theelectric motorcan provide torque without changing the speed of the engine. By leaving the engine running at the rate that generates the best gas mileage for the given operating conditions, overall mileage can be improved over a system with a smaller number of fixed gears, where the system may be operating at peak efficiency only for a small range of speeds. CVTs are also found in agricultural equipment; due to the high-torque nature of these vehicles, mechanical gears are integrated to provide tractive force at high speeds. The system is similar to that of ahydrostaticgearbox, and at 'inching speeds' relies entirely on hydrostatic drive. German tractor manufacturerFendtpioneered the technology, developing its 'Vario' transmission.

Infinitely VariableThe IVT is a specific type of CVT that includes not only an infinite number of gearratios, but an "infinite"rangeas well. This is aturn of phrase, it actually refers to CVTs that are able to include a "zero ratio", where the input shaft can turn without any motion of the output shaft while remaining in gear. Of course, the gear ratio in that case is not "infinite" but is instead "undefined".Most (if not all) IVTs result from the combination of a CVT with an epicyclic gear system with a fixed ratio. The combination of the fixed ratio of the epicyclic gear with a specific matching ratio in the CVT side results in zero output. For instance, consider a transmission with an epicyclic gear set to 1:1 gear ratio; a 1:1 reverse gear. When the CVT side is set to 1:1 the two ratios add up to zero output. The IVT is always engaged, even during its zero output. When the CVT is set to higher values it operates conventionally, with increasing forward ratios.In practice, the epicyclic gear may be set to the lowest possible ratio of the CVT, if reversing is not needed or is handled through other means. Reversing can be incorporated by setting the epicyclic gear ratio somewhat higher than the lowest ratio of the CVT, providing a range of reverse ratios.

Electric variableThe Electric Variable Transmission (EVT) combines a transmission with an electric motor to provide the illusion of a single CVT. In the common implementation, a gasoline engine is connected to a traditional transmission, which is in turn connected to an epicyclic gear system's planet carrier. An electric motor/generator is connected to the central "sun" gear, which is normally un-driven in typical epicyclic systems. Both sources of power can be fed into the transmission's output at the same time, splitting power between them. In common examples, between one-quarter and half of the engine's power can be fed into the sun gear. Depending on the implementation, the transmission in front of the epicyclic system may be greatly simplified, or eliminated completely. EVTs are capable of continuously modulating output/input speed ratios like mechanical CVTs, but offer the distinct benefit of being able to also apply power from two different sources to one output, as well as potentially reducing overall complexity dramatically.In typical implementations, the gear ratio of the transmission and epicyclic system are set to the ratio of the common driving conditions, say highway speed for a car, or city speeds for a bus. When the drivers presses on the gas, the associated electronics interprets the pedal position and immediately sets the gasoline engine to the RPM that provides the best gas mileage for that setting. As the gear ratio is normally set far from the maximum torque point, this set-up would normally result in very poor acceleration. Unlike gasoline engines, electric motors offer efficient torque across a wide selection of RPM, and are especially effective at low settings where the gasoline engine is inefficient. By varying the electrical load or supply on the motor attached to the sun gear, additional torque can be provided to make up for the low torque output from the engine. As the vehicle accelerates, the power to the motor is reduced and eventually ended, providing the illusion of a CVT.The canonical example of the EVT is Toyota'sHybrid Synergy Drive. This implementation has no conventional transmission, and the sun gear always receives 28% of the torque from the engine. This power can be used to operate any electrical loads in the vehicle, recharging the batteries, powering the entertainment system, or running the air conditioning. Any residual power is then fed back into a second motor that powers the output of the drivetrain directly. At highway speeds this additional generator/motor pathway is less efficient than simply powering the wheels directly. However, during acceleration, the electrical path is much more efficient than engine operating so far from its torque point. GM uses a similar system in the Allison Bus hybrid powertrains and the Tahoe and Yukon pick-up trucks, but these use a two-speed transmission in front of the epicyclic system, and the sun gear receives close to half the total power.

Non-directElectricElectric transmissions convert the mechanical power of the engine(s) to electricity withelectric generatorsand convert it back to mechanical power withelectric motors. Electrical or electronicadjustable-speed drivecontrol systems are used to control the speed and torque of the motors. If the generators are driven byturbines, such arrangements are calledturbo-electric transmission. Likewise installations powered bydiesel-enginesare called diesel-electric.Diesel-electric arrangements are used on many railway locomotives, ships, largeminingtrucks, and somebulldozers. In these cases, each driven wheel is equipped with its own electric motor, which can be fed varying electrical power to provide any required torque or power output for each wheel independently. This produces a much simpler solution for multiple driven wheels in very large vehicles, where drive shafts would be much larger or heavier than the electrical cable that can provide the same amount of power. It also improves the ability to allow different wheels to run at different speeds, which is useful for steered wheels in large construction vehicles.

Hydrostatic Hydrostatic transmissions transmit all power hydraulically, using the components ofhydraulic machinery. They are similar to electrical transmissions, but hydraulic fluid as the power distribution system rather than electricity.The transmission input drive is a central hydraulic pump and final drive unit(s) is/are a hydraulic motor, or hydraulic cylinder (see:swashplate). Both components can be placed physically far apart on the machine, being connected only by flexible hoses. Hydrostatic drive systems are used on excavators, lawn tractors, forklifts, winch drive systems, heavy lift equipment, agricultural machinery, earth-moving equipment, etc. An arrangement formotor-vehicle transmissionwas probably used on the FergusonF-1P99racing car in about 1961.TheHuman Friendly Transmissionof theHonda DN-01is hydrostatic.

HydrodynamicIf the hydraulic pump and/or hydraulic motor make use of thehydrodynamiceffects of the fluid flow, i.e. pressure due to a change in the fluid's momentum as it flows through vanes in a turbine. The pump and motor usually consist of rotating vanes without seals and are typically placed in close proximity. The transmission ratio can be made to vary by means of additional rotating vanes, an effect similar to varying the pitch of an airplanepropeller.Thetorque converterin most automotive automatic transmissions is, in itself, a hydrodynamic transmission. Hydrodynamic transmissions are used in many passenger rail vehicles, those that are not using electrical transmissions. In this application the advantage of smooth power delivery may outweigh the reduced efficiency caused by turbulence energy losses in the fluid.

Gear Quality

Gears are measured for variation in lead or tooth alignment the deviation of the actual helix angle from what is specified.Engineers and manufacturers often speak of gear quality. In the U.S. the term is usually associated with a quality number based on AGMA criteria this number is by no means a comprehensive indicator of every facet of the gear makeup, but provides a measure of the geometric accuracy of the teeth on a gear. In fact there are numerous characteristics weighing on gear performance, and no single specification number covers them all.The Scope of the AGMA StandardAGMA is not alone; other organizations throughout the world provide gear standards, including the International Standards Organization (ISO) and the Deutches Institute Normale (DIN). The AGMA standard is, however, the standard of choice in the U.S.In the ANSI/AGMA 2000 A88 Gear Classification and Inspection Handbook, quality numbers from Q3 to Q15 represent the accuracy of the tooth geometry; the higher the number the smaller the tolerance. The 2000 A88 standard also provides numbers that specify the type of material and the heat treatment method used in gear making. But the standard leaves out associated parameters such as general material quality and the quality of the heat treating process, which factor heavily into a gears operation. There are nonetheless other AGMA and international criteria that address issues like these.The AGMA quality numbers are intended for the classification of unassembled or loose gears supplied separately rather than in an enclosed drive. But since there is no alternative standard for enclosed gearing, manufacturers and users have taken the liberty to use the AGMA quality numbers when describing assembled gear drives as well.Truly there are many factors beyond the commonly used AGMA gear quality designation. Material quality may be influenced by the forming process (for example, forged versus cast), the cleanliness or purity of the substance, the sulfur content, and the grain size, among other things. Carburization heat treatment can be applied to varying degrees of hardness and depth, or can be a cause of mechanical or chemical material degradation if performed improperly. Manufacturing and assembly might introduce things like surface finish anomalies (nicks and burrs), handling damage, and in the case of assembled (enclosed) drives, misalignment and contamination. Lapses in quality control can let these things by.

A quick breakdown

Profiles of manufactured gear teeth are checked against the desired tooth profile; some of the possible variations are illustrated. Sometimes designers purposely alter the tooth profile from a perfect involute to compensate for load deflection.The now-familiar quality number tells of the accuracy of tooth shape and placement. The four main parameters accounted for are: Tooth lead or tooth alignment; involute profile variation; pitch or spacing variation; and radial runout. Other parameters are defined but are applied less frequently.Thetooth leadortooth alignmentcriterion applies to spur and helical-type gearing, and measures the variation between the specified lead (or helix angle) and the lead of the produced gear.Involute profile variationis the difference between the specified profile and the measured profile of the tooth.Pitch variation or spacing variationis the difference between the specified tooth location and the actual tooth location around the circumference of the gear.

Gear teeth around the gear circumference can vary in their positioning. This pitch or spacing variation can be marked in several ways. The second drawing shows pitch variation measured along the circular pitch circumference.

Radial runoutrefers to the disparity in radial position of teeth on a gear the variation in tooth distances from the center of rotation.Geometry inspections are usually made with modern equipment that measures and records all of the critical variations, and can automatically determine the AGMA gear quality level. This equipment can be accurate to within millionths of an inch and is frequently installed in environmentally controlled rooms. Gears are usually allowed to reach thermal equilibrium with the room before inspection. Most measuring machines have a stylus that follows the tooth form as the part is rotated. The details are charted at high magnification for intensive visual evaluation.Q-number ramificationsThe higher the quality number, the closer the actual geometry to what is specified. Higher geometric accuracy leads to improvements in several areas.If the gears are perfect, the driven gears angular velocity will be smooth and steady as long as the driving gear speed is constant. This comes with its rewards.With a constant angular speed, no acceleration will be imposed on the mass-elastic system of the gears and associated components. Without such acceleration, gear teeth are spared dynamic loads that deal out shock and impact, which further stress the gear teeth and generate noise. (Dynamic loads are not to be confused with the cyclic contact and bending loads gear teeth experience going in and out of mesh.)Dynamic loads that act on gear teeth are additions to the torque load. As the rotary power trains polar mass moment of inertia undergoes angular acceleration, the gears experience a dynamic torque component that couldtheoreticallybe established as:T = JaWhereJis the polar mass moment of inertia andais the angular acceleration specifically due to tooth geometry errors.Problematic gear noise is actually radiated (and amplified) by the gear drive housing; high sound levels dont come directly off the gears themselves. Nonuniform torque transmission ties in with dynamic (shock or impact) gear tooth loading that propagates into the shafts and bearings and ultimately into the housing, which then vibrates at all gear mesh frequencies, exciting the structure and the surrounding air to create noise.The problem, as noted, is rooted in the fluctuating torque transmission. This itself is caused by the involute tooth profile, tooth-to-tooth spacing variations, elastic deformation of gear teeth under load, and gear rim deflection. Some of these factors are obviously associated with AGMA quality parameters, and therefore a higher quality number means smoother torque throughput and lower noise.Designing and manufacturing for qualityWhen designing gears, the shape of the teeth under load and deflection must be considered. Gear teeth bend when transmitting torque, and thus it is the practice of designers to calculate the deflected gear shape and modify the true involute so the teeth will be correct under the operating load. There are other alterations that can be designed into the tooth geometry to minimize things like gear tip and edge loading across the face width.Some applications use adjustments down to tens of thousandths of an inch. Quality inspections of modified gear forms ensure conformance to the criteria for a given design and application rather than to the theoretically perfect shapes.As for manufacture, several common processes are used. Often gear teeth are formed on a blank by hobbing or shaping. Sometimes additional machining or finishing processes like shaving or grinding are applied, but often the hobbing or shaping is counted on to create the necessary final quality level.Surface hardening enables greater torque transmission and longer fatigue life, but can cause difficulties during processing. Surface hardness is generally instilled onto the gear teeth by heat treatment. One of the most common and effective heat-treating methods iscarburizing. In this process a heated steel gear is placed in a carburizing medium, containing carbon that diffuses into the surface (to itscase depth), enriching the surface beyond the rest of the steel in the gear. Its then quenched and tempered to approximately HRC 60. This produces high power density gearing, but the rapid quenching, which is the mechanism that develops the hardness in a carburized part, can distort the gear teeth and gear blank. Usually a grinding operation is performed after carburizing and hardening to reinstate the desired geometry. Grinding is a finishing operation, and is often costly, but it can shape with great accuracy and impart a superior surface smoothness.

ReferencesGears Educational Systems, LLCIntroduction to GearsKohara Gear Industry Co,. LTDMachine Design IIBy Prof. K.Gopinath and Prof. MayuramWikipediahttp://en.wikipedia.org/wiki/Epicyclic_gearinghttp://en.wikipedia.org/wiki/Transmission_(mechanics)

OTHERShttp://www.cam.ac.uk/research/news/functioning-mechanical-gears-seen-in-nature-for-the-first-timehttp://machinedesign.com/technologies/gear-quality-what-its-all-abouthttp://www.xtek.com/pdf/wp-gear-terminology.pdfhttp://www.me-mechanicalengineering.com/2014/06/gear-terminology.htmlhttps://www.bis.doc.gov/index.php/forms-documents/doc_view/80-gears-and-gearing-products-1992http://science.howstuffworks.com/transport/engines-equipment/gear8.htmhttp://www.cartertools.com/involute.html

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