# Gear and Gear trains

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13-Apr-2017Category

## Engineering

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Gears

Gears!

Gears are most often used in transmissions to convert an electric motors high speed and low torque to a shafts requirements for low speed high torque:Speed is easy to generate, because voltage is easy to generateTorque is difficult to generate because it requires large amounts of currentGears essentially allow positive engagement between teeth so high forces can be transmitted while still undergoing essentially rolling contactGears do not depend on friction and do best when friction is minimized

Gears A gear is a wheel with teeth on its outer edge. The teeth of one gear mesh (or engage) with the teeth of another.AboveGears meshing or engaged

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GearsDriver and Driven

Two meshed gears always rotate in opposite directions.

Driver gearDriven gear

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GearsIdler gearDriverDrivenIdler gear

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Spur GearsTeeth are parallel to the axis of the gearAdvantagesCostEase of manufactureAvailabilityDisadvantagesOnly works with mating gearAxis of each gear must be parallel

Helical GearsTeeth are at an angle to the gear axis (usually 10 to 45) called helix angleAdvantagesSmooth and quiet due to gradual tooth engagements (spur gears whine at high speed due to impact). Helical gears good up to speeds in excess of 5,000 ft/minMore tooth engagement allows for greater power transmission for given gear size.

DisadvantageMore expensiveResulting axial thrust component

Helical 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 causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears. Helical gears also offer the possibility of using non-parallel shafts. A pair of helical gears can be meshed in two ways: with shafts oriented at either the sum or the difference of the helix angles of the gears. These configurations are referred to as parallel or crossed, respectively. The parallel configuration is the more mechanically sound. In it, the helices of a pair of meshing teeth meet at a common tangent, and the contact between the tooth surfaces will, generally, be a curve extending some distance across their face widths. In the crossed configuration, the helices do not meet tangentially, and only point contact is achieved between tooth surfaces. Because of the small area of contact, crossed helical gears can only be used with light loads.Quite commonly, helical gears come in pairs where the helix angle of one is 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. If such a pair is meshed in the 'parallel' mode, the two equal but opposite angles add to zero: the angle between shafts is zero -- that is, the shafts are parallel. If the pair is meshed in the 'crossed' mode, the angle between shafts will be twice the absolute value of either helix angle.Note that 'parallel' helical gears need not have parallel shafts -- this only occurs if their helix angles are equal but opposite. The 'parallel' in 'parallel helical gears' must refer, if anything, to the (quasi) parallelism of the teeth, not to the shaft orientation.As mentioned at the start of this section, helical gears operate more smoothly than do spur gears. 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. It may span the entire width of the tooth for a time. Finally, it recedes until the teeth break contact at a single point on the opposite side of the wheel. Thus force is taken up and released gradually. With spur gears, the situation is quite different. When a pair of teeth meet, they immediately make line contact across their entire width. This causes impact stress and noise. Spur gears make a characteristic whine at high speeds and can not take as much torque as helical gears because their teeth are receiving impact blows. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity (that is, the circumferential velocity) exceeds 5000 ft/min.[3] A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding friction between the meshing teeth, often addressed with specific additives in the lubricant*

Helical GearsMating gear axis can be parallel or crossedCan withstand the largest capacity at 30,000 hp

Bevel GearsGear axis at 90, based on rolling conesAdvantagesRight angle drivesDisadvantagesGet axial loading which complicates bearings and housings

Spiral Bevel Gears

Same advantage over bevel gears as helical gears have over spur gears!!Teeth at helix angleVery StrongUsed in rear end applications (see differentials)

Worm GearsGears that are 90 to each otherAdvantagesQuiet / smooth driveCan transmit torque at right anglesNo back drivingGood for positioning systemsDisadvantageMost inefficient due to excessive friction (sliding)Needs maintenanceSlower speed applications

wormworm gear

Gears Multiple gears can be connected together to form a gear train.

Simple Gear TrainEach shaft carries only one gear wheel.Intermediate gears are known as Idler Gears.

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GearsCompound Gear TrainDriverCompound Gear DrivenIf two gear wheels are mounted on a common shaft then its a Compound Gear train.

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Gears Generally, the Gear Ratio is calculated by counting the teeth of the two gears, and applying the following formula:

Gear ratio = Number of teeth on driven gear Number of teeth on driver gearGear Ratio

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GearsGear Ratio - CalculationA 100 tooth gear drives a 25 tooth gear. Calculate the gear ratio for the meshing teeth.Gear ratio = Number of teeth on driven gear Number of teeth on driver gearGear ratio = driven25=1 driver 1004This is written as 1:4

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GearsGear Speed :- CalculationA motor gear has 28 teeth and revolves at 100 rev/min. The driven gear has 10 teeth. What is its rotational speed?Speed of driven gear = Number of teeth on driver gear x 100 Number of teeth on driven gearSpeed of driven gear = driver =28 x 100 = 280 rev/min driven10

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Gears The worm gear is always the drive gear

Worm gear and wheel

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GearsThe rack and pinion gear is used to convert between rotary and linear motion.

Rack and Pinion Heavy Duty Car Jack

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GearsBevel gears are used to transfer drive through an angle of 90o.

Bevel Gears Bevel gears

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Gears used for Speed ReducerRecall the main purpose of mating/meshing gears is to provide speed reduction or torque increase.

PinionnP NPGearnG NG

Example:Want a 3:1 reductionNP=22 teethWhat is NG?Solution:VR = 3 = NG/NP

NG = 3*22 = 66 teeth

Figure 8-15, pg. 322

EnginePump

n1, N1n2, N2n3, N3n4, N4Given:n1 = 500 rpm, N1 = 20tN2 = 70t, N3 = 18t, N4 = 54tFind: n4Example: Double Speed ReducerSolution: n2 = 500 rpm*(20/70) = 142.8 rpmn3 = n2n4 = 142.8 rpm*(18/54) = 47.6 rpmTotal reduction = 500/47.6 = 10.5 (0r 10.5:1)

Torque?? Increases by 10.5!!Power?? Stays the same throughout!

Gear NomenclatureN = Number of teethUse subscript for specific gearNP=Number of teeth on pinion (driver)NG=Number of teeth on gear (driven)NP < NG (for speed reducer)NA=Number of teeth on gear ACircular Pitch, P is the radial distance from a point on a tooth at the pitch circle to corresponding point on the next adjacent tooth P=(p*D)/N

Gear NomenclatureGear Train Rule Pitch of two gears in mesh must be identical

pDGNG=PpDPNP

GEARPINION

Gear NomenclatureDiametral Pitch, (Pd) Number of teeth per inch of pitch diameter

*Two gears in mesh must have equal Pd:

*Standard diametral pitches can be found in Table 8-1 and 8-2DN=PdDGNG==PdDPNP

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Helical 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 causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears. Helical gears also offer the possibility of using non-parallel shafts. A pair of helical gears can be meshed in two ways: with shafts oriented at either the sum or the difference of the helix angles of the gears. These configurations are referred to as parallel or crossed, respectively. The parallel configuration is the more mechanically sound. In it, the helices of a pair of meshing teeth meet at a common tangent, and the contact between the tooth surfaces will, generally, be a curve extending some distance across their face widths. In the crossed configuration, the helices do not meet tangentially, and only point contact is achieved between tooth surfaces. Because of the small area of contact, crossed helical gears can only be used with light loads.Quite commonly, helical gears come in pairs where the helix angle of one is the negative of the helix a

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