t13 introduction to gear trains

7/30/2019 T13 Introduction to Gear Trains

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Introduction toGear Trains

Zhengjian XU

29th OCT 2008


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Introduction to gear trains

Gear Types

Spur gear: gear with radial teeth parallel to its axis

Rack & Pinion a toothed wheel (pinion) engages a notched bar (rack)to convert rotary motion into linear motion

Bevel Gear Either of a pair of toothed wheels whose workingsurfaces are inclined to nonparallel axes.

pinion

Rack


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Gear Types Helical gear: a gear that has the teeth cut at an angle to the center line of the

gear. This kind of gear is useful because there is no chance of intermittent tooth-to-tooth operation because there are at least two teeth engaged at any time. It canoperate quieter than spur gear.

Worm gear:

Harmonic gear:The harmonic gear allows highreduction ratios with concentric shafts and with verylow backlash and vibration. It is based on a very simple

construction utilising metals elasto-mechanical property

A worm is used to reduce speed. Foreach complete turn of the wormshaft the gear shaft advances onlyone tooth of the gear.

Unlike ordinary gears, the motion isnot reversible, a worm can drive agear to reduce speed but a gearcannot drive a worm to increase it.


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Gear Types Herringbone gear:The two helix angle come together in the center of the gear face to form a 'V.

Differential gear: A vehicle's wheels rotate at different speeds,especially when turning corners. The differential is designed to drive a pairof wheels with equal force, while allowing them to rotate at different speeds

Input torque is applied to the ring gear (blue), which turns theentire carrier (blue), providing torque to both side gears (red andyellow), which in turn may drive the left and right wheels. If theresistance at both wheels is equal, the planet gear (green) doesnot rotate, and both wheels turn at the same rate.

If the left side gear (red) encounters resistance, theplanet gear (green) rotates about the left side gear,in turn applying extra rotation to the right side gear(yellow).


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Kinematics of Gears

Fundamental law of gearing: Angular velocity Ratio is constantthroughout the mesh.


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Gear tooth nomenclature

Pitch circle: A circle the radius of which isequal to the distance from the gear axis tothe pitch point. .

Addendum circle: A circle bounding theends of the teeth, in a right section of thegear.

Root (or dedendum) circle: The circlebounding the spaces between

the teeth, in a right section of the gear. Addendum: The radial distance between

the pitch circle and the addendum circle.

Dedendum: The radial distance betweenthe pitch circle and the root circle. Clearance: The difference between the

dedendumof one gear and the addendumof the mating gear.


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Face of a tooth: That part of thetooth surface lying outside the pitchsurface.Flank of a tooth: The part of thetooth surface lying inside the pitchsurface.Circular thickness (also called thetooth thickness) : The thickness ofthe tooth measured on the pitchcircle. It is the length of an arc andnot the length of a straight line.Fillet : The small radius thatconnects the profile of a tooth to the

root circle.


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Figure shows two teeth of a gear with thestandard nomenclature defined.

Since


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Tooth contact nomenclature

Point of contact: any point at which two toothprofiles touch each other.

Path of action: the locus of successivecontact points between a pair of gear teeth,during the phase of engagement.

Line of action:The line of action is thepath of action for involute gears. It is thestraight line passing through the pitch pointand tangent to both base circles.


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Tooth contact nomenclatureLine of contact: a line or curve along whichtwo tooth surfaces are tangent to each other

Surface of action: the imaginary surface inwhich contact occurs between two engagingtooth surfaces.

Plane of action: the surface of action forinvolute, parallel axis gears with eitherspur or helical teeth. It is tangent to thebase cylinders.

Line of contact


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Gear tooth nomenclature Generation of the Involute

Curve

This involute curve is the

path traced by a point on aline as the line rolls withoutslipping on thecircumference of a circle. Itmay also be defined as a

path traced by the end of astring which is originallywrapped on a circle whenthe string is unwrapped from

the circle. The circle fromwhich the involute is derivedis called the base circle.


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The pressure angle is the angle between the line ofaction and the common tangent. (has been standardized14.50 200 250)


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Gear tooth nomenclature Minimum number of Teeth


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Simple gear train

From the fundamental law of gearing

The sign -is necessary to take into account the change in directionof rotation.

The sign +is also to take into account the change in direction ofrotation for internal gear.


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Planar gear trainsExample: Find the output angular velocity for the planetary gear

train shown when the input angular velocity W4= 50 rad/secconterclokwise.

Solution:

The velocity of point A

Also the velocity of A can be expressed

Then we get


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Planar gear trains Letting r2=Pc*n2, r3=Pc*n3

Using the tooth relationship to replace theradii

Substituting back into the other equation


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Find the speed reductions possible for the transmission

The power is transmitted through gears

0-4-5-6-10-12 for this instant status.

From the fundamental law of gearings

We get:

If the gear 3-4 slides to the left (disengaging gear

4-5) and gear 1-2 to the left (engaging 1-9) thenthe power is transmitted through 0-1-9-6-10-12.

t13 introduction to gear trains

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