Gears Review

7/31/2019 Gears Review

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Gear trains (Chapter 6)

Change torque, speed Why we need gears

Example: engine of a containership

Optimum operating speed of the engine about400 RPM

Optimum operating speed of the propellerabout 100 RPM

Need reduction gear


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Types of gears


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Gear box

Synchronizers

Stick shift

The gear box is in first gear, second gear


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Gear Nomenclature (6.1)


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Important definitions Velocity ratio=mV=angular velocity of output

gear/ angular velocity of input gear=pitch diameter

of input gear/pitch diameter of output gear

Torque ratio=mT=torque at output gear/torque atinput gear

mT=1/mV

Gear ratio=mG=Ngear/Npinion,mG is almost alwaysgreater than one


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Fundamental law oftooth gearing (6.2 and 6.3):velocity ratio must be constant as gears rotate

Angular velocity ratio= ratio

of distances of P from centers

of rotation of input and output

gear.

If common normal werefixed then the velocity ratio

would be constant.

PO

PO

3

2

2

3

3

T

3

2


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Generating gear teeth profile

P

Steps:Select base circles

Bring common normal AB

Draw involutes CD, EF


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Gear action

Angular velocity of

Gear 3 / angular

Velocity of gear 2 =

O2P/O3P = constant


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Fundamental law of gearing:The common normal of the tooth profiles

at all points within the mesh must always

pass through a fixed point on the line ofthe centers calledpitch point. Then the

gearsets velocity ratio will be constant

through the mesh and be equal to the ratioof the gear radii.


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Base circle radius =

Pitch circle radius cos


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Path of approach: BP=ua=[(r3+a)2-rb3

2]1/2-r3sin

Path of recess: PC=ur=[(r2+a)2-rb2

2]1/2-r2sin

Final contact: CInitial contact: B


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Standard gears: American Association of Gear

Manufacturers (AGMA) (6.4)

Teeth of different gears have same profile as long as the

angle of action and pitch is the same.

Can use same tools to cut different gears. Faster and

cheaper product. Follow standards unless there is a very

good reasons not to do so.


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Template for teeth of standard gears


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AGMA Specifications

Diametral pitch, pd=1, 1.25, 1.5,,120

Addendum of pinion = addendum gear

Observations

The larger the pitch, the smaller the gear

The larger the angle of action: the larger the

difference between the base and pitch circles,the steeper the tooth profile, the smaller the

transmitted force.


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AGMA Standard Gear Specifications

Parameter Coarse pitch

(pd=N/d20)Pressure angle, 200 or 250 (not common) 200

Addendum, a 1/pd 1/pd

Dedendum, b 1.25/pd 1.25/pd

Working depth 2.00/pd 2.00/pd

Whole depth 2.25/pd 2.2/pd+0.002

Circular tooth thickness 1.571/pd (circular pitch/2) 1.571/pd

Fillet radius 0.30/pd Not standardized

Clearance 0.25/pd 0.25/pd+0.002

Minimum width at top

land

0.25/pd Not standardized

Circular pitch /pd /pd


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1/pd

1.25/pd 1.571/pd

/pd

Min: 0.25/pd

0.3/pd

0.25/pd

d=N/pd


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Planetary (or Epicyclic) Gears (10.4)

Gears whose centers can move

Used to achieve large speed reductions in

compact space

Can achieve different reduction ratios by

holding different combinations of gears

fixed

Used in automatic transmissions of cars


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Planetary gear


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Planet

CarrierInput shaft

Sun gear

Ring gear

Components of a planetary gear


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A variant of a planetary gear

Carrier


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Planetary gears

Planetary gears in automotive

transmission


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Velocity Analysis Of Planetary Gears (10.6, 10.7)

Two degrees of freedom

Given the velocities of two gears (e.g. sun

and carrier) find velocities of other gears

Approach

Start from gear whose speed is given

Use equation gear = car+ gear/car


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Velocity analysis of planetary gear


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This program finds the velocities of the remaining links giventhe velocities of two links in a planetary gear.

Input:Number of teeth of sun, planet and ring gears, N1, N3, N4,respectively.

N1 30

N3 35

N4 100

Velocities of two links: specify the known values of the inputsand guess the values of the outputs:

3 100

4 120

1 100

2 100

12 100

Given

3 0

4 1

1 2 12


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1224

1223

1221

4

1

3

1

N

N

N

N


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Find

1 2 3 4 12

3.333

1.538

0

1

1.795

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