gears review
TRANSCRIPT
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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