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OutlineGear TheoryNomenclatureGear Trains
Fundamental Law of GearingFunctionally, a gearset is a device to exchange torque for velocity
P=Tωthe angular velocity ratio of the gears of a gearset must remain constant throughout
the mesh
in
out
in
outV r
rm ==ωω
Towards the Involute ProfileA belt connecting the two cylinders
line of action, pressure angle φ
The Involute Profile
Meshing
pressure angle, line of action, length of action, addendum
Nomenclature
Figure 11-8
Ndpcπ
=
2
Pitches, Etc.
circular pitch (mm, in.)
base pitch (mm, in.)
diametral pitch (teeth/in.)
module (mm/teeth)
Ndpc
π=
φcoscb pp =
dNpd =
Ndm =
Velocity Ratiopitches must be equal for mating gears, therefore
in
out
in
outV N
Nrrm ±=±=
Contact Ratio
average number of teeth in contact at any one time =
length of action divided by the base pitch, or,
φπ cosZpm d
p =
( ) ( ) ( ) ( ) φφφ sincoscos 2222 CrarrarZ gggppp −−++−+=
where C=center distance=(Ng+Np)*1/pd*1/2
Minimum # of Teethminimum # of teeth to avoid undercutting with gear and rack
φ2min sin2
=N
OutlineGear TheoryNomenclatureGear Trains
Simple Gear Trains
3
Simple Gear Train
R
B
R
P
P
Bv N
NNN
NNm =⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
Velocity Ratio
R
B
R
G
G
P
P
Black
Black
Y
Y
Bv N
NNN
NN
NN
NN
NNm −=⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
Simple Gear TrainFine for transmitting torque between
shafts in close proximitywhen mv does not need to be too large
Use third gear (“idler”) only for directional reasons (not for gear reduction)
Reverse on a Car
Actual Manual Transmission For More OnlineAGMAHow Stuff Works Gears
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