Formula Sheet: Gear Trains | Theory of Machines (TOM) - Mechanical Engineering PDF Download

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Gear Trains
1. Types of Gear Trains
• Simple Gear Train
• Compound Gear Train
• Reverted Gear Train
• Epicyclic (Planetary) Gear Train
2. Gear Terminology
• N: Speed of rotation (rpm)
• T: Number of teeth
• ?: Angular velocity
• d: Pitch circle diameter
3. Velocity Ratio
For two meshing gears:
N
1
N
2
=
T
2
T
1
=
d
2
d
1
4. Simple Gear Train
For a train with several gears:
N
driver
N
driven
=
T
driven
T
driver
*Idler gears do not affect velocity ratio but change direction.*
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Gear Trains
1. Types of Gear Trains
• Simple Gear Train
• Compound Gear Train
• Reverted Gear Train
• Epicyclic (Planetary) Gear Train
2. Gear Terminology
• N: Speed of rotation (rpm)
• T: Number of teeth
• ?: Angular velocity
• d: Pitch circle diameter
3. Velocity Ratio
For two meshing gears:
N
1
N
2
=
T
2
T
1
=
d
2
d
1
4. Simple Gear Train
For a train with several gears:
N
driver
N
driven
=
T
driven
T
driver
*Idler gears do not affect velocity ratio but change direction.*
1
5. Compound Gear Train
If multiple gears are mounted on the same shaft:
VR =
N
1
N
4
=
T
2
· T
4
T
1
· T
3
6. Reverted Gear Train
In a reverted gear train:
VR =
T
2
· T
4
T
1
· T
3
, and d
1
+d
2
=d
3
+d
4
7. Epicyclic Gear Train
Case: Arm fixed, sun and planet gears rotating
If gear A (sun) is fixed and gear B rotates about A using arm:
N
B
- N
arm
N
A
- N
arm
= - T
A
T
B
Steps to Solve Epicyclic Gear Trains:
1. Assume arm is fixed: calculate relative motions.
2. Add a constant to all motions to account for arm rotation.
3. Use constraints to solve for unknowns.
8. Train Value
Train Value =
1
Velocity Ratio
=
N
driven
N
driver
9. Direction of Rotation
Each meshing gear reverses direction. If even number of gears: driver and driven rotate in
the same direction. If odd: opposite.
10. Torque in Gear Train
T =F · r =
P
?
Where T is torque, F is tangential force, r is pitch radius.
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