1. Gear trains (Chapter 6) Change torque, speed Why we need gears
Example: engine of a containership
Optimum operating speed of the engine about 400 RPM
Optimum operating speed of the propeller about 100 RPM
Need reduction gear

2. Connecting the main engine to the propeller through a reduction gear
Output flange
Propeller,
operates at about 100 RPM
Engine
Gear
Engine operates at
about 400 RPM

3. Types of gears

4. Gear box Stick shift Synchronizers
The gear box is in first gear, second gear

5. Gear Nomenclature (6.1)

6. 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 at input gear
mT=1/mV
Gear ratio=mG=Ngear/Npinion, mG is almost always greater than one

7. If common normal were fixed then the velocity ratio would be constant.
Fundamental law of tooth 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 were fixed then the velocity ratio would be constant. 2 T 3 3

8. If gear tooth profile is that of involute curve then fundamental law of gearing is satisfied
Involute curve: path generated
by a tracing point on a cord as the cord
is unwrapped from base cylinder

9. Generating gear teeth profile
Steps:
Select base circles
Bring common normal AB
Draw involutes CD, EF P

10. Gear action Angular velocity of Gear 3 / angular Velocity of gear 2 =
O2P/O3P = constant

11. 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 of the centers called pitch point. Then the gearset’s velocity ratio will be constant through the mesh and be equal to the ratio of the gear radii.

12. Pitch circle radius cos
Base circle radius =
Pitch circle radius cos

13. Path of approach: BP=ua=[(r3+a)2-rb32]1/2-r3sin
Initial contact: B
Final contact: C
Path of approach: BP=ua=[(r3+a)2-rb32]1/2-r3sin
Path of recess: PC=ur=[(r2+a)2-rb22]1/2-r2sin

14. Standard gears: American Association of Gear Manufacturers (AGMA) (6
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.

15. Template for teeth of standard gears

16. 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.

17. AGMA Standard Gear Specifications
Parameter
Coarse pitch (pd=N/d<20)
Fine pitch (pd=N/d>20)
Pressure angle, 
200 or 250 (not common)
200
Addendum, a
1/pd
Dedendum, b
1.25/pd
Working depth
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
Circular pitch
/pd

18. Min: 0.25/pd
1/pd
/pd
1.25/pd
1.571/pd
d=N/pd
0.25/pd
0.3/pd

19. 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

20. Planetary gear

21. Components of a planetary gear
Carrier
Input shaft
Sun gear
Ring gear

22. A variant of a planetary gear
Carrier

23. Planetary gears in automotive transmission

24. 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