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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 about 400 RPM Optimum operating speed of the propeller about 100 RPM Need reduction gear . Connecting the main engine to the propeller

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gear trains chapter 6
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
slide2

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

gear box
Gear box

Stick shift

Synchronizers

The gear box is in first gear, second gear

important definitions
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
fundamental law of tooth gearing 6 2 and 6 3 velocity ratio must be constant as gears rotate
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

if gear tooth profile is that of involute curve then fundamental law of gearing is satisfied
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

generating gear teeth profile
Generating gear teeth profile
  • Steps:
  • Select base circles
  • Bring common normal AB
  • Draw involutes CD, EF

P

gear action
Gear action

Angular velocity of

Gear 3 / angular

Velocity of gear 2 =

O2P/O3P = constant

slide11

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.

slide12

Base circle radius =

Pitch circle radius cos

slide13

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

standard gears american association of gear manufacturers agma 6 4
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.

agma specifications
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.
slide18

Min: 0.25/pd

1/pd

/pd

1.571/pd

1.25/pd

d=N/pd

0.25/pd

0.3/pd

planetary or epicyclic gears 10 4
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
slide21

Planet

Carrier

Input shaft

Sun gear

Ring gear

Components of a planetary gear

velocity analysis of planetary gears 10 6 10 7
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