Chapter 8 Notes Cams

1
MENG 372Chapter 9Gears
All figures taken from Design of Machinery, 3rd
ed. Robert Norton 2003
2
Rolling Cylinders

• Gear analysis is based on rolling cylinders
• External gears rotate in opposite directions
• Internal gears rotate in same direction

3
Gear Types

• Internal and external gears
• Two gears together are called a gearset

4
Fundamental Law of Gearing

• The angular velocity ratio between 2 meshing
  gears remains constant throughout the mesh
• Angular velocity ratio (mV)
• Torque ratio (mT) is mechanical advantage (mA)

Input
Output
5
Involute Tooth Shape

• Shape of the gear tooth is the involute curve.
• Shape you get by unwrapping a string from around
  a circle
• Allows the fundamental law of gearing to be
  followed even if center distance is not maintained

6
Meshing Action
7
Contact Geometry

• Pressure angle (f) angle between force and motion

8
Fundamental Law of Gearing

• The common normal of the tooth profiles, at all
  contact points within the mesh, must always pass
  through a fixed point on the line of centers,
  called the pitch point

9
Change in Center Distance

• With the involute tooth form, the fundamental law
  of gearing is followed, even if the center
  distance changes
• Pressure angle
• increases

10
Backlash

• Backlash the clearance between mating teeth
  measured at the pitch circle
• Whenever torque changes sign, teeth will move
  from one side of contact to another
• Can cause an error in position
• Backlash increases with increase in center
  distance
• Can have anti-backlash gears (two gears, back to
  back)

11
Gear Tooth Nomenclature

• Circular Pitch, pcpd/N
• Diametral Pitch (in 1/inch), pdN/dp/pc
• Module (in mm), md/N

12
Interference and Undercutting

• Interference If there are too few pinion teeth,
  then the gear cannot turn
• Undercutting part of the pinion tooth is
  removed in the manufacturing process

For no undercutting For no undercutting
f (deg) Min teeth
14.5 32
20 18
25 12
13
Gear Types

• Spur Gears
• Helical Gears (open or crossed)
• Herringbone Gears
• Worm Gears
• Rack and Pinion
• Bevel Gears

14
Spur Gears

• Straight teeth
• Noisy since all of the tooth contacts at one time
• Low Cost
• High efficiency (98-99)

15
Helical Gears

• Slanted teeth to smooth contact
• Axis can be parallel or crossed
• Has a thrust force
• Efficiency of 96-98 for parallel and 50-90 for
  crossed

16
Crossed Helical Gears
17
Herringbone Gears

• Eliminate the thrust force
• 95 efficient
• Very expensive

18
Rack and Pinion

• Generates linear motion
• Teeth are straight (one way to cut a involute
  form)

19
Worm Gears

• Worm gear has one or two teeth
• High gear ratio
• Impossible to back drive
• 40-85
• efficient

20
Bevel Gears

• Based on rolling cones
• Need to share a common tip

21
Other Gear Types

• Noncircular gears give a different velocity
  ratio at different angles
• Synchronous belts and sprockets like pulleys
  (98 efficient)

22
Simple Gear Trains

• Maximum gear ratio of 110 based on size
  constraints
• Gear ratios cancel each other out
• Useful for changing direction
• Could change direction with belt

23
Compound Gear Trains

• More than 1 gear on a shaft
• Allows for larger
• gear train ratios

24
Compound Train Design
2
If N2N4 and N3N5
4
3
Reduction ratio
5
Will be used to determine the no. of stages given
a reduction ratio
2 stages
25
Compound Train Design

• Design train with gear ratio of 1801
• Two stages have ratio too large
• Three stages has ratio
• At 14 teeth
• actual ratio is
• OK for power
• transmission
• not for phasing

Pinion Teeth ratio Gear teeth
12 5.646 67.7546
13 5.646 73.4008
14 5.646 79.0470
15 5.646 84.6932
16 5.646 90.3395
26
Compound Train Design Exact RR

• Factor desired ratio 18022x32x5
• Want to keep each ratio about the same (i.e.
  6x6x5)
• 14x684
• 14x570
• Total ratio

We could have used 1802x902x2x452x2x5x94x5x9
or 4.5x6x(20/3) etc.
27
Manual Transmission
28
Manual Synchromesh Transmission

• Based on reverted compound gears

29
Reverted Compound Train

• Input and output shafts are aligned
• For reverted gear trains
• R2R3R4R5
• D2D3D4D5
• N2N3N4N5
• Gear ratio is

Commercial three stage reverted compound train
30
Design a reverted compound gear train for a gear
ratio of 181

• 183x6 N36N2, N53N4
• N2N3N4N5constant
• N26N2N43N4C
• 7N24N4C
• Take C28, then N24, N47
• This is too small for a
  gear! Choose C28x4112 (say)
• N216, N396,
• N428, N584

31
Planetary or Epicyclic Gears

• Conventional gearset has one DOF
• If you remove the ground at gear 3, it has two
  DOF
• It is difficult to access w3

32
Planetary Gearset with Fixed Ring
Planetary Gearset with Fixed Arm
33
Planetary Gearset with Ring Gear Output

• Two inputs (sun and arm) and one output (ring)
  all on concentric shafts

34
Different Epicyclic Configurations

• Gear plots are about axis of rotation/symmetry

35
Compound Epicycloidal Gear Train

• Which picture is this?

36
Tabular Method For Velocity Analysis

• Basic equation wgearwarmwgear/arm
• Gear ratios apply to the relative angular
  velocities

Gear wgear warm wgear/arm Gear ratio
Gear ratio







37
Example
Given Sun gear N240 teeth Planet gear N320
teeth Ring gear N480 teeth warm200 rpm
clockwise wsun100 rpm clockwise Required Ring
gear velocity wring
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Tabular Method For Velocity Analysis
N240, N320, N480 warm -200 rpm
(clockwise) wsun -100 rpm (clockwise)
Sign convention Clockwise is negative
(-) Anti-clockwise is positive()
Gear ratio
Gear wgear warm wgear/arm
2
3
4
100
-200 -200 -200
-100
-200
- 400
-50
-250
w4 - 250 rpm
39
Tabular Method For Velocity Analysis

• N240, N320, N430, N590
• warm-100, wsun200

Gear wgear warm wgear/arm Gear ratio
Gear ratio







Gear wgear warm wgear/arm Gear ratio
2 200 -100 300 Gear ratio
2 200 -100 300 -40 20
3 -100 -600 -40 20
3 -100 -600 1
4 -100 -600 1
4 -100 -600 30 90
5 -300 -100 -200 30 90
5 -300 -100 -200
40
Equation Method For Velocity Analysis

• N240, N320, N430, N590
• warm-100rpm, wsun200