Gear Physics and Math

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Gear Physics and Math

• Peter Wittenberg

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What We Will Cover

• The Key Parameters
• Force
• Torque
• Speed
• Why We Use Gears
• Gear pairs
• Compound Gears
• Compound Gear Examples
• Compound Gear Calculations

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What You Should Know About Gears When We Finish
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The Key Gear Physics Parameters

• Force - the push or pull (pounds)
• Except for accelerating objects, forces balance
• Torque - a version of force for rotating objects
  (foot pounds)
• Torque constant anywhere on a rotating shaft
• Speed - how fast something rotates (revolutions
  per minute)

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Why do we Use Gears?

• Motor - Almost Constant Speed and Power
  Requirement
• Jet engine - 25,000 horsepower (20 MW) _at_ 6000 to
  10000 rpm
• Car engine example - 100 horsepower (75 kW) _at_
  3000 rpm
• Human bicycling - 0.1 horsepower (75 W) _at_ 80 rpm
• Power requirements vary
• Level surface power requirement
• Uphill power requirements higher
• Gears allow a Speed / Torque Tradeoff
• no free lunch - you cant increase speed and
  torque
• Gearing up reduces speed and increases torque
• Gearing down increases speed and reduces torque

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Gear pairs

• Gears Meshing on two axles
• The Gears program on the Macintosh
• Constant force - the gear teeth force must be
  equal
• Speed decreases and torque increases on move to
  larger gear
• Speed increases and torque decreases on move to
  smaller gear
• Gears on the same axle
• Constant torque and speed - the same shaft drives
  the two gears
• Force decrease on move to larger gear
• Force increase on move to smaller gear

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Breaking Compound Gears into Gear Pairs

• All compound gears are combinations of the two
  types
• Two gears with meshing teeth
• Two gears on the same shaft
• Procedure
• Start at the motor - find the first two gears
• Identify the gear that takes power from that.
  This is the next pair
• Continue in this way until the last gear in the
  chain is found.

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Compound Gear Decomposition
75
45
15
The last 75 drives the wheels

• Gears Shafts Torque Force Speed
• Motor T F S
• 15 to 45 different 3T F S/3
• 45 to 15 same 3T 3F S/3
• 15 to 75 different 53T 3F S/3/5
• 75 to 45 same 53T 3(75/45)F S/3/5
• 45 to 75 different 53(75/45)T 3(75/45)F S/3/5
  /(75/45)

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Compound Gear Examples
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Compound Gear Calculations