Air CutOff Tool

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Air Cut-Off Tool

• How, What, Why, and How Fast

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Purpose To cut things off!

• Typical applications include cutting
• mufflers and tail pipes,
• sheet metal,
• fiberglass,
• nuts,
• bolts,
• muffler clamps
• hangers,
• and grinding down burrs and rough
• edges.

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How does it work?!?
4
How does it work?!?
5
Which came first, the air motor or the air
cut-off tool?

• First patent date found for a sliding vane motor
  was 1805/1865 (date unreadable)

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How much air is consumed?

• dmc/dt rhoAsqrt(2RT(K/(K1))(2/(K1))(2/(K-1
  )))
• Initial pressure 90 PSI 621,000 Pa
• Assumed smallest hole (1 mm radius) is choke
  point
• Mol. Weight of air is .029 kg/mol
• T 273 K
• R 8.314 (Pam3)/(molK)
• Computed value of dmc/dt 4.62 x 10-3 kg/s
• ...or 8.157 CFM (air at 1.2 kg/m3 - atmospheric)
• Given value 4.4 CFM
• Error? Possibly wrong choke pointif we consider
  one with half the area, our answer would be
  correct.

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How fast?

• Revolutions/second (Input volume/second) /
  (chamber volume/revolution)
• Initial volume/second 4.62x10-3 kg/s (7.39
  kg/m3)-1
• or .000625 m3/s
• From SolidWorks initial single sealed chamber
  volume 1.51 x 10-6 m3
• Multiply volume by 4 (four chambers) multiply
  final answer by 60 (seconds to minutes)
• Result 6,210 Actual 20,000
• Error? Wrong chamber volume, or density/pressure
  of air? If air was at a fourth of the pressure,
  there would be 4 times the number of
  revolutionsa better answer.
• Reasoning Chambers do not have time to fill all
  the way when motor is spinning fast, and
  therefore pressure IS less solves error.
• Sadly, if we only accounted for one chamber, the
  number would be a lot closer

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How hard?

• Torque Force vector (cross product) moment arm
• Requires Integral Calculus(puke)
• Apply to each rotor face
• Formula after integrationPlr2/2 from rin to
  rout
• Assuming cancellation of some faces to simplify
  equations gives
• 1.73 Nm for stalled torque.

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This learned me well

• Physics can create EVIL problems
• Sliding vane motors are really cooland even
  though the physics is tough, the concept is
  fairly simple, yet truly amazing.
• I learned a lot about SolidWorks, and learned
  that some problems just get harder as they go.
  Real world models can be VERY hard to
  mathematically model
• Choked flowor at least the basics of it. Some
  of the concepts never quite made sense, no matter
  what I readand Im still unsure about whether
  the pressure drop exists...

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Bye!