Power

Determining Rotational Power Requirements

• Assumption; We know the torque (T) nad shaft rotational speed (w)
• Background;
  • Force; a push or a pull
  • W=Fxd
  • P=W/t
• Power Formula for Rotation
  • P=t*w (P - Watts, t - Newton metrers, w - radians/second)
• Qualitative Discussion Relating Power to Rotating Equipment
  • Do we have power when t=0 ?
  • Do we have power when w=0 ?
• Units
  • All units are familiar except the radian
  • Definition of a Radian
    • What is a radian an measure of ?
  • How many radians in a revolution ?
• Converting Units
  • Three principles
    • if x=y then x/y=1 or y/x=1
      • 2p radians = 1 revolution, therefore; 2p radians/1revolution =1
      • 60 seconds = 1 minute, therefore; 1minute/60seconds=1
    • you can multiply anything by 1 without changing it
      • eg 100 (rev/min)
      • =100 (rev/min)*1*1
      • =100 (rev/min)*(2p rad/rev)*(1min/60sec)
    • treat units like algebraic variables
      • 100 (rev/min)*(2p rad/rev)*(1min/60sec)
      • =100*2p/60 (rev*rad*min/min*rev*sec)
      • =100*2p/60 (rad/sec)
      •  
• Developing a Formula in Different Units using Dimensional Analysis
  • Example A Power formula using Watts, Newton meters and RPM
    • steps
      • Write out the formula with units
        • P(W)=t(Nm)*w(rad/s)
          • Writing the units only shows this makes sense since W=N*m*rad/s (note a rad is dimensionless)
      • Write out the equation with the units we wish to use
        • P(W)¹t(Nm)*w(rev/min)
          • [note: This is an inequality since the units on the RHS dont match with the units on the LHS of the equal sign.]
        • Look at only the units
          • W¹N*m*rev/min
          • Since a watt is a N*m*rad/s we must add conversions to make rev/min to rad/s, therefore multiply by 1min/60s*2prad/1rev
        • P(W)=t(Nm)*w(rev/min)*1min/60s*2prad/1rev [note: this an equality since units match]
        • P=2p/60*t*w for P - (W), t - (Nm), w - RPM
        • P=p/30*t*w for P - (W), t - (Nm), w - RPM ,(final equation)
          • to check do the equation with units only including conversion factors(W)=(N*m*rev*min*rad/min*sec*rev)
          • (W)=(N*m*rad/s), checks out
• Note 1HP = 745.7 W
• Assignment
  • Calculate the power required in each joint of the robot arm.
  • Bonus; Complete this calculation on a spreadsheet.
• Efficiency
  •  
  • n=Output Power/Input Power