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2/19/2008
Calculations for Accumulator Sizing
Based on the following input:
      Engine: CAT 3512 - 3158 cu.in. displacement
      Min Cranking RPM: 120
      Number of Teeth on Flywheel: 183
      Number of Teeth on Starter Pinion: 11
      Ambient Temp: 100°F (560°Rankin)
      Accumulator Precharge: 1650psi w/N2
      Accumulator Gross Volume: 60 gal ((4) 15 gal units)
      Starter Motor Displacement: 5.1 in³/rev
      Accumulator Pressure - Hydraulic (fully charged): 2800psi
      Cranking Time Required: 30 seconds ((3) 10 second cranks)
      Customer prefers (3) accumulators, (4) max
 
Cranking Oil Volume Required:
      Cranking speed times the ratio of teeth in the drive gears
      120 rev/min x 183/11 = 1996 rpm
 
Flow Rate of Oil Required:
      Displacement of the cranking motor divided by 231 to convert to gallons times motor rpm
      5.1 in³/rev x 1996 rpm / 231 in³ per gallon = 44 gpm
 
Gallons of Oil Required:
      Flow rate times cranking time required
      44 gal/min x 30 seconds / 60 seconds per min = 22 gallons
 
Accumulator Volume Available:
      Using the equation: (P1V1) / T1 = (P2V2) / T2
 
      Where P = Pressure is in psi
            V = Volume is in gallons
            T = Temperature is in degrees Rankin (F+460 = Degrees
Rankin)
            to derive the nitrogen volume.
 
      Nitrogen volume from fully charged to fully discharged is:
      2800V1 / 560 = 1650 x 60 / 528
      V1 = 37.5
 
      Oil volume from fully charged to fully discharged is:
      60 total volume - nitrogen volume = 60 - 37.5 gallons = 22.5 gallons
 
CONCLUSION:
With 22.5 gallons available and 22 gallons required, the use of (4) 15 gallon accumulators is adequate for the required cranking speed and time.


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