Calculations for Accumulator Sizing
Posted: Friday, February 01, 2008
by Tim New
Hydra Kinetics, Inc.
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: