Force on the Core
Before determining the requirements of the side-action, calculating force on the core is essential. Seal offs, core length and other factors notwithstanding, the designer can simply use maximum projected area and injection pressure to calculate core force.

• Maximum Projected Area (C) in square inches is found by sectioning the core at the largest point exposed to plastic.
• Maximum Injection Pressure (P) is nozzle pressure in psi (hydraulic ram injection pressure x 10).
• Core Force (F) = P x C.
  For 20,000 psi and a 2" dia. pin:
  F = (20,000 psi)(3.14 sq.in.) = 62,800 lbs.

While methods 1 and 2 use heel blocks to final position the core, flex and compression is often a problem. More robust preloading methods 3 (with pressure) and 4 (without pressure), eliminate these issues, but require the ability to calculate core and cylinder forces.

Cylinder Basics
Cylinder Push/Extend Force (M) and Cylinder Pull/Retract Force (N) is calculated as follows:

M = H x [(3.14xB})/4]
N = H x [(3.14xB})/4 - (3.14xR2)/4]
H = Hydraulic supply pressure (psi)
B= Bore diameter of cylinder (in.)
R= Rod diameter of cylinder (in.)

Note for pull, rod area subtracts from the piston area. Retract Force is critical when considering friction from material shrinkage.

Cylinder Sizing

• Standard Cylinders: If the machine cylinder hydraulic pressure is known (and available during injection), minimum bore size is:
  B = SQRT[(4 x F)/(H x 3.14)]
  
  For 2" dia. core and H = 1,500 psi:
  B = SQRT[(4 x 62,800)/(1,500 x 3.14)]
  = 7.3 inches (8" bore cylinder)
  
  For other injection pressures and core area, see Chart 1.

  Chart 1: Cylinder bore chart for other injection pressures and core areas.

• Nonstandard Cylinders: Preloading side-action cylinders generate the large output forces of large bore cylinders in a smaller bore package. A typical preload side-action system produces 60,000 lbs of output force with a bore diameter of two inches, and total outside diameter of five inches, easily fitting inside bore of the eight-inch standard cylinder in the example. Nonstandard cylinders may also maintain output force with zero psi hydraulic pressure.