plunger (DIS.PPHPL2) into spool settings (SPOOL. PLUNGER. S and SPOOL.PLUNGER.E) 

 for valves controlling flow into and out of the kicker port (VALVE.PLUNGER.S and 

 VALVE. PLUNGER.E, respectively). 



Leakage from the kicker port to exhaust was modeled by a small non-zero offset in the 

 exhaust curve (CURVE. PLUNGER.E) leaving the exhaust valve partially open at all times. A 

 similar offset in the supply curve (CURVE. PLUNGER. S) provided for supply leakage. Leakage 

 values of 2 percent for the supply and exhaust side of the plunger were determined to yield a 

 truer match to empirical data. However, the model was extremely sensitive to changes in this 

 parameter. 



Line element (LINE2) represents fluid passage between the supply and the kicker port. 

 An additional line element (LINE3) was added between the poppet chamber and the plunger 

 drive chamber to provide information on the pressure drop and flow across the supply poppet, 

 and thus the pressure in the poppet chamber (PPO). The line element (LINE4) added between 

 the plunger drive chamber and the exhaust orifice allowed for a more accurate exhaust behavior 

 and produced a desired lag to the drive chamber discharge. This element provided information 

 on the pressure drop and flow to the exhaust orifice, and thus the pressure in the exhaust 

 chamber (PEY). Later, a line element (LINE5) was added between the plunger and the kicker 

 port on the supply side. This line element served to reduce pressure pulsation in the kicker port 

 to match empirical data. 



The drive chamber pressure (PPL), which is a function of the poppet setting, is 

 continuously exhausted through an open orifice (VALVE. EXHAUST). The exhaust condition 

 is represented by a near-infinite volume accumulator (EXHAUST) at ambient pressure (PEY). 

 The drive chamber pressure is applied to the plunger through an actuator (ACT. PLUNGER), and 

 a small force is created by the exhaust pressure acting on the back side of the plunger head 

 (PFORCE.PL). 



Figure A-4 shows the working of the piston. The line element (LINE1) represents the 

 fluid between the supply and the piston chamber. The pressure in the piston chamber (PPI) is 

 applied to the differential piston area (ACT. PISTON). The force from this actuator 

 (ACT.FORCE.PISTON), which is calculated as a by-product of the element, is multiplied by 

 a fraction, then applied as a seal friction force (FFORCE.PI). The sign of the piston velocity 

 (DISD.PHPI1) is used to set the sign of the friction force to oppose motion. 



Motion of the poppet, plunger, piston, and anvil was limited by hard stops at the upper 

 and lower limits of body motion from housing contact. Hard contacts were also implemented 

 at the interfaces for plunger to piston, and piston to anvil. These hard contacts were 

 implemented through a set of control elements which created a compression only spring damper 

 force. A typical hard-stop control element diagram is shown in Figure A-5. The string labeled 

 "XY" represents the names for the two bodies such as "PLPI" for plunger to piston contact. The 

 displacement (DIS.XY) causes a force (F) to be applied between the two bodies only for values 

 less than zero. The damping coefficient is a function of velocity (DISD.XY). 



The coordinate system locations for the noncentroidal reference frames and centers of 

 gravity for the redesign model are shown in Figure A-6. Figure A-7 shows the locations for the 

 hard stops as they were modeled. 



A-2 



