~ Pergamon Mech. Math. TheoO' Vol. 30, No. 4, pp. 599-612, 1995 Copyright ~(~ 1995 ElsevierScienceLtd 0094-114X(94)00057-3 Printed in Great Britain. All rights reserved 0094-114X/95 $9.50 + 0.00 MODELLING AND SIMULATION OF AN AXIAL PISTON VARIABLE DISPLACEMENT PUMP WITH PRESSURE CONTROL P. KALIAFETIS and TH. COSTOPOULOS Mechanical Design and Control Systems Section & Machine Design Laboratory, Mechanical Engineering Department, National Technical University of Athens, Patission 42, 106 82 Athens, Greece (Received 1 October 1993; in revised form 15 July 1994; received for publication 20 September 1994) Abstract--Static and dynamic characteristics of an axial piston variable displacement pump with pressure regulator are studied. The governing equations of the pump complete unit are derived and analysis is performed by computer simulation through which significant parameters of the pump complete unit are identified. A standard variable displacement pump is simulated and the results show good agreement with the manufacturer's dynamic operating curves. A--cross sectional area (m 2) C---Coulomb friction coefficient (N) D--viscous friction coefficient (Ns/m) d--pipe internal diameter (m) E--modulus of elasticity (N/m 2) e--pipe wall thickness (m) F--force (N) f--pipe friction coefficient -- g--acceleration of gravity (m/s 2) K--spring constant (N/m) L--pressure pipe length (m) m--mass (kg) n--Poisson's ratio -- P--pressure (N/m 2) Q--volume flowrate (m3/s) R--radius of control valve supply and leakage line (m) s~ischarge coefficient -- t--time (s) V--discrete volume (m 3) v--velocity of oil flow (m/s) x--piston position (m) ~--velocity of pressure wave (m/s) A--real distinct value (Ns/m 3) p~ensity of oil (kg/m 3) Subscripts l--piston 1 2--piston NOMENCLATURE 3--proportional control valve spool 3 CF~oulomb friction JET--orifice q~ 0.6 mm L--outlet of the pump LEAK--leakage OIL--oil P--pump PIPE--pressure pipe line SW--swash plate T--tank val--control valve VF--viscous friction Notation Q--leakage coefficient of the pump (mS/Ns) Cop--flow gain of the pump (m3/s/m) Fro--intrinsic displacement force (N) fiD-----coefficient of the position dependent intrinsic force (N/m) Gei--pressure dependent internal leakage coefficient (m~/Ns) ktD--coefficient of the pressure dependent intrinsic force (m:) P(I)--pressure at internal point (N/m 2) PP(I)--pressure at the intersection of characteristics (N/m 2) v(I)--velocity of oil flow at internal point (m/s) vP(1)--oil flow velocity at the intersection of characteristics (m/s) xT~displacement where the flow to the tank is sealed (m) XRrv--spring preload of control valve spool spring (m) ~=dP/dt /: =dx/dt .;:" = d2x/dt 2 INTRODUCTION In modern hydraulic systems axial piston variable displacement pumps are widely used in most applications of which pressure control is utilised [I, 2]. Such a pump with pressure control produces only the flow actually needed by the consumer, resulting in better power efficiency and low oil temperature. These variable displacement pumps in conjunction with proportional valves or servovalves make modern hydraulic systems more effective and flexible. 599