Modelling and experimental validation of a nonlinear proportional solenoid pressure control valve
Keywords:Nonlinear modelling, solenoid, pressure control valve, linear analysis
This paper investigates the static and dynamic behaviour of a pressure control valve with nonlinear negative characteristics. The pressure control valve has both reducing and relieving capability and is actuated by a solenoid. The static characteristics have been measured over the entire working range, covering the dynamic response of the solenoid, as well as the complete valve. A model is proposed that considers the flow as a mix of laminar and turbulent flow and flow forceswith a flow angle that varies with the stroke of the spool. The model shows good agreement with measurements. The investigations show that the flow forces decrease with higher flow rates as a result of a flow angle that tends to go towards a vertical angle. This results in an increase in pressure with flow during pressure reducing mode. A linear analysis is also presented, explaining this as a negative spring constant in the low frequency range. Stability is, however, maintained.
Åman,R., Handroos,H., and Eskola, T., 2008. Computionally
efficient two-regime flow orifice model for real-time
simulation. Simulation modelling practice and theory, 16,
Amirante, R., Vescovo, G.D., and Lippolis, A., 2006. Flow
forces analysis of an open center hydraulic directional
control valve sliding spool. Energy conversion and
management, 47, 114–131.
Borghi, M.,Milani, M., and Paoluzzi, R., 2000. Stationary flow
force analysis on compensated spool valves. International
journal of fluid power, 1 (1), 17–25.
Borutzky, W., Barnard, B., and Thoma, J., 2002. An
orifice flow model for laminar and turbulen conditions.
Simulation modelling practice and theory, 10, 141–152.
Branciforte, M., Meli, A., Muscato, G., and Porto, D., 2011.
Annand non-integer order modeling of abs solenoid valves.
IEEE transactions on control systems technology, 19 (3),
Dasgupta, K., and Watton, J., 2005. Dynamic analysis of
proportional solenoid controlled piloted relief valve by
bondgraph. Simulation modelling practice and theory, 13,
Dell’Amico, A., 2013. Pressure control in hydraulic power
steering systems. Lic. thesis No. 1626. Linköping University.
Ellman, A., and Piché, R., 1996. A modified orifice flow
formula for numerical simulation of fluid power systems.
Fluid power systems and technology, 3, 59–63.
Erhard, M., Weber, J., and Schoppel, G., 2013. Geometrical
design and operability verification of a proportional
pressure relief valve. In: The 13th Scandinavian
international conference on fluid power, SICFP2013, 3–5
June, Linköping, Sweden, 365–376.
Merritt, H.E., 1967. Hydraulic control systems. New York:
Palmberg, J.-O., Andersson, B., and Malmros, C., 1983.
Analysis and synthesis of hydraulic pressure regulators. In:
IASTED, international conference ACI’83. Köpenhamn.
Vaughan, N. and Gamble, J., 1996. The modeling and
simulation of a proportional solenoid valve. Transactions of
the ASME Journal of Dynamic Systems, Measurements and
Control, 118, 120–125.
Walker, P.D., Zhu, B., and Zhang, N., 2014. Nonlinear
modeling and analysis of direct acting solenoid valves
for clutch control. Transactions of the ASME journal of
dynamic systems, measurements and control, 136, 051023-
Wu, D., Burton, R., and Schoenau, G., 2002. An empirical
discharge coefficient model for orifice flow. International
journal of fluid power, 3 (3), 13–18.