• Andrea Vacca Industrial Engineering Department – University of Parma, Italy
  • Matteo Cerutti Industrial Engineering Department – University of Parma, Italy


hydraulic valves, priority valves, flow divider valves, optimization, design of experiments, response surface methodology


This paper describes the use of a numerical procedure developed by the authors for the analysis and optimization of hydraulic components. The element taken as reference is a two-way priority spool valve, typically utilized in steering systems with a load sensing control strategy in the presence of other actuators. The valve’s purpose is to control the primary port flow rate, the exceeding flow being discharged to the secondary output port. The optimization algorithm is based on Response Surface Methodology techniques, adopting the path search method known as Steepest Descent. For this purpose, the component’s behaviour is analytically described by means of a properly defined objective function. The procedure approximates this objective function with a simple model whose coefficients are evaluated using an AMESim® model of the valve, previously verified using test results. The simulations required to find the fitting model are planned using Design Of Experiments (DOE) methods. Because of the large number of factors characterizing valve design a preliminary analysis (screening) based on DOE algorithms was performed in order to identify the parameters which significantly influence valve behaviour. This allows the important factors to be considered for the optimization phase. The entire numerical procedure was implemented through MATLAB® scripts which automatically execute the AMESIM® simulations to perform the screening analysis or optimization. Considering a configuration pertinent to a stock version of the valve as starting point of the procedure, the paper proposes an optimal configuration. Experimental investigations performed on a prototype reveal the improved performance achieved with the proposed design in comparison with the behaviour observed in different stock versions of the valve, highlighting the potential of the optimization procedure developed. Moreover, the results presented in the paper illustrate how the procedure can also be utilized to perform other analyses of component behaviour, for example, proving, useful guidelines for the definition of dimensional tolerances.


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Author Biographies

Andrea Vacca, Industrial Engineering Department – University of Parma, Italy

Andrea Vacca He received his Master’s degree in Mechanical Engineering in 1999, at the University of Parma (Italy). In 2005 he became Ph. Doctor, at University of Florence, with a thesis in the field of Heat Transfer and Gas Turbine Blade Cooling Technology. Now he is Assistant Professor at the Industrial Engineering Department, University of Parma (Italy), where his main research interests are the analysis and simulation of fluid power systems and components, such as valves, gear and piston pumps.

Matteo Cerutti, Industrial Engineering Department – University of Parma, Italy

Matteo Cerutti He acquired his Master’s degree in Mechanical Engineering in 2005 at the University of Parma (Italy), with a thesis on Designed Experiment techniques applied to hydraulic components. He is now a Ph.D student at the Dep. of Energetics of the University of Florence (Italy) and cooperates with the Dep. of Industrial Engineering of the University of Parma for his research activities.


Antony J. 2003. Design of Experiments for Engineers

and Scientists. Butterworth-Heinemann Elsevier.

Berta, G. L., Vacca, A., Franzoni, G. and Guidetti,

M. 2003. Load Sensing-Prioritätsventile – Model

fűr die Funktionssimulation. O+P, Ölhydraulik und

Pneumatik, No. 10.

Box, G. E. P. and Wilson, K. B. 1951. On the

Experimental Attainment of Optimum Conditions

(with discussion). Journal of the Royal Statistical

Society, Series B 13(1), pp. 1-45.

Box, G. E. P. and Draper, N. R. 1987. Empirical

Model Building and Response Surfaces Methodology.

J. Wiley & Sons.

Casoli, P., Vacca, A. and Franzoni, G. 2003. A Numerical

Model for the Simulation of Load Sensing

Spool Valves. The 18th Int. Conference on Hydraulics

and Pneumatics, Prague, Czech Republic.

Dahlén, L. and Crlsson, P. 2003. Numerical Optimization

of a Distributor Valve. Int. Journal of Fluid

Power, Vol. 4, No. 3, pp. 17-25.

Eschenauer, H., Koski, J. and Osyczka, A. 1990.

Multicriteria Design Optimization. Berlin, Springer


Fisher, R.A. 1935. The Design of Experiments. Edinburgh:

Oliver & Boyd. RE, RI.

Frangopoulos, C. A. 2003. Methods of Energy System

Optimization. Proc. of the Summer School Optimization

of Energy Systems and Processes, Gliwice,


Karnopp, D. 1985. Computer Simulation of Stick Slip

Friction in Mechanical Dynamic Systems. Trans. of

ASME, Journal of Dynamic Systems, Measurement

and Control, Vol. 107, pp. 100-103.

Kleijnen, J. P. C., Hertog, D. and Angün E. 2002.

Response Surface Methodology’s Steepest Ascent

and Step Size Revisited. Proc. of the 2002 Winter

Simulation Conference, pp. 377-383.

Myers, R. H. 1999. Response Surface Methodology -

Current Status and Future Directions (including discussion),

Journal of Quality Technology, 31, No. 1,

pp. 30-74.

Myers, R. H. and Montgomery, D. C. 2002. Response

Surface Methodology: Process and Product Optimization

Using Designed Experiment. J. Wiley and


Montgomery, D. C. 1997. Design and Analysis of

Experiments. J. Wiley & Sons.

Nervegna, N. 2003. Oleodinamica e Pneumatica:

Sistemi, Componenti, Esercitazioni. Vol. 1 and 2,

Politeko, Turin (Italy).

Papadopoulos, E. and Davliakos, E. 2004. A Sistematic

Methodology for Optimal Component Selection

of Electrohydraulic Servosystems. Int. Journal

of Fluid Power, Vol. 5, No. 3, pp. 15-24.

Ranjit, R. K. 2001. Design of Experiments Using the

Taguchi Approach: 16 Steps to Product and Process

Improvement. J. Wiley & Sons.

Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H.

P. 1989. Design and Analysis of Computer Experiments.

Statistical Science, 4, No. 4, pp. 409-435.

Simpson, T. W., Mauery, T. M., Korte, J. J. and

Mistree, F. 2001. Kriging metamodels for Global

Approximation in Simulation-Based Multidisciplinary

Design Optimization. American Institute

of Aeronautics and Astronautics Journal.

Vacca A. 2006. Proposal of a Load Sensing Two-Way

Valve Model, Applying “Design of Experiments”

Techniques to Simulations. IMECE2006, 2006

ASME Int. Mech. Eng. Congress and Expo., Chigago

(IL), USA.

Vesely F. 2003. Design of Pilot Operated Relief Valve

by Use of the Simulation, The 18th Int. Conference

on Hydraulics and Pneumatics, Prague, Czech Republic.

Wiens, T., Burton, R., Schoenau, G. and Ruan J.

Optimization and Experimental Verification

of a Variable Ratio Flow Divider Valve. Int. Journal

of Fluid Power, Vol. 6, No. 3, pp. 45-53.






Original Article