Comparison of Numerical Effectiveness of Three Methods for Modelling 2-Way Flow Control Valves Rafael Åman and Heikki Handroos Department of Intelligent Machines, Lappeenranta University of Technology, Lappeenranta, Finland, aman@lut.fi Abstract In simulating the dynamics of 2-way flow control valves using semi-empirical model [6] the integration of pressure in small fluid volume between the pressure compensator and control throttle causes numerical problems. The system stiffness approaches infinity as the fluid volume approaches zero. Using semi-empirical model with description of the two orifices in series [6] the integration of the pressure in the small fluid volume between the pressure compensator and the main orifice can be avoided. The drawback of this method is that this pressure is needed in dynamic equation for the pressure compensator. This again leads into numerical problems when control throttle has a small cross-section area. The method proposed in this paper uses pseudo-dynamic solver to calculate the pressures in small volumes of flow control valve as individual static solutions at each time step of the actual solver that is solving the dynamics of complete valve. The key advantage of the method is that the numerical problems caused by the small volumes are completely avoided. The superiority of pseudo-dynamic method comes from the fact that the method is freely applicable regardless of used integration routine. The present paper describes the algorithm in general level and how it applies to a 2-way flow control valve model. Results obtained with the three methods are compared. Keywords: Fluid power, 2-way flow control valve, simulation, small volume, pseudo-dynamic solver, static solution 1 Introduction The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step ODE-algorithms are used the stability would easily be lost when integrating pressures in small volumes. In case of using variable step algorithm the step size is decreasing into its minimum as the fluid volume decreases towards zero. This results in very long simulation times. Krus has developed the modified Heun-method that utilizes the partial derivatives of flows with respect to pressures [7]. This method has been quite successful in solving pressures in small volumes, but it still requires very small integration time steps when the volumes are very small. Ellman postulated an iterative algorithm for pressures in volumes that can be approximated zero volumes to be used in conjunction with modified Heun-method [2]. This method also requires a small integration time step and is applicable only with modified Heun-method. To solve the problem caused by small fluid volumes the present paper proposes a pseudo-dynamic solver that instead of integrating the pressure in small volume solve the pressure as a static pressure at each time step by using pseudo-dynamic solver. This can also be called as steady-state solving method [2]. Pseudo-dynamic solver has been used in [9] for solving statics of fluid power circuits. The static solution is obtained by firstly giving reasonable parameter values to all volumes (e.g one litre) and then solving the steady-state pressures by numerical integration and then by picking up the steady-states of the pressures after transient state. In this method the dynamic simulation is only used by producing the static solution. The pseudo-dynamic solver is based on the basic assumption that if the volume in the system to be described is small enough, the pressure can be expressed by a static pressure, as explained in [2]. The method has two key ideas. Firstly, the nominal frequency (time constant), which is created by the small volume, is not significant in comparison with the dynamics of the whole system. Secondly, instead of integrating the equations for pressure gradients in such volumes, their pressures are