Physics-Based Modeling and Friction Parameter Identification of a Proportional Spool Valve

This paper presents the development of a physics-based model of a proportional directional valve with the aim of describing its dynamic behavior while accounting for the influence of friction forces acting on the spool. The model is derived from the spool’s equation of motion, and in order to achieve accurate parameter tuning, an experimental analysis of the individual forces acting on the spool was carried out. Particular attention is given to the parameters of the friction force, as this component represents a key factor affecting the dynamic response of the system. Due to the difficulty of direct measurement, the identification of friction parameters was performed through a combined numerical–experimental comparison of the system’s response to step control inputs. A significant advantage of the proposed model lies in its capability to parameterize the individual force components independently, which facilitates straightforward adaptation to different operating conditions or valve types. For experimental validation, a series of dynamic measurements was conducted on a specialized hydraulic test rig. The acquired data were used both to identify the friction model parameters and to validate the simulation model. A comparison of the simulation results with experimental data demonstrates good agreement across a wide range of operating conditions. The proposed model therefore provides a flexible and accurate tool for predicting the behavior of proportional directional valves, applicable both in the design of control algorithms and in the optimization of valve construction.