Distributed parameters modeling for the dynamic stiffness of a spring tube in servo valves

The stability and dynamic performance of a flapper-nozzle servo valve depend on several factors, such as the motion of the armature component and the deformation of the spring tube. As the only connection between the armature component and the fixed end, the spring tube plays a decisive role in the dynamic response of the entire system. Aiming at predicting the vibration characteristics of the servo valves to combine them with the control algorithm, an innovative dynamic stiffness based on a distributed parameter model (DPM) is proposed that can reflect the dynamic deformation of the spring tube and a suitable discrete method is applied according to the working condition of the spring tube. With the motion equation derived by DPM, which includes the impact of inertia, damping, and stiffness force, the mathematical model of the spring tube dynamic stiffness is established. Subsequently, a suitable program for this model is confirmed that guarantees the simulation accuracy while controlling the time consumption. Ultimately, the transient response of the spring tube is also evaluated by a finite element method (FEM). The agreement between the simulation results of the two methods shows that dynamic stiffness based on DPM is suitable for predicting the transient response of the spring tube.