Mathematical Modeling of an Armature Assembly in a Flapper–Nozzle Servo Valve Based on the Finite Element Method

The self-excited oscillation of an electro-hydraulic servo valve is a crucial factor that affects the operational stability of both the servo valve and the entire servo system. As the intermediary for electromagnetic force, hydraulic force, and feedback force, the dynamic characteristics of the armature assembly play a pivotal role in the emergence of self-excited oscillations. In this article, a mathematical model of the armature assembly is developed using the finite element method (FEM), which establishes a connection between the input signal and the dynamic characteristics of the armature assembly. The structure of the parameter matrix and the recursive relationship of discrete time steps are derived, while the discrete method of the feedback rod and the discrete time format of the FEM model are also analyzed to enhance the prediction accuracy of the model. To validate the efficacy of the FEM model, a numerical simulation model, a classical mathematical model, and an experimental platform are constructed to simulate or measure the dynamic characteristics of the armature assembly. Through the comparison of the dynamic characteristics obtained by the abovementioned methods, it is confirmed that the FEM model effectively predicts both the static and dynamic characteristics of the armature assembly. To suppress the vibration magnitude within the natural frequency range of the armature assembly, the external load that can effectively mitigate the resonance amplitude is calculated based on the FEM model, and the aim of ensuring the stable functionality of the armature assembly throughout its operational range is achieved.