# Modeling the Dynamic Behavior of a Pilot-Operated Solenoid Valve for an Ultra-High Pressure Vessel
###### Abstract  
A pilot-operated solenoid valve is used to control ultra-high pressure vessels. However, it is difficult to understand its dynamic behavior because the valve operates under ultra-high pressure conditions and the driving unit moves in a multi-step fashion in a tight hidden space. This study aims to identify the system coefficient, especially the damping coefficient, required to analyze the dynamic behavior of a solenoid driving unit. Experiments to measure the dynamic behavior of the driving unit are conducted using two laser sensors and one accelerator. The damping coefficient is estimated using Matlab Simulink, by varying the damping coefficient to match the experimental results. The obtained system coefficients are modeled as equations of motion. It is verified that the valve motion consists of two sequential movements--Phase 1 by pilot plunger and Phase 2 by main plunger, pilot plunger, and the valve initiation time is as fast as 9.9 ms. The damping coefficient of each phase is estimated 0.001 N \(\cdot\) s/mm for Phase 1, 0.004 N \(\cdot\) s/mm for Phase 2.  
modeling dynamic behavior; pilot-operated solenoid valve; ultra-high pressure cylinder +
Footnote †: journal: Applied  
1
Footnote 1: email: _Applied_  
Received: 26 January 2021  
Accepted: 3 March 2021  
Published: 5 March 2021  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.  
**Published:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.  
similar to Kajima for air-gap and bilinear transformation [6]. [PERSON] experimented with the direct acting valve used in CRHDM according to the shape of the contact surface and compared it with the results of ANSYS analysis, but did not identify system variables in the form of equations of motion [7]. [PERSON] conducted a study to create a motion equation for dynamic performance analysis of the pilot operated solenoid valve of a spacecraft conversion engine, and analyzed the effect of parameters [8]. [PERSON] conducted a study to simulate the prediction of the single-phase solenoid plunger position of the PWM method using the SIMON tool [9]. [PERSON] analyzed the factors of the system using Matlab Simulink to analyze the dynamic response characteristics of the solenoid valve, including the electro pneumatic valve model and the pneumatic hydraulic valve mode [10]. However, these studies were done for relatively low pressures. [PERSON] designed a pilot-operated solenoid valve for use in ultra-high pressure vessels. However, he did not analyze the dynamic behavior to improve performance [11,12]. Because the valve operates under ultra-high pressure conditions and the drive unit moves in several stages in a tight hidden space. The dynamic motion of plungers is very hard to be investigated.  
In this study, the dynamic behavior of the pilot-operated solenoid valve is analyzed with the equation of motion under normal pressure in order to identify the accurate valve actuation time sequence based on measurements of the moving parts of the solenoid, pilot plunger and main plunger, as well as solenoid attraction force. Matlab Simulink is used to compare the experimental results and the simulation results for identifying the damping coefficients.