Simulation and optimization practice of electromagnetic force stroke characteristics of the pilot solenoid valve in an electronic controlled air suspension gas distribution valve

The pilot solenoid valve is a critical component of the electronic controlled air suspension (ECAS) air distribution valve, governing the inflation and deflation processes and, consequently, the inflation and deflation rates. Its electromagnetic force–stroke profile directly determines the accuracy and stability of spool-position control, which in turn affects the rapid and precise regulation of ECAS ride height and air-spring stiffness. Owing to the limited load capacity of commercial vehicle electrical systems, the available drive current is constrained, resulting in insufficient electromagnetic force at the beginning of the armature stroke and excessive force near the final pull-in. During the initial motion, an inadequate electromagnetic driving force cannot effectively overcome resistance, thereby deteriorating the armature start-up behavior, manifested as a delayed response or even start-up failure. During final pull-in, the electromagnetic force increases rapidly as the air gap decreases, causing the armature to accumulate excessive kinetic energy and collide with the stationary core at high speed. This induces stop-pin impact and energy loss, thereby reducing the operational stability and reliability of the solenoid valve. Therefore, without increasing the drive current, this study aims to improve the electromagnetic force–stroke distribution and to conduct structural optimization of the pilot solenoid valve.

Based on equivalent magnetic-circuit theory, the magnetic-circuit characteristics of the pilot solenoid valve were systematically analyzed. A finite-element electromagnetic model was established, considering magnetic nonlinearity and variations in the working air gap, and its accuracy was validated through comparison with static electromagnetic force experiments. On this basis, evaluation indices for characterizing the electromagnetic force–stroke distribution were defined. Pearson correlation coefficients were employed to perform sensitivity analyses of key structural parameters, and parameters with high sensitivity were selected as optimization variables to clarify the relationships between structural parameters and electromagnetic force distribution. Considering the coupling effects among multiple structural parameters, a response-surface prediction model for the average electromagnetic force over typical working air-gap intervals was developed using a Box–Behnken design. To maximize the average electromagnetic force in the initial and mid-stroke air-gap intervals and minimize it in the final pull-in interval, the NSGA-II multiobjective optimization algorithm was adopted to search for Pareto-optimal combinations of design variables. Subsequently, electromagnetic force simulations were conducted for the optimal parameter combination, and the simulation results were compared with the corresponding response-surface predictions to verify the effectiveness of the proposed optimization method.

The optimization results indicate that, under an unchanged drive current, the average electromagnetic force in the initial working air-gap segment increased by 31.83% compared with the pre-optimization design, while it increased by 25.72% in the mid-stroke working air-gap segment. In contrast, the average electromagnetic force in the final pull-in air-gap segment was reduced by 20.98%. The improved electromagnetic force–stroke distribution effectively alleviates the imbalance between insufficient driving force at the initial stage and excessive pull-in force at the final stage. Consequently, the start-up capability of the pilot solenoid valve under current-limited conditions is significantly enhanced, the responsiveness and stability of armature motion in the intermediate stroke are improved, and the end-stage impact and associated energy loss are effectively reduced.

This study addressed the suboptimal electromagnetic force–stroke distribution of a small-orifice pilot solenoid valve in an ECAS air distribution valve under current-limited conditions through modeling, experimental validation, simulation, and optimization. The proposed method significantly improved the force distribution across the full stroke, providing a valuable reference for the design, simulation, testing, and application of pilot solenoid valves. Additionally, it serves as a typical case for solenoid valve simulation experiment teaching, enhancing students’ engineering analysis skills and innovative thinking.