Novel modulation approach of flat force–displacement characteristic of linear electro-mechanical converter for electro-hydraulic servo-proportional valve

Flat force–displacement characteristic has crucial influence on the performance of linear electro-mechanical converter of electro-hydraulic servo-proportional valves. The commercial proportional solenoids obtain such features by welding a non-magnetic separator ring, which is complicated and time-consuming. This article presents a novel modulation approach to obtain the flat force–displacement characteristic of linear electro-mechanical converter by constructing a by-pass air gap. Taking an existing linear force motor as an example, the force–displacement characteristic curves of the linear force motor with by-pass air gap and without by-pass air gap are both studied using magnetic circuit analysis and finite element method under different excitation currents. Based on the finite element method simulated data, the response surface method is used to perform the experiment design for structure parameters of linear force motor with by-pass air gap, and the quadratic fitting equations are obtained for further optimization. To balance conflicted design objectives such as linearity, mean value of output force and power-to-weight ratio, the structural parameters of the linear force motor with by-pass air gap are optimized using a multi-objective optimization algorithm based on particle swarm. Prototypes of linear force motor with by-pass air gap and without by-pass air gap are both manufactured, and a special test rig is built. The static and dynamic experimental results are consistent with the theoretical analysis. The former proves that the linear force motor with by-pass air gap can obtain a nearly flat force–displacement curve with reasonable parameter optimization and also improve output force, and the latter reveals that a linear electro-mechanical converter with flat–displacement characteristic has better working stability over common ones. The proposed modulation approach provides a new approach for the design of flat force–displacement characteristic of linear electro-mechanical converter.