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A novel formula easily applied with high precision is proposed in this paper to fit the -curve of soft magnetic materials, and it is validated by comparison with predicted and experimental results. It can accurately describe the nonlinear magnetization process and magnetic saturation characteristics of soft magnetic materials. Based on the electromagnetic transient coupling principle, an electromagnetic mathematical model of a high-speed solenoid valve (HSV) is developed in Fortran language that takes the saturation phenomena of the electromagnetic force into consideration. The accuracy of the model is validated by the comparison of the simulated and experimental static electromagnetic forces. Through experiment, it is concluded that the increase of the drive current is conducive to improving the electromagnetic energy conversion efficiency of the HSV at a low drive current, but it has little effect at a high drive current. Through simulation, it is discovered that the electromagnetic energy conversion characteristics of the HSV are affected by the drive current and the total reluctance, consisting of the gap reluctance and the reluctance of the iron core and armature soft magnetic materials. These two influence factors, within the scope of the different drive currents, have different contribution rates to the electromagnetic energy conversion efficiency.

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In this article, a mathematical fluid–structure–thermal model for fuel leakage of piston couples was developed, with consideration of the physical properties of fuel, elastic deformation, and temperature distribution along the seal length. The calculated results were compared with experimental static fuel leakage data. Based on this model, the effects of various factors on the fuel leakage were investigated. The results showed, at pressures under 100 MPa, the most dominant influence on the fuel leakage of a piston couple was the initial clearance; however, as the pressure increased from 100 to 200 MPa, the influence of the initial clearance gradually weakened, while the effects of the piston diameter, elastic modulus, and diameter of the piston sleeve increased and became more significant; in this case, the piston diameter replaced the initial clearance as the most dominant factor. At a pressure range of 200–300 MPa, the effects of the elastic modulus exceeded the effects of the initial clearance and became the second most important factor. Therefore, simply adjusting the initial clearance is not an effective method to reduce fuel leakage. An increase in the seal length significantly influences the fuel leakage only under relatively low-pressure conditions, as the effect weakens with increasing pressure. As a result, under high-pressure conditions, it is necessary to consider both the diameter of the piston and the elastic modulus to reduce the fuel leakage.

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