Modeling and analysis of electromagnetic force approximate model of high-speed solenoid valve

High-speed solenoid valve (HSV) is the key component of electronic control fuel injection system for diesel engine. Improving the dynamic response speed of HSV will be able to achieve higher injection precision and more flexible fuel injection law, thus reducing gas emissions of diesel engine and improving its fuel economy. However, HSV is the complex coupling system of electric field, magnetic field, mechanical movement and flow field, and the interactions of multiple parameters exist between the fields for HSV. To improve the dynamic response speed of HSV is a complex optimization problem of multiple physical field and multiple parameters. A zero-dimensional approximation coupling model of HSV can be developed instead of the CAE (computer aided education) models or physical experiments, which conduces to achieve the efficient prediction and global optimization of performances. So the approximation model method was employed in this paper. First, the structure and principle of HSV for electronic unit pump of diesel engine were presented. Second, the three-dimensional (3D) finite element model of HSV was developed to calculate the electromagnetic force, and its accuracy was verified by means of the comparison with experimental data. Third, 3 major methods of experimental design, i.e. central composite faced-centered design (CCF), central composite inscribed design (CCI) and optimal latin hypercube design (OLH), and 3 typical approximation methods, i.e. quadratic polynomial response surface model (RSM), Kriging model (KR) and radial basis function model (RBF) were introduced. Fourth, 6 key parameters including 2 field coupling parameters, i.e. working air gap and drive current, and 4 structure parameters, i.e. coil turns, side pole radius, thickness and radius of armature were determined for establishing the approximate models. Next, 6 groups of sample points were designed, whose response values of electromagnetic forces were obtained by the 3D finite element model of HSV. Four of the groups were designed with different sizes by the OLH, and the other 2 groups were designed by the CCF and CCI. Then, 18 groups of electromagnetic force approximation models were developed by combining the 6 groups of experimental design with the 3 typical approximation methods introduced. To compare the accuracy of approximation models, 3 kinds of evaluation indices were introduced. They were multiple correlation coefficient, average absolute error and root mean square error respectively. In the end, the effects of different sample point sizes, experimental design methods and approximate methods on the accuracy of electromagnetic force approximation models were analyzed in detail. It is concluded that the accuracy of approximate model doesn't increase monotonically with the increase of the set size of sample points, and too many sample points maybe leads to the decrease of the accuracy of approximate model; the OLH has good adaptability with the KR and RBF, and can be given priority for developing approximation models. In addition, the best solution for establishing electromagnetic force approximation model of HSV is the combination of the KR and OLH, whose size of sample points is 1.5 times of the minimum sample points required by the quadratic polynomial response surface model. Its multiple correlation coefficient, average absolute error and root mean square error are 0.97, 0.06 and 0.09 respectively. It provides a theoretical guidance for the establishment of the zero-dimensional approximation coupling model and the optimization of HSV.