Mathematical Problems in Engineering

Volume 2017, Article ID 9078598, 10 pages

https://doi.org/10.1155/2017/9078598

## Investigation on Electromagnetic Models of High-Speed Solenoid Valve for Common Rail Injector

^{1}College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China^{2}College of Power Engineering, Bauman State Technical University, Moscow 115569, Russia

Correspondence should be addressed to Liyun Fan; moc.361@10_ylnaf

Received 26 December 2016; Revised 10 April 2017; Accepted 20 April 2017; Published 12 June 2017

Academic Editor: Francesco Braghin

Copyright © 2017 Jianhui Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

The fuel system has a vital impact on the overall performance of a diesel engine, and a high-pressure common rail system enables the cyclic injection quantity, injection timing, and fuel injection law to be controlled exactly and flexibly. Therefore, a diesel engine that is equipped with a high-pressure common rail system has the potential to achieve the optimized design goals of high-efficiency combustion and ultralow emission [1–5]. The common rail injector is one of the high-pressure common rail system’s critical components, with a direct influence on the cycle fuel injection quantity fluctuation, gas-liquid two-phase flow characteristics of high-pressure fuel in the nozzle, fuel atomization characteristics in the cylinder, and air-fuel mixture quality [6–9]. The common rail injector is a complex, nonlinear, and multidimensional system that couples electromagnetic, mechanical, and hydraulic phenomena. To study the dynamic characteristics of the common rail injector in detail and optimize it, the simulation analysis of its dynamic performance is an effective method. A simulation model of the HSV that has high accuracy is thus indispensable.

The dynamic response characteristic is an important evaluation index of the HSV in the fuel injector. This is because a fast response speed of the HSV is beneficial to achieve multiple injections and more precise control of the fuel injection timing of the high-pressure common rail system. The dynamic response of the HSV is determined by both its electromagnetic force characteristic and moving part quality, but the former has a more significant impact. Only when the maximum static electromagnetic force of the HSV meets its requirements can the response time requirements of the opening and closing phases of the HSV be met by using the drive circuit. Hence, research on the electromagnetic force is of great importance for the design of the HSV.

In research on the static electromagnetic force of the HSV, most scholars used the finite element method (FEM). Liu et al. [10] studied the influence rules of the main structure parameters and the interaction between them on the electromagnetic force using a combination of response surface design and FEM. Sun et al. [11] studied the influence rules of the iron core length, the cross-sectional areas of the main and side poles, the coil turns, and the air gap width on the electromagnetic force of an E-shaped HSV for an electronic unit pump by FEM. It was discovered that the drive current significantly impacts the electromagnetic energy conversion, as increasing the drive current unnecessarily does not improve the electromagnetic force of the HSV but only increases the power consumption and thus reduces the electromagnetic energy conversion efficiency. Cheng et al. [12] studied using FEM the flux density distribution of an HSV whose iron core is made of a nano-based soft magnetic material. It was discovered that solenoid valves with different soft magnetic materials have different characteristics of electromagnetic force. Miller et al. [13], Shin et al. [14], and Bianchi et al. [15] carried out optimization research on the static electromagnetic force of an HSV to obtain the optimal structure parameters by FEM. However, because of the long solution time and high requirements for computer performance of FEM, the efficiency of research on the optimization and analysis of the structural parameters is low, especially when carrying out an iterative structural analysis for the detailed parameter design of HSV. Therefore, the development of a static electromagnetic mathematical model for an HSV that can be applied conveniently with high accuracy has become an important research direction.

Elmer and Gentle [16] put forward a relatively simple mathematical model of a proportional solenoid valve. The model simplified the electromagnetic process calculation of the solenoid valve as the calculation of an RL equivalent circuit. Ma et al. [17], Shamdani et al. [18], and Bianchi et al. [19] determined the influencing relation of drive current and air gap on electromagnetic force by a polynomial fit technique based on test data of the static electromagnetic force. Wang et al. [20] and Chung et al. [21] considered the magnetic saturation characteristics of an HSV by adjusting the coefficient of the fitting formula to limit the maximum electromagnetic force of the valve. Huber and Ulbrich [22] and Chung et al. [23] developed a dynamic characteristic mathematical model for the common rail injector. Its electromagnetic submodel was built based on a map chart consisting of the electromagnetic force, drive current, and air gap. However, the HSV electromagnetic characteristics are not only a simple function relationship between the electromagnetic force and the drive current and air gap. In the high-pressure common rail system, the nonlinear transient coupling characteristics of the electromagnetic, mechanical, and hydraulic systems determine the electromagnetic characteristic transformation of the HSV. Therefore, this method meets the demands of engineering application, but it cannot reveal the intrinsic electromagnetic properties of the HSV, both the static electromagnetic characteristics and the dynamic electromagnetic characteristics.

Most of the literature on the HSV tends to ignore the influence of the soft magnetic material reluctance in developing the electromagnetic model of the solenoid valve. Topçu et al. [24], Jin et al. [25], Naseradinmousavi and Nataraj [26], and Mehmood et al. [27] considered that the reluctance of the iron core magnetic material is much less than that of the air gap; therefore, the nonlinear magnetization process and magnetic saturation characteristics of the iron core magnetic material can be ignored. Sefkat [28] assumed that the magnetic field is not saturated in the whole working process of the solenoid valve, and the magnetic induction intensity always linearly increases with the increasing magnetic field intensity; that is to say, the saturation phenomenon of the electromagnetic force did not happen for their model. However, Wang et al. [29] and Sun et al. [11] discovered that a saturation phenomenon of the electromagnetic force for the solenoid valve existed in their experimental research, and the magnetic saturation of the HSV soft magnetic materials was the main cause of this. In the actual control process of the HSV, to improve the opening speed, a high voltage was loaded on the HSV to quickly obtain a large current. In this way, it is easy to achieve magnetic saturation for the solenoid valve. When the solenoid valve reached magnetic saturation, with the increase in the drive current, the electromagnetic force of the HSV will increase very slowly; therefore, the economy of the HSV decreased. Simply dealing with the magnetic saturation characteristic or taking no account of it will lead to obvious calculation errors in determining the electromagnetic force characteristics. Therefore, it is necessary to take the nonlinear magnetization characteristics and magnetic saturation characteristics of the solenoid valve magnetic materials into account upon building a mathematical model of an HSV.

Coppo et al. [30] established a complete mathematical model for a common rail injector. For its electromagnetic submodels, the magnetization process of the solenoid valve was divided into a linear magnetization phase and a saturation magnetization phase, which are described by simple piecewise lines. In the mathematical model of an HSV developed by Liu et al. [31], the reluctance of the soft magnetic materials was included to consider the nonlinear magnetization characteristic, but the most important - magnetizing curve was determined based on - experimental data by a trial and error method for calculating the reluctance of soft magnetic materials. The mathematical models of a solenoid valve developed by Jin et al. [25] and Vu et al. [32] considered the magnetic saturation characteristics, edge effect of the air gap, and flux leakage, but a detailed description of the - magnetizing curve that determines the reluctance of the soft magnetic materials and calculates their transient permeability was not provided.

It can be found from the above references that a certain research insufficiency on the electromagnetic mathematical model of the HSV still exists. Some electromagnetic mathematical models use an electromagnetic force fitting formula based on experimental data, some models do not consider the reluctance of the soft magnetic materials, and some only took segmental magnetic properties of the magnetic materials into account. Therefore, to provide more valuable information on the electromagnetic energy conversion of the HSV and more deeply understand the solenoid valve’s electromagnetic conversion process, more detailed research on the electromagnetic mathematical model of the HSV has been carried out in this paper. The resulting model considers the nonlinear magnetization characteristics and magnetic saturation characteristics of the HSV. Based on this mathematical model, research on the electromagnetic force characteristics of the common rail injector HSV and its key influence factors can follow. It provides a certain theoretical basis and design tools for the design of HSVs.

#### 2. The Electromagnetic Model of HSV

##### 2.1. Magnetic Circuit Model of HSV

Figure 1 shows the structure schematic of a HSV. It mainly consists of an iron core, coil, and armature. To obtain a strong electromagnetic force, a soft magnetic material with a high saturation induction density and low remanence is often applied for the iron core and armature.