# Effects of Valve, Armature, and Armature Pin Guidance on Diesel Injector Performance
## 1 Introduction  
### Literature Review  
The development of internal combustion engines (ICEs) spans several centuries and has significantly influenced modern society by broadening transportation and mechanization horizons. Despite their benefits, ICEs are associated with substantial gas and particle emissions, prompting ongoing research into innovative technologies and strategies to mitigate these effects. Fuel injectors are critical in this context, impacting engine efficiency and emissions [1, 2]. In diesel engines, particularly within the common-rail (CR) fuel injection system, critical parameters such as injection timing, injection, and duration are controlled to enhance efficiency and minimize emissions [3]. Extensive research indicates that delayed injection timing is effective in reducing NOx emissions by lowering peak combustion temperatures and pressures within the cylinder [4, 5, 6, 7]. Increasing injection pressure improves fuel atomization, which facilitates a more uniform fuel-air mix, decreasing ignition delays and promoting complete combustion [8, 9]. However, higher injection pressures may also lead to increased NOx emissions [10, 11, 12]. Adopting multiple injection strategies offers another approach to optimize injection timing and reduce emissions from compression-ignition engines [13]. [PERSON] et al. investigated the effects of various injection timings and quantities--main, pilot, and post-injection--in a four-cylinder diesel engine [14]. Their findings suggest that an early pilot injection coupled with a delayed main injection can decrease both NOx emissions andcombustion noise. Additionally, they observed that incorporating post-injection with delayed main injection further contributes to reductions in NOx and soot emissions. Precise control over injection parameters is critical for achieving optimal combustion efficiency and maximum energy output. This study examines factors that influence injector precision, such as armature closing time, needle opening time, and flow rate. Fuel injection is a crucial factor in controlling combustion within diesel engines. The CR fuel injection system enables precise control of fuel injection speed, which is essential for enhancing engine performance and reducing exhaust emissions. [PERSON] et al. examined the effects of high injection pressures (ranging from 400 to 1600 bar) on injection rate characteristics using a six-hole solenoid CR injector with a fixed injector energization time of 1.5 ms [15]. Their findings indicated that higher injection pressures significantly shortened the hydraulic injection delay from 0.5 to 0.25 ms. The profile of fuel injection speed serves as a direct indicator of the fuel injection process and significantly influences the atomization and combustion within the engine. [PERSON] et al. utilized an empirical calculation method to analyze the fuel injection speed profiles of high-pressure injectors [16]. By adjusting the injection pressure and energization time, they determined the fuel injection duration, the maximum speed of fuel injection, and the dynamics of the rise and fall curves in the fuel injection profile. Notably, they observed that under conditions with shorter energization times, injection duration increased with higher injection pressures. Conversely, marginally extending the energization time led to a decrease in injection duration as the pressure increased. Moreover, the injection duration exhibited varied growth trends under different rail pressures and energization durations. [PERSON] et al. highlighted an often-overlooked aspect in literature: the impact of hydrodynamic forces on injector dynamic characteristics [17]. They noted that during the armature's opening phase, the exiting fuel acts as a cushion between the armature's upper surface and the electromagnet, which mitigates the impact force on the armature and considerably inhibits cavitation. To explore this phenomenon further, they simulated the interaction between hydrodynamic forces and the movement of the injector armature and electromagnet.