# Effects of Valve, Armature, and Armature Pin Guidance on Diesel Injector Performance
## 2 Materials and Methods  
### System and Problem Definition  
In this study, a magnetically triggered solenoid CR diesel injector (Bosch), designed to operate at a pressure of 2000 bar, was utilized. This injector is currently in mass production and is distributed globally to various well-known vehicle brands. For further investigation and replication of the study, it can be obtained from the aftermarket with the type definition BX-CRI2-20 (0 986 435). Figure 1 provides a cross-sectional view of the injector, highlighting its key components, including the complete injector, armature, armature pin, and valve. The working principle of the CR injector is based on generating a hydraulic pressure difference. As illustrated in Figure 1, when the magnetic group is triggered, the armature moves upward, causing fuel in the valve area to be discharged back through the A-throttle [25; 29]. This action forms a low-pressure zone in the pressure chamber. The high-pressure force acting on the tip of the injector needle then overcomes the opposing spring force in this low-pressure region, allowing the needle to open. When the magnetic triggering ceases, the armature moves downward under the influence of the spring, creating a seal on the A-throttle and preventing low-pressure formation. Consequently, the vertical spring force returns the needle to the closed position. The injector assembly and testing process is depicted in Figure 2a. Sub-components are delivered to assembly lines through three different paths. As shown in Figure 2a, the armature, armature pin, and valve parts are produced in-house to their final form using various machining processes, including turning, washing, hardening, milling, drilling, and brushing. Parts are measured using a coordinate measurement machine (Zeiss, Oberkochen, Germany) and tactile measurement devices (Heidenhain, Traunreut, Germany) to define the desired inner/outer diameter and length. A schematic of the injector-function measurement device, which serves as the core measurement tool for this study, is shown in Figure 2b. Figure 1: Cross-sectional view of complete injector, armature, armature pin, and valve. Figure 2: Cont. The HDA device (Moehwald, Homburg, Germany), where HDA stands for \"Hydraulischer Druckanstieg\" (a German abbreviation for hydraulic pressure increase), is employed to measure the injection rate and mass. This device operates by detecting changes in hydraulic pressure as the liquid is injected into a sealed chamber filled with liquid. The primary measurement principle is based on monitoring pressure and the speed of sound within a constant volume chamber. The injection mass flow rate, assuming reversible, adiabatic (isentropic) injection into the chamber, can be expressed as follows:  
\[\frac{dm}{dt}=\frac{V\frac{dP}{dt}}{\frac{dP}{d\rho}}=\frac{V}{c^{2}}\frac{dP} {dt}, \tag{1}\]  
where \(m\) is fuel mass in the chamber, \(V\) is chamber volume, \(t\) is time, \(\rho\) is fuel density, \(c\) is the speed of sound in the fuel, and \(P\) is chamber pressure. Integrating this equation between two points in time (and two different pressures) yields the cumulative mass:  
\[m_{1-2}=\int_{\tau_{1}}^{\tau_{2}}\frac{dm}{dt}dt=V\int_{P_{1}}^{P_{2}}\frac{1 }{c(P(t))^{2}}\frac{dP}{dt}dP. \tag{2}\]  
Mass flow rate and cumulative mass can be calculated for a specific chamber volume, provided that the time-dependent pressure and pressure-dependent speed of sound are known. The HDA measures the speed of sound directly, which mitigates the influence of other variables, such as density and mass, on the results. The schematic of the HDA, shown in Figure 2b, illustrates its key components. The test chamber has a volume of 128 mL and is temperature-regulated by an external heat pump. A piezoresistive pressure sensor located in the cylinder wall measures the pressure signal. This signal is filtered through an anti-aliasing filter with a cutoff frequency of 25 kHz, then digitized at a 16-bit resolution and a sampling rate of 100 kHz.