International Journal of Automotive Technology, Vol. 17, No. 4, pp. 567−579 (2016) DOI 10.1007/s12239−016−0057−2
Copyright © 2016 KSAE/ 091−03 pISSN 1229−9138/ eISSN 1976−3832
EFFECT OF INJECTOR PARAMETERS ON THE INJECTION QUANTITY OF COMMON RAIL INJECTION SYSTEM FOR DIESEL ENGINES Y. BAI, L. Y. FAN*, X. Z. MA, H. L. PENG and E. Z. SONG College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China (Received 5 August 2015; Revised 11 December 2015; Accepted 21 December 2015) ABSTRACT−In this paper, the bond graph model of common rail injector was proposed in consideration of the effects of variable liquid capacitance and fuel physical property on the injection characteristics of the injector. State equations were derived based on the model, which were numerically solved by programming in Matlab. Comparisons between the simulation results and the experimental data show that the numerical model can effectively predict the injection quantity of the system. Effect of variation of delivery chamber diameter, needle seat semi-angle, needle cone semi-angle, ball valve seat semi-angle, nozzle hole diameter, inlet orifice diameter and outlet orifice diameter on fuel injection quantity had been analyzed. The influence rules of various parameters on the fuel injection quantity had been established. The experiments were conducted using face centered central composite design. A second order polynomial response surface model had been developed for predicting fuel injection quantity, as a function of the independent variables. Analysis of variation was used to determine the significance interactions which primarily affect the fuel injection quantity. It had been concluded that six interaction factors including delivery chamber diameter with nozzle hole diameter, needle seat semi-angle with needle cone semi-angle, needle seat semi-angle with nozzle hole diameter, needle cone semi-angle with nozzle hole diameter, nozzle hole diameter with inlet orifice diameter, and nozzle hole diameter with outlet orifice diameter have significant effect on the fuel injection quantity of the system. KEY WORDS : Common rail injection system, Injector, Bond graph, Response surface, Interactive effect
1. INTRODUCTION
significant reduction of experimental tests (Ferrari et al., 2013). Many research activities are carried out to modeling the common rail injector. Caika and Sampl (2011) developed a common rail injector model based on the 1D fluid flow and multi-body dynamics approach in BOOSTHYDSIM, including numerous hydraulic, mechanical and electrical components. The model was validated by comparing the measured and calculated injection rate for different load cases. Through co-simulation with AVL FIRE, the cavitations occurrence at needle seat and in the nozzle hole had been analyzed. Payri et al. (2012) proposed a one-dimensional model for standard common rail diesel injection system. The comparison of the injection rate proportionate by the model with the experimental data for different injection conditions showed a good performance of the model and therefore the ability of it to predict the injection rate with high level of accuracy. Boudy and Seers (2009) presented the modeling results of a common-rail diesel injection system validated with the experimental results. Based on the model, the influence of fuel properties in the injector feed pipe and injector mass flow rate were evaluated. Coppo and Dongiovanni (2006) refined a previously developed numerical model of a common-rail type diesel injector in order to obtain accurate predictions of injector operation in its entire application field. Experimentally measured and numerically obtained values
Common rail injection system (CRIS) is earning popularity due to the depleting nature of fossil fuels and adverse environmental effect of exhaust emissions from petroleum fuelled diesel engines (Nikzadfar and Shamekhi, 2014; Jeong et al., 2014; Jo et al., 2015). It is a state-of-the art technology that enables better fuel economy, lower emissions and higher power of the diesel engines, the superiority of which has been proved by practice (Kannan et al., 2013; Qian and Liao, 2015). The injector used in CRIS has a strong influence on the characteristic of the system and thus in phenomena such as spray atomization, combustion and emissions (Wang et al., 2015). The inconsistency in manufacture process and wear of the components during long time continuous operating will lead to the variations of injector parameters. These parametric variations result in an inconsistency of fuel injection quantity (FIQ) and cause the working stability of diesel engines to deteriorate. Thus, an investigation on FIQ caused by the variations in the injector parameters has significant importance in practice and theory. Numerical simulation offers the means of evaluating the geometry and operation on the injector, allowing a *Corresponding author. e-mail:
[email protected] 567
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of injected volume per stroke were compared, showing the ability of the model to reproduce with good accuracy the injector operation in its entire working field, which was explored in terms of energization time and working pressure. Bond graph is a system dynamic graphical modeling method which describes various energy domains in the system (Rosenberg, 1971; Kurniawan et al., 2012). It classifies a variety of physical quantities involved in the system into four kinds of variables, that is, effort, flow, momentum and deflection, viewed from the perspective of power flow. Power bonds, effect, power source, junction, transformer and gyrator are used to represent the basic physical characteristics and the relations of energy conversion and conservation of the system (GamezMontero and Codina, 2007; Bera et al., 2012). Thus, this method describes the composition, transformation, logical relations and physical characteristics of power flow in the system. However, it is observed that bond graph technique used for common rail injector modeling is insufficient. Therefore, in this paper, a bond graph model of common rail injector has been proposed according to the multiphysics field characteristic of the system. The state equations have been obtained, considering the effects of variable liquid capacitance and fuel physical property on the injection characteristics of the injector. Experiments are
conducted at the same model conditions to validate the accuracy of the numerical model. The influence rules of the variations in the injector parameters and the significant interactive effect between parameters on FIQ of the system are analyzed in detail, combining design of experiments and response surface methodology (RSM). The results can provide a theoretical guidance for the design and optimization of the system. Figure 1 shows the entire research method and process in the present work.
2. OPERATING PRINCIPLE OF COMMON RAIL INJECTOR Figure 2 presents the modeled injector and its corresponding main components. As the electric current to the injector is supplied by the electronic control unit, the control valve moves upwards, the lift of the ball valve opens the outlet orifice and makes it operative for the discharge. This connects the control chamber to the tank through a return pipe and allows the control chamber to be emptied. The fuel pressure in control chamber decreases, as does the hydraulic force, which acts on the control piston. As soon as the force due to the difference between the control chamber, nozzle volume, needle chamber and delivery
1: Low pressure fuel outlet; 2: High pressure fuel inlet; 3: Control piston; 4: Nozzle volume; 5: Nozzle; 6: Nozzle hole; 7: Delivery chamber; 8: Needle chamber; 9: Needle; 10: Control chamber; 11: Inlet orifice; 12: Outlet orifice; 13: Control valve; 14: Solenoid valve. Figure 1. Research flowchart.
Figure 2. Schematic of common rail injector.
EFFECT OF INJECTOR PARAMETERS ON THE INJECTION QUANTITY OF COMMON RAIL INJECTION SYSTEM
chamber pressures prevails over the needle-spring preload, the needle moves upwards and fuel is injected, through the nozzle holes, into the cylinder. The injection process stops when the solenoid valve is deactivated. The control valve is forced downwards by the spring that acts on it and there is a renewed buildup of pressure in control chamber, which is caused by the fuel flowing in from inlet orifice. The hydraulic force acting on the control piston, pluses the needle-spring preload, overcome the force due to the hydraulic force acting on the shoulder of the needle in the nozzle volume and on part of the needle tip in the delivery chamber. The needle returns to its initial position and stops fuel injection (Catania et al., 2008; Chung et al., 2008).
3. BOND GRAPH AND NUMERICAL MODEL OF COMMON RAIL INJECTOR The injector in question is not large in scale, but rather complicated to model in that it involves different fields such as electric, magnetic, mechanical movement and flow fields coupled together. In this paper, the injector illustrated in Figure 2 is modeled using the bond graph methodology. Based on the bond graph method and the relations of injector components, the bond graph models of the subsystems were developed firstly, and then, they were coupled together according to the flow direction of the power flow in the system and the causalities between the variables, finally, the complete bond graph model of the system was obtained. The basic bond graph elements used in the components of the injector are listed in Table 1, and Figure 3 shows the complete bond graph model of the injector. The effort equations and flow equations can be obtained based on the energy-stored elements in the proposed bond graph model, and then the whole bond graph numerical model of the injector can be written in the uniform state equations. As shown in Figure 3, based on the causalities between variables and the flow direction of the power flow, the state equations of the system are obtained as follow;
Table 1. Basic bond graph elements for the components of the injector. Components
Basic bond graph elements
Solenoid valve
R, I, C, TF, Se
Fuel pipeline
R, I, C
Joint of pipeline and injector
R, I, C
Control chamber
R, C, TF
Needle moving part
R, I, C
Nozzle volume
C, TF
Nozzle
R, I, C, TF
⎞ dp5 1 ⎛ p4 − p5 p5 − p6 = ⎜ − − v1 A1 ⎟ dt C5 ⎝ R22 R23 ⎠
(7)
dp6 1 ⎛ p5 − p6 p6 − p7 ⎞ = ⎜ − ⎟ dt C6 ⎝ R23 R24 ⎠
(8)
⎞ dp7 1 ⎛ p6 − p7 2 p7 − p8 − v1 A2 ⎟⎟ = ⎜ − Cd2 f 2 dt C7 ⎝ R24 ρ ⎠
(9)
⎞ dp8 1 ⎛ 2 2 p7 − p8 − Cd3 f3 p8 − p9 − v1 A3 ⎟⎟ (10) = ⎜ Cd2 f 2 dt C8 ⎜⎝ ρ ρ ⎠ ⎞ dp9 1 ⎛ 2 2 = ⎜ Cd3 f 3 p8 − p9 − Cd4 f 4 p9 − pc − v1 A4 ⎟⎟ dt C9 ⎜⎝ ρ ρ ⎠
dF10 1 = v1 dt C10
(13)
⎞ dp11 1 ⎛ 2 2 = p3 − p11 + v1 A5 − Cd5 f 5 p11 − pl − v2 A6 ⎟⎟ ⎜ Cd1 f1 dt C11 ⎜⎝ ρ ρ ⎠
(14) (15) (16)
(1)
dv2 1 = ( p11 A6 + Fs − R30v2 − F12 ) dt I16
dp2 1 ⎛ p − p3 ⎞ = ⎜ q14 − 2 ⎟ dt C2 ⎝ R19 ⎠
(2)
dF12 1 = v2 dt C12
dq13 1 = ( pr − R17 q13 − p1 ) dt I13
(3)
The liquid capacitance of a chamber is calculated by the formula C=
(4)
dp3 1 ⎛ p2 − p3 2 p − p4 ⎞ = ⎜ − Cd1 f1 p3 − p11 − 3 ⎟ dt C3 ⎝ R19 ρ R21 ⎟⎠
(5)
dp4 1 ⎛ p3 − p4 p4 − p5 ⎞ = − ⎜ ⎟ dt C4 ⎝ R21 R22 ⎠
(6)
(11)
dv1 1 = ( p5 A1 + p7 A2 + p8 A3 + p9 A4 − F10 − R28v1 − p11 A5 ) (12) dt I15
dp1 1 = ( q13 − q14 ) dt C1
dq14 1 = ( p1 − R18q14 − p2 ) dt I14
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V E
(17)
where V is the volume of the chamber and E the fuel bulk modulus. If V changes slightly, it thinks that C is only related to E. However, in injection process, the volumes of control chamber etc. change relatively greatly with the movement of needle moving part. Thus, the variable liquid capacitance is given by the following equation;
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Figure 3. Complete bond graph model of the injector.
C=
V0 + Ax E
(18)
where V0 is the initial volume of the variable chamber, A and x are the effective pressure bearing area and the displacement of the moving part, respectively. There are a number of throttled orifices in the injector, such as inlet orifice, outlet orifice, and nozzle hole and so on. The flow rate of the fuel which flows through the throttled orifice can be expressed by the relation
q = Cd f
2 pu − pd ρ
(19)
where Cd and f are the flow coefficient and the flow area of the throttled orifice, ρ is fuel density, pu and pd are the pressure upstream and down-stream of the throttled orifice. In the present work, the needle of the injector is a double cone needle with nozzle holes located on the needle seat, as shown in Figure 4, σ is the needle seat angle, α is the needle
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Figure 4. Schematic of the nozzle. cone angle and de is the delivery chamber diameter. The nozzle includes two chambers which are intermediate chamber and delivery chamber, respectively. There are two restrictive areas between the needle and its seat, which are the throttled areas f3 and f4 (Hardenberg, 1984, 1985; Groen and Kok, 1996). The injection characteristic of the injector is influenced by the fuel properties (Tat and Gerpen, 2003; Boehman et al., 2004). Therefore, dynamic variations of keys fuel properties including density and bulk modulus during fuel injection process and varying pressures have been included in modeling using following empirical formulas (Nikolić et al., 2012); ρ = ρ0 + ρ1 p + ρ 2 p 2
(20)
E = E0 + E1 p + E2 p 2
(21)
Figure 5. Test bench of common rail system. nozzle holes. In this paper, for the hydraulic system, flow is fuel flow rate, effort is fuel pressure, for the mechanical system, flow is velocity of the moving part, effort is force. 16 state variables have been selected, including fuel pressure and flow rate in pipes and chambers denoted as p1, p2, p3, p4, p5, p6, p7, p8, p9, p11, q13, q14, velocity of needle and solenoid valve moving part denoted as v1 and v2, spring force of needle and solenoid valve denoted as F10 and F12. Rail
where p is the transient pressure in injector. ρ0, ρ1, ρ2, E0, E1 and E2 are the empirical coefficients whose values are 839.44, 0.48, − 5.32 × 10−4, 1.55, 1.07 and − 2.69 × 103, respectively.
4. EXPERIMENTAL SETUP AND MODEL VALIDATION Figure 5 shows the experimental setup for the injector tests, which consisted of the injector test bench, the injection flow meter, the rail pressure regulator, the injector solenoid valve control module and the terminal monitoring system. The test bench was designed to reproduce the operating condition of a CRIS. The high pressure pump is driven by a motor, which provides a precise rotational speed. The EFS 8246 flow meter is used to measure the injection rate. The entire injected volume is also available. The high pressure sensor mounted on common rail gives the feedback signal for the rail pressure regulation loop. The injector is controlled by the EFS 8233, which provides the power interface for the control of the solenoid valve and generates the logical signal to drive the injector. The PC terminal monitoring system displays the working conditions of the test bench and stores the data during the experiments. The diameter of the test injector nozzle holes is 0.15 mm with 7
Figure 6. Flowchart of the injector bond graph model simulation.
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Figure 7. Model validation at different injection pressures and injection durations.
Figure 8. Effect of delivery chamber diameter on FIQ.
pressure, cylinder pressure, electromagnetic force and low chamber pressure are chosen as input variables, and fuel injection quantity of the system is chosen as the output variable. The state equations of the common rail injector mentioned aboved were numerically solved by manual writing codes in m-file in Matlab. Figure 6 shows the flowchart of the injector bond graph modeling and gives the computational details of algorithm used for the model. In order to validate the proposed numerical model, several experimental tests were carried out. Three injection pressures are explored: 30, 90 and 160 MPa. For each of these pressures, eight different injection durations are considered. Experimental results are compared to those obtained by the proposed numerical model in Figure 7. As shown in the figure, the numerical predictions and experimental data for the injection quantity are in good agreement, which highlights the ability of the model to predict the actual FIQ of the injector with a considerable level of accuracy.
between needle chamber and delivery chamber as well as the increase in fuel pressure peak in the delivery chamber increases the injection pressure and fuel flow rate peak. These results in the flow rate of the fuel injected through the nozzle holes to the cylinder increased. In addition, with an increase in delivery chamber diameter, the flow area from intermediate chamber to delivery chamber increases at the same lift of the needle. Therefore, as shown in Figure 8, FIQ increases from 55.57 mm3 to 60.05 mm3 with increase in delivery chamber diameter from 0.6 mm to 1 mm.
5. EFFECTS OF PARAMETERS ON FIQ During the manufacture and assembly processes, there may be inconsistency in the parameters of the injector. In addition, at the running times of the injector, mechanical wear also leads to the parametric variations. Variations in the parameters of the injector influence the injection characteristics and lead to the variation in FIQ, which is very critical for the coherence and stability of the system. Therefore, in this section, the influence of the variations of injector parameters on FIQ was analyzed in detail. 5.1. Effects of Single Parameter 5.1.1. Delivery chamber diameter The volume of delivery chamber increases due increased diameter of the delivery chamber. This results in a reduction of intermediate chamber volume when the other parameters remain invariant. The shorten in the channel
5.1.2. Needle seat semi-angle Figure 9 shows the effect of needle seat semi-angle on FIQ. It is clear from the figure that with increasing needle seat semi-angle from 13˚ to 25˚, the FIQ is increased from 55.47 mm3 to 61.65 mm3. However, the increment of FIQ caused by the variation of needle seat semi-angle reduced gradually. Furthermore, increase in needle seat semi-angle from 25˚ to 29˚, leads to decrease in FIQ from 61.65 mm3 to 60.05 mm3. This could be due to the following fact: the flow area between needle chamber and intermediate chamber increases with an advancement of the needle seat semi-angle, whereas, the flow area between intermediate chamber and delivery chamber does not vary in different needle seat semi-angle. Thus, with increase in needle seat semi-angle, the decline in the throttled effect between needle chamber and intermediate chamber as well as the reduction of the flow resistance decreases the fuel pressure drop from needle chamber to intermetiate chamber. These result in a increase of the fuel pressure in intermetiate chamber, which causes a increase in fuel pressure in delivery chamber and leads to FIQ increases with the increase of needle seat semi-angle. Further increase of needle seat semi-angle, which is close to needle cone semiangle, decreases the volume of intermetiate chamber. At this condition, the intermetiate chamber plays the dominant role in throttling. This leads to the evidently increase in
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Figure 9. Effect of needle seat semi-angle on FIQ.
Figure 11. Effect of ball valve seat semi-angle on FIQ.
throttled effect from needle chamber to delivery chamber and the pressure loss of the fuel flowed through the intermetiate chamber increased. Therefore, FIQ is increased by increasing of needle seat semi-angle, whereas further increase in needle seat semi-angle leads to the decrease of FIQ.
that the FIQ increases from 60.05 mm3 to 63.49 mm3 with the increase of needle cone semi-angle from 30˚ to 46˚, and the increment amplitude of FIQ decreases gradually.
5.1.3. Needle cone semi-angle The variation of needle cone semi-angle mainly influences the flow area from intermediate chamber to delivery chamber. The initial volume of intermediate chamber increases with an increase in needle cone semi-angle which results in the increase of the flow area from intermediate chamber to delivery chamber. However, the increment amplitude of flow area from intermediate chamber to delivery chamber caused by the same increased angle of needle cone decreases gradually. This results in a decrease of throttled effect when the fuel flows through intermediate chamber to delivery chamber as well as a decline in pressure loss. Fuel pressure in delivery chamber increased at the same lift of the needle. Thus, Figure 10 demonstrates
Figure 10. Effect of needle cone semi-angle on FIQ.
5.1.4. Ball valve seat semi-angle Control chamber and low pressure fuel chamber are connected by the outlet orifice which is controlled by the on-off of ball valve. The minimum distance between ball valve and valve seat during the movement of the ball valve determines the throttling characteristics. Figure 11 clearly demonstrates that FIQ decreases from 62.16 mm3 to 59.53 mm3 with advancement of ball valve seat semi-angle from 51˚ to 59˚. This can be attributed to the fact that, the angle between the center line of injector and the contact point of ball valve and ball valve seat decreases with the increase of ball valve seat semi-angle. At a constant maximum lift of control valve, the maximal flow area between ball valve and ball valve seat decreases which results in an enhance of throttled effect. The pressure loss of the fuel flowed through the throttled area increases and the pressure of the fuel in control chamber drops reduces as a consequence. In addition, increasing the ball valve seat semi-angle causes a decrease in pressure bearing area of the ball valve closed to control chamber. This leads to a decrease in hydraulic force acted on ball valve from the fuel in control chamber when the ball valve is not opened. Thus, the opening moment of ball valve delayed. However, the variation of ball valve seat semi-angle has no significant effect on the movement of ball valve after the ball valve is opened. An increase in ball valve semi-angle results in a shorten in the whole movement of ball valve, that is, a reduces in discharge time of the high pressure fuel in control chamber. This finally leads to a decrease in fuel injection time through the nozzle holes, and reduces the FIQ. 5.1.5. Nozzle hole diameter Figure 12 shows the effect of nozzle hole diameter on FIQ. It can be observed that there is a linear increase in FIQ
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the pressure loss when fuel flows through it. In discharge process of the fuel in control chamber when the outlet orifice is opened by the ball valve, pressure drop of the fuel in control chamber reduces. The delay in the moment of nozzle holes completely opened as well as the ahead of time of nozzle holes closed absolutely results in the shorten in effective working time of the needle. Figure 13 presents the effect of inlet orifice diameter on FIQ. It can be seen that an increase in outlet orifice diameter from 0.16 mm to 0.24 mm leads to FIQ decreases from 83.82 mm3 to 60.05 mm3.
Figure 12. Effect of nozzle hole diameter on FIQ.
from 35.15 mm3 to 85.40 mm3 when the nozzle hole diameter is increased from 0.11 mm to 0.19 mm. The augmentation of nozzle hole diameter results in a decrease in throttled effect of nozzle hole. The fuel pressure in nozzle volume, needle chamber, intermediate chamber and delivery chamber reduces after the opening of nozzle hole. The moment when the needle reaches its maximum lift delay and the moment when the nozzle hole closed completely advanced. This leads to a shorten in the injection time of the nozzle hole. Whereas, the diameter of nozzle hole has influence on the flow area of the fuel in delivery chamber injected into the cylinder. An increase in nozzle hole diameter enhances the flow area of the fuel injected into the cylinder and leads to an increase in FIQ.
5.1.7. Outlet orifice diameter The diameter of outlet orifice has significant influence on its flow characteristics, and affects the discharge rate of the fuel in control chamber. Discharge area of the high pressure fuel in control chamber increases with increase in outlet orifice diameter. Thus, the throttled effect declines as well as the pressure loss of the fuel flowed through the outlet orifice reduces results in an increase in discharge rate in unit time. Meanwhile, the fuel discharge rate speeds up and the moment when needle reach its maximum lift is in advance. Due to the diameter variation of outlet orifice has less influence on the closure of the nozzle holes covered by the needle, the whole time from the nozzle holes begin to open to it is closed completely is prolonged. Therefore, as shown in Figure 14, it is vivid that an increase in outlet orifice diameter from 0.27 mm to 0.35 mm causes the increase of FIQ from 60.05 mm3 to 63.32 mm3.
5.1.6. Inlet orifice diameter Inlet orifice connects the control chamber and the inlet of injector. It plays an important role in throttling and has a direct influence on the flow area when fuel flows into control chamber. Advancement of inlet orifice diameter may lead to a decline of throttled effect which decreases
5.2. Interactive Effects of Two Parameters The above “one-factor-at-a-time” technique involves altering one factor at a time while keeping all the other parameters constant. This approach is timing consuming and often leads to an incomplete understanding of the system behavior, resulting in confusion and a lack of predictive ability. RSM is an effective tool when a response variable is influenced by several independent variables. The three-dimensional response surface is the most useful
Figure 13. Effect of inlet orifice diameter on FIQ.
Figure 14. Effect of outlet orifice diameter on FIQ.
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Table 2. Variables and their levels in the experimental design. Variables
Units
Symbols
Delivery chamber diameter
mm
Needle seat semi-angle
Code levels −1
0
1
X1
0.6
0.8
1
˚
X2
13
21
29
Needle cone semi-angle
˚
X3
30
38
46
Ball valve seat semi-angle
˚
X4
51
55
59
Nozzle hole diameter
mm
X5
0.11
0.15
0.19
Inlet orifice diameter
mm
X6
0.16
0.2
0.24
Outlet orifice diameter
mm
X7
0.27
0.31
0.35
approach in terms of visualization of the response, because it gives the simultaneous dependence from the two most significant parameters which affect the response. In this paper, based on face centered central composite design, experiments were conducted to develop the response surface model for FIQ in terms of two independent variables with minimum number of experiments. The second order polynomial equation in the following form is assumed to map the response surface n
n
i =1
i =1
n −1
be explained by the model. The ANOVA revealed that the developed response surface model is adequate and high significance to express the actual relationship between the FIQ and the independent variables. Table 3 lists the model items and the corresponding pvalues for the response surface model. It can be seen that the coefficients of all the linear terms, the quadratic terms for X12 and X72, and the interaction terms in X1X5, X2X3, X2X5, X3X5, X5X6 and X5X7 have significant effect on FIQ (p-value < 0.05). Thus, the interactive effect of delivery chamber diameter and nozzle hole diameter, needle seat semi-angle and needle cone semi-angle, needle seat semi-angle and nozzle hole diameter, needle cone semi-angle and nozzle hole diameter, nozzle hole diameter and inlet orifice diameter, and nozzle hole diameter and outlet orifice diameter have significant effect on FIQ. In this section, the FIQ response surface will be constructed and the significance interaction between these independent variables will be analyzed in detail. The analysis is limited to the interaction between two parameters only, therefore, the values of other parameters have been assigned their appropriate intermediate values.
n
Y = β 0 + ∑ β i X i + ∑ β ii X i2 + ∑ ∑ βij X i X j
(22)
i =1 j=i +1
where Y is the response variable, β0, βi, βii and βij are the coefficient of the response surface model, n is the number of independent variables and Xi is the independent variable. The independent variables and their levels in the experimental design are given in Table 2. Analysis of Variance (ANOVA) is used to verify model adequacy which provides numerical information about pvalue (Hirkude and Padalkar, 2014; Lee and Lee, 2015). Based on the ANOVA, the model was found to be significant as the value of p is less than 0.0001. Furthermore, the regression statistics goodness of fit (R2) and the goodness of prediction (Adjusted R2) are 0.998 and 0.995 respectively, which indicates that 99.8 % of the variability in FIQ could
5.2.1. Interactive effect of delivery chamber diameter and nozzle hole diameter
Table 3. Coefficients and their significant values of the model. Model item Constant
X1
X2 2.859
X3
X4
X5
X6
X7
1.692 − 0.883 26.395 − 9.264 1.513
Coefficient
71.344
3.326
p
< 0.05
< 0.05 < 0.05 < 0.05 < 0.05 < 0.05 < 0.05 < 0.05
Model item
X1X6
X1X7
X2X3
X2X4
X2X5
Coefficient
0.464
0.347
0.957
0.544
2.516 − 0.649 − 0.675 0.134
p
0.229
0.377
< 0.05 0.176 < 0.05
Model item Coefficient p
X4X6
X4X7
X5X6
X5X7
− 0.503 − 0.569 − 3.596 1.509 0.177
0.171
X6X7
X2X6 0.103 2 1
X
X2X7 0.087 2 2
X
X3X4 0.726 2 3
X
0.455 − 2.693 − 2.399 0.511
< 0.05 < 0.05 0.260
< 0.05
0.068
0.663
X1X2
X1X3
X1X4
X1X5
0.214 − 0.065 − 0.071 2.315 0.571
0.859
0.856
< 0.05
X3X5
X3X6
X3X7
X4X5
0.894 − 0.310 0.243 − 0.189 < 0.05 2 4
X
0.433 2 5
X
0.521 2 6
X
0.629 X72
0.761
1.271 − 0.986 − 3.093
0.496
0.251
0.443
< 0.05
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Figure 15. Interactive effect of delivery chamber diameter and nozzle hole diameter.
Figure 16. Interactive effect of needle seat semi-angle and needle cone semi-angle.
The interactive effect of delivery chamber diameter and nozzle hole diameter on FIQ is depicted in Figure 15. As seen in the three dimensional plot, at high nozzle hole diameter, the FIQ increases with increase in delivery chamber diameter. Whereas, at a low nozzle hole diameter, the FIQ increases with increase in delivery chamber diameter (from 0.6 mm to 0.8 mm) and decreases slightly with further increase in delivery chamber diameter (from 0.8 mm to 1 mm). In addition, for all delivery chamber diameter from 0.6 mm to 1 mm, the FIQ resulted in a linear increase in nozzle hole diameter. This could be due to the fact that FIQ increases with the increase of delivery chamber diameter and nozzle hole diameter. Therefore, for a given FIQ, delivery chamber diameter and nozzle hole diameter are negatively correlated when the nozzle hole diameter is high, that is, the nozzle hole diameter decreases with increase in delivery chamber diameter. However, there is a threshold value for delivery chamber diameter when nozzle hole diameter is low. There is a negative correlation between delivery chamber diameter and nozzle hole diameter, where the delivery chamber diameter is under the threshold value. This means that delivery chamber diameter increases despite of the decrease of nozzle hole diameter. There is a positive correlation between delivery chamber diameter and nozzle hole diameter, where the delivery chamber diameter is above the threshold value. This means that delivery chamber diameter increases with the increase of nozzle hole diameter.
in FIQ when the needle seat semi-angle is increased from 13˚ to 25˚ and later gradually decreases when the needle seat semi-angle is further increased to 29˚. This could be attributed to the fact that FIQ increases with the increase of needle cone semi-angle, and with increase in needle seat semi-angle, FIQ increases firstly and then decreases. A threshold value exists in the needle seat semi-angle. On one hand, in case of the specified FIQ, when the needle seat semi-angle is less than the threshold value, needle seat semi-angle decreases despite of the increase of the needle cone semi-angle. On the other hand, when the needle seat semi-angle is more than the threshold value, needle seat semi-angle increases with the increase of the needle cone semi-angle.
5.2.2. Interactive effect of needle seat semi-angle and needle cone semi-angle Figure 16 shows the effect of the interaction between needle seat semi-angle and needle cone semi-angle on FIQ. It is observed that FIQ increases with an increase in needle cone semi-angle at any designed values of needle seat semi-angle. It is clearly shown that there is a steady increase
5.2.3. Interactive effect of needle seat semi-angle and nozzle hole diameter
Figure 17. Interactive effect of needle seat semi-angle and nozzle hole diameter.
EFFECT OF INJECTOR PARAMETERS ON THE INJECTION QUANTITY OF COMMON RAIL INJECTION SYSTEM
Figure 17 shows the interactive effect of needle seat semiangle and nozzle hole diameter over FIQ. As seen from this figure, at high nozzle hole diameter, FIQ increases with increase in needle seat semi-angle. At a low nozzle hole diameter, as the needle seat semi-angle increases from 13˚ to 21˚, there is a increase in FIQ. However, beyond 21˚ of the needle seat semi-angle, an opposite trend prevailed in the FIQ. Furthermore, for a given needle seat semi-angle, the FIQ resulted in a linear increase in nozzle hole diameter. This may be because of the fact that, for a given FIQ, the nozzle hole diameter decreases with increase in needle seat semi-angle when the nozzle hole diameter is high. They are negatively correlated in this condition. A threshold value also exist in the needle seat semi-angle when the nozzle hole diameter is low. Below the threshold value, the nozzle hole diameter decreases gradually with the increase of needle seat semi-angle, while above the threshold value, the nozzle hole diameter increases with the increase of the needle seat semi-angle. 5.2.4. Interactive effect of needle cone semi-angle and nozzle hole diameter The FIQ three dimensional response surface plot of interaction between needle cone semi-angle and nozzle hole diameter is presented in Figure 18. As illustrated in the figure, the FIQ is increased on the advancement of nozzle hole diameter from 0.11 mm to 0.19 mm at all needle cone semi-angle. Meanwhile, during advancement of needle cone semi-angle from 30˚ to 46˚, the FIQ is increased slightly at all nozzle hole diameter. The possible reason for this trend could be that, at a given FIQ, with an increase in needle cone semi-angle, the nozzle hole diameter increases due to the negative correlation between them.
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Figure 19. Interactive effect of nozzle hole diameter and inlet orifice diameter. orifice diameter on FIQ is shown in Figure 19. It was observed that for nozzle hole at any diameter, increasing the inlet orifice diameter has a negative effect on FIQ. However, for a given inlet orifice diameter, increasing the nozzle hole diameter, has a positive effect on FIQ. These relations can be explained as follows. FIQ increases with increase in nozzle hole diameter, whereas, increasing the inlet orifice diameter decreases FIQ. Therefore, at a given FIQ, increase in inlet orifice diameter, leads to increase in nozzle hole diameter. A positive correlation can be observed between nozzle hole diameter and inlet orifice diameter.
5.2.5. Interactive effect of nozzle hole diameter and inlet orifice diameter The interactive effect of nozzle hole diameter and inlet
5.2.6. Interactive effect of nozzle hole diameter and outlet orifice diameter Figure 20 demonstrates the interactive effect of nozzle hole diameter and outlet orifice diameter on FIQ. It is obvious from the figure that an increase of nozzle hole diameter evidently increases FIQ at a constant outlet orifice diameter.
Figure 18. Interactive effect of needle cone semi-angle and nozzle hole diameter.
Figure 20. Interactive effect of nozzle hole diameter and outlet orifice diameter.
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At a constant nozzle hole diameter, FIQ increases with outlet orifice diameter, and then decreases with further increase of outlet orifice diameter. The above results could be due to the fact that FIQ increases with the increase of either nozzle hole diameter or outlet orifice diameter. There is a threshold value for the outlet orifice diameter. For a given FIQ, the nozzle hole diameter decreases with increase in outlet orifice diameter when the outlet orifice diameter is less than the threshold value. Thus, in this situation, nozzle hole diameter and outlet orifice diameter are negatively correlated. Whereas, there is a positive correlation between nozzle hole diameter and outlet orifice diameter, where the outlet orifice diameter is above the threshold value. This means that outlet orifice diameter increases with the increase of nozzle hole diameter.
6. CONCLUSION A numerical model of common rail injector has been developed using bond graph methodology, which can predict the FIQ of CRIS accurately. It provides an effective platform for the research on FIQ of the system. The influence rules of various parameters on FIQ have been obtained. It has been found that FIQ increases with the increase of delivery chamber diameter, needle cone semi-angle, nozzle hole diameter and outlet orifice diameter, whereas, an increase in ball valve seat semi-angle and inlet orifice diameter decreases the FIQ. Moreover, FIQ increases firstly and then decreases with an increase in needle seat semi-angle. Experiments have been conducted based on face centered central composite design. A second order polynomial response surface model is proposed for the purpose of predicting FIQ, as a function of the independent variables. ANOVA is used to determine the significance interactions between parameters which primarily affect FIQ. It is concluded that the interactive effect of delivery chamber diameter and nozzle hole diameter, needle seat semi-angle and needle cone semi-angle, needle seat semi-angle and nozzle hole diameter, needle cone semi-angle and nozzle hole diameter, nozzle hole diameter and inlet orifice diameter, and nozzle hole diameter and outlet orifice diameter have significant influences on FIQ of the system. ACKNOWLEDGEMENT−This research was supported by the National Natural Science Foundation of China (grant number NSFC 51279037, 51379041) and the Key Project of Chinese Ministry of Education (grant number 113060A).
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