Journal of Mechanical Science and Technology 30 (7) (2016) 3365~3377 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online)

DOI 10.1007/s12206-016-0646-z

Analysis upon fuel injection quantity variation of common rail system for diesel engines† Liyun Fan*, Yun Bai, Xiuzhen Ma and Enzhe Song School of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, China (Manuscript Received August 29, 2015; Revised February 14, 2016; Accepted March 8, 2016) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Fuel injection quantity variation of common rail system has effect on the stability and reliability of diesel engines. For purpose of investigating the influence rule and mechanism of fuel injection quantity variation caused by parameters, taking account of the influence of fuel physical properties on dynamic injection characteristics of the system, a bond graph model of common rail injector has been proposed based on bond graph methodology and the state equations of the system are obtained. Comparisons between calculated fuel injection quantities by the numerical model and experimental measurements at different rail pressures and injection pulse widths indicate that the developed model can reasonably predict the fuel injection quantity characteristic of the system. Fuel injection quantity variation characteristics caused by the parameters of common rail injector have been analyzed in entire operating conditions. The selected parameters are 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. The variation rules of quantitative percentages are obtained by quantitative analysis upon fuel injection quantity variation influential factors. It is concluded that ball valve seat semi-angle, nozzle hole diameter, inlet orifice diameter and outlet orifice diameter have the most significant effect on fuel injection quantity variation, and the followed are delivery chamber diameter and needle seat semi-angle. In addition, needle cone semi-angle also results in the variation of fuel injection quantity, but the effect is insignificant. Keywords: Bond graph methodology; Common rail system; Fuel injection quantity variation; Injector; Quantitative analysis ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction As environmental problems and energy crisis become more severe, the exhaust emission reduction technology and improvement of fuel consumption have become the major topics of diesel engines [1-4]. Diesel engine manufacturers have concentrated their efforts on the development of advanced fuel injection systems by raising the level of injection pressure considerably to obtain better atomization of the injected fuel [5-7]. Common rail injection system which is considered to be the most promising electronic control technology for diesel engines has obvious and outstanding advantages in reducing environmental pollution and saving energy [8-10]. As the critical component for common rail injection system, variation of injector parameters has significant influence on the coherence of fuel injection quantity. Traditional test research method is time-consuming, and subjects to the experimental conditions it is difficult to analyze the fuel injection quantity variation characteristic in depth [11, 12]. Therefore, numerical *

Corresponding author. Tel.: +86 151 2458 8186, Fax.: +86 451 82568316 E-mail address: [email protected] † Recommended by Associate Editor Kyoung Doug Min © KSME & Springer 2016

simulation for common rail injector is of great significance in both of theory and practice. In order to evaluate the influence of physical properties of biodiesel on injection process in a common-direct injection system with second generation solenoid injectors, Payri et al. [13] proposed a one-dimensional model. Several experimental measurements were performed using the injection rate test bench. The comparison of the injection rate proportionated 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. Chung et al. [14] developed a full-circuit numerical model of an indirect acting piezo injector with bypass-circuit by using AMESim code which is used to predict the dynamic flow characteristics of hydraulic components. The model had been verified by comparison with the experimental results. Xu et al. [15] developed a novel common-rail type DME injector. In order to validate the feasibility of the proposed design and investigate the influence of structure parameters on injector performance, a simulation model is established based on Flowmaster coupled Maxwell. An injector prototype was built to carry out experimental tests as the fuel of DME. The results showed that the simulation results

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are in agreement with the experimental results, therefore, the simulation model can better predict the novel injector performance. Catania et al. [16] applied a multijet CR injectionsystem mathematical model to better understand the cause and effect relationships for nozzle opening and closure delays. Parametric numerical tests were carried out to identify configurations useful for minimizing the nozzle closure delay. As common rail injector involves electromagnetic, mechanical and hydraulic domains with precision components, the variation of its parameter has influence on fuel injection quantity of the system which leads to the diesel engines working performance becomes deteriorated. Investigation upon effects of common rail injector parameters on fuel injection quantity variation is of great importance to optimally design and improve parameters of the system, as well as the coherence of the injection system. In this paper, a numerical model of common rail injector has been developed based on bond graph methodology. The accuracy of the model is validated by comparing the calculated fuel injection quantities with the experimental measurements at different rail pressures and injection pulse widths. The variation characteristics of fuel injection quantity caused by 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 have been studied in entire operating conditions. The variation rules of quantitative percentages are obtained by quantitative analysis upon fuel injection quantity variation influential factors.

2. Bond graph methodology and common rail injector Bond graph methodology is an energy flow chart which describes the composition, transformation and logical relations of power flow in the system [17]. Various of physical variables are classified as effort, flow, momentum and deflection from power flow perspective. The flow, collection and distribution of power and the energy conversion can be represented by bond graph methodology when the dynamic characteristics of the system are investigated [18]. In bond graph methodology, power bond, effect element, power source, junction, transformer and gyrator are used to represent the basic physical characteristics and relations of energy conversion and conservation in the system. Fig. 1(a) is power bond. It is denoted by a line segment, and the arrow denotes the flow direction of power. The efforts at 0 junction are identical, but the sum of the flows at 0 junction equal to 0, as shown in Fig. 1(b). Similarly, the flows at 1 junction are identical, but the sum of the efforts at 1 junction equal to 0, as shown in Fig. 1(c). Transformer TF is an energy transformer which is used to transform different kinds of energy or convert energy of the same type based on the law of conservation of energy, as shown in Fig. 1(d). Gyrator GY converts the effort or the flow on its power bond according to the proportionality coefficient, as shown in Fig. 1(e). The effect elements in bond graph methodology mainly include resistive effect, capacitive

(a) Power bond

(b) Bond graph of 0 junction

(c) Bond graph of 1 junction

(d) Bond graph of TF transformer

(e) Bond graph of GY gyrator

(f) Bond graphs of effect elements

(g) Bond graphs of power sources Fig. 1. Schematic of bond graph basic elements.

effect and inductive effect, as shown in Fig. 1(f). Resistive effect consumes energy, and capacitive effect and inductive effect store energy. These effect elements have influence on energy transfer process. Fig. 1(g) shows the power sources which include effort source and flow source. It is denoted by a power bond with power source written at one end, and represents the input power to the system. The characteristic equations between variables of 0 junction, 1 junction, transformer TF, gyrator GY, resistive effect, capacitive effect and inductive effect are as follow: e2 = e3 = e4 f 2 - f3 - f 4 = 0 f5 = f6 = f7 e5 - e6 - e7 = 0 e8 × m = e9 f8 / m = f9 e10 × r = f11 f10 / r = e11

(1) (2) (3) (4)

e12 = Rf12 1 t f13dt C òt0 1 t f14 = ò e14 dt I t0

e13 =

(5)

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proposed based on its composition and operating principle mentioned above, as shown in Fig. 3. According to the bond graph model in Fig. 3, the state equations of the system can be obtained. The state equations of high pressure fuel pipeline are:

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 Fig. 2. Schematic of common rail injector.

where ei (i = 2, …, 14) is the effort, fj (j = 2, …, 14) is the flow, m and r are the proportionality coefficients of the transformer and the gyrator, R is the resistive effect, C is the capacitive effect, I is the inductive effect, and t0 and t are the time bounds of integration, respectively. Common rail injector is mainly composed of injector body, solenoid valve components, control piston assembly and needle matching parts, as shown in Fig. 2. When the solenoid valve is power disconnected, outlet orifice is closed by the ball valve, nozzle holes are sealed by the needle and the injector does not inject fuel. As control signal is sent out to the injector by electronic control unit, control valve moves upwards, as well as the ball valve, the outlet orifice is opened. The high pressure fuel in control chamber flows into the low pressure chamber. 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 chamber pressures prevails over the needle spring preload, nozzle holes are opened by the needle and fuel is injected into the cylinder. When the solenoid valve is power disconnected again, control valve together with ball valve move downwards, and the outlet orifice is closed. When the hydraulic force acting on the control piston pluses the needle spring force overcome the force due to the hydraulic force acting on the shoulder of the needle in nozzle volume and on part of the needle tip in delivery chamber, the needle returns to its initial position and stops fuel injection.

3. Mathematical model of common rail injector The bond graph model of common rail injector has been

dp1 1 = ( q13 - q14 ) dt C1

(6)

dp2 1 æ p2 - p3 ö = çç q14 ÷ dt C2 è R19 ÷ø

(7)

dq13 1 = ( pr - R17 q13 - p1 ) dt I13

(8)

dq14 1 = ( p1 - R18q14 - p2 ) dt I14

(9)

where p1, p2, q13, q14, C1, C2, I13, I14, R17 and R18 are fuel pressures, flow rates, liquid capacitances, liquid inductances and liquid resistances of the two segments of the high pressure fuel pipeline, p3 and R19 are fuel pressure and liquid resistance of the high pressure fuel pipeline joint, and pr is the rail pressure. The state equation of high pressure fuel pipeline joint is: dp3 1 æ p2 - p3 2 p - p4 = - Cd 1 f15 p3 - p11 - 3 ç dt C3 çè R19 R21 r

ö ÷÷ ø

(10)

where p4 and p11 are fuel pressures in the pipeline from injector inlet to nozzle volume and control chamber, C3 is liquid capacitance of the high pressure fuel pipeline joint, R21 is half of the liquid resistance of the pipeline from injector inlet to nozzle volume, Cd1 and f15 are flow coefficient and flow area of the inlet orifice, and ρ is the fuel density. The state equation of the pipeline from injector inlet to nozzle volume is: dp4 1 æ p3 - p4 p4 - p5 ö = ç ÷ dt C4 è R21 R22 ø

(11)

where p5 is fuel pressure in nozzle volume, C4 is liquid capacitance of the pipeline from injector inlet to nozzle volume, and R22 is half of the liquid resistance of the pipeline from injector inlet to nozzle volume. The state equation of nozzle volume is: ö dp5 1 æ p4 - p5 p5 - p6 = - v1 A1 ÷÷ çç dt C5 è R22 R23 ø

(12)

where p6 is fuel pressure in the pipeline from nozzle volume to needle chamber, C5 is liquid capacitance of the nozzle volume, R23 is half of the liquid resistance of the pipeline from nozzle volume to needle chamber, v1 is velocity of the needle moving part, and A1 is the pressured area of the needle in nozzle volume.

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Fig. 3. Bond graph of common rail injector.

The state equation of the pipeline from nozzle volume to needle chamber is: dp6 1 æ p5 - p6 p6 - p7 ö = ç ÷ dt C6 çè R23 R24 ÷ø

(13)

where p7 is fuel pressure in needle chamber, C6 is liquid capacitance of the pipeline from nozzle volume to needle chamber, and R24 is half of the liquid resistance of the pipeline from nozzle volume to needle chamber. The state equations of nozzle are: ö dp7 1 æ p6 - p7 2 = - Cd 2 f16 p7 - p8 - v1 A2 ÷ ç ÷ dt C7 è R24 r ø

dp8 1 æ 2 = p7 - p8 ç Cd 2 f16 dt C8 çè r Cd 3 f17

(14)

(15)

ö p8 - p9 - v1 A3 ÷ ÷ r ø 2

where p8 and p9 are fuel pressures in intermediate chamber and delivery chamber, C7, C8 and C9 are liquid capacitances of the needle chamber, intermediate chamber and delivery chamber, pc is the cylinder pressure, Cd2, Cd3, Cd4, f16, f17 and f18 are flow coefficients and flow areas from needle chamber to intermediate chamber, from intermediate chamber to delivery chamber and nozzle holes, A2, A3 and A4 are the pressured areas of the needle in needle chamber, intermediate chamber and delivery chamber. As shown in Fig. 4, a double cone needle is investigated in this paper. Fig. 5 shows that there are two restrictive areas between needle and needle seat which change with needle lift. Therefore, the flow areas in the nozzle can be obtained by the following formulas [19-21]: b s b tan 2 - tan 2 m¢ = ( d a - d e ) cos s 2

(17)

2 tan

ö dp9 1 æ 2 2 = p8 - p9 - Cd 4 f18 p9 - pc - v1 A4 ÷ çç Cd 3 f17 ÷ dt C9 è r r ø

(16)

2 é b æ d e sin 1ê 2 çç1 + 1 M1 = ê b 4 ê x sin b + m¢ ç tan 2 ç êë 1 2 2 è

ö ÷ 1 ÷÷÷ tan b 2 ø

ù ú ú ú ûú

(18)

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Fig. 6. Schematic of ball valve flow area. Fig. 4. Schematic of nozzle.

dv1 1 = ( p5 A1 + p7 A2 + p8 A3 + p9 A4 - F10 - R28v1 - p11 A5 ) dt I15

(27) dF10 1 = v1 dt C10

where C10 and F10 are flexibility and force of the needle spring, I15 and R28 are mass and viscous damping coefficient of the needle moving part, and A5 is the pressured area of control piston. The state equation of control chamber is:

Fig. 5. Schematic of nozzle flow area.

tan b1 = M 1 f16 =

M 12 -

1 2

(19)

p

b æ ö ç x1 sin + m¢ ÷ëéd e cos b1 è 2 ø b b b æ öæ öù ç x1 sin + m¢ ÷ç cos + sin tan b1 ÷ ú 2 2 2 è øè øû

é 1 ê da M2 = ê 4 ê x1 ëê

æ ç 1 ç1 + b çç tan 2 2 è

tan b 2 = M 2 f17 =

M 22 -

p x1 s sin cos b 2 2

ö ÷ 1 ÷+ ÷÷ tan b 2 ø

ù ú ú ú ûú

1 2

(20)

(21)

(22)

é sæ s s öù ê d a + x1 sin ç cos - sin tan b 2 ÷ ú 2è 2 2 øû ë

(23) where da and de are diameters of the needle cone and delivery chamber, β and σ are angles of the needle cone and needle seat, and x1 is the needle lift. The pressured areas of the needle in nozzle can be calculated by the following relations: æ da - de ç 1 x0 = ç 2 ç tan s - tan b ç 2 2 è A3 = A4 =

p

{d 4

p

2 a

(28)

ö ÷ ÷ ÷÷ ø

- éë d e - ( x1 + x0 ) sin b ùû

(24)

2

}

2

é d e - ( x1 + x0 ) sin b ùû . 4ë

The state equations of needle moving part are:

(25) (26)

dp11 1 æ 2 = p3 - p11 + v1 A5 ç Cd 1 f15 dt C11 çè r ö 2 Cd 5 f19 p11 - pl - v2 A6 ÷ ÷ r ø

(29)

where pl is fuel pressure in low pressure chamber, C11 is liquid capacitance of the control chamber, Cd5 and f19 are flow coefficient and flow area of the ball valve, v2 is velocity of the solenoid valve moving part, and A6 is the pressured area of the ball valve at outlet orifice side. The outlet orifice of the injector is sealed by the ball valve. As shown in Fig. 6, the flow area of the ball valve changes with the variation of ball valve lift. It can be calculated by the following equation: f19 = p x2 ( d + x2 cos a ) sin a cos a

(30)

where x2 and d are lift and diameter of the ball valve, α is the angle between axial direction of the injector and distance from the centre of ball valve to ball valve seat. The state equations of solenoid valve are: dv2 1 = ( p11 A6 + Fs - R30v2 - F12 ) dt I16

(31)

dF12 1 = v2 dt C12

(32)

where C12 and F12 are flexibility and force of the solenoid valve spring, I16 and R30 are mass and viscous damping coefficient of the solenoid valve moving part, and Fs is electromagnetic force of the solenoid valve.

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The injection characteristics of common rail system are influenced by the fuel properties [22, 23]. Therefore, the dynamic variations of the key fuel properties including density and bulk modulus during fuel injection process have been considered in modeling in this paper using the following empirical formulas [24]:

Table 1. Variation range of the selected parameters. Parameter

Variation range

Delivery chamber diameter (mm)

0.6-1

Needle seat semi-angle (˚)

13-29

Needle cone semi-angle (˚)

30-46

Ball valve seat semi-angle (˚)

51-59

r = r 0 + r1 p + r 2 p 2

(33)

Nozzle hole diameter (mm)

0.14-0.16

E = E0 + E1 p + E2 p 2

(34)

Inlet orifice diameter (mm)

0.16-0.24

Outlet orifice diameter (mm)

0.27-0.35

where p is the transient fuel pressure in the 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 The state equations of common rail injector mentioned above are numerically solved by programming in Matlab. In order to validate the accuracy of the numerical model, a test bench of common rail injection system has been established, as shown in Fig. 7. The high pressure pump is driven by a motor which provides a precise rotational speed. During the experiments, the instantaneous injection volumes are measured with EFS 8246 flow meter which measures stroke-bystroke. For each injection cycle, five instantaneous injection volumes are measured which makes possible to control the fluctuation of the injection curve stroke-by-stroke. The high pressure sensor mounted on the common rail gives the feedback signal for the regulation loop. The injector is controlled by EFS 8233 which generates the logical signal to drive the injector. The PC terminal monitoring system displays the working condition of the test bench and stores the data during the experiments. The calculated fuel injection quantities by the bond graph numerical model and experimental measurements at different rail pressures and injection pulse widths have been compared, as shown in Fig. 8. The results indicate that the numerical predictions and experimental data of the fuel injection quantity are in good agreement, which demonstrates the acceptable accuracy of the proposed numerical model of common rail injector, and it can be used to reasonably predict the fuel injection quantity of the system at different working conditions.

5. Fuel injection quantity variation influential factor Fuel injection quantity is the key injection characteristic of common rail system. The variations of parameters in manufacture and application process result in fuel injection quantity variation and lead to the working stability of the injection system reduction which has influence on the working performance and economy of diesel engines. In this paper, the effects of fuel injection quantity variation caused by common rail injector parameters have been analyzed in entire operating conditions. The variation ranges of the selected parameters are

Fig. 7. Test bench of common rail injection system.

Fig. 8. Comparisons between calculated fuel injection quantities and experimental measurements.

listed in Table 1. 5.1 Delivery chamber diameter Delivery chamber is the last chamber in the injector for fuel injecting. Fuel injection quantity and injection rate of the system depend on the fuel pressure in delivery chamber. Therefore, the volume of delivery chamber has influence on fuel

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Fig. 9. The fuel injection quantity variation caused by delivery chamber diameter.

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With an increase in injection pulse width, increasing rail pressure causes an increase in fuel injection quantity variation, but the velocity of the variation declines obviously. Fuel injection quantity variation increases with an increase in injection pulse width at different rail pressure. The needle cannot reach its maximum lift at small injection pulse width. With the increasing of needle seat semi-angle, the opening moment of the needle remains invariant, whereas the flow area from needle chamber to intermediate chamber increases which leads to the fuel pressures in intermediate chamber and delivery chamber increase. This means that the moment when the nozzle holes are sealed by the needle delay. The movement time of the needle extends with increase in needle lift, as well as the injection duration. This influence becomes seriously with the increasing of rail pressure, consequently results in the fuel injection quantity varies drastically with the variation of rail pressure when the injection pulse width is small. Further increase in injection pulse width, the needle reaches its maximum lift. At this condition, increasing needle seat semi-angle causes an advance in the moment when the needle reaches its maximum lift and a shortening of its rising time. However, the moment when the nozzle holes are sealed by the needle delay and its decline time extends which leads to an increase in injection duration. This influence increases with the increasing of rail pressure, while the variation comparatively less. 5.3 Needle cone semi-angle

Fig. 10. The fuel injection quantity variation caused by needle seat semi-angle.

injection quantity variation. The volume of delivery chamber is increased with increasing of delivery chamber diameter, which results in a rising of peak pressure in delivery chamber. The fuel injection rate injected through the nozzle holes increases at the same differential pressure. Fig. 9 shows the fuel injection quantity variation caused by delivery chamber diameter in entire operating conditions. Increasing rail pressure and injection pulse width causes an increase in fuel injection quantity of the system. Therefore, the fuel injection quantity variation is approximating linear increase with the increase in rail pressure and injection pulse width. At a rail pressure of 160 MPa and an injection pulse width of 3 ms, the maximum fuel injection quantity variation is 7.56 mm3. 5.2 Needle seat semi-angle Fig. 10 shows the fuel injection quantity variation characteristic in entire operating conditions when needle seat semiangle is 13˚, 21˚ and 29˚, respectively. Fuel injection quantity varies drastically with the increasing of rail pressure when the injection pulse width is small, and the maximum is 7.42 mm3.

Needle cone semi-angle affects the flow characteristic from intermediate chamber to delivery chamber. Increasing needle cone semi-angle leads to an increase in initial volume of the intermediate chamber, which causes an increase in flow area from intermediate chamber to delivery chamber and results in an increase in fuel pressure in delivery chamber. The fuel pressure in the system is fluctuant due to the reciprocating motion of the moving parts, which leads to the variation of fuel injection quantity at low rail pressure. However, increasing rail pressure and injection pulse width result in an extending in needle working time which restrains the pressure fluctuation in the system. At this condition, the variation of needle cone semi-angle no longer has significant effect on fuel injection quantity variation. Fig. 11 shows the fuel injection quantity variation caused by needle cone semi-angle in entire operating conditions. Needle cone semi-angle has significant effect on fuel injection quantity variation at low rail pressure, and the maximum is 0.30 mm3. Increasing of rail pressure leads to a decrease in fuel injection quantity variation, and fuel injection quantity of the system does not vary obviously with the increasing of injection pulse width at different needle cone semi-angle. 5.4 Ball valve seat semi-angle The fuel injection quantity variation characteristics at different ball valve seat semi-angle in entire operating conditions

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Fig. 11. The fuel injection quantity variation caused by needle cone semi-angle.

Fig. 13. The fuel injection quantity variation caused by nozzle hole diameter.

fuel injection quantity variation reduces. 5.5 Nozzle hole diameter

Fig. 12. The fuel injection quantity variation caused by ball valve seat semi-angle.

are shown in Fig. 12. The fuel injection quantity varies significantly at small injection pulse width, and the maximum is 8.42 mm3. Fuel injection quantity does not vary obviously with the increasing of injection pulse width and linearly increases with the increasing of rail pressure, but the increment amplitude is relatively small. Ball valve seals outlet orifice and then determines the fuel pressure in control chamber relief or not. The minimum distance between ball valve and valve seat determines the flow characteristic of the fuel flowed through the outlet orifice in control chamber. At the same lift of ball valve, increasing of ball valve seat semi-angle decreases the flow area between ball valve and valve seat, and reduces the fuel pressure drop in control chamber. This leads to a delay of ball valve opening moment and a reduction of fuel pressure relief time in control chamber which results in a decrease in injection duration. At small injection pulse width, with micro-displacement of the needle, ball valve seat semiangle has significant effect on fuel injection quantity, therefore, the fuel injection quantity varies obviously. Both of injection pressure and injection duration increase with the increasing of rail pressure and injection pulse width, the influence of ball valve seat semi-angle on injection process decreases and the

Nozzle hole determines the injected fuel flow characteristic, therefore has direct and significant influence on fuel injection quantity of the system. With decreasing of nozzle hole diameter, the flow area of nozzle hole is reduced which results in a obvious throttle. Thus, the flow coefficient of nozzle hole decreases, as well as the peak injection rate. At small injection pulse width, the flow area between needle and needle seat is less than that of the nozzle holes. At this condition, the throttling action between needle and needle seat is the main influential factor on fuel injection quantity, thus, the fuel injection quantity varies slightly at different nozzle hole diameter. However, with the increasing of injection pulse width, the needle lift is increased and reaches its maximum, the flow area between needle and needle seat is more than that of the nozzle holes. The size of the nozzle hole becomes the main influential factor on fuel injection quantity. Fig. 13 shows the fuel injection quantity variation characteristic in entire operating conditions when nozzle hole diameter is 0.14 mm, 0.15 mm and 0.16 mm, respectively. At a rail pressure of 160 MPa and an injection pulse width of 3 ms, the maximum fuel injection quantity variation is 22.41 mm3. Increasing rail pressure and injection pulse width lead to a linear increase in fuel injection quantity variation. 5.6 Inlet orifice diameter Inlet orifice diameter affects its flow characteristic and has influence on the fuel pressure in control chamber. When outlet orifice is open, increasing inlet orifice diameter reduces the relief velocity of the pressure in control chamber and decreases the rise velocity of the needle moving part. While the buildingup velocity of the fuel pressure in control chamber is accelerated which promotes the needle seals the nozzle holes quickly when outlet orifice is close. Therefore, increasing inlet orifice

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Fig. 14. The fuel injection quantity variation caused by inlet orifice diameter.

Fig. 15. The fuel injection quantity variation caused by outlet orifice diameter.

diameter reduces the injection duration and then decreases the injected fuel quantity. As shown in Fig. 14, inlet orifice diameter has significant effect on fuel injection quantity variation at small injection pulse width, and the maximum is 20.82 mm3. However, the variation of fuel injection quantity is relatively small at large injection pulse width and varies smoothly. Increasing rail pressure causes an increase in fuel injection quantity variation. The variation of inlet orifice diameter mainly affects the injection duration, thus the fuel injection quantity is influenced by the rail pressure. At small injection pulse width, fuel injection quantity of the system is extremely sensitive to the variation of fuel pressure. The reciprocating motion of the moving parts results in the pressure fluctuates drastically in control chamber. The fuel pressure fluctuations in control chamber are difference at different inlet orifice diameter, which have significant effect on injection duration and cause an obvious variation in fuel injection quantity.

pressure fluctuation in control chamber is extended. This decreases the influence of outlet orifice diameter on fuel pressure in control chamber at end of the fuel injection. Thus, the fuel injection quantity varies smoothly. As shown in Fig. 15, outlet orifice diameter has significant effect on fuel injection quantity variation at small injection pulse width. With the increasing of injection pulse width, the variation amplitude is increased, and the maximum is 11.94 mm3. However, the fuel injection quantity variation is comparatively small and varies slightly at large injection pulse width. Outlet orifice diameter affects the injection duration which results in the variation of fuel injection quantity. Increasing rail pressure leads to an approximate linear increase in fuel injection quantity, but the rate of the variation is relatively small.

5.7 Outlet orifice diameter Outlet orifice connects control chamber and low pressure chamber, and the diameter has influence on its flow characteristic. Increasing outlet orifice diameter causes an increase in relief velocity of fuel pressure in control chamber which results in an earlier moment of fuel injection. Simultaneously, the rise rate of the fuel pressure in control chamber in the process of ball valve sealed outlet orifice decrease and the end moment of fuel injection delay. At small injection pulse width, outlet orifice diameter not only has influence on the opening velocity of the needle, but also affects the lift of the needle. In addition, the injection duration is short at small injection pulse width, as well as the adjustment time of the fuel pressure in control chamber. The reciprocating motion of moving parts results in the pressure fluctuating drastically in control chamber. At this condition, the variation of outlet orifice diameter has significant effect on the fuel pressure in control chamber which leads to an obvious variation in fuel injection quantity. At large injection pulse width, the stabilization time of the fuel

6. Quantitative analysis upon influential factor Quantitative analysis is a method which applies quantitative percentage to evaluate the influence of influential factor on response. The variation rules of quantitative percentages are obtained by quantitative analysis upon fuel injection quantity variation influential factors. Fig. 16 shows the quantitative percentage of the injector parameters at different injection pulse width and rail pressure of 40 MPa, 100 MPa and 160 MPa, respectively. As shown in Fig. 16(a), the quantitative percentages of delivery chamber diameter, needle seat semiangle, needle cone semi-angle, ball valve seat semi-angle, nozzle hole diameter, inlet orifice diameter and outlet orifice diameter at different injection pulse width and rail pressure of 40 MPa are 0% to 5.4%, 0.2% to 6.4%, 0.1% to 0.7%, 3.0% to 55.4%, 0% to 60.0%, 8.6% to 41.8% and 3.1% to 35.1%, respectively. Both of the quantitative percentages of delivery chamber diameter and nozzle hole diameter increase with an advancement of injection pulse width, but the increasing rates is reduced. In addition, the quantitative percentage increment of delivery chamber diameter is smaller than that of the nozzle hole diameter. Increasing injection pulse width decreases the quantitative percentage of ball valve seat semi-angle. The

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quantitative percentage of ball valve seat semi-angle decreases rapidly with the increasing of injection pulse width from 0.2 ms to 0.6 ms. Further increase in injection pulse width reduces the decreasing rate of the quantitative percentage of ball valve seat semi-angle. The quantitative percentages of needle seat semi-angle, needle cone semi-angle and inlet orifice diameter fluctuate obviously from injection pulse width of 0.2 ms to 0.8 ms. However, these three quantitative percentages decrease with the increasing of injection pulse width when it is more than 0.8 ms. The quantitative percentage of outlet orifice diameter also fluctuates significantly with increasing injection pulse width from 0.2 ms to 0.8 ms. While it hardly varies with the increasing of injection pulse width when it is more than 0.8 ms. As shown in Fig. 16(b), the quantitative percentages 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 at different injection pulse width and rail pressure of 100 MPa are 0.5% to 5.9%, 4.1% to 6.6%, 0.2% to 0.4%, 3.4% to 25.8%, 5.6% to 65.4%, 18.8% to 42.9% and 2.3% to 26.1%, respectively. The variation characteristics of the quantitative percentage of delivery chamber diameter and nozzle hole diameter are identical with those at rail pressure of 40 MPa. Increasing injection pulse width causes a decrease in quantitative percentages of ball valve seat semi-angle and outlet orifice diameter. Both of these two quantitative percentages decrease rapidly with the increasing of injection pulse width from 0.2 ms to 0.4 ms. Further increase in injection pulse width reduces the decreasing rate of these quantitative percentages. Moreover, these quantitative percentages fluctuate firstly with the increasing of injection pulse width from 0.4 ms to 2 ms, and then decrease approximate linearly. The quantitative percentages of needle seat semi-angle, needle cone semi-angle and inlet orifice diameter increase with increasing injection pulse width from 0.2 ms to 0.4 ms. However, these three quantitative percentages decrease with the increasing of injection pulse width when it is more than 0.4 ms. As shown in Fig. 16(c), the quantitative percentages 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 at different injection pulse width and rail pressure of 160 MPa are 2.2% to 6.0%, 3.8% to 5.5%, 0.2% to 0.3%, 4.3% to 30.1%, 24.5% to 66.8%, 16.7% to 35.2% and 2.3% to 23.6%, respectively. The variation characteristics of the quantitative percentage of delivery chamber diameter, nozzle hole diameter and outlet orifice diameter are identical with those at rail pressure of 100 MPa. Increasing injection pulse width from 0.2 ms to 1.2 ms decreases the quantitative percentages of needle seat semiangle, needle cone semi-angle and inlet orifice diameter. Further increase in injection pulse width reduces the decreasing rate of these three quantitative percentages. The quantitative percentage of ball valve seat semi-angle increases firstly and then decreases with the increasing of injection pulse width

(a) Rail pressure of 40 MPa

(b) Rail pressure of 100 MPa

(c) Rail pressure of 160 MPa 1. Delivery chamber diameter, 2. Needle seat semi-angle, 3. Needle cone semi-angle, 4. Ball valve seat semi-angle, 5. Nozzle hole diameter, 6. Inlet orifice diameter, 7. Outlet orifice diameter Fig. 16. Quantitative analysis upon influential factors at different rail pressures.

from 0.2 ms to 0.6 ms, and the variation rate is obvious. Further increase in injection pulse width reduces the decreasing rate of the quantitative percentages of ball valve seat semiangle. Fig. 17 shows the quantitative percentages of the injector

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parameters at different rail pressure and injection pulse width of 0.4 ms, 1.6 ms and 3 ms, respectively. As shown in Fig. 17(a), the quantitative percentages 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 at different rail pressure and injection pulse width of 0.4 ms are 0.4% to 3.3%, 4.8% to 6.6%, 0.3% to 1%, 5.9% to 30.1%, 4.7% to 36.1%, 28.3% to 43.0% and 3.7% to 30.7%, respectively. Both of the quantitative percentages of delivery chamber diameter and nozzle hole diameter increase with the increasing of rail pressure from 30 MPa to 100 MPa. These two quantitative percentages are invariable and independent of the rail pressure from 100 MPa to 150 MPa. However, further increase in rail pressure decreases these quantitative percentages with a faster decreasing rate. The quantitative percentages of needle seat semi-angle and inlet orifice diameter decrease with advancement of rail pressure from 30 MPa to 60 MPa. Further increase in rail pressure causes these two quantitative percentages increase firstly and then decrease. Increasing rail pressure causes a decrease in quantitative percentage of the needle cone semi-angle. The quantitative percentage of needle cone semi-angle decreases rapidly at first with increasing rail pressure from 30 MPa to 60 MPa, and then the decreasing rate reduces with further increase in rail pressure. The quantitative percentage of ball valve seat semi-angle fluctuates slightly with increasing rail pressure from 30 MPa to 60 MPa. When the rail pressure is increased from 60 MPa to 70 MPa, this quantitative percentage decreases rapidly, but increases with further increasing rail pressure. The quantitative percentage variation characteristic of outlet orifice diameter is similar with that of the ball valve seat semi-angle. The quantitative percentage of outlet orifice diameter fluctuates slightly with the increasing of rail pressure from 30 MPa to 60 MPa. Further increase in rail pressure leads to a decrease in quantitative percentage of the outlet orifice diameter with a faster decreasing rate. In addition, the quantitative percentage of outlet orifice diameter is invariable and independent of the rail pressure from 100 MPa to 160 MPa. As shown in Fig. 17(b), the quantitative percentages 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 at different rail pressure and injection pulse width of 1.6 ms are 1.7% to 4.2%, 4.6% to 6.8%, 0.3% to 0.7%, 4.5% to 13.3%, 11.2% to 43.8%, 32.4% to 42.9% and 3.7% to 31.6%, respectively. The quantitative percentages of delivery chamber diameter and nozzle hole diameter increase with the increasing of rail pressure. Moreover, the variation amplitude of the quantitative percentage of delivery chamber diameter is relatively small. Increasing rail pressure from 30 MPa to 60 MPa, the quantitative percentages of needle seat semi-angle, needle cone semiangle and inlet orifice diameter decrease firstly and then increase. Further increase in rail pressure reduces these three quantitative percentages with a slower decreasing rate. The

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(a) Injection pulse width of 0.4 ms

(b) Injection pulse width of 1.6 ms

(c) Injection pulse width of 3 ms 1. Delivery chamber diameter, 2. Needle seat semi-angle, 3. Needle cone semi-angle, 4. Ball valve seat semi-angle, 5. Nozzle hole diameter, 6. Inlet orifice diameter, 7. Outlet orifice diameter Fig. 17. Quantitative analysis upon influential factors at different injection pulse widths.

quantitative percentage of ball valve seat semi-angle fluctuates with the increasing of rail pressure, and the fluctuation amplitude decreases with increasing rail pressure. The quantitative percentage of outlet orifice diameter increases slightly at first and then decreases rapidly with increasing rail pressure from

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30 MPa to 60 MPa, and it fluctuates slightly with further increase in rail pressure. As shown in Fig. 17(c), the quantitative percentages 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 at different rail pressure and injection pulse width of 3 ms are 3.0% to 4.3%, 5.1% to 6.4%, 0.3% to 0.7%, 3.2% to 9.2%, 29.5% to 43.7%, 32.3% to 41.6% and 3.6% to 23.9%, respectively. The quantitative percentages of delivery chamber diameter and nozzle hole diameter increase with the increasing of rail pressure, but the increasing amplitude is obvious smaller than those of rail pressure of 100 MPa. Increasing rail pressure from 30 MPa to 40 MPa, both of the quantitative percentages of needle seat semi-angle and inlet orifice diameter is increased. However, these two quantitative percentages decrease with further increase in rail pressure. The quantitative percentages of needle cone semi-angle and outlet orifice diameter decrease with increasing rail pressure. Increasing rail pressure from 30 MPa to 40 MPa, the quantitative percentage of outlet orifice diameter decreases rapidly at first and then the decreasing rate reduces obviously. The quantitative percentage of ball valve seat semi-angle increases firstly and then decreases with the increasing of rail pressure from 30 MPa to 60 MPa, and increases with further increase in rail pressure.

7. Conclusions A numerical model of common rail injector has been proposed based on bond graph methodology. Comparisons between the calculated fuel injection quantities by the model and experimental measurements at different rail pressures and injection pulse widths indicate that the numerical model has an acceptable accuracy. The fuel injection quantity variation characteristics caused by the injector parameters such as 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 are investigated in entire operating conditions. The influence mechanism of different parameters on fuel injection quantity variation of the system has been analyzed in detail. The variation rules of quantitative percentages are obtained by quantitative analysis upon fuel injection quantity variation influential factors. At different rail pressure and injection pulse width, the quantitative percentages 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 are 0% to 6.0%, 0.2% to 6.8%, 0.1% to 1%, 3.0% to 55.4%, 0% to 66.8%, 8.6% to 43.0% and 2.3% to 35.1%, respectively. The results show that ball valve seat semi-angle, nozzle hole diameter, inlet orifice diameter and outlet orifice diameter have the most significant effect on fuel injection quantity variation, followed by the delivery chamber diameter and needle seat semi-angle. In

addition, needle cone semi-angle also results in the variation of fuel injection quantity, but the effect is insignificant.

Acknowledgment This work supported by the National Nature Science Foundation of China (NSFC 51279037, 51379041 and 51475100), China; Key Project of Chinese Ministry of Education (113060A), China.

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Liyun Fan received his B.S. degree in Power and Energy Engineering in 2003 and Ph.D. degree in Power Machinery and Engineering in 2008 from Dalian University of Technology, China. Dr. Fan is current a professor of power machinery and engineering in the College of Power and Energy Engineering, Harbin Engineering University, China. His research interests include electronically controlled fuel injection technology of advanced diesel engines and modeling and simulation of diesel engine power plants. Yun Bai received his B.S. degree in Engineering Mechanics in 2011 from Shenyang Aerospace University, China. Mr. Bai is currently a Ph.D. student at Institute of Engine Electronic Control Technology in the College of Power and Energy Engineering, Harbin Engineering University, China. His research interests include modeling and simulation of diesel engine power plants, and optimization of diesel engines fuel injection system.