Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science http://pic.sagepub.com/
Virtual prototype modeling and performance analysis of the air-powered engine Xu Qiyue, Shi Yan, Yu Qihui and Cai Maolin Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2014 228: 2642 originally published online 29 January 2014 DOI: 10.1177/0954406214520818 The online version of this article can be found at: http://pic.sagepub.com/content/228/14/2642
Published by: http://www.sagepublications.com
On behalf of:
Institution of Mechanical Engineers
Additional services and information for Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science can be found at: Email Alerts: http://pic.sagepub.com/cgi/alerts Subscriptions: http://pic.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav Citations: http://pic.sagepub.com/content/228/14/2642.refs.html
>> Version of Record - Sep 4, 2014 OnlineFirst Version of Record - Jan 29, 2014 What is This?
Downloaded from pic.sagepub.com by guest on September 5, 2014
Original Article
Virtual prototype modeling and performance analysis of the air-powered engine
Proc IMechE Part C: J Mechanical Engineering Science 2014, Vol. 228(14) 2642–2651 ! IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406214520818 pic.sagepub.com
Xu Qiyue, Shi Yan, Yu Qihui and Cai Maolin
Abstract For accurate modeling and optimization of the air-powered engine, the basic model of the air-powered engine’s working process was established at first. Experiments on a prototype modified from an internal combustion engine were carried out to verify the air-powered engine’s feasibility and the basic model’s validity. Based on the experimental results, a balanced valve was designed. Afterward, the virtual prototype with the newly designed valve system was built and relative simulations were conducted to analyze the dynamic performances of the air-powered engine. Results show that the valve controlling model is easy to achieve parameterization. The output performance of the designed valve is superior to that of a solenoid valve. Furthermore, the inertia moment of the flywheel is analyzed to balance the starting performance and speed fluctuations. At last, orthogonal design and gray relation analysis were utilized to optimize the valve timing parameters, and optimized values of the cam rise angle and the cam return angle are proposed. This research can provide theoretical supports to the new air-powered engine prototype’s design and optimization. Keywords Air-powered engine, dynamic, virtual prototype, performance analysis Date received: 22 July 2013; accepted: 19 December 2013
Introduction As a new type of power equipment, the air-powered engine (APE) is driven by compressed air that can be obtained from the power generation process of renewable energies, such as solar energy, wind energy and tidal energy. The compressed air, as a kind of medium, can store these unstable energies in the form of pressure energy in large scale.1,2 Its energy release process can be completely free from contamination. The compressed air expands in the APE’s cylinder, driving the piston to output work and is discharged in the form of breathable gas at low temperature. Serving as engines of motor vehicles, the APE can achieve zero carbon emissions. So in recent years, research on the APE have been widely carried out.3–5 MDI, a French company designing air-powered vehicles, developed a series of APEs.6,7 In China, some universities and companies also successfully manufactured different types of APEs.8–10 But generally limited by low working efficiency of the compressed air, low-temperature ice block and critical parts’ performance, the APE is still in the development stage. Therefore, precise modeling and simulation can not only lay a foundation for the design of
the APE but also save development costs. The displacement and stroke-bore ratio of the APE were studied by Liu et al.11 The influence of inlet and outlet valve’s open timing on pneumatic engine and their optimal design were researched by Nie et al..12 Simulation and experimental studies of electro-pneumatic valve used in APE were carried out by Chen et al.13 However, simulation researches of the APE’s working process in these studies are mainly based on steady-state modeling and the hypothesis that the angular velocity is constant. Under the above-mentioned conditions, parameters and performances are analyzed. Multi-body dynamics model about detail structures has not been set up; therefore, dynamic performances of the APE such as the startup process and speed fluctuations cannot be analyzed. Structure rationality related to the vibratory impulse is not considered. In addition, performance optimizations11–14 School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China Corresponding author: Shi Yan, School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China. Email:
[email protected]
Downloaded from pic.sagepub.com by guest on September 5, 2014
Qiyue et al.
2643 2. The air in the cylinder is uniform during the thermodynamic process. 3. The airflow in and out of the cylinder is considered as quasi-steady, one-dimension and isentropic. 4. The air’s kinetic energy and potential energy are ignored. 5. There is no leak during the working cycle.
Energy equation. The energy equation can be given as dU dQ dm1 dm2 dW ¼ þh1 þ h2 þ d d d d d Figure 1. Working cycle of the APE. APE: air-powered engine.
are mainly analyses of the independent effect of a single parameter, and the parameters’ coupling and the comprehensive performance evaluation are ignored. This study focuses on the virtual prototype modeling method and the multi-parameter and multi-objective performance analyses of the APE. Results of the study can be used to evaluate the APE’s dynamic performances and provide solutions for the optimization of crucial parameters, especially the valve timing parameters.
Basic modeling and experimental verification
where U is the internal energy of the air in the cylinder, Q is the heat absorbed by the air from outside, h1 and h2 are the specific enthalpy of the air flow in and out of the cylinder, respectively, m1 and m2 are the mass of the air flow in and out, respectively, W is the work and is the crank angle. The heat capacity of the engine body made of metal is much bigger than that of the air; so the temperature of the internal walls can be considered to be constant. Thus the heat transfer is dQ=dt ¼ cAh ðÞT ¼ ct Ah ðÞðTa TÞ
For a single-stage piston-type APE, its operation is controlled by the valve system as shown in Figure 1. In the suction power stroke, the compressed air enters the cylinder through the intake valve because of the pressure difference, driving the piston downward. Then the intake valve closes after a specific crank angle while the compressed air continues to push the piston down and output work. When the piston is near the bottom dead center (BDC), the exhaust valve opens so that the air with residual pressure discharges under the impetus of the piston. After the piston moves back to the top dead center (TDC), the APE completes a work cycle.
The steady-state model based on the crank angle was built at first. In the modeling process, the following assumptions are made: 1. The compressed air is ideal, which means specific heat u and specific enthalpy h are only related to the temperature.
ð3Þ
where m is the mass of the air in the cylinder. For ideal air, it can be yielded du ¼ Cv dT
ð4Þ
where Cv is the constant volume specific heat. Substituting equation (4) into equation (3) yields dU ¼ mCv dT þ Cv T dm
ð5Þ
The work done by the compressed air is described by dW¼ p dV
Basic model of the working process
ð2Þ
where ct is the heat transfer coefficient, Ah ðÞ is the total heat transfer area, Ta is the temperature of the internal walls and T is the temperature of the air in the cylinder. The internal energy of gas can be expressed as dU ¼ dðmuÞ ¼ m du þ u dm
Working principle of the APE
ð1Þ
ð6Þ
Substituting equations (2)–(6) into equation (1) yields dT 1 dV ¼ uG ct Ah ðÞT þ h1 G1 þ h2 G2 p d mCv d ð7Þ where G1 ¼ dm1 =d, G2 ¼ dm2 =d, G ¼ dm=d.
Downloaded from pic.sagepub.com by guest on September 5, 2014
2644
Proc IMechE Part C: J Mechanical Engineering Science 228(14)
Continuity equation. The intake and exhaust air flow rate of the APE can be calculated as follows 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kþ1 > > 1 k 2 k1 > > AðÞ pi , > > > ! Rg Ti kþ1 > > k > > > 2 k1 > po > > < pi 4 kþ1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gi ¼ " 2 kþ1 #ffi u > u > 1 2k 1 po k po k > > , AðÞ pi t > > >! k1 Rg Ti pi pi > > > > k > > po 2 k1 > > 4 : kþ1 pi
Figure 2(b) shows the schematic diagram of the test bench.
Results and analyses
ð8Þ where ! is the angular speed of the crank shaft, A() is the effective sectional area of the intake or exhaust valve, it is a function of the crank angle and for simplicity can be set as a step function in the simulation, k is the adiabatic exponent of the air, Rg is the gas constant, pi and Ti are the upstream pressure and temperature, respectively, they express the air state of the air source during the intake phase and of the air in the cylinder during the exhaust phase, and po is the downstream pressure.
1. After adjusting the valve timing, the prototype can operate smoothly. When the source air pressure ps was 0.35 MPa, the rotation speed n was 200 r/min and the average output torque was approximately 2 N m. Since the effective sectional area of the solenoid valve is too small, the pressure loss due to the throttling is severe. Figure 3 shows a curve of the cylinder pressure p intercepted during the operation in the above condition. As can be seen, the peak pressure is only about 0.24 MPa. 2. To verify the basic working model, the valve phase configuration of the model was made the same as the solenoid valves’, the inlet pressure pin was set equal to the peak cylinder pressure in the experiments. When pin¼0.24 MPa and n ¼ 200 r/min, the cylinder pressure data was obtained by the simulation and converted to the curve with time as shown in Figure 3. The experimental and
State equation. Ideal air meets the equation of the state pV ¼ mRg T
ð9Þ
where Rg is the gas constant of air (J(kgK)-1). Torque equation. Force analysis is carried out on the piston crank connecting rod mechanism, and the ideal torque output can be described by M ¼ ðFg þ Fj Þ
sin½ þ arcsinð sin Þ r cos
ð10Þ
where Fg is the driving force of the compressed air on the piston along the axis of the cylinder, Fj is the reciprocating inertial force, is the crank ratio and r is the crank radius.
Experimental verification To verify the feasibility of the APE and the accuracy of the basic model, a prototype was modified from a single cylinder piston-type internal combustion (IC) engine by transforming its valve system. For ease of control, the original mechanical valves were replaced by solenoid valves whose actions were controlled according to the crank angle detection and the phase configuration. After that a dedicated test bench for the APE was designed and built to measure the APE’s inlet pressure, temperature, cylinder pressure, rotation speed, power, torque and other parameters (as shown in Figure 2a).
Figure 2. The validation prototype of the APE and its test bench: (a) photograph of the experimental setup and (b) schematic diagram of the test bench. APE: air-powered engine.
Downloaded from pic.sagepub.com by guest on September 5, 2014
Qiyue et al.
2645
0.25
340 simulation curve experimental curve
320 300
p/MPa
-
n/(r·min 1)
0.2
0.15
280 260 240 220
0.1
200 0
0.1
0.2
0.3
0.4
0.5
0.6
0.35
0.7
0.4
0.45
0.5
0.55
0.6
0.65
0.7
ps /MPa
t/s
Figure 3. Cylinder pressure curves from the experimental testing and the simulation.
simulation curves have similar trends. Both pressure curves rise rapidly during the intake process and have a first quick drop due to the air expansion driving the piston downward and then a second quick drop due to the opening of the exhaust valve. But since the valves’ actions are step-type and the sectional areas are idealized in the model, the pressure change is faster than that in the experiment. The simulated pressure curve reaches its peak faster and then descents slowly due to the low piston speed around the TDC after the intake valve closes. And owning to the idealization of the exhaust valve, the residual pressure release process completes more quickly in the simulation. In the same condition, the average output torque according to the simulation is 2.11 N m and matches with the experimental data; so the model of the APE’s working cycle is reliable. 3. In the experiment, ps was raised while the load remained about 2 N m, the rotation speed increased but the growth rate reduced, as shown in Figure 4. So the power output of the crankshaft is considerably limited. In addition to the throttle pressure loss, it is mainly due to the response delay of the angular sensor and solenoid valves. From the above analysis it is concluded that solenoid valves cannot meet the performance demand of the APE. This article redesigns the APE focusing on the mechanical valve system’s improvements. The intake valve of conventional IC engines can prevent the gas leaking from inside the cylinder. But in APEs, the pressure outside the intake valve is always higher than that inside the cylinder. This situation can lead to problems like leakage from the intake valve or excessive preload of the spring that will further affect the performance of the valve system. A balanced valve was designed to prevent the high pressure difference on the intake valve and ensure the seal when it is closed, as shown in Figure 5. The valve rod
Figure 4. Rotational speed at different source air pressures, while the load remains 2 Nm.
6HDOJXLGH VOHHYH 9DOYH URG %DODQFHG DLUFKDPEHU
$LULQ OHW
)
)
)
)
Figure 5. Schematic diagram of the balanced valve.
is driven by the cam-plunger-rocker mechanism. Since the valve timing of APEs is considerably different from that of the IC engines, parameters of the valve phase need to be analyzed after the virtual prototype is built.
Modeling method of the virtual prototype There are many ways of multi-computational domain modeling of the mechanical system.15–18 SIMULINK is an easy way to realize the design of control models. SimMechanics, a mechanical dynamics simulation tool, provides CAD interfaces allowing importing three-dimension solid models into SIMULINK and connecting them with control models. Then mechanical dynamics models can be established.
Mechanism of the virtual prototype The air-working model and the valve-controlling model of the APE are built using SIMULINK,
Downloaded from pic.sagepub.com by guest on September 5, 2014
2646
Proc IMechE Part C: J Mechanical Engineering Science 228(14)
Figure 6. Mechanism of APE’s virtual prototype. APE: air-powered engine.
outputting the cylinder pressure and the movement of the valve driver, respectively, as inputs of the dynamics model. The physical model based on the imported solid models feeds back crank angle and angular velocity according to dynamic principles. Figure 6 shows the mechanism of the virtual prototype.
Dynamic modeling method Unlike steady-state engine modeling based on crank angle, time is treated as the independent variable in dynamic modeling. During the dynamic simulation, the state variables of the physical model are measured by corresponding sensor modules in real time. The APE remains stationary until an instant starting torque is applied on the crankshaft. Therefore, the rotational speed is unstable under the combined effect of real-time torques and the inertial moment.
Figure 7. Physical model of the APE. APE: air-powered engine.
Table 1. Major structural parameters. Parameter
Value
Piston stroke (m) Cylinder diameter (m) Cylinder’s initial volume (m3) Crank ratio Reciprocation (mass/kg)
0.050 0.052 0.00003 0.263 0.143
Reaction forces from followers are detected by force sensor modules and then applied on the camshaft. In this way the valve-controlling model is also parameterized. The motion of the valve lift is expressed as SðÞ ¼ i½Hð þ a Þ3 =3o 15Hð þ o Þ4 =4o
Virtual prototype Physical model
þ 6Hð þ a Þ5 =5o
The APE’s 3D solid model was built with Solidworks based on structures of the validation prototype and the newly designed balanced valve. Figure 7 shows parts of the APE’s model. The main structures include: cylinder cover, 2; cylinder, 3; crankshaft, 4 and crank piston mechanism, 5. The valve system includes: timing gears, 6; camshaft, 7; cam follower, 8; tunable rocker mechanism, 9 and balanced valves, 1. Major structural parameters are shown in Table 1.
Valve-controlling model Dynamic performances of the valve system based on cams are crucial in the design of the virtual prototype. This article establishes virtual cams and cam followers as well as valves of the virtual prototype are driven by the motion equation of the virtual cams.
ð11Þ
where i is the drive ratio of the rocker, H is the cam lift, o is the cam rise angle and a is the advance angle. For the intake valve, the advance angle means the advanced crank angle relative to the TDC when the intake valve starts to open. And for the exhaust valve, it means the advanced crank angle relative to the BDC when the exhaust valve starts to open. The motion of the valve fall can be described in symmetrical form. Thus the valve timing can be defined by these parameters: the rise angle o , the return angle c , the duration angle l and the advance angle a . For the balanced valve shown in Figure 5, its effective sectional area can be described by AðÞ ¼ SðÞ½D þ sinð2v ÞSðÞ=2 cos v
Downloaded from pic.sagepub.com by guest on September 5, 2014
ð12Þ
Qiyue et al.
2647
where D is the valve diameter and v is the valve contact angel. Equations (11), (12), and (8) form a complete valve-controlling model.
Table 2. Main valve timing parameters. pin (MPa)
ina ( )
inl ( )
outa ( )
outl ( )
0.24
15
30
20
110
Crankshaft dynamic model Dynamic analysis of the APE is focused on torques on the crankshaft. Differential equations of the crankshaft are
0.2
where ! is the angular velocity, t is time, Mp is the driving torque generated by the expansion of the compressed air, Ms is a tunable instant stating torque, Mn is a tunable load torque that is related to the rotation speed and the damping coefficient, Mi ði ¼ 1, 2Þ is the real-time torque caused by the reaction force of the intake or exhaust valve, Me is the torque due to friction loss and the mechanical efficiency and ICr is the total moment of inertia of rotating parts on the crankshaft. With dynamic simulation tools, these torques are applied on the crankshaft of the virtual prototype through corresponding sensors and driving modules without building their analytical expressions.
Dynamic model of the working process Based on the form of equations in ‘‘Basic model of the working process,’’ the dynamic model takes time as the independent variable instead of the crank angle. For example, the differential equation of air temperature becomes dT 1 dV ¼ cAh ðtÞðTa TÞ þ h1 G1 þ hG2 p uG dt mCv dt ð14Þ where G1 ¼ dm1 =dt, G2 ¼ dm2 =dt and G ¼ dm=dt. The virtual prototype of the APE was established by connecting the above-mentioned physical model and control models, and all control variables and most of the structure variables were parameterized.
Performance analysis of the virtual prototype Operating status of the virtual prototype After debugging, the virtual prototype can be started and it can gradually achieve stable operation. It is possible to control the valve system by adjusting the parameters of the valve-controlling model. Compared with the previous experiment, the main parameters like intake advance angle ina , intake duration angle inl , exhaust advance angle outa and exhaust duration
p/MPa
ð13Þ
0.15
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t/s (b)
8
6
M/(N·m)
8 d > > ¼! < dt d! Mp þ Ms Mn Mi Me > > : ¼ dt ICr
(a) 0.25
4
2
0
-2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t/s
Figure 8. Cylinder pressure and instantaneous torque of the virtual prototype when main valve parameters are set as in Table 2: (a) cylinder pressure and (b) instantaneous torque.
angle outl were set as shown in Table 2. Rise angle and return angle of the valve were set to 45 to simulate the solenoid valve delay. The inlet pressure pin was set to 0.24 MPa and the load damping was adjusted until average rotational speed of the crank was about 200 r/min. A curve of the cylinder pressure is plotted in Figure 8(a) when the virtual prototype operates stably, and corresponding output torque M is shown in Figure 8(b). As can be seen from Figure 8(a), the virtual prototype’s cylinder pressure changes rapidly during the intake and exhaust process in spite of the big rise angle and return angle. That’s because the valve’s cross-sectional area changes quickly at the opening and closing moment. In addition, due to the reasonable configuration of the valve timing, the residual pressure is relatively low, leading to the high
Downloaded from pic.sagepub.com by guest on September 5, 2014
2648
Proc IMechE Part C: J Mechanical Engineering Science 228(14) Table 3. Speed fluctuation amplitude at different inertial moments of flywheel.
250
Ic =ðkg m2 Þ n=ðr min1 Þ
0.05 64
0.10 33
0.15 22
0.20 16
150
-
n/(r·min 1)
200
100
200 50
180 0
5
10
15
0.05kg·• 0.10kg·• 0.15kg·• 0.20kg·•
20
160
-
t/s
n/(r·min 1)
0
Figure 9. Rotational speed of the virtual prototype during startup.
140
120
expansion efficiency of the air. The ideal average torque Me can be calculated using the following expression Z
100 0
2
4
6
8
10
t/s
2T
Me ¼ 1=ð2TÞ
M dt
ð15Þ
0
where M is the instantaneous torque and T is the period. In the above conditions, the ideal average torque of the virtual prototype is 2.35 N m, higher than the experimental prototype’s data. As shown in Figure 8(b), the resistance torque during return stroke of the piston is small, so the working efficiency of the compressed air is high. Figure 9 shows the rotational speed of the crankshaft during the starting process. About 5–6 s after the startup, the average speed tends to stabilize but the fluctuation is quiet apparent.
Analyses on the inertial moment of flywheel Starting speed and smoothness are two important indicators of engines’ dynamic performance and related to the value of inertial moment. The inertial moment can be adjusted by the flywheel after the structure and size of engines are determined. The inertial moment of the flywheel Ic corresponding to the rotational speed shown in Figure 9 is 0.1 kg m2. As can be seen, the start time is short but speed fluctuation amplitude is large after the engine reaches stable state. With other parameters unchanged, Table 3 shows the fluctuation amplitude of the rotational speed n when Ic ¼ 0.05, 0.10, 0.15, 0.20 and 0.25 kg m2, respectively. And corresponding curves of the average rotational speed during startup are shown in Figure 10. The speed fluctuation amplitude is inversely proportional with the flywheel inertial moment, but the starting process becomes slower when the inertial moment increases. In conventional IC engines, size of the flywheel is generally expected to be reduced
Figure 10. Average rotational speed during startup at different inertial moment of flywheel.
considering structure’s compactness, so the rated speed is high. But in APEs, the expansion of the compressed air becomes less efficient when the rotational speed increases, so the designed speed is relatively low. This situation results in bigger size and weight of the flywheel and then greater stress load on the crankshaft. Through simulation tests with the dynamic virtual prototype, the inertial moment of the flywheel at different speed levels can be designed by balancing the start speed, the rotational fluctuation and the flywheel’s size. At present, the designed inlet pressure of the APE is 1 MPa. The rotational speed is about 1100 r/min when the output power is 1 kW. In this condition, the optimal flywheel’s inertial moment is 0.057 kg m2.
Analyses of the valve timing parameters based on performance optimization The APE’s performance indicators includes ideal power output Pe , working efficiency e , which represents the ratio of the ideal power output and the air power19 consumed, and average air temperature av , which affects mechanical behaviors of the engine. These indicators can be calculated by the following expressions 8 Z 2 > > > P ¼ 1=T pV d e > > < 0 ¼ Pe T=½min R1 lnð pin =p0 Þ > Z 2 > > > > : av ¼ 1=ð2Þ d
Downloaded from pic.sagepub.com by guest on September 5, 2014
0
ð16Þ
Qiyue et al.
2649
where V is the instantaneous volume of the cylinder, min is the mass of the intake air during one cycle, 1 is the inlet air’s temperature, p0 is the atmospheric pressure and is the instantaneous temperature in the cylinder. Structural parameters of the engine cannot be changed easily; in addition, simulation analysis shows that the inlet pressure and valve timing are key factors that influence the APE’s performances. So the major valve timing parameters as shown in Table 2 were analyzed. Ranges of the parameters are shown in Table 4. The independent analysis of individual parameters shows that different indicators of the APE cannot reach optimum at the same time. For example, Figure 11(a) shows the opposite trends of the ideal
Table 4. Ranges of the parameters. pin (MPa)
ina ( )
inl ( )
outa ( )
outl ( )
0.8–1.5
5–25
10–50
0–40
100–180
(a) 2.5
0.6
ideal power working efficiency 0.55
ηe
Pe/(kW )
2
1.5
0.5
1 0.8
0.9
1
1.1
1.2
1.3
1.4
power and the working efficiency at different inlet pressures. The coupling between parameters has no explicit expressions but do affect the performance optimization. For example, at different inlet pressures, the optimal value of the intake duration angle changes when the working efficiency is analyzed (as shown in Figure 11b). So the inlet pressure needs to be considered during the design of the intake duration angle and vice versa. In conclusion, the design of the APE is a multiparameter and multi-objective optimization problem. The coupling of the parameters should be considered and an effective comprehensive evaluation method is indispensable. In this article, orthogonal design20 was carried out to cover the discrete combinations of different parameters. The optimal parameter combination for the expected indicators was obtained using gray relation analysis.21–23 The orthogonal array can uniformly extract the representative combinations of minimum number from all parameter combinations. Table 5 is a part of the orthogonal array formed by the parameters in Table 4. To evaluate the N groups of parameter combinations in the orthogonal array, the evaluation set E ¼ ðPe , e , av Þ ¼ ðE1 , E2 , E3 Þ is formed by the indicators in equation (16). Dij is the calculated value of Ej through the virtual prototype’s running with No. i parameter combination, and then D ¼ ðDij ÞN3 is called gray relational decision matrix. The vector of expected indicators is expressed as D0 ¼ ðD01 , D02 , D03 Þ whose value is set according to design requirements and can be adjusted after each optimization calculation. The gray relational decision matrix is made dimensionless
0.45 1.5
Ddij ¼ Dij =D0j ,
Pin/(MPa)
(b)
i ¼ 1, 2, . . . , N; j ¼ 1, 2, 3
ð17Þ
0.7 inlet pressure 0.8MPa inlet pressure 0.6MPa 0.68
Table 5. Orthogonal array of the APE’s parameters (partial).
ηe
0.66
0.64
0.62
0.6 10
20
30
40
50
φinl /(°)
Figure 11. Optimization curves of some performance indicators: (a) ideal power and working efficiency at different inlet pressures and (b) working efficiency of the APE at different intake duration angles and inlet pressures. APE: air-powered engine.
No.
pin (MPa)
ina ( )
inl ( )
outa ( )
outl ( )
1 2 3 4 5 6 7 8 9 10
0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0
5 10 15 20 25 15 20 25 5 10
10 20 30 40 50 40 50 10 20 30
0 10 20 30 40 10 20 30 40 0
100 120 140 160 180 140 160 180 100 120
APE: air-powered engine.
Downloaded from pic.sagepub.com by guest on September 5, 2014
2650
Proc IMechE Part C: J Mechanical Engineering Science 228(14)
The gray relational coefficient between the dimensionless value Ddij and its corresponding expected indicator is expressed as fij , representing the match degree between Dij and D0j . The commonly used calculation formula for fij is min min1 Ddij þ max max1 Ddij i j i j fij ¼ 1 Ddij þ max max1 Ddij i
j
i ¼ 1, 2, . . . , N; j ¼ 1, 2, 3 ð18Þ Then the matrix Fr ¼ ð fij ÞN3 is called gray relation judgment matrix. The weight for different indicators is set according to engine’s design requirements. In this article, the vector of weights is v ¼ ð!1 , !2 , !3 ÞT ¼ (0.31, 0.53, 0.16). Then the relational degree between the calculated indicators of corresponding parameter combination and the expected indicators can be calculated by Ri ¼
3 X
i ¼ 1, 2, . . . , N
fij Wj
working efficiency of the compressed air. For example, Figure 12 shows the working efficiency at various rotational speeds and intake rise angles with other timing parameters set, as shown in Table 7. Therefore the magnitudes of o and c are expected to be small to achieve better performance. However, reducing the magnitudes of o and c will result in a steep transitional curve of the cam, increasing pressure between the cam and the followers and even affecting the structural feasibility. Furthermore, fast movement of the valves brings about great impact forces on the valve system. Because virtual cams are applied in the model, this study tried to set the rise angles and the return angles of both the intake and the exhaust valves to 15 without considering the structural rationality. After the virtual prototype operated stably, the force between the rocker and the pushrod of the intake valve during two opening and closing processes were measured. As can be seen in Figure 13, the instantaneous impact force due to the movement of the valve is much larger than the preload force of the
ð19Þ
j¼1
sffiffiffiffiffiffiffiffiffiffiffi 3 P !2j is called projection weight
0.56
1
0.54
vector of the gray relation. The optimal parameter combination then can be determined by the value of Ri . The bigger Ri is, the more the calculated indicators are fit with the expected indicators. In addition, the optimal indicators Di can be obtained. Through simulating calculations with the virtual prototype and adjustments of the expected indicators, the optimal performance indicators and corresponding combination of parameters within the ranges are obtained and shown in Tables 6 and 7. In addition to the main valve timing parameters, the rise angle o and the return angle c have influences on the output performance by affecting the valves’ operating speed. Low operating speed of the APE’s valves leads to more throttling loss and air consumption, which reduces the torque output and
0.52
ηe
where Wj ¼ !2j =
10° 20° 30° 40° 50°
0.58
0.5 0.48 0.46 0.44 0.42 0.4 800
900
1000
1100
1200
1300
1400
1500
1600
-
n/(r·min 1)
Figure 12. Working efficiency at various rotational speeds when the intake rise angle changes from 10 to 50 .
2000 1500 1000
Table 6. Optimal performance indicators. e
Pe (kW)
av (K)
F/N
500 0 -500
1.31
51.1%
234
-1000 -1500 -2000 0
Table 7. Optimal combination of the parameters.
0.01
0.02
0.03
0.04
0.05
0.06
t/s
pin (MPa)
ina ( )
inl ( )
outa ( )
outl ( )
1.0
5
46
0
124
Figure 13. Impact force between the rocker and the pushrod of the intake valve.
Downloaded from pic.sagepub.com by guest on September 5, 2014
Qiyue et al.
2651
valve’s spring. It will bring great wear and impact load to the mechanism. Through simulation analyses, considering the influences on the performance output and the impact force mentioned above, the values of the rise angle and the return angle are designed to be approximately 30
Conclusions In this article, a virtual prototype of the APE with newly designed valve system was proposed based on experimental studies. Dynamic performances of the APE were simulated and the valve timing parameters’ optimization was calculated considering multi-parameter coupling and multi-performance evaluation. Conclusions are summarized as follows: 1. The simulation results have a good consistency with the experimental results, which verifies the basic model of the APE’s working process. 2. The output performance of the designed valve is superior to that of the experimental prototype’s solenoid valve. 3. Designed inertia moment of the flywheel is 0.057 kg m2 when the rotational speed is about 1100 r/min. 4. Within a certain parameter range, when the inlet pressure is 1 MPa, the intake advance angle is 5 , the intake duration angle is 46 , the exhaust advance angle is 0 and the exhaust duration angle is 124 , optimal output performances indicators are obtained: the ideal power equals 1.31 kW, the working efficiency equals 51.1% and the average air temperature equals 234 K. 5. Optimized rise angle and return angle of the valve are approximately 30 . The virtual prototype of the APE can make the simulation more precise and reduce the cost of the design. This research can provide theoretical supports to the new APE prototype’s design and optimization. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
References 1. Ibrahim H, Ilinca A and Perron J. Energy storage systems-characteristics and comparisons. Renew Sustain Energy Rev 2008; 12: 1221–1250. 2. Lund H and Salgi G. The role of compressed air energy storage (CAES) in future sustainable energy systems. Energy Convers Manag 2009; 50: 1172–1179. 3. Zuo CJ, Qian YJ, An D, et al. Experimental study on airpowered engine. Chin J Mech Eng 2007; 43: 93–97. 4. Papson A, Creutzig F and Schipper L. Compressed air vehicles. Transp Res Rec J Transp Res Board 2010; 2191: 67–74.
5. Huang CY, Hu CK, Yu CJ, et al. Experimental investigation on the performance of a compressed-air driven piston engine. Energies 2013; 6: 1731–1745. 6. Motor Development International (MDI). Home page, http://www.mdi.lu/index.php (2013, accessed 2014). 7. Motor Development International (MDI). Web page. AIRPod, http://www.mdi.lu/2014%20airpod.php (2014, accessed 2014). 8. He W, Wu Y, Ma C, et al. Research of air powered engine system using two-stage single screw expander. Chin J Mech Eng 2010; 46: 139–143. 9. Liu H. Research on air powered vehicle engine. PhD Thesis, Zhejiang University, China, 2004. 10. Wang Y, Liu XY and Zhou Y. Design and performance analysis of a triangle rotary piston air-powered engine. Mech Sci Technol Aerosp Eng 2009; 28: 950–954. 11. Liu H, Tao G and Chen Y. Research on displacement and stroke-bore ratio of air-powered engine. J Eng Des 2006; 13: 012. 12. Nie XH, Yu XL, Hu JQ, et al. Influence of inlet and outlet valve’s open timing on pneumatic engine and their optimal design. J Eng Des 2009; 16: 16–20. 13. Chen P, Yu X and Liu L. Simulation and experimental study of electro-pneumatic valve used in air-powered engine. J Zhejiang Univ Sci A 2009; 10: 377–383. 14. Chen Y, Liu H and Tao G. Simulation on the port timing of an air-powered engine. Int J Vehicle Des 2005; 38: 259–273. 15. Wang YB, Huang QT, Zheng ST, et al. Dynamic modeling and analysis of a parallel manipulator using Simulink and SimMechanics. J Harbin Eng Univ 2012; 33: 100–105. 16. He L, Gu L, Long K, et al. Simulative analysis of dynamic characteristics of automobile shock absorbers based on fluid-structure interaction. Chin J Mech Eng 2012; 48: 96–101. 17. Yang C, Ye Z, Peter OO, et al. Modeling and simulation of spatial 6-DOF parallel robots using Simulink and Simmechanics. In: 3rd IEEE international conference on computer science and information technology, Chengdu, China, 9–11 July 2010, pp. 444–448. 18. Zhan JC, Guo XS and Yang YN. New multi-software environment for collaborative modeling and simulation of mechatronic systems. J Syst Simul 2008; 21: 5816–5828. 19. Cai ML, Kawashima K and Kagawa T. Power assessment of flowing compressed air. J Fluids Eng 2006; 128: 402–405. 20. Chen JL, Au KC, Wong YS, et al. Using orthogonal design to determine optimal conditions for biodegradation of phenanthrene in mangrove sediment slurry. J Hazard Mater 2010; 176: 666–671. 21. Xia XT and Li JH. Influence of vacuum on friction torque of rolling bearing for space applications based on optimum grey relational space. J Grey Syst 2011; 23: 327–334. 22. Wei GW. GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowl Based Syst 2010; 23: 243–247. 23. Xu QY, Cai ML, Yu QH, et al. Multi-parameter and multi-objective optimization method for air powered engine. J Beijing Univ Aeronaut Astronaut 2013; 39: 803–807.
Downloaded from pic.sagepub.com by guest on September 5, 2014
