J. Cent. South Univ. (2016) 23: 825-833

DOI: 10.1007/s11771-016-3129-6

An investigation of cam-roller mechanism applied in sphere cam engine

ZHANG Lei(张雷), PAN Cun-yun(潘存云), XU Xiao-jun(徐小军),

XU Hai-jun(徐海军), ZHANG Zheng-zhou(张正洲)

College of Mechatronic Engineering and Automation, National University of Defense Technology,Changsha 410073, China

 Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: As an alternative power source for hybrid electrical vehicle(HEV), electric generating system(EGS) driven by sphere cam engine(SCE) is said to own higher power density and integration. In this work, the structure and working principle of EGS were introduced, based on which the advantages of EGS were displayed. The profile of sphere cam was achieved after the desired motion of piston was given. After establishing the dynamic model of power transmission mechanism, the characteristics of cam-roller mechanism were studied. The results show that the optimal cam profile of SCE is a sinusoid curve which has two peaks and two valleys and a mean pressure angle of 47.19°. Because of the special cam shape, the trace of end surface center of piston is an eight-shape curve on a specific sphere surface. SCE running at speed of 3000 r/min can generate the power of 33.81 kW, which could satisfy the need of HEVs. However, the force between cylinder and piston skirt caused by Coriolis acceleration can reach up to 1182 N, which leads to serious wear between cylinder liner and piston skirt and may shorten the lifespan of SCE.

Key words: sphere cam engine; hybrid electrical vehicle; cam-roller mechanism; kinetic analysis

1 Introduction

With more strict emission limits and eager expectation on higher fuel efficiency, pure electrical vehicles (EVs) and hybrid-electric vehicles (HEVs) become more and more popular for better overall performance compared with vehicles driven by traditional internal combustion engines (ICEs) [1-3]. Many vehicle manufacturers have produced all kinds of passenger cars powered partially or fully by battery, such as the Honda Insight and the Toyota Prius [4]. As an obvious shortage of ICEs using gasoline or diesel as primary fuel, the energy conversion efficiency is pretty low at low speed and light load, which covers the most range of cars running in the city. Unlike ICEs, the electrical driving systems have almost constant power efficiency in all kinds of working conditions [5]. Furthermore, electrical driving system makes the energy recovery during braking process possible, which avoids unnecessary energy lost. According to recent studies, the vehicle transportation consumes 68% of all available petroleum and the overall energy conversion coefficient is only 20% which is far from expected [6-8]. What is worse, SO_x, NO_x and soot emitted from the passenger vehicles powered by ICEs are the main sources of city atmosphere pollution [5]. Pure electric vehicles can alleviate this air pollution for transferring the pollution to the electric plant and increasing the overall energy conversion efficiency [9]. However, affected by the energy density of battery and the lack of charging equipments, pure electrical passenger cars are blamed for too long charging duration and limited range, which holds back the application of EVs [10]. As a way to overcome the shortages of EVs in range, HEVs which combine smaller ICEs and batteries together are proposed to extend the range of the vehicles [3, 11-12]. However, most of the existing studies on the HEVs focus on the control strategy of hybrid power system. A novel EGS which integrates the generator to SCE is proposed in this work. SCE works as a spark-ignite four-stroke engine using gasoline as fuel, which is said to have high power density and high overall efficiency. Different from the traditional engine, SCE applies a sphere cam and a pair of rotors as the main energy conversion mechanism, which is smaller and can be integrated to the EGS effectively.

The working principle of EGS was described and analyzed at first. The structure and working principle of EGS powered by SCE were presented, based on which the novelty of EGS was analyzed. Furthermore, the energy conversion mechanism, cam-roller mechanism, which allowed the axial arrangement of cylinders and increased power density of SCE was studied, the kinematic model of cam-roller mechanism was established to study the motion characters of piston. Under the effect of the special motion of power transmission mechanism, the Coriolis acceleration of piston might cause obvious lateral force between cylinder liner and piston skirt, which might cause heavy friction and thus decrease the overall efficiency. The performance of SCE, such as the torque and power, was evaluated in the end.

The results show that the special cam-roller mechanism makes the high power density of SCE possible. The center trace of piston end surface is an eight-shape curve on a sphere surface. The velocity of piston is the main reason of Coriolis force between cylinder liner and piston skirt, which has a maximal value of 1182 N. Further study shows that the torque of SCE running at the speed of 3000 r/min could be 107.648 N·m. The average power of SCE is 33.801 kW, which could satisfy the power need of HEVs well.

2 Structure introduction of SCE

Unlike the traditional reciprocating engine, SCE is mainly used to generate electrical power to drive the HEV as an assistant power source when the battery of hybrid vehicle runs out [4]. Therefore, SCE should have high power density and be easily integrated to EGS. Different from the engines used in vehicles which work under a varying working condition, SCEs have the relative higher energy conversion efficiency for running at a constant speed in higher efficiency area. Benefiting from the novel cam-roller mechanism, SCE could achieve the higher power density and better integration.

As to the traditional EGS, engines are connected to the generator by coupler, which increases the total volume and lowers the reliability of EGS. In order to decrease the total volume of EGS and achieve higher power density, the electric generating system is designed to be a part of SCE. The stator coil of electric generating system is installed on the outer shell of SCE directly, while the rotor coil is fixed to the cylinder shell which could rotates around the center axis of SCE. When the rotor coil is connected to the electric supply, a strong electric magnetic field is formed. Once the engine starts, the magnet field rotates with the rotor of SCE. As a result of relative movement between stator coil and magnet field, the mechanical power of engine is converted to the electric power. The structure of EGS is shown in Fig. 1(a), and the main parts of SCE are shown in Fig.1(b).

As shown in Fig. 1, the sphere cam is installed on the shell of SCE, which is fixed to the ground. The rotor of SCE includes a pair of cylinders, four pistons, two piston-supports and a rotor coil, among which the two piston-supports are in contact with the sphere cam by rollers directly. And the rotor coil is installed on the cylinder body directly, which avoids the waste of space and reduces the oscillation of rotor by increasing the rotational inertia of rotor. Two pistons are installed oppositely in the same cylinder, which reduces the heat loss by removing the cylinder cover away. When the gas in cylinder burns, pressure in cylinder goes up very quickly, the pistons are pushed away under the force of burned gas. The circumference forces from the sphere cam drive the rotor of SCE to rotate around the center axis. The gas exchange between cylinder and atmosphere is through a specially designed component called gas distribution valve which has two gas ports and a spark installation hole. The gas distribution valve is installed in the socket of cylinder body under the force of flanges connected to the body of SCE directly. The relative movement between cylinder and valve controls the open and close of intaking and exhausting ports, which are connected to the cylinder in a specific order. The spark plug used to generate electrical spark to ignite the mixture gas in cylinder is installed in the spark hole and controlled by a high-voltage coil.

Fig. 1 Overviews:

The high power density of SCE originates from the novel power transmission mechanism which is very compact and simple, as shown in Fig. 2. A pair of piston-supports is pinned to the cylinder body and in contact with the sphere cam at the same time. When the cylinder body rotates, pistons installed in cylinder move back and forth, which results in the variation of cylinder volume. Similar to the traditional reciprocating engine, top dead center (TDC) is defined as the position of piston where the volume of cylinder has the minimal value; while the bottom dead center (BDC) is defined as the position of piston where the volume of cylinder has the maximal value. At first, the volume of cylinder expands under the force from cam, the combustion chamber is connected to the intaking port; as a result, fresh mixture is sucked in. Then the intaking port is closed as a result of relative movement between cylinder body and gas distribution valve. While the volume of cylinder decreases as a result of movement of two pistons in the same cylinder, the gas in cylinder is compressed. Just a little moment before the volume of cylinder decreases to the minimal value, the spark is excited to ignite the mixture in cylinder. The temperature and pressure of gas in cylinder increase sharply as a result of rapid heat release by combustion process. The pressure exerting on the surface of piston pushes the pistons away, then the thermodynamic energy of burned gas is converted to the mechanical energy. When the volume of cylinder reaches the maximal value the exhausting port opens, gas in cylinder is exhausted out by the movement of piston from BDC to TDC. Up to now, the whole cycle of SCE has been finished. The working consequence in the other cylinder is similar, and the only difference lies in shifting angle of 90° between those two cylinders.

Compared with the traditional engine, SCE is more simple and reliable for removing complex and damageable valve system away. The pistons of SCE are oppositely arranged both in cylinder and on the piston-support, which is obviously different from the traditional engine. The opposite arrangement of piston in cylinder removes the cylinder cover away, which would increase the heat efficiency and simplify the structure at the same time. In addition, the opposite arrangement of piston on the piston support makes the forces exerting on the cam well balanced. The piston-supports are connected to the cylinder body though a center pin which is used to transmit the force from the cam to the rotor coil. Therefore, the lateral force between piston and cylinder becomes much smaller which will increase the overall efficiency of SCE. The cross-section view and mechanical schematic diagram of SCE are shown in Fig. 2.

Fig. 2 Mechanical schematic diagram of SCE

As shown in Fig. 2, the power transmission mechanism of SCE is mainly made up of a pair of piston-supports, a sphere cam and two cylinders, which is very simple and reliable. The sphere cam with sinusoid profile is located in the middle of two cylinders. As the main parts of power transmission mechanism, cam is well manufactured and under special heat treatment it could ensure the strength of the cam surface under heavy load. While the rollers in contact with the cam directly have a special shape which is carefully designed to ensure the reliable contact and avoids the sliding wear. Powered by gasoline, SCE works as a four-stroke spark-ignite nature-inspired engine, which is very light and produces less air pollution. The air ports are controlled by the rotary valve on which the intaking hole, the exhausting hole and the spark hole are manufactured in a specific order. Just a little moment before the piston reaches TDC, mixture in cylinder is ignited by the spark located at the center of cylinder. The mixture burns to generate high temperature and pressure. So the pistons are pushed away from each other under the force of burned gas; the cylinder body driven by the pistons rotates faster. At the same time, the temperature and pressure in cylinder decrease as a result of energy conversion from internal energy of burned gas to the mechanical energy of rotary cylinder.

3 Determination of key parameters of SCE

Benefiting from the special power transmission mechanism, SCE is believed to own higher power density and can be easily integrated to electric generating system. However, the line contact between roller and cam may cause much larger contact stress, compared with traditional reciprocating engine, which may be the main reason for the failure of SCE. In order to determine the proper parameters of power transmission mechanism of SCE, the pressure angle of cam is studied. Furthermore, the trace of mass center of piston is calculated after establishing the kinematic model of SCE.

3.1 Profile of cam of SCE

As shown in Fig. 3, the piston is connected to the piston-support which is in contact with the cam by the conical roller. As a way to alleviate the abrasion between cam and roller, the shape of roller is specially designed to avoid the relative sliding between roller and cam. The conical roller instead of cylindrical roller is accepted here to satisfy the surface of sphere cam as shown in Fig. 3(b).

As mentioned before, SCE has only one degree of freedom, the volume of cylinder, the kinematic parameters of piston and the position of piston-supports can be expressed as the functions of angle displacementof rotor. Since the two conical rollers installed on the same piston-support are in contact with the cam at the same time, the angle displacement can be determined by the profile of sphere cam. Therefore, the motion of piston must be determined in advance. The motion of piston is described using the trigonometric function for its simplicity and being free from hard or soft impact. And according to the special structure of SCE, the motion of piston is similar to the motion of roller, which can be expressed using the following equation:

                               (1)

where n is the oscillation cycle of piston per revolution; α is the angle displacement of piston; θ is the angle displacement of rotor; and δ is the angle between axes of two rollers on the same piston-support.

Fig. 3 Structure and power transmission mechanism of SCE:

The trace of big end surface center of roller is located on the sphere surface which has two valleys and two peaks as shown in Fig. 4.

As shown in Fig. 4, the shape of end surface center is saddle-like. As for another roller installed on the same piston-support, the trace of end center is similar. During one revolution of rotor, SCE completes one working cycle, the volume of cylinder varies twice. When the roller runs to the peak point, the piston is located at TDC; when the roller goes to the valleys point, the piston is located at BDC. Compared with the motion of roller, themovement of piston, which can be deprived from the kinematic model of the power transmission mechanism, catches much attention.

Fig. 4 Trace of center of roller

The surface of the cam, which is in contact with the two rollers at the same time, can be deduced from the trace of the roller. The contacting line between roller and cam can be calculated from the following equation:

(2)

where r is the radius of contacting point; σ can be deprived from the following expression –arctan (sinφ·dθ/dφ); θ is the angle displacement of rotor; φ is the angle displacement of roller; and β is the half cone angle.

Supposing β is equal to π/18, r is defined in the range from 100 mm to 120 mm; the surface of cam can be displayed in Fig. 5. It can be concluded that the shape of cam is similar to the trace of the center point of roller surface.

Fig. 5 surface of sphere cam

As to the cam-roller mechanism, pressure angle defined as the angle between the velocity and the contacting force at the contacting point is the key parameter to evaluate the transmission efficiency. As to cam-roller mechanism, smaller pressure angle means bigger transmission efficiency [13-14]. The pressure angle can be deprived from the following equation:

                 (3)

The relationship between pressure angle and angle displacement of rotor when the parameter n is set to 4 can be displayed in Fig. 6. It can be concluded that during one revolution of outer rotor, there are four dead points which correspond to the sum of valleys and peaks of cam. Actually when roller is located at the valley or peak point, the velocity of roller is perpendicular to the contact force, indicating the lowest transmission efficiency of cam-roller mechanism. The minimal pressure angle is 31.6°, while the average pressure angle is 47.19° which is acceptable but not satisfying as the main power transmission mechanism of engine.

Fig. 6 Relationship between pressure angle and angle displacement of rotor

The pressure angle of cam-roller mechanism depends on such parameters like the number of peaks of cam, the stroke of piston and the radius of cam, etc. Among those parameters, changing the number of cam peaks is the easiest way to adjust the pressure angle of the power transmission mechanism. However, too many peaks and valleys may cause the difficulty in cam manufacture. So the variation of pressure angle with the number of cam peaks and valleys are studied, as displayed in Fig. 7.

As shown in Fig. 7, with the increase of the peaks and valleys, the oscillation frequency of pressure angle during one revolution of rotor gets bigger, and the minimal pressure angle gets smaller. In Fig. 7, n indicates the sum of the peaks and valleys. As to the situation, when n is equal to 8, the minimal pressure angle is about half of the pressure angle when the cam has only one peak and one valley. Taking the mechanical transmission efficiency and the difficulty in manufacture into consideration at the same time, the optimal value of parameter n should be set to two.

Fig. 7 Influence of peaks number of cam on pressure angle

3.2 Kinematical model of cam-roller mechanism

In order to study the kinematical characters of rollers, a cartesian coordinate system o-xyz with the origin located at the geometry center of cam is established. Then the center point of roller can be expressed as

                                 (4)

where r is the distance between mass center of piston and coordinate origin; θ is the angle displacement of rotor; and φ is the stroke of piston.

The velocity of center point of roller can be deprived by differentiating the both sides of Eq. (4), which is displayed as

          (5)

Similarly, the acceleration of center point of roller can be deprived, which is displayed like below:

           (6)

By setting the radius of center point of piston to 75 mm, the kinematic characters can be deduced as displayed in Fig. 8. As shown, the trace of center point of roller is an eight-shape curve on a sphere along which the center point of piston runs round and round. The components of center point trace of piston along three axes are shown in Fig. 8 (b), among which the oscillation amplitude along y-axis is the biggest.

Fig. 8 Center point trace of end surface of piston:

As to SCE, the cylinder bodies rotate around the center axis of engine shell, which means that the variation of rotary inertia around center axis of shell has a big effect on the dynamic performance of engine. The movement of mass center relative to the cylinder body along x-direction changes the inertia of rotary parts, while the relative movement along y-direction leads to the vibration of cylinder body. The moving parts of power conversion mechanism include pistons which reciprocate along the cylinder liner and the piston-supports which rotate around the center pin. The mass of piston which is made up of aluminums is 0.33 kg, while the piston-support composed of cast iron material weights 1.9 kg. Therefore, the mass center of moving parts can be presented in Fig. 9. The trace of mass center relative to the cylinder body is shown in Fig. 9(a), and the velocities along different axes are shown in Fig. 9(b).

Fig. 9 Trace and velocity of mass center of power transmission mechanism:

It can be concluded from Fig. 9 that the mass center of moving part oscillates around the geometrical center of cam, the trace of mass center is half-elliptical. The mass center moves along the trace cycle-by-cycle. The motion along x-direction would lead to the variation of inertial moment which may cause the lateral force between cylinder liner and piston skirt by means of Coriolis acceleration. Fortunately, the magnitude of vibration along x-axis, which has amplitude smaller than 2 mm, is much smaller compared with the vibration along y-axis, which is 21 mm. According to the velocity analysis along both directions, the frequency of vibration along x-axis is about twice the vibration frequency along y-axis. That is the reason why the trace is a half ellipse instead of a whole ellipse.

4 Dynamic model analysis of SCE

The inertial forces applied on the power transmission mechanism are the main reason of vibration. As to the internal combustion engine, the fast increasing of pressure in cylinder is another reason of vibration and noise. In order to evaluate the dynamic performance of SCE, the kinetic model is built using Lagrange method, based on which the dynamic performance of engine is numerically simulated.

According to the Lagrange principle, the total energy of mechanism includes the potential energy and kinetic energy, of which the potential energy caused by the variation of mass center along y-direction is much smaller compared with the kinetic energy of rotary cylinder assemblies. For convenience, the potential energy is dismissed when building the dynamic model of mechanism which is presented like below:

                                      (7)

where I_c is the rotational inertia of cylinder body; I_puy, I_pdy and I_csy are the rotational inertia of upper piston, down piston and piston-support along y-axis, correspondingly; I_puz, I_pdz and I_csz are the rotational inertia of upper piston, down piston and piston-support along z-axis, respectively; θ is the angle displacement of cylinder body; α is the angle displacement of piston-supports along z-axis; T is the equivalent torque of all forces applied on the cylinder body.

As an obvious advantage, SCE always works at a constant speed in full load. To value the performance of SCE, the torque and the power under the constant speed should be taken into consideration at first. The equivalent torque in Eq. (7) includes contribution of gas force applied on piston and the output torque. However, the lack of physical prototype of SCE makes the calibration of pressure curve in cylinder impossible. The pressure data used in simulation are derived from the reciprocating engine with the same displacement of 0.52L [15-18]. And the equivalent torque of gas force on rotor can be deprived from the virtual work theory, which can be displayed as

                               (8)

where θ is the angle displacement of rotor, φ is the stroke angle of piston, P is the pressure in cylinder, and S is the surface area of piston.

Based on the special structure of SCE, the volume variations of two cylinders are opposite to each other, which leads to the phase angle shift of 90° in working consequence between two cylinders. When cylinder one is under explosion stroke cylinder, cylinder two is under exhausting stroke; and when cylinder two is under explosion stroke cylinder, cylinder one is under compression stroke. The working consequence in cylinders is listed in Table 1.

The pressures in cylinders are shown in Fig. 10. As to the cylinder one, gas in cylinder has been ignited during period from 0 to π/2. The pressure in cylinder one increases sharply to the maximal value which is 3.05 Mpa; while the waste gas in cylinder two is exhausted out. As to cylinder two, gas pressure increases quickly to the maximal value of 3.05 Mpa during the period from 3π/2 to 2π. the pressure in cylinder one increases to 1.6 Mpa as a result of compression stroke.

Table 1 Working consequence in cylinders

Fig. 10 Pressure in cylinders of SCE

The equivalent torque of gas pressure is the displayed in Fig. 11. There are two peaks during one revolution of rotor, a bigger one and a smaller one. Affected by phase angle shifting of 90° between two cylinders, the peak values are different. When the gas in cylinder is compressed, the piston does negative work to compress the gas in cylinder, which will cause a negative pressure peak.

Fig. 11 Equivalent force of gas applied on rotor

As shown in Fig. 11, the negative pressure peaks appear at 250° and 350° of rotor angle, which are the ends of compression strokes of two cylinders correspondingly. Figure 11 shows that an additional mass should be added to the rotor to overcome the resistance of gas during compression stroke. Fortunately, the coil of rotor fixed to the cylinder body could be used as the flywheel of SCE. The values of two torque peaks are 218 N·m and 262 N·m, respectively, while the average value of pressure is 107.648 N·m. SCE runs at the speed of 3000 r/min, so the power of SCE could be 33.81 kW.

According to the analysis before, the Coriolis force between piston and cylinder liner may be the main reason of wear and tear of cylinder surface. So much attention should be put on the lateral force caused by Coriolis acceleration. The figure below explains the origin of Coriolis force. As the piston rotates with cylinder body, the variation of distance between piston and center axis will cause the change of tangential velocity of piston. Therefore, a lateral force is needed to accelerate or decelerate the piston to satisfy the constraint of cylinder.

Fig. 12 Coriolis acceleration analysis

The relationship between Coriolis force and angle displacement of rotor is displayed in Fig. 13. The Coriolis force varies four times during one revolution of rotor, the same as the displacement variation of piston. The maximal value of Coriolis force is 1182 N which appears in the middle point of piston stoke. When thepiston is located at the TDC or BDC, the Coriolis force decreases to zero and changes the direction. Since the magnitude of Coriolis force is pretty large, which may cause an obvious energy loss during working process; the lubrication system of SCE piston should be carefully designed to alleviate this shortage.

Fig. 13 Relationship between Coriolis force and angle displacement of rotor

5 Conclusions

1) Benefiting from the novel power transmission mechanism, SCE has bigger power density and can be integrated to the electric generating system easily, which could decrease the total mass of SCE and increase the reliability effectively at the same time. Therefore, SCE is more suitable to drive HEVs for its smaller volume and special structure.

2) The surface model of cam is established after choosing the trigonometric function as the primary motion law of piston, based on which the influence of peaks and valleys of cam on the pressure angle is studied. The results show that there are four dead points during one revolution of rotor. The minimal pressure angle is 31.6° and the mean pressure angle is 47.19°. The minimal pressure angle and mean pressure angle both decrease with the increase of peaks and valleys’ number, however, more peaks and valleys mean more difficulties in manufacture. So the optimal peaks and valleys’ number should be set to two.

3) The kinematic and dynamic models of SCE are established to analyze the characteristics of SCE arising from the novel power transmission mechanism. The end surface center’s trace of piston is an eight-shape curve on the sphere surface. As to the moving parts of power transmission mechanism, the motion of mass center relative to the cylinder is much obvious in y-direction compared with x-direction, which may decrease the lateral force caused by Coriolis acceleration between piston liner and cylinder skirt.

4) The torque of SCE running at the speed of 3000 r/min could be 107.648 N·m, which is 33.81 kW if counting in power. As the assistant power source is used to drive HEV when the battery runs out, SCE with the power of 33.81 kW can satisfy the power need well.

References

[1] AXSEN J, Kurani K S. Hybrid, plug-in hybrid, or electric-what do car buyers want? [J]. Energy Policy, 2013, 61: 532-543.

[2] RUI Xian-hong, YAN Qing-yu, MARIA S K, LIM T M. Li₃V₂(PO₄)₃ cathode materials for lithium-ion batteries: a review [J]. Journal of Power Sources, 2014, 258: 19-38.

[3] VERHELST S, SHEPPARD C G W. Multi-zone thermodynamic modelling of spark-ignition engine combustion—an overview [J]. Energy Conversion and Management, 2009, 50(5): 1326-1335.

[4] HANNAN M A, AZIDIN F A, MOHAMED A. Hybrid electric vehicles and their challenges: a review [J]. Renewable and Sustainable Energy Reviews, 2014, 29: 135-150.

[5] GUPTE S. Experimental analysis and feasibility study of 1400CC diesel engine car converted into hybrid electric vehicle by using BLDC hub motors [C]// 4 International Conference on Advances in Energy Research (Icaer 2013). Mumbai, India: Indian Inst Technology Bombay Department-Energy Sci & Engn, 2014, 54: 177-184.

[6] KIM J, JEONG Y H, JEON Y H, KANG J H, LEE S, PARK J Y. Development of a switched reluctance motor-based electric AC compressor drive for HEV/EV applications [J]. Journal of Magnetics, 2014, 19(3): 282-290.

[7] NIETO N, DIAZ L, JOHN G, BLANCO F, RAMOS J C, RIVAS A. Novel thermal management system design methodology for power lithium-ion battery [J]. Journal of Power Sources, 2014, 272: 291-302.

[8] VERHELST S, SIERENS R. A quasi-dimensional model for the power cycle of a hydrogen-fuelled ICE [J]. International Journal of Hydrogen Energy, 2007, 32(15): 3545-3554.

[9] RIBAU J P, SILVA C M, SOUSA J M C. Efficiency, cost and life cycle CO₂ optimization of fuel cell hybrid and plug-in hybrid urban buses [J]. Applied Energy, 2014, 129: 320-335.

[10] SEAMAN A, DAO T S, MCPHEE J. A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation [J]. Journal of Power Sources, 2014, 256: 410-423.

[11] SUN Hong-guang, DIXON R. Development of cooling strategy for an air cooled lithium-ion battery pack [J]. Journal of Power Sources, 2014, 272: 404-414.

[12] Choi Y S, KANG D M. Prediction of thermal behaviors of an air-cooled lithium-ion battery system for hybrid electric vehicles [J]. Journal of Power Sources, 2014, 270: 273-280.

[13] RICHARD V B, FRED S. Internal combustion engine handbook basics, components, systems, and perspectives [M]. Warrendale: SAE International, 2004: 437-454.

[14] NOAH D, MANRING, MEHTA V S, BRYAN E, NELSON, KEVIN J G, JEFF L. KUEHN. Scaling the speed limitations for axial-piston swash-plate type hydrostatic machines [J]. Journal of Dynamic Systems, Measurement, and Control, 2014, 136(3): 031004.

[15] ZHANG Lei, Xu Hai-jun, Pan Cun-yun, Xu Xiao-jun. Combustion simulation and key parameter optimization for opposite axial piston engine in small scale [J]. Journal of Central South University, 2015, 22(9): 3397-3408.

[16] DENG Hao, PAN Cun-yun, WANG Xiao-Cong, ZHANG Lei, Deng li. Comparison of two types of twin-totor piston engine mechanisms [J]. Journal of Central South University, 2013, 20(2): 363-371.

[17] SHI Chun-tao, Qin De, TANG Qi, TIAN Xiao-song. Developments in combustion modeling in ICE [J]. Agriculture mechanical engineering, 2013, 38(4): 181-185. (in Chinese)

[18] OPPENHELM A K. Dynamics of combustion systems [M]. Heidelberg: Springer-Verlag, 2007: 3-61.

(Edited by FANG Jing-hua)

Foundation item: Projects(51475464, 51175500, 51575519) supported by the National Natural Science Foundation of China

Received date: 2015-03-03; Accepted date: 2015-07-22

Corresponding author: PAN Cun-yun, PhD;Tel: +86-731-84574932;E-mail: pancunyun@sina.com