J. Cent. South Univ. (2013) 20: 3536−3544 DOI: 10.1007/s117710131879y
Mathematical modeling and analysis of gas torque in twinrotor piston engine
DENG Hao(邓豪) 1, 2, PAN Cunyun(潘存云) 1, XU Xiaojun(徐小军) 1, ZHANG Xiang(张湘) 1 1. College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, China; 2. Naval Aeronautical Engineering Institute, Qingdao Branch, Qingdao 266041, China © Central South University Press and SpringerVerlag Berlin Heidelberg 2013
Abstract: The gas torque in a twinrotor piston engine (TRPE) was modeled using adiabatic approximation with instantaneous combustion. The first prototype of TRPE was manufactured. This prototype is intended for high power density engines and can produce 36 power strokes per shaft revolution. Compared with the conventional engines, the vector sum of combustion gas forces acting on each rotor piston in TRPE is a pure torque, and the combustion gas rotates the rotors while compresses the gas in the compression chamber at the same time. Mathematical modeling of gas force transmission was built. Expression for gas torque on each rotor was derived. Different variation patterns of the volume change of working chamber were introduced. The analytical and numerical results is presented to demonstrate the main characteristics of gas torque. The results show that the value of gas torque in TRPE falls to be less than zero before the combustion phase is finished; the time for one stroke is 30° in terms of the rotating angle of the output shaft; gas torque in one complete revolution of the output shaft has a period which is equal to 60° and it is necessary to put off the moment when gas torque becomes zero in order to export the maximum energy.
Key words: rotor; piston engine; gas torque; power density; adiabatic process
of 1930−1970 [8, 10]. However, with the maturity of the 1 Introduction conventional engine as well as the difficulty of developing a radicallychanged new engine, ORE was To this day, existing successful piston engines are gradually abandoned in the 1970s. reciprocating piston engine, Wankel rotary engine [1], However, with the predicted fuel crisis, air pollution cam engine [2] and swash plate engine [3]. These and the new visions of the future engine with higher engines still stop short from fulfilling the requirements power density and higher efficiency, people have been imposed on prime moves [4−7]. A breakthrough can only devoted to reconsidering ORE. Efforts to develop an be achieved by a radical departure from the conventional innovative ORE have been continued in recent years, and piston engine design. many patents have been carried out. LIBROVICH et al For decades, corporations and individual inventors [11] proposed a novel rotary vane engine using all over the world have been coming up with other types noncircular gears for torque transmission. LIANG [12] of internal combustion engines with a view of providing proposed a rotary engine with two rotors and its design a lightweight, economical and high fuel efficient engine. method. SAKITA [13] described his cat and mouse type The most promise is the rotary engine, which achieves a rotary engine and its performance evaluation. WIESLAW more direct power transmission without using the [14] presented a new conception of oscillating engine. reciprocating pistons and the valve mechanism. The best American inventor MORGADO [15] built a series of known rotary engines [7−8] disclosed to date can be ORE prototype (named by MYT engine). However, it classified into three types, Wankel type, sliding vane appears from the published literature that ORE shows a type and oscillatory rotating type. promised future but many proposals have not been The engine proposed in this work belongs to a exposed to a deep analysis. category generally known as oscillatory rotating engine The basic structure, work principles and comparison (ORE, also known as catandmouse type engine). This of two types of twin rotor piston engine (TRPE) have type of engine was originally proposed by been introduced [16−17]. TRPE exhibits many BULLINGTON [9], and developed rapidly in the period advantages that belong to Wankel engine, such as no
Foundation item: Project(51175500) supported by the National Natural Science Foundation of China Received date: 2012−07−02; Accepted date: 2012−08−14 Corresponding author: DENG Hao, Lecturer, PhD; Tel: +86−731−84574932; Email: [email protected] J. Cent. South Univ. (2013) 20: 3536−3544 3537 reciprocating pistons, and no intakeexhaust valve strokes per shaft revolution, thus may display V24 mechanism. In addition, TRPE has been proved to have engine smoothness while its size is much smaller. the potential of higher power density due to multiple utilization of work space and higher uniformity of torque 3 Gas torque modeling in TRPE due to more than two symmetrical working chambers exporting power at any time. In this work, mathematical 3.1 Combustion gas force transmission modeling and analysis of gas torque were presented. The primary source of torque for the engine is generated from the forces produced by the expansion of 2 First prototype of TRPE burning gases in combustion chambers. So it is necessary to analyze the combustion gas first. As shown in Fig. 2, in order to get the turning force, TRPE is intended for high power density engines. all piston engines rely on the expansion pressure created Its construction is based on some newly invented by the combustion gas. Expansion pressure is denoted by mechanisms [18−19]. As shown in Fig. 1, the first p in Fig. 2(a). The difference among the mechanisms of prototype is manufactured. As the job of equipping with ig the three engines is in the way that the expansion auxiliary systems is not finished, the engine is only pressure is used. In the reciprocating (or Wankel) engine, allowed to run by the help of the motor temporarily. In pig generated in the combustion chamber forces the this design, TRPE has two mechanical systems. One is piston down (or turn the rotor). The mechanical force energy conversion system (ECS), and the other is (denoted by F) is transferred and decomposed into two differential velocity mechanism (DVM). ECS is designed components. One is the force toward the output shaft to convert heat energy into mechanical energy, and DVM center (denoted by Fn) and the other is the tangential is designed to merge nonuniform rotations of two parts force (denoted by Ft). Only Ft rotates the output shaft. into uniform rotation of one part. DVM is coaxial with In the case of the spark ignition engine with six ECS. It interconnects the two rotors and makes them alternately speed up and slow down at a certain time.
Fig. 1 Proto of TRPE
The ECS shown in Fig. 1 has two identical opposed rotors, the former rotor and the latter rotor. Each rotor has six vane pistons. The space between the two rotors and the housing provides twelve working chambers for internal combustion and the pressure of expanding gases serves to turn the rotors. So, at any time, one set of six separated working chambers is close together while the other set of six separated working chambers is wide apart. Fig. 2 Comparison of gas pressure acting on reciprocating TRPE of the presented prototype can produce 36 power engine: (a) Wankel engine; (b) TRPE 3538 J. Cent. South Univ. (2013) 20: 3536−3544 vane pistons per rotor, as shown in Fig. 1, the inside space of the housing is always divided into twelve working chambers. In operation, those twelve working chambers are always in motion and successively execute the four processes of intake, compression, ignition and exhaust. Compared with reciprocating engine, where those four processes are carried out within each cylinder, each process is carried out in a different place in TRPE. Based on the working principle of TRPE [16], three ignition devices (Pig1, Pig2 and Pig3), three intake ports (Pin1, Pin2 and Pin3), and three exhaust ports (Pex1, Pex2 and Pex3) should be radially located at the circumference of the housing, as shown in Fig. 2(b). Each stroke is commenced or completed while any working chamber travels close to the ports. Figure 2(b) also shows the moment when combustion takes places in three even spaced working chambers simultaneously. Fig. 3 Schematic diagram of former rotor under gas pressure
F1, F2 and F3 denote the composition of combustion gas pressure force which is applied to the surface of the where h is the width of working chambers, r is the radius former rotor. R1, R2 and R3 denote the composition of of the rotor, d2 and d1 are the internal and external combustion gas pressure force which is applied to the diameters of vane pistons. The variables (pig(t), pcp(t), surface of the latter rotor. It is a valid assumption that the pin(t) and pex(t)) are the gas pressures in the working gas pressures of working chambers with the same engine chambers during combustion, compression, intake and stroke are the same at any time. So exhaust, respectively. It is assumed that the difference between pressure in F1=F2=F3, R1=R2=R3 (1) the intake chambers, exhaust chambers and ambient On the other hand, the two rotors rotate with pressure is small, so p ≈p ≈p (p is atmospheric relatively slower speed than the sonic, therefore, pressure in ex a a pressure). Thus, can be considered to be uniform in the chambers. So 3 2 2 Fj =R j ( j = 1,2,3) (2) M ≈ ( p − p )(d − d ) h (4) YP 8 ig cp 2 1 As the direction of gas pressure acting on the rotors Gas pressure inside working chambers (including is always perpendicular to the surfaces, effects of driving the combustion working chambers) is on average the former rotor from three gas forces F1, F2 and F3 (or spatially constant. Moreover, gas pressures of working R1, R2 and R3) are the same. Moreover, based on Eqs. (1) chambers are the same, i.e., the torques on adjacent and (2), it can be seen that the vector sum of combustion vanes in each chamber are equal and opposite. Thus, gas gas forces acting on each rotor is a pure torque. torque acting on the latter rotor (MLP) is equal by Theoretically, energy generated by the gas combustion magnitude and opposite by direction to gas torque on the can be completely transmitted out by the two rotors, and former rotor. there exist no radial contact forces between the two M = − M (5) rotors and the housing and no radial bearing forces. So LP YP this design also provides a balance pressure forces within Thus, TRPE suffers very little from imbalances working chambers of the engine. because the acceleration of an oscillating member is In addition, because of the large area of vane piston balanced by an equal deceleration of another identical contacting the inner surface of the housing, as opposed to member. a line contact. The sealing problems of TRPE are To describe the gas torque acting on the former potentially much easier to solve than those of other rotor, several assumptions are made. rotary engines. 1) The working chambers are perfectly sealed; 2) The velocities of the two rotors are relatively 3.2 Gas torque acting on rotors high, so the total heat flux into the walls of the chamber Gas torque on the rotor is the sum of torques due to can be omitted; all four engine regimes. As shown in Fig. 3, gas torque 3) Gas proceeds at rates much faster than the transit on the former rotor can be written as time of vanes across intake and exhaust ports.
d 2/2 So adiabatic approximation is used to calculate the M YP (t) = 3 [ pig (t) − pcp (t) + pin (t) − pex (t)]hrdr (3) ∫ d1 / 2 gas pressure in the combustion and compression working J. Cent. South Univ. (2013) 20: 3536−3544 3539 chamber at each output shaft angle, i.e., pV κ =R (κ is In a practical gasoline engine, the maximum of gas polytropic index and R is a constant). pressure pmax is usually equal to 8.5 MPa [20]. As pa= 2κ Let Vj denote the volume of the jth working 0.1 MPa, so ck=pmax/pa=85. If MYP>0, then ε < ck . In chamber labeled between the vane pistons Yj and Lj, and general, κ is set to be equal to 1.5 [21]. So ε should be let Vj+1 denote the volume of the (j+1)th working less than 4.4. chamber labeled between the vane pistons Yj+1 and Lj. As we know, ε is limited by the airfuel mixture For example, suppose that the combustion takes places in entering the cylinders. The lower ignition temperature of the jth working chamber while compression takes places gasoline will cause it to burn at a compression ratio of in the (j+1)th working chamber. So less than 12. On the other hand, compression ratio represents the efficiency of the engine. The bigger the V min κ pig = pm ax ( ) compression ratio is, the higher the efficiency is. In V j Ref. [20], a compression ratio of an average gasoline (6) V engine should be bigger than 6. Thus, the compression p = p ( max ) κ cp a ratio of TRPE utilized as a gasoline engine should be less V j +1 than 12 and bigger than 6, namely, ε ∈ [6,12]. where pmax is the maximum pressure in working chamber, Based on the analysis above, if TRPE is utilized as a Vmin and Vmax are the extreme volumes of the working gasoline engine, which adopts the present technology, the chamber. value of MYP falls to be less than zero before the time Without a loss of generality, assuming the jth when the combustion phase is finished. Thus, after the working chamber is at the combustion phase, then the moment when MYP=0, the gas pressure in the (j+1)th working chamber is at the compression phase compression chamber is bigger than the pressure in the accordingly. Thus, in the above course, Vj is continuously combustion chamber. The forward motion of the former increasing, Vj+1 is continuously decreasing. According to rotor and the energy of compressing the gas are provided Eq. (6), there may exist a moment when MYP<0. by the flywheel. Substituting Eq. (6) into Eq. (4), it is easy to show For an example, ε of TRPE is set to be 6. When that κ κ κ MYP=0, km=ck. As km = ε V j /V j +1 , V min κ M YP ≈ M c ( ) [ck − k m ] V j κ κ V j ( ) = c k / ε (8) V j +1 2 2 M c = 3h(d2 − d1 ) pa / 8 (7) Substituting the values of ε, c , and κ into Eq. (8), it ck = pmax / pa k can be seen that V /V = 3.2. k = ε κV κ / V κ j j +1 m j j +1 Based on the definition of the compression ratio, where M is a gas torque constant determined by c Vmax/Vmin=ε=6, and there always exists an equation: atmospheric pressure and some geometric structure V +V = V + V (9) parameters; ck is determined by the variable pmax; km is max min j j +1 determined by the compression ratio of the engine (ε) So when MYP=0, Vj=5.3Vmin. This means before the and the volume of the working chamber (Vj), as 2κ moment when the volume of the combustion chamber 1/ε
efficient. The maximum of gas pressure pmax is usually 3.3 TRPE utilized as practical engine equal to 14 MPa in this type of engine. So, when TRPE
1) TRPE utilized as gasoline engine is utilized as a diesel engine, if MYP>0, according to 3540 J. Cent. South Univ. (2013) 20: 3536−3544 ε 2κ< c , then ε<5.2. Thus, similar with TRPE utilized as a π/3 − 2 β c ε k M (θ ) ≈ M [ ]κ [ k − ( )κ ] gasoline engine, the value of M falls to be less than YP c YP (ε + 1) δ j (θ ) π/3 − 2β − δ j (θ ) zero before the time when the combustion phase is (12) finished. For example, ε of TRPE diesel engine is set to be where Mc, β, ε, ck and κ are constants with respect to time. Only δj(θ) is the only variable parameter with respect to 12. When MYP=0, according to Eq. (8), Vj/Vj+1=2.3, and time or the output shaft angle θ. Obviously, when δj is at according to Eq. (9), it can be seen that Vj=9Vmin. This means before the moment when the volume of the its maximum, namely, δj(θ)=δmax, MYP achieves its combustion chamber achieves the value which is 9 times maximum, and when δj is at its minimum, namely, δj(θ)= of its minimum, the gas pressure rotates the former rotor δmin, MYP achieves its minimum. The extreme of MYP can and the flywheel while compresses the gas in the be given by compression chamber. After this moment, the next travel (M YP )max = M c (c k − 1) which is 3 times of the minimum of the volume, the c k κ (13) forward motion of the former rotor and the energy of (M YP )min = M c ( − ε ) ε κ compressing the gas are provided by the flywheel. Figure 4 shows the maximum of combustion gas Thus, both the maximum and the minimum of MYP pressure (pmax) with respect to the compression ratio ε. It have no relationship with the function of δj(θ). In can be concluded that if TRPE is utilized as a practical addition, (MYP)max even has no relationship with the engine which adopts the present engine technology, the compression ratio. value of MYP falls to be less than zero before the time when the combustion phase is finished. 4.2 Different variation patterns of δj(θ) in TRPE Without a loss of generality, a complete combustion stroke in TRPE is defined as follows: At the beginning of
the combustion stroke, θ=0, and δj(0)=δmin; At the end of
the combustion stroke, θ=π/6 and δj(π/6)=δmax. Based on Eq. (12), it can be seen that MYP(θ) is determined by the variation function of δj(θ). For better understanding of the gas torque dynamics, different variation patterns of the volume of working chamber are selected. Each pattern can be realized by its respective differential velocity mechanism [22]. In this work, in
Fig. 4 Maximum of combustion gas pressure pmax with respect order to compare these variation functions, Mc, β, ε, ck to compression ratio ε and κ are assumed to be the same, and δj(θ) is respectively defined as a circulararc function, sine 4 Gas torque analysis function, linear function, power function and exponential function. 4.1 Extreme value of gas torque 4.2.1 Circulararc function
In general, volume of working chamber (Vj) in In this section, δj(θ) is defined as a function with a 2 2 2 TRPE is assumed to be a function of the output shaft circulararc form (x−a) +(y−b) =R . As given in Table 1, angle θ. Vj(θ) is proportional to the relative angle of two this type of function may have three patterns (denoted by adjacent vane pistons δj(θ), namely, Vj=kδj, where k is a CF1, CF2 and CF3, respectively) due to the difference of structure parameter. Thus, according to Eq. (9), the center and the radius of arcs. Obviously, there always exists an equation: δmin + δmax = δ j (θ ) + δ j +1 (θ ) (10) π = δ − δ (14) In Ref. [16], it is concluded that 6 max min 2π / N − 2 β δ = With Eq. (11), β can be determined by ε as min ε + 1 (11) π(ε − 3) 2π / N − 2 β β = (15) δmax = ε 2N (ε − 1) ε + 1 where N is the number of vane pistons per rotor, and in Figure 5 shows the maximum of δ, the minimum of this work, N=6; β is the span angle of each vane piston. δ, and the span angle of vane pistons β with respect to So Eq. (7) can be expressed as the compression ratio ε. It can be seen that ε should be bigger than 3 as β>0. In addition, β should be chosen big J. Cent. South Univ. (2013) 20: 3536−3544 3541 Table 1 Three patterns of circulararc function Name Characteristic Radius of circle: π/6 Center of circle: (π/6, δ ) CF1 min π π Function: δ (θ ) = ( )2 − (θ − ) 2 + δ j 6 6 min Radius of circle: π/6 Center of circle: (0, δ ) CF2 min π Function: δ (θ ) = − ( )2 −θ 2 + δ j 6 max Radius of circle: π/12
Center of circle: (0, (δmin+δmax)/2), and (π/6, (δmin+δmax)/2） Function: Fig. 6 Relative angle function δ(θ) generated by three types of CF3 when θ∈[0, π/12], π π circulararc function curve (CF1, CF2 and CF3) with respect to δ (θ ) = ( )2 − (θ − ) 2 + δ j 6 6 min flywheel angle θ in combustion stroke when θ∈[π/12, π/6],
π 2 π 2 δmin + δ max 4.2.2 Sine function δ j (θ ) = ( ) − (θ − ) + 12 6 2 In this section, δj(θ) is defined as a sine function y = asin(Nx +ϕ ) + b, denoted by SF. δj(θ) varies from
δmin to δmax in a combustion stroke. δmin and δmax are also determined by Eq. (11). In addition, based on the work
principle of TRPE, the period of δj(θ) is equal to π/3 [16]. So
δ − δ π δ + δ δ (θ ) = max min sin(6θ − ) + max min (16) j 2 2 2 4.2.3 Linear function
In this section, δj(θ) is defined as a linear function,
y=ax+b, denoted by LF. δj(θ) varies from δmin to δmax in a
combustion stroke. δmin and δmax are also determined by Eq. (11). So
Fig. 5 Maximum of δ, minimum of δ and span angle of vane 6θ (δ − δ ) δ (θ ) = δ + max min (17) piston β with respect to compression ratio ε j min π 4.2.4 Power function enough to assure the strength of the vane piston. But on In this section, δ (θ) is defined as a power function, the other hand, as shown in Fig. 5, while the value of β j denoted by PF. As the need for bigger rate of volume increases, the value of δ decreases. Too small δ may min min change at the beginning of combustion stroke in TRPE, cause the interference between the two adjacent vane δ (θ) is assumed to have a form such as y=2x a+ b. δ (θ) pistons. So for balance, ε ∈ [5, 20]. In this work, ε of j j varies from δ to δ in a combustion stroke. δ and TRPE is chosen to be 10 for example, and β = 11.67° , min max min δ are also determined by Eq. (11). So accordingly. max
Substituting ε=10 and β=11.67° into Eq. (11), then (ln(δ max / 2− δ min / 2) / ln(π/6)) δ j (θ ) = 2θ + δ min (18) δmin and δmax of TRPE can be obtained. After that, it is easy to determine the circulararc function in Table 1. 4.2.5 Exponential function
Figure 6 shows the relative angle function δ(θ) generated In this section, δj(θ) is defined as a exponential by three types of circulararc function curve (CF1, CF2 function (denoted by EF). Similar with the need in and CF3) with respect to the flywheel angle θ in a Section 4.2.4, δj(θ) is assumed to have a form such as combustion stroke. y=0.2a x+ b. So 3542 J. Cent. South Univ. (2013) 20: 3536−3544 6θ / π δ j (θ ) = 0.2((δmax − δmin + 0.2) / 0.2) + δ min − 0.2 (19) minimum. So the simulation results verify the conclusion that both the maximum and the minimum of MYP have no
In this work, for simplicity and comparison, ε of relationship with the function of δj(θ). In addition, Fig. 9
TRPE is chosen to be 10, and β is chosen to be 11.67°. shows the minimum and maximum of MYP with respect Each function of δj(θ) is obtained respectively. Figures 6 to ε. It can be seen that the increase of ε proportionally and 7 show the relative angle function δ(θ) generated by causes the decease of (MYP)min. different function curve with respect to the flywheel angle θ in one combustion stroke.
Fig. 8 Comparison of gas torque MYP due to difference of relative angle function δ(θ) with respect to flywheel angle θ in one combustion stroke Fig. 7 Relative angle function δ(θ) generated by four types of function curve (LF, SF, PF and EF) with respect to flywheel angle θ in one combustion stroke
4.3 Results of gas torque analysis Pressure decreases adiabatically in the combustion chamber (denoted by Vj) and increases in the following compression chamber (denoted by Vj+1). In the case of the proposed TRPE, with parameters from Section 4.2, gas torques of MYP(θ) obtained from Eq. (12) are given in Fig. 8. It is obvious that MYP(θ) varies according to the different function patterns of δj(θ). For each curve, at some moment (denoted by θb), pressure in Vj is balanced by pressure in Vj+1, which means a zero gas torque on the rotor. Furthermore, the gas torque becomes negative when gas pressure in Vj+1 becomes larger than the pressure in the adjacent Vj chamber. Fig. 9 Minimum and maximum of gas torque MYP with respect
However, θb is different for each function pattern of to compression ratio ε
δj(θ). Obviously, θb of curve CF2 is the biggest, and θb of curve CF1 is the smallest. On one hand, it is necessary to As shown in Fig. 10, gas torque in one complete put off the moment when the gas torque becomes zero in revolution of the output shaft has a period which is equal order to export the maximum of energy. On the other to 60°. After the end of combustion in Vj, the beginning hand, the curve of MYP(θ) should be changed gently to of combustion in Vj+1 occurs, and after the end of avoid vibration. It can be seen that the curves SF, LF, PF combustion in Vj+1, the beginning of combustion in Vj+2 and EF show less vibration. In all, the volume change occurs. Combustion of other working chambers occurs in should be as small as possible at the beginning of the sequence. The time for one stroke is 30° in terms of the combustion stroke. rotating angle of the output shaft, and there are three
Moreover, for every curve shown in Fig. 8, MYP(θ) explosion strokes simultaneously, namely, the expansion begins from the same maximum and to the same stroke overlaps so the torque fluctuation is low. The J. Cent. South Univ. (2013) 20: 3536−3544 3543
Fig. 10 Gas torque in one complete revolution of output shaft (CP: Compression stroke; CB: Combustion stroke; IN: Intake stroke; EX: Exhaust stroke) discontinuities of gas torque shown in Fig. 10 at the 4) Both the maximum and the minimum of gas transition points due to the combustion model is assumed torque have no relationship with the function of working to be an instantaneous process in this work. chamber volume change.
5 Conclusions References
1) The vector sum of combustion gas forces acting [1] YAMAMOTO K. Rotory engine [M]. Tokyo, Japan: Sankaido Co., on each rotor is a pure torque. So there exist no radial Ltd, 1981: 2−12. contact forces between the two rotors and the housing [2] YUAN Peng, WANG Deshi, WANG Shuzong. Kinematics and and no radial bearing forces theoretically. dynamics of contrapositive cam engine [J]. Torpedo Technology, 2007, 15(6): 13−16. 2) The combustion gas torque in TRPE rotates the [3] LIAN Yongqing, WANG Shuzong, MA Shijie. Dynamic rotors and the flywheel while compresses the gas in the simulation of the airpowered swashplate engine [J]. Chinese Journal compression chamber at the same time. The value of gas of Mechanical Engineering: Chinese Edition, 2008, 44(1): 243−246. torque in TRPE falls to be less than zero before the time (in Chinese) when the combustion phase is finished. The combustion [4] XIAO Jin, LI Qingfeng, HUANG Zheng. Motion characteristic of a stroke and the compression stroke overlap so the torque free piston linear engine [J]. Applied Energy, 2010, 87(4): fluctuation in TRPE is lower than that in reciprocating 1288−1294. engine. [5] KORAKIANITIS T, BORUTA M, JEROVSEK J, MEITNER P L. 3) The variation pattern of the volume of working Performance of a single nutating disk engine in the 2 to 500 kW power range [J]. Applied Energy, 2009, 86(10): 2213−2221. chamber significantly affects the gas torque. It is [6] KARHULA J. Cardan gear mechanism versus slidercrank necessary to put off the moment when the gas torque mechanism in pumps and engines [D]. Finland: Lappeenranta becomes zero in order to export the maximum of energy. University of Technology, 2008. The volume change should be as small as possible at the [7] HUDSON B. The production of power by pure rotary means [D]. beginning of the combustion stroke. These conclusions Melbourne, Australia: RMIT University Architecture and Design, are prepared for the optimum design of differential 2008. velocity mechanisms. [8] ASHLEY S. A new spin on the rotary engine [J]. Mechanical 3544 J. Cent. South Univ. (2013) 20: 3536−3544
Engineering, 1995, 117(4): 80−82. engine [J]. Chinese Journal of Mechanical Engineering: Chinese [9] BULLINGTON F. Internal combustion engine: USA, US Patent Edition, 2012, 48(1): 64−68. (in Chinese) 1821139 [P]. 1925−08−24. [17] DENG Hao, PAN Cunyun, WANG Xiaocong, ZHANG Lei, DENG [10] NORBYE J. Rivals to the wankel: A roundup of rotary engines [J]. Li. Comparison of two types of twinrotor piston engine mechanisms Popular Sci, 1967: 80−85. [J]. Journal of Central South University, 2013, 20(2): 363−371. [11] LIBROVICH B, TUCKER R W, WANG C. On gear modelling in [18] PAN C Y, DENG H, XU H J. Power transmission equipment multistage rotary vane engines [J]. Meccanica, 2004, 39(1): 47−61. composed of a pericycloidal mechanism and two double crank [12] LIANG L. A rotary engine with two rotors and its design method: Mechanisms: CN Patent 201110072149.7 [P]. 2011−03−24. WO Patent 2005/124122 A1 [P]. 2005−10−06. [19] PAN Cunyun, DENG Hao, XU Haijun. A piston engine with [13] SAKITA M. A catandmouse type rotary engine: Engine design and annular connecting cylinders: CN Patent 201110331226.3 [P]. performance evaluation [J]. Proceedings of the Institution of 2011−10−27. Mechanical Engineers, Part D: Journal of Automobile Engineering, [20] ZHOU Longbao. Internal combustion engine [M]. Beijing: China 2006, 220(Compendex): 1139−1151. Machine Press, 2009: 15−18. (in Chinese) [14] OLEDZKI W J. About a new conception of internal combustion [21] MIKALSEN R, WANG Y D, ROSKILLY A P. A comparison of engine construction I: Rotary engines [C]// 2008 ASME International Miller and Otto cycle natural gas engines for small scale CHP Mechanical Engineering Congress and Exposition. Boston, applications [J]. Applied Energy, 2009, 86: 922−927. Massachusetts, USA: 2009: 1456. [22] DENG Hao, PAN Cunyun, XU Xiaojun. A twinrotor piston engine [15] MORGADO R G. Internal combusiton engine and method: USA, US with annular connecting chambers [J]. Proceedings of the Institution Patent 20070199537A1 [P]. 2007−08−30. of Mechanical Engineers, Part C: Journal of Mechanical Engineering, [16] DENG Hao, PAN Cunyun, XU Haijun, ZHANG Xiang. Theoretical 2013, 227(5): 1080−1089. research on the power transmission system of a twinrotor piston (Edited by FANG Jinghua)