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.