WO1998058167A1

WO1998058167A1 - Rotary engine

Info

Publication number: WO1998058167A1
Application number: PCT/PL1998/000028
Authority: WO
Inventors: Stanislaw Kulka
Original assignee: Stanislaw Kulka
Priority date: 1997-06-16
Filing date: 1998-06-16
Publication date: 1998-12-23
Also published as: PL320581A1; PL191001B1; AU7679198A

Abstract

The rotary engine operates in the four-phase work cycle and reaches the efficiency of the order of 48 % up to 64 % (according to the type), this resulting from engine geometry. The cylinder (1) has hole cylindrical in shape, this hole being tightly closed at both sides by two flat heads (2). The cross section of the cylinder (1) hole is the closed plane curve determined by the equation in the polar co-ordinates (r, f): r(f) = R1 + aR1sin f; for: f⊂∫0; 2Π⊃ where: R1 > 0, 0 < a ≤ 0,5. The shaft (3) crosses the cylinder (1) hole and is supported in the holes of both heads (2), and its axis is in line with the axis of said cylinder (1) hole. The section of the shaft (3) between the heads (2), i.e. inside said cylinder (1), is rectangular in cross section and cubicoid-shaped. The rotor (4) installed in said cylinder (1), made in form of an arm, divides the cylinder (1) from inside into two chambers each other sealed. The shape of the inside wall of said rotor (4), in its cross section, is defined by the closed plane broken line defined by the function in polar co-ordinates (r1, f): the engine achieves much higher efficiency than the piston engines owing to the course of the gas pressure force moment exerted against the shaft (3) during the work phase, this being a result of the engine geometry and the thermodynamic process.

Description

ROTARY ENGINE

This invention relates to a rotary internal-combustion engine for driving machines and vehicles. In this field, most known designs are piston engines and Wankel engine. The effective efficiency for various types of engine according to the invention, ranges between 48% up to 64%, that results from the geometry of the engine design. The work cycle of the single-cylinder rotary engine is similar to that of a two-cylinder four-stroke piston engine.

The rotary engine consists of the following units:

1. cylinder unit,

2. working mechanism: the shaft and the rotor,

3. mechanism controlling the rotor,

4. systems of: supply, exhaust, lubrication, sealing, cooling, and others. The design, described below as the "Rotary Engine", refers to single-cylinder engines in particular, because multi-cylinder engines (with more than one cylinder) can be provided with a shaft (of a different design) to control the rotor without any driving mechanism, provided that rotors in particular cylinders are phase shifted each other. Such a solution requires a separate elaboration as a "Rotary Engine II".

Construction Of The Engine

1. The cylinder unit consists of the cylinder itself and two identical heads closing tightly, at both sides, the cylinder hole with two parallel flat surfaces vertical to the cylinder hole axis. The cylinder hole is a cylindrical in shape: its cross-section (in a plane vertical to the cylinder axis) constitutes a closed plane curve according to the function equation in polar coordinates (r, f), with centre 0 in the point of intersection of the cylinder hole axis and the plane of its cross- section: r(f) = R_j + aR_jSin f; where: fe<0; 2π>, R_λ > 0, 0 < a < 0.5. The r(f) closed plane curve defines the contour of the cylinder internal wall. The cylinder height, H, should be not bigger than dimension 2R_j of the cylinder hole: 0 < H < 2R_j. Each head has a round port coaxial with the axis of the cylinder hole of diameter D equal to: 2aR_j < D < 2R_j(l - a). The engine shaft is mounted in said ports. Besides that, at least two openings, closed with valves and serving as the supply and exhaust system ducts, are made in the heads or in the cylinder body.

2. The working mechanism of the engine consists of the shaft and the rotor.

The shaft of the engine supported in the ports of both heads, and protrudes through the cylinder hole, and its axis is coaxial with the cylinder hole axis. The engine shaft, in the section between both heads, i.e. inside the cylinder, is of cubicoid shape, its cross-section is rectangular and symmetrical to the shaft axis. In other sections the shaft is circular. The cubicoidal part of the shaft is used to connect the shaft itself with the rotor. Three ports are made in the shaft for the rotor driving mechanism. One of the ports, in the form of longitudinal slot, is located symmetrically along the shaft axis. This slot intersects symmetrically the middle part of the shaft, i.e. its rectangular prism, parallel to longer sides of the rectangular shaft cross-section and reaches symmetrically farther at its both sides outside the cylinder to a length depending on the parameters of the rotor driving mechanism, not reaching, however, the shaft ends. The remaining two ports in the shaft are identical having a circular cross-section, and their axes are parallel each other, whereby crossing vertically the shaft axis. They are located symmetrically at both sides, outside the cylinder, and they protrude crosswise through the along-axis-opening and parallel to the shorter sides of the rectangular cross-section of the shaft. The distance between these hole axes depends on cylinder height, H, thickness of the heads, and technical parameters of the rotor driving mechanism.

The rotor, seated on the shaft inside the cylinder, is made in the form of an arm dividing the cylinder into two tightly separated chambers. The rotor has got two parallel flat bases co-operating with two flat surfaces of the heads and makes a solid body of cylindrical and prismatic features, wherein all generating lines and side edges constitute sections of straight lines being parallel each other and vertical to both bases. The rotor height is equal to the cylinder height H. The rotor axis is verdical to its flat bases and parallel to the cylinder axis, and it is the axis of symmetry for the rotor solid. The contour of the rotor side wall at its cross-section (in a plane parallel to its both bases) constitutes a closed plane broken curve, according to the equation in polar coordinates (r_lr f), with the centre Oj in the intersection point of the rotor axis with the cross-section plane: for fe<0; π/2), rι(f) = R_j + aR_jsin f - b, where b - clearance between the wall of the cylinder hole and the side-wall of the rotor; for fe(π/2; π) the course of the r_j(f) curve depends on compression ratio and a shape of the combustion chamber; for fe(π; 2π) the course of the r_j(f) curve is centrally symmetrical in relation to the O_j point towards the course within the range fe(0; π). The ends of the rotor arm are determined by two points: r_j(0) and r_j(π) and its length is: (2R_j - b). The rotor has got a hole, coaxial with the rotor axis, of a rectangular cross-section, situated in such a manner that longer sides of the rectangle are parallel to the rotor length. The rotor is mounted on the engine shaft in such a manner that the cubicoidal member of the shaft is located in the rectangular hole of the rotor; where the hole width is equal to the rectangle width and the length of the hole is longer by at least 2aRr_j than the shaft cubicoid length. The cubicoidal member of the shaft serves as a guide, along which the rotor moves radially with a reciprocating motion in relation to the shaft axis whereby rotating together with the shaft around its axis.

3. Rotor controlling mechanism controls the reciprocating radial motion of the rotor in relation to the shaft axis, shifting the rotor upon the cubicoidal member of the shaft. The control mechanism consists of the following components: slide (lpc), connecting-rod (1 pc), guiding shaft (2 pcs), bevel gear (2 pcs), toothed ring (2 pcs).

The cubicoidal slide length is equal to the length of the rectangular hole in the rotor, and its width is equal to that of the along-axis-opening in the shaft; it is rigidly mounted in the rectangular port of the rotor and protrudes through along- axis-opening in the engine shaft.The port of a circular section with its centre at the point O_j is made in the slide. Two identical guiding shafts are journalled in two round ports in the shaft, crosswise to its axis. They operate like connecting- rods, having one crank each of a radius R2 = aR_j. Cranks of both guiding shafts are located in the along-axis-opening of the shaft, and they are connected with the bar-shaped connecting-rod going through the port in the slide. The distance between the ports for crank-pins in the connecting-rod (i.e. theoretical length of the connecting-rod) is equal to that between the axes of the guiding shafts. Two bevel gears are rigidly mounted at opposite ends of the guiding shafts, and two toothed rings are rigidly mounted on both heads at both sides, outside the cylinder and they constitute two rectangular bevel gear transmissions of a transmission ratio i = 1 each. Due to rotary motion of the shaft, both bevel gears roll over both toothed rings. The cranks of both guiding shafts, coincident in phase, move the connecting-rod in such a way that its axis is always parallel to the axis of the engine shaft and always in line with the rotor axis. The diameter of the connecting-rod bar is equal to that of the port in the slide, and the connecting-rod moving with a reciprocating motion in the port of the slide forces a radial reciprocating motion of the rotor on its shaft by means of the slide.

The design of the controlling mechanism provides a mechanical feedback of the radial motion of the rotor, in relation to the shaft axis, with the rotary motion of the rotor (together with its shaft) around the shaft axis. It means that each position of the rotor, in its rotary motion, corresponds with specific position of the rotor in its radial motion on the shaft cubicoid, and vice versa. The controlling mechanism controls the motion of the rotor in such a way that ends of the rotor arm circumscribes the closed plane curve: r(f) = R_j+ R2 sin f - b and the point 0_t circumcircles the circle defined by the equation: r₀(f) = I R2 sin f | from the point 0, i.e. the radial motion of the rotor is not forced by the internal wall of the cylinder. The ends of the rotor arm move along the internal wall of the cylinder but do not exert a pressure on the wall (from inertia of the rotor mass); a contact of the rotor with the internal wall of the cylinder hole is needed to achieve compression in both chambers of the cylinder (at both sides of the rotor), and it is tealized by sealing-lubricating members.

4. Other sub-units of the engine are the following systems: supply, exhaust, ignition, lubrication, sealing, cooling, and starting.

The supply system feeds both chambers of the cylinder with fuel and air at appropriate phase of engine operation. Widely known schemes generally employed in piston engines can be adapted to the supply system, taking into consideration kind of fuel and type of engine (compression ratio, supercharging, carburettor, injection, etc.).The supply system comprises channels made in the cylinder body and/or heads, these channels being closed with valves. Valve drive can be transmitted mechanically from the engine shaft, or electronically- controlled electromagnetic drive may be designed for the valves. The exhaust system is used to remove exhaust gas from the chamber of the engine; similarly to the supply system, the exhaust system comprises channels closed with valves. One supply system and one exhaust system serve for both chambers of the single cylinder.

The ignition system: depending on the engine type, various types can be used, based on known systems used in four-stroke piston engines.

The lubrication system provides continuous lubrication for friction parts in the engine. The way in which the rotor co-operates with the shaft allows to use the working mechanism as a pump to force oil circulation in the lubrication system.

The rotor sealing is effected by means of sealing members joined with the rotor to separate and seal both chambers of the cylinder closed with heads. The sealing members, constituting sealing/lubricating components and connected with forced oil circulation system, provide lubrication to the internal surfaces of the cylinder and heads.

The cooling system: well known designs are used, such as air flow and/or closed liquid circulation; however; required cooling intensity is much smaller compared with piston engines because the course of the thermodynamic process allows to achieve much higher efficiency at a cost of smaller heat losses.

The starting system - well known designs are used.

Principles Of Operation

As it arises out of the engine design description according to the invention, a cyclic change of volume takes place in both cylinder chambers, and the work cycle of a single-cylinder engine is similar to the work cycle of a double-cylinder four-stroke piston engine during the rotor-shaft rotary motion. The full work cycle of one cylinder chamber is effected during the rotation of the shaft by the angle f = 4π, and it can be divided into four phases: suction, compression, work and exhaust.

The suction phase: the chamber is supplied with fuel and air while increasing the cylinder chamber volume from V_Ωήn to V^,,; the rotor rotates by an angle f_j = π.

The compression phase: the rotor rotates with the shaft by an angle of about f₂ = [4/5 ÷ 5/6 jπ (depending on angular velocity of the shaft), the volume of the chamber is reduced from V_max to V ₂ (to the volume corresponding with angle f₂); the compression phase ends when the rotor is close to the position of V^.

The work phase: ignition is effected with advance to the angle f₂, and the work phase commences when the rotor is in the position corresponding with the angle f₂, just before reaching the V_min. In result of combustion, the pressure of the gas (exhaust gas), p(f), acts against the arm of the rotor and, starting from the position for the angle f₂, the rotor acts with the moment of a positive force against the shaft, according to the engine geometry. The volume of the cylinder chamber changes from V_f2 to V,^ (i.e. at first, it decreases from V_f2 to V,^, and, next, it is increased up to V^^), and the rotor-shaft unit rotates by the angle f₃ = 2π - f₂. Released internal (chemical) energy of fuel, amounting to 48% ÷ 64%, is transformed into mechanical energy.

The exhaust phase: the volume in the cylinder chamber decreases from ^max ^to min' exhaust gases are exhausted, and the rotor-shaft unit rotates by the angle f₄ = π.

The full cycle of one cylinder chamber is completed, and the same cycle is repeated. Operation of the valves is synchronised with the movement of the engine shaft: valves open and close the holes of the suction and exhaust channels according to the phase of the given chamber of the cylinder. The said cycle represents the operation of one chamber; the work cycle of the second chamber of the cylinder is identical, however being phase-shifted by the angle f = π in relation to the first chamber.

Advantages Of The Rotory Engine

The engine according to the invention, as compared with engines in common use, has many essential advantages, such as: one cylinder has two chambers; the rotor turns the shaft directly and the main working motion of the rotor is the rotary motion; the rotor-shaft unit can be used as a pump to force an oil flow in the lubrication system; the rotor does not exert pressure onto the wall of the cylinder hole and no excessive friction occurs; and the most important advantage is high overall (effective) efficiency of the engine.

Effective (total) efficiencv of the engine according to the invention varies from 48% to 64%, i.e. it is nearly twice as high as efficiency of engines currently in use, and it depends on the thermodynamic process resulting from the geometry of -_ t -_

the engine construction. Efficiency can be easily calculated by traditional methods or by computer simulation, both giving the same results.

The most important factor determining the level of efficiency is the course of the curve of the exhaust gas pressure force moment, M(f), acting against the shaft axis during the work phase. The work phase starts before V^, when rotor is in the position f = -π/6, assuming f = 0 for V_min. The moment, M(f), commences to increase rapidly, starting from f = π/6 (at an appropriate angle of advance of ignition or injection) to reach the value of ( .7÷0.8)V_max for f = 0, i.e. for V_ΠJJ_U, and to reach the maximal value, M,^, when the rotor is in position f = π/6. It happens so is effected because when the rotor is in the position f = -π/6, the part of the cylinder chamber is a long and narrow gap, and combustion takes place in a wider part of the cylinder chamber, in the combustion chamber. At such a position of the rotor, the gap is not being filled with gas of a high pressure and when the rotor reaches V^ for f = 0 the gap is reduced to null (taking no account of the clearance b); after reaching V_min the gap is made up again but it is filled with gas of a high pressure with a delay when the rotor overpasses the position f = π/6 or, further on, depending on the angular velocity of the shaft. It can be assumed that from the position f = π/6 up to the end of the work phase for f = π, i.e. till reaching V_max, the pressure in the whole chamber of the cylinder is equalised.

The course of the force moment, M(f), in the function of shaft rotation angle f, this shaft acting against the shaft axis during the work phase for fe<-π/6; π), is described by the equations:

M(f) = pff) HR_j ² a (1 - a/2 + a sin f) for fe ( -π/6; π/6>

M(f) = 2p(f) RRx² a sin f for fe < -π/6; π>, where: p(f) is an equation of the gas pressure for fe ( -π/6; π). As the equations M(f) allow to determine an average force moment M_s, the latter acting on the shaft axis during the whole work cycle for f = 4π, and average torque M₀, the effective efficiency and the effective power of the engine N = M₀ ω, where ω is the angular velocity of the shaft, can be calculated from the M(f) moment curve. The effective efficiency S of the engine according to the invention is determined by the equation: S = (1.6÷2.0)S_t, where S_t is effective efficiency of a four-stroke piston engine. The coefficient: (1.6÷2.0), for engines of a high compression ratio with a pressure ignition is to be assumed from the lower limit 1,6, and greater values up to 2.0 are to be taken for engines of a low pressure ratio with spark ignition.

The course of the work phase and of the moment curve M(f), as result from design features of the engine and as compared with piston engines, allow for a significant reduction of energy loss carried by exhaust gases and transferred to the cooling medium; therefore the efficiency of the said engine increases significantly and varies from 48% to 64%.

Explanations To The Drawings

The drawings are made in the orthogonal projection, and they consists of 4 sheets. They show 5 figures.

The reference marks represent the following units:

1. engine cylinder (1 pc),

2. cylinder head (2 pcs),

3. engine shaft (1 pc),

4. rotor (1 pc),

5. slide (1 pc),

6. connecting-rod (1 pc),

7. guiding shaft (2 pcs),

8. bevel gear (2 pcs),

9. toothed ring (bevel crown gear) (2 pcs),

10. suction valve (2 pcs),

11. exhaust valve (2 pcs).

Sheet 1/4:

Fig. l: assembly drawing: the engine according to the invention is shown in

+l - a --.vi ol o--i +ι -» - rx-T 4*lt/-fc (. h oTr l-Ll-V HΛ U1 O HUll Kf L lll-V C-i.it4.J-t.

Sheet 2/4:

Fig.2: the section in the plane perpendicular to the engine shaft axis shows the closed plane curve r(f), this curve forming the contour of the cylinder hole wall,

Fig.3: the section in the plane perpendicular to the engine shaft axis ( marked BB in the Fig.1) shows the guiding shaft. Sheet 3/4:

Fig.4: rotor - the view: projection on the plane perpendicular to the shaft axis shows the rotor in the cylinder, where point O_λ coincides with point O; besides, the contour of the rotor side wall is shown as curve r_λ (f).

Sheet 4/4:

Fig.5: shows the diagram of force moments M(f₇) and M(f₉) of gas pressure exerted against the shaft axis, at both chambers of the cylinder; the work cycle of the chamber 1 is phase-shifted by the angle f = π in relation to the work cycle of the chamber 2.

Exemplary Design Of The Invention

The invention is shown in the Figure 1, Figure 2 and Figure 3, as an exemplary design of a single-cylinder two-chamber rotary engine.

The cylinder 1, having the cylinder hole of a shape determined by the r(f) curve, is rigidly connected with two heads 2. The shaft 3 is journalled in the holes of both heads 2, and its axis is in line with the axis of the cylinder 1. The rotor 4 is seated on the cubicoidal member of said shaft 3, inside the cylinder 1, and divides said cylinder 1 into two chambers tightly separated. The slide 5 is rigidly mounted in the rectangular port of said rotor 4, and protrudes through the along-axis-opening of said shaft 3. In both transverse openings of the shaft 3 (at its both ends) there are supported two guiding shafts 7 (their axes are parallel each other), being a type of crankshafts. The cranks of said shafts 7 are connected with the connecting-rod 6 protruding through the opening of said slide 5, and its axis is always parallel to the axis of the shaft 3. At the opposite ends of the shafts 7, there are installed rigidly two bevel gears 8 operating with two toothed rings 9 installed rigidly on both heads 2 whereby constituting two rectangular bevel gear transmissions of a transmission ratio i = 1 each. The rotary motion of said shaft 3 forces the bevel gears 8 to roll over both toothed rings 9, and said connecting-rod 6, shifting (in an reciprocating motion) in the opening of said slide 5, controls the radial motion (reciprocal motion) of said rotor 4, shifting it along the rectangular member of said shaft 3 according to its position in the rotary motion; therefore the radial motion of said rotor 4 is independent to the cylinder 1 hole wall shape of said cylinder 1. In the chambers of said cylinder 1, a cyclic change of their volume takes place, and both chambers perform the four-ph^se work cycle φiring the rotation of said shaft 3 by the angle f = 4π, where botø work cycles* are pilose-shifted by the angle f= π. The supply and exhaust systems in the exemplary design (as one of the most optimal designs) have two suction and two exhaust channels made in the body of said cylinder 1, these channels being closed with suction valve 10 and exhaust valve 11. These valves are the slidable, and they open and/or close the channels at appropriate phases of the cycle to supply both chambers of the cylinder 1 and/or remove exhaust gas.

Claims

PATENT CLAIMSWhat I Claim Is:

1. A rotory internal-combustion engine, in witch the cylinder (1) has got a cylindrical hole closed tightly two-sided by two flat heads (2) perpendicular to the axis of the cylinder hole, the cross-section where of is the closed plane curve described by the equation in polar coordinates (r, f) and with the centre at the point 0 being crossed by the cylinder axis: r(f) = R_╧ç + aR_jSin f; for: fe<0; 2╧Ç>, where: _x > 0, 0 < a < 0,5; the shaft (3) of the engine is mounted in the ports in both heads (2) and its axis is coaixial with the cylinder axis; inside the cylinder (1), the rotor (4) in the form of an arm dividing the cylinder (1) into two sealed chambers is installed on the shaft (3); the rotor (4) is joined with the shaft (3) in such a way that it turns together with the shaft (3) around its axis, and concur moving radially (reciprocating motion) to the shaft axis; the radial motion of the rotor (4) is independent of the shape of the cylinder hole and is controlled by the rotor controlling mechanism according to its position in the rotary motion; during the motion of the rotor (4) in the cylinder (1), a cyclic change of the volume of both chambers occurs, at the both sides of the rotor arm, and both chambers perform, separately, four-phase work cycles being phase-shifted by the angle f = ╧Ç, during the shaft (3) turn for the angle of f = 4╧Ç (similarly to four-stroke two-cylinder piston engine).

2. The engine according to the Claim 1, whose shaft section between the heads (2), i.e. inside the cylinder (1), is rectangular in cross-section and symmetrical in relation to the shaft axis, serving to join with the rotor (4); in the shaft (3) there are three port holes designed for the rotor controlling mechanism, one port hole is made in the form of along-axis-opening slot symmetrical along the shaft axis and crossing the rectangular prism and going outside the cylinder (1) symmetrically at its both sides for a distance depending on the engine's parameters; the remaining two ports are circular in cross-section, with their axes parallel each other and crossing perpendicular the shaft axis, and they go across the along-axis-opening, being located symmetrically at both sides of the cylinder (1).

3. The engine according to the Claim 1 and the Claim 2, whose rotor (4) has got two flat surfaces parallel each other and perpendicular to the rotor axis, being the axis of symmetry for the rotor solid and parallel to the cylinder axis; the height of the rotor (4) is equal to the height of the cylinder (1); the shape of the side wall of the rotor (4) in a cross-section (perpendicular to the rotor axis) is the closed plane broken curve, defined by the function in polar coordinates (r f) with the centre at the point 0_L being crossed by the rotor axis: r_t(f) = R_j - aR^in f - b for fe(0; ╧Ç/2), where b means a clearance; for fe(╧Ç/2; ╧Ç>, the curve r^f) course varies depending on a compression ratio and a shape of the combustion chamber; for fe<╧Ç; 2╧Ç), the course of the r_x(f) curve is centrally symmetrical in relation to the 0_L point towards the course within the range fe(0; ╧Ç>; in the rotor (4) the port hole is made of a rectangular cross-section with the centre at the point ; inside the rectangular hole of the rotor (4) there is placed the rectangular prism of the shaft (3) appropriately matched to the hole servings, a guide for the rotor (4) moving on it radially (reciprocating motion) to the shaft axis.

4. The engine according to the Claim 1, and the Claim 2, and the Claim 3, whose rotor controlling mechanism provides coupling of the rotary motion of the rotor (4) with its axial motion, owing to which the radial motion does not depend on the shape of the cylinder (1) hole and the rotor (4) does not exert the pressure (resulting from inertia of the rotor mass) upon the wall of the cylinder (1) wall; the rotor controlling mechanism consists of the slide (5), connecting-rod (6), two guiding shafts (7), and of two rectangular bevel gear transmissions of a transmission ratio i = 1 each, consisting of two bevel rings (8) and two toothed gears (9); the slide (5), cubicoidal in shape, has a length equal to that of the rectangular port hole in the rotor (4), and it is rigidly mounted in this port hole, whereby protruding through the co-axial opening of the shaft (3); the slide (5) has the port hole of a circular cross-section with its centre at the point O_j, this slide being crossed by the connecting-rod (6), round in cross- section and of diameter equal to that of the opening in the slide (5); two guiding shafts (7) are journalled in round openings in the shaft (3) whereby constituting connecting-rods of a radius R₂ = aR_l5 the cranks of the both guiding shafts (7) are located in the co-axial opening of the shaft (3), and they are connected with the connecting-rod (6); two bevel gears (8) are mounted rigidly at opposite ends of the guiding shafts (7), co-operating with two toothed rings (9) rigidly mounted on both heads (2), outside the cylinder (1); rotary motion of the shaft (3) forces the bevel gears (8) to roll over the both bevel rings (9), and the cranks of the both guiding shafts (7) move the connecting-rod (6), the axis of which is in line with the rotor (4) axis and always parallel to shaft (3) axis; the connecting-rod (6) moving (with reciprocating motion) in the opening of the slide (5), forces radial (reciprocating) motion of the rotor (4) on the shaft (3), and each position of the rotor (4) in its rotary motion corresponds with the specific position in its radial motion; hence the rotor (4) moves in such a way that point O_j circumscribes the circumference defined by the equation: r₀( ) = ! R₂ sin/1 , and the ends of the rotor (4) arms circumscribe the closed curve: r( ) = R_j + R₂ sin/- b; the contact of the rotor (4) with the internal wall of the cylinder (1) hole and the surfaces of the heads (2) is effected by means of sealing/lubricating members to achieve compression in both chambers.