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Title:
VOLUME SCREW MACHINE OF ROTARY TYPE
Document Type and Number:
WIPO Patent Application WO/2004/007967
Kind Code:
A1
Abstract:
A rotary screw machine comprises an outer enclosing element (1, 101) having a profiled inner surface (201, 1201), an inner enclosed screw element (4, 104'), having a profiled outer surface (104, 1104) and intermediate screw elements such as a two-sided rotor (3, 103') and a rotor-satellite (102). The screw elements (1, 2, 3, 4) and (101, 102, 103, 104) form a series of elements of which each enclosed element is housed in a respective next enclosing element. According to the invention, the inner enclosed screw element (4, 104) is a planetarily moving screw element.

Inventors:
GORBAN ALEXANDER (UA)
Application Number:
PCT/IB2003/003427
Publication Date:
January 22, 2004
Filing Date:
July 14, 2003
Export Citation:
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Assignee:
ELTHOM ENTPR LTD (CY)
GORBAN ALEXANDER (UA)
International Classes:
F01C1/107; F01C1/22; F01C17/06; F04C2/00; F04C2/08; F04C2/10; F04C2/107; F04C2/22; F04C11/00; F04C18/22; (IPC1-7): F04C2/16
Foreign References:
US6195990B12001-03-06
EP0069604A11983-01-12
RU2140018C11999-10-20
DE19945871A12001-03-29
US1968113A1934-07-31
Attorney, Agent or Firm:
Intes, Didier (Paris Cedex 07, FR)
Download PDF:
Claims:
CLAIMS
1. A rotary screw machine, comprising: an outer enclosing screw element (1, 101 having a profiled inner surface (201,1201), an inner enclosed screw element (4, 104') having a profiled outer surface (104,1104), at least two intermediate screw elements (2,3 ; 102', 103') which are both enclosing and enclosed and have both a profiled inner (202,203 ; 1202,1203) and profiled outer surface (102,103 ; 1102,1103), all screw elements (1,2, 3,4 ; 101', 102', 103', 104#) form a series of elements of which each enclosed element is housed in the respective next enclosing element, wherein the inner enclosed screw element (4, 104') is a planetarily moving screw element.
2. The rotary screw machine of claim 1, wherein said inner enclosed element (4, 104') is hinged on a crank (5, 105') which is coupled to an output shaft (6,106).
3. The rotary screw machine of claim 2, wherein a rotor (3, 1039 rotating about the axis of said output shaft (6,106) encloses said inner enclosed screw element (4, 104'), and wherein a planetarily moving screw element (2, 102') encloses said rotor (3, 103') and is enclosed by said outer enclosing screw element (1, 101') which acts as a stator.
4. The rotary screw machine of any of claims 1 to 3, wherein the motion of an output shaft (6,106) is coupled to the motion of screw elements of said machine in such a manner that a working medium propagating in a first group of working chambers (300) formed between screw elements of said machine in a first direction propagates further in a second group of working chambers (500) by a first group (300,400) formed between screw elements of said machine in a second direction opposite to said first direction.
5. The rotary screw machine of claim 4, wherein an outer body (7,107) of said machine comprises a cavity (12) in which the working medium can turn in order to change its propagation direction.
6. The rotary screw machine of any of claims 13, wherein the motion of an output shaft (6,106) is coupled to the motion of particular screw elements (101', 103 in such a manner that the portions of a working medium propagating in the different working chambers (1300,1400, 1500) between the screw elements all propagate from one side of the machine to the opposite side.
7. The rotary screw machine of claim 6, acting as a pump pumping a medium from a stub tube (109) on one side of the machine to a stub tube (111) on the other side of the machine.
8. The rotary screw machine of claim 7, wherein the output shaft (106) driven by a handle (112) into rotation.
9. The rotary screw machine of claim 4 or 6 with the features according to claim 3, in which the motion of the rotor (3, 103') and the stator (1, 101') is coupled to the motion of the output shaft (6,106).
10. A rotary screw machine, comprising at least three screw elements having each at least one profiled surface, in which a working medium propagates in working chambers formed between two screw elements, wherein the screw elements are coupled in such a manner that upon rotation, the working medium which propagates in a first direction in a first group of working chambers (300,400) propagates in a second direction opposite thereto in a second group (1300,1400) of working chambers.
11. A rotary screw machine, comprising at least three screw elements each having at least one profiled surface, in which the motion of at least two of said screw elements is coupled in such a manner that portions of working medium propagating in different working chambers formed between two screw elements propagate from one side of the machine to the opposite side such as to obtain a substantially constant flow of said working medium from one side of the machine to the other side.
Description:
VOLUME SCREW MACHINE OF ROTARY TYPE FIELD OF THE INVENTION The invention relates to a volume screw machine of rotary type (rotary screw machine).

PRIOR ART Volume screw machines of rotary type comprise conjugated screw elements, namely an enclosing (female) screw element and an enclosed (male) screw element. The enclosing (female) screw element has an inner profiled surface (female screw surface), and the enclosed (male) screw element has an outer profiled surface (male screw surface). The profiled surfaces (screw surfaces) are non-cylindrical (curvilinear shape) and limit the elements radially. They are centred around respective axes which are parallel and which usually do not coincide, but are spaced apart by a length E (eccentricity).

A rotary screw machine of three-dimensional type of that kind is known from US 3,168, 049 and also from US 5,439, 359, wherein an enclosed element surrounded by a fixed enclosing element is in planetary motion relative to the enclosing element.

A first component of this planetary motion drives the axis of the male surface to make this axis describe a cylinder of revolution having a radius E around the axis of the female surface, which corresponds to an orbital revolution motion. In other words, the axis of the enclosed (male) element rotates around the axis of the enclosing (female) element, wherein the latter axis is the principal axis of the machine.

A second component of this planetary motion drives the male element to make it rotate around the axis of its screw surface. This second component (peripheral rotation) can also be called swivelling motion.

Instead of providing a planetary motion, a differential motion can be provided. Usually, synchronizing coupling links are used therefore.

However, the machines can also be self-synchronized by providing suitable screw surfaces.

In most cases, the screw surfaces of the rotary screw machines have cycloidal (trochoidal) shapes as it is for example known from French patent FR-A-997957 and US 3,975, 120 and in the article by

Clarce I. M., Walker D. F., Hamilton P. H.,"New class of rotary piston machine suitable for compressors, pumps and Internal Combustion <BR> <BR> engines", Proc. Inst. Mech. Eng. , 1972, V. 186 N62, p. 743-753 as well as in "Geometry for trochoidal-type machines with conjugate envelopes"by J. V.

Shung and G. R. Pennock, Mech. Mach. Theory, Vol. 299, pp. 25-42,1994.

Rotary screw machines of volume type of the kinds described above are known for transforming energy of a working substance (medium), gas or liquid, by expanding, displacing, and compressing the working medium into mechanical energy for engines or vice versa for motors, compressors, pumps, superchargers, detanders, etc. They are in particular used in downhole motors in petroleum, gas or geothermal drilling.

The transformation of a motion as used in motors has been described by V. Tiraspolskyi,"Hydraulical Downhole Motors in Drilling", the course of drilling, p. 258-259, published by Edition TECHNIP, Paris.

The effectiveness of the method of transforming a motion in the screw machines of the prior art is determined by the intensity of the thermodynamic processes taking place in the machine, and is characterized by the generalized parameter"angular cycle". The cycle is equal to a turn angle of any rotating element (enclosing element, enclosed element or synchronizing link) chosen as an element with an independent degree of freedom.

The angular cycle is equal to a turn angle of a member with independent degree of freedom at which an overall period of variation of the cross section area (or overall opening and closing) of the working chamber, formed by the enclosing and enclosed elements, takes place, as well as an axial movement of the working chamber by one period Pm in the machines with an inner helical screw surface or by one period Pf in the machines with an outer helical screw surface, wherein Pm, Pf are pitches (periods) of a screw turn of the end sections around central axes of the respective elements.

The known methods of transforming a motion in volume screw machines of rotary type with conjugated elements of the curvilinear shape realized in the similar volume machines have the following drawbacks: - limited technical potential, because of an imperfect process of organizing a motion, which fails to increase a quantity of

angular cycles per one turn of the drive member with an independent degree of freedom, in particular when a large volume and masses of working substance passing through a machine are required; - limited specific power of similar screw machines; - limited efficiency and inefficient employing of the constructional volume of the machine; - existence of reactive forces on the fixed body of the machine.

SUMMARY OF THE INVENTION It is an object of the invention to provide a very compact rotary screw machine having a high technical potential, a high specific power and working stably in a very efficient way.

The rotary screw machine according to the invention comprises an outer enclosing screw element having a profiled inner surface and an inner enclosed screw element having a profiled outer surface as well as (at least) two intermediate screw elements which are both enclosing and enclosed and have both a profiled inner and a profiled outer surface. All screw elements form a series of elements of which each enclosed element is housed in a respective next enclosing element. According to the invention, the inner enclosed screw element is a planetarily moving screw element.

Due to the planetary motion of the inner enclosed screw element, working chambers are formed between that inner enclosed screw element and the next enclosing element subsequently at opposite sides of the machine. If one wants to provide an outlet for a working medium which is transported in the working volumes, that outlet need not be as large as in the case in which the inner enclosed screw element rotates without planetary motion about a fixed axis. At a particular moment, the inner enclosed screw element which moves away from the upper portion of the machine and makes it possible that the working medium transported in the upper portion of the machine exits through an outlet. Shortly thereafter, the planetarily moving inner enclosed screw element is once again moved to the upper portion of the machine, thereby providing for the possibility that a working medium which is transported in

working volumes in the lower portion of the machine can exit the machine via the same outlet. In other words, the machine according to the invention can be built in a very compact manner, namely as regards the provision of outlets which at the same time permits the provision of sufficiently large inlets.

Preferably, the inner enclosed element is hinged on a crank which is coupled to an output shaft. The output shaft can be driven and thereby cause the rotation of other screw elements, or a motion of these screw elements is transferred to the output shaft if the machine works inversely.

In a preferred, very simple embodiment, the inner enclosed screw element is enclosed of a rotor rotating about the axis of the output shaft. That rotor is surrounded by a planetarily moving screw element, and the planetarily moving screw element is then surrounded by the outer enclosing screw element which acts as a stator which might be rotatable.

In other words, the most compact rotary screw machine according to the present invention comprises two different mechanisms, a first mechanism being comprised of the stator, the planetarily moving screw element and the rotor (one side of that rotor), whereas the second unit is comprised of the rotor (inner side thereof) and the inner enclosed element together with the output shaft.

The mere combination of particular screw elements does not unambiguously define a single rotary screw machine. Rather, different embodiments can be provided. The particular embodiment is defined by the manner how single screw elements of the rotary screw machine are coupled, i. e. what kind of synchronization of the single screw elements is provided.

In a first embodiment, the motion of an output shaft is coupled to the motion of screw elements of the machine in such a manner that a working medium propagating in a first group of working chambers formed between screw elements of the machine in a first direction thereafter propagates in a second group of working chambers which are formed between screw elements of the machine in a second direction which is opposite to the first direction. In other words, some of the screw elements can be coupled with the output shaft in such a manner that an alternating motion of the working medium takes place, i. e. that the working medium

moves back and forth in the machine. An outer body of the machine should comprise a cavity in which the working medium can turn around such as to change its propagation direction, i. e. to feed the working medium which has propagated through the first group of working chambers into the second group of working chambers.

In an alternative embodiment, the motion of an output shaft is coupled to the motion of particular screw elements in such a manner that portions of a working medium propagating in the different working chambers formed between the screw elements all propagate from one side of the machine to the opposite side. One then has to provide an inlet on one side and an outlet on the other side. The rotary screw machine might then act as a pump which pumps a medium from a stub tube on side of the machine to a stub tube on the other side of the machine. The output shaft may be driven by a handle.

If the above-mentioned embodiment comprising four screw elements (inner enclosed element, rotor, planetarily moving element, stator) is used, both these alternative embodiments have in common that the motion of the rotor and the stator is coupled to the motion of the output shaft. That coupling takes place by means of a reducer (first embodiment) or an inverter (second embodiment).

According to another aspect of the present invention, in a rotary screw machine which comprises at least three screw elements having each at least one profiled surface, and in which a working medium propagates in working chambers formed between two screw elements, the screw elements are coupled in such a manner that upon rotation, the working medium which propagates in a first direction in a first group of working chambers propagates in a second direction opposite thereto in a second group of working chambers. In other words, according to that aspect of the invention, different screw elements of a rotary screw machine are coupled in a particular way such as to obtain an alternating motion back and forth of the working medium in the rotary screw machine.

According to a further aspect of the present invention which corresponds to the contrary of that aspect, in a rotary screw machine which comprises at least three screw elements each having at least one profiled surface, the motion of at least two of these screw elements is

coupled in such a manner that portions of a working medium propagating in different working chambers formed between two screw elements propagate from side of the machine to the opposite side such as to obtain a substantially constant flow of the working medium from one side of the machine to the other side. In other words, that aspect of the present invention provides for a rotary screw machine which transports a working medium from one side of the machine to the other side in an optimized manner, i. e. in a manner in which the working medium is not transported in a plurality of different portions. Rather, a continuous flow of working medium can be obtained by a suitable design of the shape of the screw elements and an optimized coupling.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will become more easily apparent from the following description of preferred embodiments thereof, which is given by way of example only, and in which reference is made to the drawings, in which: Fig. 1 shows a longitudinal section of a rotary screw machine according to a first embodiment of the invention of the rotary screw machine of fig. 1 along the line II-II in fig. 1, Fig. 2 shows the cross section of the rotary screw machine of fig. 1, Fig. 3 shows a longitudinal section of a second embodiment of a rotary screw machine according to the invention, Fig. 4 shows a cross section of the rotary screw machine of fig. 3 along the line IV-IV of fig. 3, and Fig. 5 shows a cross section of the rotary screw machine of fig. 3 along the line V-V of fig. 3.

DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION Fig. 1 shows a longitudinal section of a first preferred embodiment of the present invention. The rotary screw machine comprises a fixed base 8 in which a movable outer body 7 of the machine is supported. In the movable outer body, a stator 1 having a profiled inner surface 201 is provided. The stator 1 encloses a two-sided rotor-satellite 2

having an outer profiled surface 102 and an inner profiled surface 202.

The two-sided rotor-satellite 2 encloses a two-sided central rotor 3 having an outer profiled surface 103 and an inner profiled surface 203. In the interior of the machine, an inner enclosed screw element which is planetarily moving is provided: A rotor-satellite 4 is hinged to rotate on a crank 5 of an output shaft 6.

A reducer 10 is provided which is capable to transfer a rotation of the output shaft 6 to the rotor 3 (with decreasing rotation velocity twice, i. e. without inversion, +2) and which is capable to transfer a rotation of the output shaft 6 to the body 7 (with decreasing the rotation velocity twice, with inversion, i. e.-2).

On one side of the rotary screw machine, stub tubes 9 for inputting a working medium are provided. More in the interior of that machine, but on the same side, a stub tube for outputting the working medium is provided.

On the opposite side of the rotary screw machine, a cavity 12 is provided in which the working medium which is input via the stub tube 9 and which propagates in working chambers formed between the stator 1 and the rotor-satellite 2 can turn in order to change its propagation direction and to continue its flow in working chambers formed between the two-sided rotor 3 and the rotor-satellite 4 such as to exit via the stub 11.

Therefore, the screw elements form two different groups of kinematic planetary differential mechanisms, namely a first group comprised of the elements 1,2 and the outer profile 103 of the two-sided rotor 3 and the second group formed of the inner profile 203 of the two- sided rotor, and the elements 4 and 6.

The profiles of the different elements are rotationally symmetrical. In particular, the symmetry order of the inner profile 201 of the stator 1 is 6, the symmetry order of the outer and inner profiles 102 and 202, respectively, of the rotor-satellite 2 is 5, the symmetry order of the outer profile 103 and the inner profile 203 of the two-sided rotor 3 is 4, and the symmetry order of the outer profile 104 of the rotor-satellite 4 is 3. In other words, the symmetry order of the profiles of the respective screw elements increases from the inside to the outside of the machine.

The stator 1 and the two-sided rotor 3 rotate about the axis Z, whereas the rotor-satellite 2 is placed with eccentricity E2 from that axis and whereas the rotor-satellite 4 is placed with eccentricity E4 from that axis. E2 and E4 are chosen in such a manner as to obtain a statical and dynamical balance of the machine, i. e. such that the centre of gravity of these two rotor-satellites falls into the axis Z.

The inner and outer profiles of all the screw elements 1,2, 3,4 have portions in the form of circular arcs with radius rn (Z) which can be mathematically expressed by the following parametric equations: ry=rn (Z) sin t rx=nmE+rn (Z) cos t and have portions in the form of the transitive arcs between the circular arcs at the end of the screw element. These can be mathematically expressed by the following parametric equations: x (t) =Ecos (nm-1) t+E (nm-1) cost-rn (Z) sin [(nm-2)/2] t y (t) =Esin (nm-l) t-E (nm-l) sint+rn (Z) sin [(nm-2)/2] t where: rn (Z) -radii of the circular arcs which change monotonically along axis Z.

In compressor mode, the machine of fig. 1 and fig. 2 operates as follows : The output shaft 6 is rotated with an angular velocity 6. Via the reducer 10, it rotates the body 7 (together with the stator 1) with an angular velocity col=-w6/2 and at the same time the rotor 3 with an angular velocity 3=6/2. The rotation of the rotor 3 is a first independent rotary motion, simultaneously for both groups of planetarily differential mechanisms 1,2, 3 and 3,4, 6, respectively. The rotation is transferred via the outer surface 103 into the group of differential elements 3,2, 1 and via the inner surface 203 into the group of differential elements 3,4 and 6. The rotation of the body 7 together with the stator 1 is a second independent rotary motion for the group of elements 1,2, 3, and the rotation of the output shaft 6 is the second independent rotary motion for the group of elements 3,4 and 6. The directions and values of the angular velocities of the independent rotations in each group of differential mechanisms are chosen such that the rotors- satellites 2 and 4 execute a planetary motion in opposite directions about the revolution centres 02 and 04, respectively.

Between the stator 1 and the rotor-satellite 2, working chambers 300 are formed, between the rotor-satellite 2 and the two-sided rotor 3, working chambers 400 are formed, between the rotor 3 and the rotor-satellite 4, working chambers 500 are formed.

In view of the fact that the rotors-satellites 2 and 4 execute planetary motion in opposite directions, the working chambers 300 and 400 on the one hand and 500 on the other hand move the working medium along the Z-axis as well as in opposite directions. Jointly, all the conjugated elements 1 to 4 advance (by motion of their conjugation contacts) the working medium from the stub tube 9 into the chambers 300,400 and thereafter into the chambers 500 and further through the stub tube 11 to the outside.

A complete cycle of an axial movement of the six working chambers 300 (with the working medium) between the elements 1 and 2 occurs, when the symmetry orders of the machine elements and their kinematic interaction is given as described above, in 180° of rotation of the shaft 6, i. e. twice during one rotation of the shaft 6.

A complete cycle of an axial movement of the five working chambers 400 between the elements 2 and 3 occurs under the same circumstances in 150° of rotation of the output shaft 6, i. e. 2.4 times during one rotation of the shaft 6.

A complete cycle of an axial movement of the four working chambers 500 between the elements 3 and 4 occurs at the given circumstances in 720° of rotation of the output shaft 6, i. e. half a time during one rotation of the shaft 6.

For the angular velocities of the different screw elements of the rotary screw machine of fig. 1, one obtains the following relation : If the relative angular velocity rotation Me of the shaft 6 is taken to be unity, @6=1 one obtains C03=0. 5 and @1=-0. 5. The relative angular velocity of the revolution mure. 2 of a line 02-0 of the rotor-satellite 2 about the axis Z is then given by (3-re. 2)/(X1-core 2) =nm 1/nm 3 or Mre. 2=-2. 5, wherein nm. 1=6 is the symmetry order of the element 1 and nm. 3=4 is the symmetry order of the element 3. The relative angular velocity of the swivelling motion °s. 2 of the rotor-satellite 2 about its centre 02 is given by (cos. 2-Mre. 2)/ (Mi- (Dre. 2) =nm. i/nm. 2 or (Os. 2=-l/10, wherein nm. 2=5 is the symmetry order of the element 2.

In the machine of fig. 1, the relative angular velocity of the rotation 003 of the central rotor 3 is (A) 3=0. 5, and the relative angular velocity of the revolution of a line 04-0 of the rotor-satellite 4 about the axis Z is given by o) re. 4=o) 6=l. The rotor-satellite 4 swivels about the axis 04 with a relative angular velocity o 54 which is given by (Ws. 4~ (Ore. 4)/ (W3- re4) =nm3/nm4 or co54=1/3, wherein 0) 4=3 is the symmetry order of the element 4.

As already mentioned above, the directions of an axial movement of a gas provided by a couple of working chambers 300 and 400 are the same and are defined by the direction of revolution of the centre 02 of the element 2. The directions of an axial movement of a gas by a couple of working chambers 500 and 600 are the same and are defined by the direction of the revolution of the centre 04 of the element 4. The different sides of the angular velocity of the counter-rotative revolution of the centre 02 of the element 2, which is equal to wre. 2=-2.5, on the one hand, and of the angular velocity of the centre 04 of the element 4, which is equal Wre. 4=1, on the other hand, testify that the direction of the axial movement of a gas by a couple of chambers 300 and 400 is opposite to the direction of the axial movement of a gas by a couple of chambers 500, as shown by the arrows in fig. l.

The invention has the advantage that the angular extent of the thermodynamic cycles is decreased, that the resultant moment of momentum is decreased, and that the total volume of the rotary screw machine is used in an optimized manner.

A second preferred embodiment of the invention is in the following described with respect to figs. 3 to 5. Figs. 3 to 5 show a rotary screw machine acting as a pump. The order of the screw elements is the same as that of the first embodiment described with respect to figs. 1 and 2. Like parts of the machine are given the same reference numerals increased by 100. In particular, the rotary screw machine according to the second embodiment comprises a stator 101'as an outer enclosing screw element which has a profiled inner surface 1201, a two-sided rotor- satellite 102 having an outer profiled surface 1102 and an inner profiled surface 1202, a two-sided central rotor 103 having an outer profile 1103 and an inner profile 1203, and a rotor-satellite 104 which is hinged to rotate on a crank 105'of a shaft 106 which has an outer profiled surface

1104. The elements are placed in a movable outer body 107 of the machine supported in a fixed base 108. On one side of the machine, a stub tube for inputting a working medium is provided, and on the other side of the machine, a stub tube 111 for outputting the working medium is provided.

Via an inventor, a rotation of the shaft 106 which is at first transferred to the body 107 can be transferred to the rotor 103 without inversion.

As shown in fig. 4, the inner profile 1202 of the stator 101'has a symmetry order of 6, the profiles of the two-sided rotor-satellite 102 have a symmetry order of 5, the profiles of the two-sided rotor 103 have a symmetry order of 4, and the profile 1104 of the rotor-satellite 104 has a symmetry order of 3.

Between the rotary screw elements 101', 102', 103'and 104', working chambers 1300,1400 and 1500 are formed. If a working medium (i. e. water) is supplied through the inlet stub tube 9 in the body 7 to the open right-end surface of the elements 1, 101', 102', 103'and 104', that working medium is supplied through the working chambers 1300,1400 and 1500 to the left-open end surface of the elements 101', 102', 103'and 104'and to the outlet stub tube 111 in the body 107.

The pump of fig. 1 operates as follows : Upon rotation of the shaft 106 by means of the handle 112, the body 107 is rotated, together with the stator 101', with an angular velocity Me. Via the inventor 110, the body 107 rotates the rotor 103 with an angular velocity (A) 3=-(1) 6. The rotation of the rotor 103 is a first independent rotary motion for two groups of planetary differential mechanisms at the same time, namely for the first group consisting of elements 101', 102'and 103'and for the second group consisting of the elements 103', 104'and 105'. The rotation is transferred through the outer surface 1103 into the group of differential elements 103', 102', 101'and through the inner surface 1203 into the group of differential elements 103', 104'and 105'. The rotation of the body 107 together with the stator 101 is the second independent rotary motion for the group of elements 101,102 and 103, and the rotation of the crank 105 is the second independent rotary motion for the group of elements 103,104 and 105. The directions and values of the angular velocities of the independent rotations in each group of differential

mechanisms are chosen in such a manner that the rotors-satellites 102' and 104'execute a planetary motion in equal direction about revolution centres 02 and 04 which are chosen in such a manner that a statically and dynamically balanced system is provided. The working chambers 1300, 1400 and 1500 move the working medium along the Z-axis in equal directions. That is, the conjugated elements 101'to 104'advance, by the motion of their conjugation contacts, the working medium from the stub tube 109 into the chambers 1300,1400, 1500 and further through the ports of the body 107 and the stub tube 111 to the outside.

A complete cycle of an axial movement of the six working chambers 1300 (with working medium) between the elements 101', 102' occurs, when the symmetry orders of the pump elements and the scheme of their kinematic interaction is given as described above, in 90° of rotation of the shaft 106 (i. e. four times during one rotation of the shaft 106).

A complete cycle of an axial movement of the five working chambers 1400 between the elements 102', 103'occurs under the same circumstances in 75° of the rotation of the output shaft 106, i. e. 4.8 times during one rotation of the shaft 106.

A complete cycle of an axial movement of the four working chambers 1500 between the elements 103', 104'occurs under the same circumstances in 180° of rotation of the output shaft 106, i. e. twice during one rotation of the shaft 106.

In the pump of fig. 3, the stator 101 is movable. If its angular velocity w, as well as the angular velocity of rotation °6 of the shaft 106 is taken to be unity, @6=l and wl=l, then the relative angular velocity of rotation of the rotor 103 equals W3=-l. The relative angular velocity of the revolution (Ore. 2 of a line O2-O (see fig. 4) of the rotor-satellite 102 about the axis Z is then given by (W3-Wre. 2)/ (Wl-Wre. 2) =nm. 1/nm. 3 or rez=5/ wherein nm. =6 and is the symmetry order of the element 1 and nm. 3=4 is the symmetry order of the element 3. The relative angular velocity of the swivelling wus. 2 of the rotor-satellite 102 about its centre O2 is given by Ws. 2-Mre. 2)/ (Mi-Mre. 2) =nm. i/nm. 2 or or. 2=5, wherein nm. i=6 is the symmetry order of the element 1 and nm.3=4 is the symmetry order of the element 3. The relative angular velocity of the swiveling wus. 2 of the rotor- satellite 102'about its centre 02 is given by (Ms. 2=Mre. 2)/ (Mi-

#re2)=nm.1/nm.2, or, #s.2=1/5, wherein nm.2=5 is the symmetry order of the element 2.

In view of the fact that the relative angular velocity of the central rotor @3=-1, the relative angular velocity of the revolution of a line 04-0 of the rotor-satellite 104 about the axis Z is Ore4=O6=1. The rotor- satellite 104 swivels about the axis 04 with a relative angular velocity Cl) s. 4 which is given by (#s.4 - #re.4)/(#3 - #re.4)=nm.3/nm.4 or 5. 4=5/3. This embodiment has the advantage that the angular extent of the thermodynamic cycles is decreased, and that the resultant momentum is decreased and that at the same time the reactive forces on the machine supports are also decreased, thereby improving the specific characteristics of the screw volume machine according to the invention.