WO2008036004A1 - Machine volumique rotative avec une chambre bisphérique - Google Patents

Machine volumique rotative avec une chambre bisphérique Download PDF

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Publication number
WO2008036004A1
WO2008036004A1 PCT/RU2007/000511 RU2007000511W WO2008036004A1 WO 2008036004 A1 WO2008036004 A1 WO 2008036004A1 RU 2007000511 W RU2007000511 W RU 2007000511W WO 2008036004 A1 WO2008036004 A1 WO 2008036004A1
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WO
WIPO (PCT)
Prior art keywords
rotor
housing
axis
piston
rotation
Prior art date
Application number
PCT/RU2007/000511
Other languages
English (en)
Russian (ru)
Inventor
Alexandr Vladimirovich Didin
Original Assignee
Yanovsky, Ilya Yakovlevich
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Yanovsky, Ilya Yakovlevich filed Critical Yanovsky, Ilya Yakovlevich
Publication of WO2008036004A1 publication Critical patent/WO2008036004A1/fr

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01C—ROTARY-PISTON OR OSCILLATING-PISTON MACHINES OR ENGINES
    • F01C9/00—Oscillating-piston machines or engines
    • F01C9/005—Oscillating-piston machines or engines the piston oscillating in the space, e.g. around a fixed point
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01C—ROTARY-PISTON OR OSCILLATING-PISTON MACHINES OR ENGINES
    • F01C11/00—Combinations of two or more machines or engines, each being of rotary-piston or oscillating-piston type
    • F01C11/002—Combinations of two or more machines or engines, each being of rotary-piston or oscillating-piston type of similar working principle

Definitions

  • volumetric rotary machine with bisphere chamber Volumetric rotary machine with bisphere chamber.
  • the invention relates to the field of engineering, namely to rotary volumetric machines that can be used as pumps, hydraulic drives, etc., in particular in multi-stage submersible plants.
  • Known volumetric rotary machine (OPM) (SU 2004133654, SU 2004124353 (1)), which has a housing with an internal cavity of an annular shape. In this cavity, a spiral-shaped separator is installed in which the rotor is mounted.
  • the working surface of the rotor is a surface of revolution, in which there is at least one groove along the axis of rotation of the rotor, in each of which a piston is installed that can rotate partially protruding from one side of the rotor.
  • the piston has at least one through-cut along the perimeter, interacting with the separator, to synchronize the rotation of the piston with the rotation of the rotor.
  • Car entry window and the exit window of the machine are spaced along the axis of the rotor and are separated from each other by a separator.
  • the piston of such a machine rotates in one direction relative to the rotor, and, together with the rotor, rotates relative to the housing.
  • Such a machine has the following advantages.
  • the piston is securely installed in the slot of the rotor, protruding from it by a part of about half.
  • the spacing of the entry and exit windows along the axis of the rotor makes it easy to combine such machines into multi-stage ones, including with a common rotor for many stages. Such machines are used in submersible installations.
  • the common rotor allows you to remove the load from the radial, and often from the thrust bearings of the rotor due to balancing the loads of the individual stages when they are rotated relative to each other.
  • a significant advantage of the pump, created on the basis of such a machine, is the constant flow.
  • Known OPM (GB 1 458 459 and similar to it DE 32 06 286A1), in which the body has a cavity in the form of a segment of a sphere in which a separator is installed along the axis of symmetry of the cavity in the form of a steep sector overlapping the cavity; a rotor mounted rotatably in the housing, with a working surface in the form of two truncated cones, supported by vertices on a sphere from opposite sides, and on the surface of the sphere (within the working cavity), at an angle to the axis of symmetry of the rotor, there is an annular groove made tangentially to to both cones.
  • a piston is fixed rotatably relative to the rotor, in which there is a slot capable of passing the separator.
  • the piston interacts with the separator through the sealing synchronizing element (SSE), made in the form of a cylinder, cut in half, with a groove starting at one end and going almost to the second end.
  • SSE sealing synchronizing element
  • the entrance window of the working fluid and the corresponding exit window is located on one side of the piston.
  • On the other side of the piston there are a couple more entry and exit windows.
  • the piston of such a machine oscillates relative to the housing, and the rotor of the machine rotates relative to the oscillating piston.
  • OPM also has disadvantages: the inconvenience of combining such a machine into a multi-stage machine, due to the fact that the entry and exit windows are on one side of the piston, and for passage from stage to stage, it is necessary to make a channel bypassing the spherical cavity of the housing along the axis of the rotor. Disadvantages are uneven delivery, poor piston fastening (only by the part sitting in the groove on the sphere), which also weakens the shaft due to the annular groove, unreliable fastening of the sealing force element in the piston groove (jamming with increasing load is possible).
  • Known OPM (DE 3146782 Al), which has a housing with a cavity in the form of a segment of a sphere, a rotor mounted for rotation, in which a through cut is made along the axis of the rotor. Also there is a piston in the form of a disk mounted in the groove of the rotor with the possibility of rotation, a camera in the form of a spherical segment, partitioned by a separator in the direction of rotation of the rotor, exit and entrance windows, located before and after the separator, respectively. Moreover, the rotation of the piston is synchronized with the rotation of the rotor by means of a shaft motionlessly moving through the rotor and a system of gears, one of which is mounted on the piston. The piston of such a machine rotates in one direction relative to the rotor, and, together with the rotor, rotates relative to the housing.
  • the advantages of this machine are the spherical contact of the piston and the chamber, the reliability of the fastening of the piston protruding on both sides of the shaft, the presence of a strong shaft (the longitudinal groove weakens it a little), the ability to bring out (open) the entry and exit windows along the shaft to combine several steps on one shaft , independence of leaks from wear of the synchronization mechanism, the possibility of high revolutions.
  • the disadvantage is the unreliable synchronization mechanism, especially if you need to pass the gear shaft through several stages.
  • the aim of this invention is to provide a high-performance, easy to manufacture volumetric rotary machine (OPM). It is supposed to be used in multistage submersible pumps and hydraulic drives. In this OPM, two pistons are installed in the rotor groove, which perform rotational vibrations, however, it turned out that they do not experience large inertial loads even at high OPM speeds. Because masses distributed near the line (plane), which in the middle position of each piston passes through its axis of rotation perpendicular to the axis of rotation of the rotor, these oscillations are performed, largely due to the action of centrifugal forces arising from the rotation of the piston together with the rotor. Those. the natural period of oscillation of the piston is close to the period of revolution of the rotor.
  • the OPM working cavity is limited by geometrically simple surfaces: two segments of the housing sphere, limited by inclined, generally curved (with slight deviations from the plane), and in many particular cases by flat housing surfaces, rotor rotation surfaces, consisting of in most cases, from a cylindrical and, in some cases, spherical surfaces.
  • the inclined surface of the housing can be made flat due to the fact that the center of rotation of the piston is located in the chamber above this surface.
  • the inclined surface of the housing and the face of the SSE interacting with it can be made flat due to the fact that the SSE rotates with respect to the piston around a geometric axis passing through the center of rotation of the piston.
  • the objective of the invention is also achieved due to the fact that when the inclined surface of the housing is displaced outside the center of the working chamber OPM (center of rotation of the piston), it becomes possible to perform reciprocal of the inclined surface of the housing on the piston of the surface.
  • the objective of the invention is also achieved due to the fact that on the piston the surfaces reciprocal to the inclined surface of the housing are executed, interacting with it during OPM operation and being sealing surfaces of the piston.
  • the objective of the invention is also achieved due to the fact that when the inclined surface of the housing is displaced outside the center of the working chamber OPM (center of rotation of the piston) of the surface, the response of the inclined surface of the housing is part of the cylinder.
  • the objective of the invention is also achieved due to the fact that the piston has connectors for installing SSEs, which improve the contact of the piston with the inclined surface of the housing, and reduce the internal flow of the working fluid through the contact point.
  • the objective of the invention is also achieved due to the fact that the piston is executed with a mass distribution as close as possible to the axis passing through the center of the piston along its plane.
  • the objective of the invention is also achieved due to the fact that the piston is executed with the distribution of masses as approximating as possible. ellipsoid of inertia of the piston to the axis passing through the center of the piston perpendicular to its plane and its plane of symmetry.
  • Fig. 1 shows an isometric volumetric rotary machine (OPM) with the longitudinal part (half) of the body removed. Further, in all figures, the rotor rotates clockwise when viewed from above.
  • OPM isometric volumetric rotary machine
  • Figure 2 is an exploded view of the OPM of Figure l; Fasteners and bearings are not shown.
  • FIG. 3 two steps of an OPM variant with a cylindrical shaft are shown in isometric view. For clarity, the longitudinal halves of the cases and the halves of the two extreme limiters of the cameras are cut off.
  • Figure 4 is an exploded perspective view of the OPM of Figure 3;
  • a piston and its two sealing synchronizing elements (SSEs) OPM in Fig. 1 are shown in exploded perspective.
  • Figure 6 presents in isometric disassembled form another version of the piston and SSE.
  • Figure 7 presents in isometric disassembled form a piston with SSE in the form of rollers.
  • Volumetric rotary machine (Fig. 1, 2) consists of a housing 1, a rotor 2 with an output shaft 3 and two pistons 4 which include synchronization sealing elements (SSEs) 5.
  • Housing 1 consists of two longitudinal halves and two inserts - limiters of the chamber 14 and has an internal cavity 6 bounded by two intersecting spherical surfaces 7.
  • the axis passing through the centers of the spheres 7 is the geometric axis of the OPM, the housing and the axis of rotation of the rotor 2.
  • the nickels of the chamber 14 are made in the form of sphere segments bounded, in the general case, by two curved surfaces 8.
  • these surfaces 8 are flat.
  • a spherical recess 10 (figure 2), from which there is also an opening 11 for the exit of the rotor 2.
  • the limiters of the chamber 14 are mounted concentrically to the spherical surfaces 7, so that their surfaces 8 are at an angle (in this example 40 degrees) to the geometric axis 15 and facing surfaces 8 to each other.
  • the rotor 2 is made in the form of a set of coaxial elements (Fig.
  • the piston 4 (Fig. L - 7) is made in the form of a disk with a spherical lateral surface 19, a smaller part of which is cut off by a chord.
  • the radius of the surface 19 is approximately equal to the radius of the surface 7 for the possibility of rotation of the piston in the housing when creating a seal between the surfaces 7 and 19.
  • the end surfaces 20 of the piston 4, in this design, are flat and parallel to each other.
  • K mounted on them spherical platforms 22, concentric surfaces 19 adjoin the connectors 21, for contact with the spherical recess 10 of the housing 1.
  • the pistons 4 are installed in the through groove 16 of the rotor 2 with the possibility of performing rotational vibrations in the plane of the groove 16 relative to the geometrical axes 23 passing approximately (with accuracy to play, tolerances, wear) through the centers of the central spheres 12 of the rotor 2 (relative to the center of the surface 19).
  • the thickness of the piston 4 is approximately equal to the width of the groove 16 for sealing by the piston 4 of the groove 16.
  • the pistons 4 are installed in the rotor 2 overlapping each other, therefore, for their central location in the groove 16 of the rotor 2, on their end surfaces
  • the SSE 5 (Fig. L - 7) has one flat face 24 for contact with the flat surface 8 of the housing 1, one concave spherical face 25 for contact with the Central sphere 12 of the rotor 2, one convex spherical face 26 for contact with the spherical surface 7 of the housing 1 and on another face made a hinge connector 27 reciprocal to the hinge connector 21 of the piston 4. Hinge connector
  • the protrusion 21 on the piston 4 consists of two coaxial cylindrical protrusions 28, between which there is a coaxial cylindrical recess 29.
  • the hinge connector 27 on the SSE 5 consists of two coaxial cylindrical recesses 30, between which a cylindrical protrusion 31 is located coaxially with it.
  • the protrusion 31 holds the SSE 5, mainly from moving the perpendicular flat face 24 and fastens the two halves of the SSE 5, and the recesses hold the SSE 5, mainly from moving along the flat face 24 and from turning in the plane of this face.
  • both hinge connectors 21 are on the same axis 32 and the axis 32 of the hinge connectors 21 and 27 intersects (with precision to play, tolerances, wear) the axis 23 of the oscillatory rotation of the piston 4. It is due to this fact , face 24 of SSE 5 may be in constant contact with the flat surface 8 of the housing 1.
  • the axis 32 is in the inner cavity 6 above the flat surface 8 and approximately parallel to her.
  • the windows of the entrance 33 and the exit 34 of the working fluid (Fig. 1, 2) are located on opposite flat surfaces 8.
  • the window of the entrance 33 is located mainly in that part of the surface 8, which is measured by the distance along the axis 15 when moving along the shaft rotation
  • the working cavity 37 OPM is limited to two; spherical surfaces 7 of the housing 1, two surfaces 8 of the inserts and two central spheres 12 of the rotor 2 and its cylindrical surface 13.
  • the working surface of the rotor 2 i.e. the surface bounding the working cavity 37 and interacting with the housing 1 for sealing the chamber consists of surfaces 12 and 13.
  • the working chamber 37 is sealed by the surface (recess) of the housing 10 along the surface 12 of the rotor 2, the piston surface 20
  • the pistons 4 may have rotation axes 50, which are pressed into the holes 49 and rotate in the holes of the rotor 2, or, in another embodiment, the axes 50 are pressed into the rotor 2, and the pistons 4 rotate around them.
  • the pistons 4 create a pressure drop only when passing the working section 38 located between the inlet window 33 and the exit window 34 in places where the cross-sectional area (passing along axis 15 of rotor 2) of the working cavity is close to its maximum and minimum values. There they divide the working cavity 37 into cameras suction (during operation their volume increases) 39 and discharge chambers (during operation their volume decreases) 40.
  • maximum OPM feed minimal friction losses, because the speed of the piston 4 relative to the rotor 2 is close to zero, the maximum seal between the piston 4, SSE 5 and the housing 1 due to inertia.
  • the supply of such OPM is all the more constant, the shorter the working section 38, i.e. the angular dimensions of the windows 33 and 34 are larger. If the working section 38 has a greater angular extent (smaller windows 33 and 34), the OPM feed becomes less uniform.
  • This OPM can be used as part of a multi-stage machine or independently. With the independent use of one stage, it does not create a pressure drop throughout the cycle, but the movement of the working fluid can be maintained due to the inertia of the liquid column in the line.
  • the cycles of the individual stages are displaced in phase (for example, due to the rotation of the rotors of different stages) so that at any part of the cycle a part of the stages creates a pressure drop.
  • two or more steps are required.
  • the housing 1 of each stage is made in the form of a cylinder with a cavity 6 bounded by two intersecting spherical surfaces 7, cut off symmetrically from both sides by planes inclined under the corner to its axis 15 and passing beyond the centers of the surfaces 8.
  • the housing 1 of each stage is made in the form of a cylinder with a cavity 6 bounded by two intersecting spherical surfaces 7, cut off symmetrically from both sides by planes inclined under the corner to its axis 15 and passing beyond the centers of the surfaces 8.
  • the surface 8 is made on two sides (for two adjacent steps).
  • On the limiters of the chambers 14 one hole is made which is an exit window 34 for one stage and an entrance window 33 of the next stage.
  • the rotor 2 of the OPM is cylindrical.
  • a hole 11 is made in the cylindrical limiters of the chambers 14.
  • the grooves 16 of the adjacent steps are made with an angle turn equal to (if the steps are rotated in phase due to the rotation of the stage bodies) or close to 90 degrees ( for reversing the phase of the steps of the machine and due to the reversal of the rotors of the steps).
  • Pistons 4 can be used both with SSE 5 of various types and without SSE 5.
  • FIG. Figure 6 shows an example of a SSE 5 swinging on an axis 47 protruding from a piston 4.
  • Axis 47 may be part of a piston 4 (a stronger connection, but a more complicated manufacture), or it can be inserted into the hole in the piston 4 either motionless or rotatable. In each case, this is determined by materials, loads, required strength.
  • SSE 5 is made in the form of a tube 48 with a flat plate. It has the same functional surfaces 24, 25, 26 as on the previous SSE 5.
  • the tube 48 is put on the axis 47 either stationary (then the axis 47 rotates in the piston 4), or with the possibility of rotation.
  • the hole 49 When the hole 49 is made in the center of the piston 4, it can be fixed in the rotor 2 using an axis (pin) 50, which can be pressed into the hole 49 or be able to rotate in it. Moreover, on the central sphere 12 of the rotor 2, a hole 46 is also made under the axis 50.
  • FIG. 7 shows an example of SSE 5 made in the form of a roller 51 mounted on an axis 47 protruding from the piston 4.
  • a roller 51 for example, carbide, plastic or rubber bushing.
  • the roller 51 can be mounted on the axis 47 with the possibility of rotation or motionless.
  • the pistons 4 of different OPMs can be combined into one piston 4. This reduces the load on the common piston 4, but due to the fact that the axis 32 of the SSE 5 of both OPMs cannot, being parallel to the surface 8, simultaneously pass through the center of the piston 4; measures have to be taken to maintain the contact seal of the piston 4 (SSE 5) - surface 8. Here are some of them. Passing through the center of the piston 4 axles 32 of only one of the two OPMs (asymmetric piston 4) and laying the main load on them for synchronizing the piston 4.
  • Design SSE 5 in which SSE 5 selects the gap between piston 4 and surface 8. Introduction of a small deviation from flatness surface 8 on one of the surfaces 8 (reduces manufacturability, the resource of the friction pair). Pressing (for example, a pressure drop) to the surface 8 of only the side of the piston 4 creating a pressure drop (a backlash appears in the system).
  • the combination on a common axis 32 passing through the center of the piston 4 SSE 5 different OPM (increases the thickness of the piston, complicates the design).
  • the OPM of FIG. 1 operates as follows.
  • the pistons 4 are located on the working section 38 in the state of their maximum deflection (at the rocking point) in the areas of the maximum (on one side of the rotor closest to us) and minimum (on the other side of the rotor) section of the working chamber 37, overlapping her passage.
  • the camera 37 is closed in a ring.
  • the pistons 4 share the chamber 37 in two opposite places into two cavities - a rarefaction chamber 39 (to the right of the pistons 4) and a compression chamber 40 (to the left of the pistons 4).
  • SSE 5 improve the contact of the pistons 4 with the flat surfaces 8.
  • the size of the rarefaction chamber 39 increases and the working fluid enters through the entrance window 33.
  • the size of the compression chamber 40 decreases, and the working the body leaves it through the exit window 34.
  • the cross section of the working chamber 37 when moving the part of the piston 4 closest to us, begins to decrease.
  • the piston 4 is forced to begin to turn so that the proximal part of the lower piston 4 is shifted up from us, and the proximal part of the upper piston 4 is shifted down from us.
  • the back of the SSE 5 of the upper piston runs into the exit window 34, the overlapping of the working cavity 37 by the pistons 4 is stopped.
  • the OPM does not create a differential pressure (in fact, a small differential remains, as with a fan-type machine).
  • the movement of the working fluid in the line at this time should be supported either by the inertia of its movement, or by other successively established OPMs.
  • this section of the cycle can be eliminated, but then the OPM supply will become forcibly pulsating and the feed will be lost, the efficiency will decrease due to the load on the piston 4 when it moves relative to the rotor 2.
  • the front the edge of the SSE 5 of the second end of the piston 4 slides off the inlet window 33 and runs into the working platform 38. Now this end of the pistons 4 overlaps the cross section of the working chamber 37, pushing the working medium through it from the inlet window 33 to the exit window 34.
  • the OPM of FIG. 3 works similarly to the OPM of FIG. The difference is that it has many steps (two of them are shown) and the pressure drop is maintained throughout the cycle by at least one step.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Hydraulic Motors (AREA)
  • Rotary Pumps (AREA)
  • Reciprocating Pumps (AREA)

Abstract

L'invention concerne une machine volumique rotative dont la chambre de travail a la forme de deux sphères chevauchant partiellement, qui sont limitées par des plans inclinés. Le rotor se présente comme un cylindre comportant un logement longitudinal traversant qui comporte deux pistons effectuant des mouvements en oscillation dans le plan dudit logement, qui recouvrent la chambre de travail et créent une différence de pression lorsqu'ils se trouvent près de leurs points d'oscillation extrêmes, à savoir lorsque leur vitesse est minimale par rapport au rotor et que, partant, les pertes de frottement et d'usure sont également minimales. On obtient ainsi une machine volumique rotative à nombre de tours élevé relativement bon marché, qui possède de bonnes caractéristiques spécifiques (rapport de la puissance à la taille et au poids, rapport de la capacité à la taille), avec une durée de vie utile et une fiabilité élevées, qui possède des surfaces de travail simples du point de vue de la géométrie (plan sur plan, sphère sur sphère). Il est prévu d'utiliser largement la machine volumique rotative dans des pompes immergées à étages multiples.
PCT/RU2007/000511 2006-09-22 2007-09-20 Machine volumique rotative avec une chambre bisphérique WO2008036004A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
RU2006133843/06A RU2382204C2 (ru) 2006-09-22 2006-09-22 Объемная роторная машина с бисферной камерой (варианты)
RU2006133843 2006-09-22

Publications (1)

Publication Number Publication Date
WO2008036004A1 true WO2008036004A1 (fr) 2008-03-27

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Application Number Title Priority Date Filing Date
PCT/RU2007/000511 WO2008036004A1 (fr) 2006-09-22 2007-09-20 Machine volumique rotative avec une chambre bisphérique

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EA (1) EA014046B1 (fr)
RU (1) RU2382204C2 (fr)
WO (1) WO2008036004A1 (fr)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2469212C1 (ru) * 2011-09-07 2012-12-10 Закрытое Акционерное Общество "Новомет-Пермь" Роторная объемная машина

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2708413A (en) * 1949-09-26 1955-05-17 Loewen Edward Rotary piston, power transferer
US2832198A (en) * 1954-03-15 1958-04-29 Pichon Gabriel Joseph Zephirin Hydraulic rotary pump and motor transmission
US3121399A (en) * 1960-10-31 1964-02-18 Hartley E Dale Fluid handling device
DE2334233A1 (de) * 1973-07-05 1975-04-03 Wilhelm Wanke Maschine mit kugelsegmentaxialringkolben und in der mittelwelle vorzugsweise fest gelagerten lamellen sowie mit dichtungsanordnung ausserhalb der hauptkraftwirkungslinien, vorzugsweise fuer arbeitsverfahren mit drucksteigerungs-, druckminderungs- oder drehmomentuebertragungsprinzip
RU2140543C1 (ru) * 1998-08-18 1999-10-27 Позднеев Авенир Иванович Роторный двигатель внутреннего сгорания

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2708413A (en) * 1949-09-26 1955-05-17 Loewen Edward Rotary piston, power transferer
US2832198A (en) * 1954-03-15 1958-04-29 Pichon Gabriel Joseph Zephirin Hydraulic rotary pump and motor transmission
US3121399A (en) * 1960-10-31 1964-02-18 Hartley E Dale Fluid handling device
DE2334233A1 (de) * 1973-07-05 1975-04-03 Wilhelm Wanke Maschine mit kugelsegmentaxialringkolben und in der mittelwelle vorzugsweise fest gelagerten lamellen sowie mit dichtungsanordnung ausserhalb der hauptkraftwirkungslinien, vorzugsweise fuer arbeitsverfahren mit drucksteigerungs-, druckminderungs- oder drehmomentuebertragungsprinzip
RU2140543C1 (ru) * 1998-08-18 1999-10-27 Позднеев Авенир Иванович Роторный двигатель внутреннего сгорания

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EA200800673A3 (ru) 2008-08-29
EA200800673A2 (ru) 2008-06-30
RU2006133843A (ru) 2008-03-27
EA014046B1 (ru) 2010-08-30
RU2382204C2 (ru) 2010-02-20

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