EP2929549A1 - Correction des erreurs angulaires d'aimants permanents - Google Patents

Correction des erreurs angulaires d'aimants permanents

Info

Publication number
EP2929549A1
EP2929549A1 EP13811147.1A EP13811147A EP2929549A1 EP 2929549 A1 EP2929549 A1 EP 2929549A1 EP 13811147 A EP13811147 A EP 13811147A EP 2929549 A1 EP2929549 A1 EP 2929549A1
Authority
EP
European Patent Office
Prior art keywords
partial
magnet
magnetization
magnets
magnetizability
Prior art date
Legal status (The legal status 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 status listed.)
Withdrawn
Application number
EP13811147.1A
Other languages
German (de)
English (en)
Inventor
Frank Grunwald
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Continental Teves AG and Co OHG
Original Assignee
Continental Teves AG and Co OHG
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 Continental Teves AG and Co OHG filed Critical Continental Teves AG and Co OHG
Publication of EP2929549A1 publication Critical patent/EP2929549A1/fr
Withdrawn legal-status Critical Current

Links

Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F7/00—Magnets
    • H01F7/02—Permanent magnets [PM]
    • H01F7/0273—Magnetic circuits with PM for magnetic field generation
    • H01F7/0278—Magnetic circuits with PM for magnetic field generation for generating uniform fields, focusing, deflecting electrically charged particles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F3/00—Manufacture of workpieces or articles from metallic powder characterised by the manner of compacting or sintering; Apparatus specially adapted therefor ; Presses and furnaces
    • B22F3/02—Compacting only
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F3/00—Manufacture of workpieces or articles from metallic powder characterised by the manner of compacting or sintering; Apparatus specially adapted therefor ; Presses and furnaces
    • B22F3/10—Sintering only
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F3/00—Manufacture of workpieces or articles from metallic powder characterised by the manner of compacting or sintering; Apparatus specially adapted therefor ; Presses and furnaces
    • B22F3/12—Both compacting and sintering
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F13/00—Apparatus or processes for magnetising or demagnetising
    • H01F13/003—Methods and devices for magnetising permanent magnets
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F41/00—Apparatus or processes specially adapted for manufacturing or assembling magnets, inductances or transformers; Apparatus or processes specially adapted for manufacturing materials characterised by their magnetic properties
    • H01F41/02—Apparatus or processes specially adapted for manufacturing or assembling magnets, inductances or transformers; Apparatus or processes specially adapted for manufacturing materials characterised by their magnetic properties for manufacturing cores, coils, or magnets
    • H01F41/0253—Apparatus or processes specially adapted for manufacturing or assembling magnets, inductances or transformers; Apparatus or processes specially adapted for manufacturing materials characterised by their magnetic properties for manufacturing cores, coils, or magnets for manufacturing permanent magnets
    • H01F41/0266—Moulding; Pressing
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F7/00—Magnets
    • H01F7/02—Permanent magnets [PM]
    • H01F7/0205—Magnetic circuits with PM in general
    • H01F7/021—Construction of PM
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T29/00—Metal working
    • Y10T29/49—Method of mechanical manufacture
    • Y10T29/49826—Assembling or joining
    • Y10T29/49828—Progressively advancing of work assembly station or assembled portion of work

Definitions

  • the invention relates to a magnet arrangement and to a method for producing a magnet arrangement.
  • the object of the invention has been found to propose a magnet arrangement and a method for producing a magnet arrangement, which is relatively inexpensive and / or simple and / or a relatively high precision of magnetization and / or magnetization with respect to a main magnetization direction and / or main direction of magnetizability entire magnet arrangement allows.
  • substantially balanced is preferably the formulation at least partially compensated and / or reduced and / or understood at least partially compensated.
  • the term length of the partial magnet is alternatively understood as meaning preferably a mechanical axis of symmetry and / or a length and / or longitudinal direction of the body geometry of the partial magnet. With the formulation direction and / or main direction of the
  • Magnetizability or magnetisable is expediently the direction or main direction in which the magnetic material or the magnetic particles are aligned, in particular special in terms of a preferred direction of their orientation.
  • Deviations of the magnetic fields generated by the partial magnets are at least partially compensated in the interaction of the partial magnets.
  • the magnet arrangement is preferably designed such that the partial magnets are substantially anisotropic with regard to their magnetic material or the magnetic particles or crystals.
  • the at least two partial magnets are manufactured with the same tool, in particular with regard to their magnetization and / or magnetizability.
  • the partial magnets are in each case substantially cylindrical or cylindrical-segment-shaped or hollow-cylindrical or guader-shaped or prism-shaped with a polygon, in particular an equilateral polygon, as the base surface.
  • the magnet arrangement preferably comprises a plurality of partial magnets, of which in each case adjacent or adjoining partial magnets are mechanically connected to one another.
  • Each partial magnet is preferably designed in such a way that, relative to its main magnetization direction and / or main direction of its magnetizability, ie in particular with respect to its length, it has magnetization and / or magnetizability essentially orthogonal thereto, which expediently understood as orthogonal direction component of the magnetization or magnetizability is, which in particular as radial angular error of the magnetization or magnetizability is called, wherein
  • one partial magnet is arranged rotated relative to the adjacent other partial magnet by an angle between 140 ° and 220 °, in particular by an angle of substantially 180 °, relative to the length or about the length or Longitudinal axis of the partial magnets.
  • each partial magnet is formed such that its one side has a higher degree of the anisotropic and / or rectified orientation of the magnetic particles and / or the corresponding magnetic material arranged in this side and / or in the region than its other side , which is particularly referred to as north-south fault, wherein the side with the higher degree of anisotropic and / or rectified orientation of the magnetic particles and / or the corresponding magnetic material is defined as a strong pole of the partial magnet and corresponding to the side with the lower degree of anisotropic and / or rectified alignment of the
  • Magnetic particles and / or the corresponding magnetic material is defined as a weak pole of the partial magnet, wherein the magnet assembly is formed so that adjacent partial magnets are aligned and arranged such that two weak poles or two strong poles of the two partial magnets adjoin one another and connected to each other.
  • the magnet arrangement is designed so that the two aforementioned formations or arrangements of the partial magnets are combined, so that both the radial
  • the partial magnets consist of sintered powder or plastic-injected or plastic-bonded magnetic material.
  • each partial magnet is formed so that its first or second side a higher degree of anisotropic or Having substantially parallel or rectified orientation of the arranged on this side or in the region of this page magnetic particles, as in the second or first side, ie in the other side.
  • the side with the higher degree of the anisotropic or rectified orientation of the magnetic particles is particularly preferably referred to as the strong pole of the partial magnets and correspondingly the side with the lower degree of the anisotropic or rectified orientation of the magnetic particles is particularly preferably referred to as the weak pole of the partial magnet.
  • this degree of orientation of the magnetic particles is very particularly preferably understood a measure of the anisotropy of the magnetic particles with respect to their similar or rectified alignment.
  • the magnet arrangement is designed so that the two strong poles or the two weak poles of the two partial magnets or adjacent or respectively all of the adjacent partial magnets adjoin one another. In this way, in particular the north-south fault of the magnet arrangement can be avoided or reduced or. be substantially balanced.
  • Each partial magnet is in particular designed in such a way that, with respect to its length or longitudinal extent, it has an essentially orthogonal or a radial magnetization or radial magnetizability or a radial angular error with respect to its magnetization or magnetizability.
  • this radial magnetization or radial magnetization or this radial angular error of a partial magnet relative to the adjacent other partial magnet by an angle between 140 ° and 220 ° or by an angle between 170 ° and 190 ° or to a Angle of substantially 180 ° twisted, in particular twisted about the length or longitudinal axis of the partial magnet as the axis of rotation, is arranged.
  • an angle error or radial angle error of the magnet arrangement can be avoided or reduced.
  • the magnet assembly is formed so that
  • both the two strong poles or the two weak poles of the two partial magnets or adjacent partial magnets adjoin one another and
  • the partial magnets of the magnet arrangement are arranged substantially centered one behind the other with respect to their central axis in the longitudinal direction or in the direction of their length.
  • the at least two partial magnets of the magnet arrangement are preferably connected to one another by an adhesive or adhesive bonding.
  • the magnet arrangement is expediently bipolar, thus comprises two magnetic poles.
  • the method for producing the magnet arrangement is preferably so pronounced
  • the at least two partial magnets are produced in the same part magnet manufacturing tool.
  • the method is expediently designed such that the impressing and / or strengthening of the orientation of the magnetic particles and / or of the magnetic material takes place by being pressed and / or sintered and / or baked and / or heat-treated and / or cured and / or is cooled.
  • each partial magnet is formed so that its one side a higher degree of anisotropic and / or rectified Alignment of arranged in this side and / or in the region of this side magnetic particles and / or the corresponding magnetic material, as its other side, wherein the side with the higher degree of anisotropic and / or rectified alignment of the magnetic particles and / or the corresponding magnetic material as is defined strong pole of the partial magnet and, accordingly, the side with the lower degree of anisotropic and / or rectified orientation of the magnetic particles and / or the corresponding magnetic material is defined as a weak pole of the partial magnet, wherein the magnet assembly thus formed et, that adjacent partial magnets are aligned and arranged to each other, that two weak pole
  • the magnetic material in particular formed as a powder, is expediently compressed after the alignment of the magnetic material or the magnetic particles by an externally applied magnetic field or pressed into shape, in particular by mechanical force. Subsequently, such a pressed blank magnet is preferably sintered or heat-treated. It is expedient that after the production of at least a first and a second partial magnet, the first and the second partial magnet with respect to their orientation in the partial magnet manufacturing tool and with respect to their length or
  • the first or second partial magnet is reversed in its longitudinal direction with respect to its two ends, so that, for example, its lower end is rotated at the top or the other way round, and / or the first and / or second partial magnet are rotated and / or aligned relative to one another with respect to their longitudinal axis or longitudinal axis Length or substantially more common
  • the at least two partial magnets are usefully connected together.
  • the at least two partial magnets are each produced by compression or in the form of pressing, after which the relative arrangement between at least the first and second partial magnet is carried out and then particularly preferably the at least two partial magnets are baked together or sintered to be permanently connected to each other ,
  • the radial angle error and / or north-south error of each partial magnet in the course of manufacture after the alignment of the particles or the magnetic material is formed and / or changes and / or amplified or attenuated by pressing during pressing and / or sintering and / or baking and / or cooling the respective partial magnet mechanically deformed.
  • the component of the main magnetization direction or the main direction of the magnetizability of one or each partial magnet is stronger than in other directions, in particular as in the orthogonal or radial direction, particularly preferred is the ratio of the magnetization strength or strength of the magnetizability or the magnetic remanence or the magnetic remanence due to a magnetization along the main magnetization direction, the component in the main direction to the component in the orthogonal or radial direction at least 95 to 5.
  • the magnet arrangement is expediently designed as a permanent magnet or permanent magnet.
  • the radial angle error is alternatively or alternatively referred to as axial angle error.
  • the invention also relates to the use of the magnet arrangement in motor vehicles, in particular in position sensor arrangements.
  • Fig. 3 shows an exemplary magnet arrangement, with a compensated or reduced north-south fault
  • Fig. 4 shows an example of a magnet arrangement, with a
  • Hall-effect sensor the direction of the magnetic field, for example by means of an AMR sensor, or exploits the magnetizing effect, for example by means of a "flux gate sensor” or an inductive sensor from often rotationally symmetric magnetic fields are required by Permanent magnets in the form of blanks or rings or
  • Cylinders are generated. These rings or blanks or cylinders are axially, ie magnetized in their longitudinal direction. Desired or necessary is that the mechanical and the magnetic axis of symmetry or longitudinal or main direction are congruent or rectified. Unfortunately, due to the manufacturing process, it is often not possible for the magnetic and mechanical axes of symmetry to be rectified or identical, as exemplified with reference to FIG. 2.
  • Both errors, the radial angle error see Fig. 2, and the north-south error see Fig. 1, are based on the defective, that is: not exactly parallel alignment of the magnetic particles during pressing of the magnetic blanks.
  • a strong magnetic field is applied during the pressing of the magnetic powder in order to align the particles of the powder.
  • this magnetic field is not homogeneous but slightly divergent. This results in a strong pole on the bottom and a weaker, so weak pole on the top, see Fig. 1. This is the mentioned north-south fault.
  • the radial angle error is also based on a misalignment of the particles of the magnetic powder. Cause here is an angle between the axis of symmetry of the magnetic tool and the aligning magnetic field ( Figure 2) Both errors are impressed after sintering in the magnet and not to compensate by a special magnetization.
  • the magnet is replaced for example by two magnets, which have half the height.
  • the second magnet is "turned upside down” so that two similar poles, Regardless of their orientation in the part magnet manufacturing tool, touch (either the weaker ones or the stronger ones).
  • the north-south fault is compensated, as shown by way of example with reference to FIG. 3.
  • the upper magnet In order to compensate for the radial or axial angle error, as shown in FIG. 4, the upper magnet must still be oriented such that the undesired radial components of the magnetization face in the opposite direction. As a result, these components weaken and virtually extinguish themselves in the "far field".
  • the method presented here or the magnet arrangement makes it possible to drastically reduce the unwanted angular error or radial angle error and / or the north-south error.
  • the zone in which the magnet is pressed is not in the center of the coil, which aligns the magnetic powder prior to pressing. The result is that the strong pole of the magnet is always stronger than the weak pole of the magnet. Since the
  • FIG. 1 illustrates the exemplary production of a partial magnet 2, 3, the material of which is arranged in tool 8 in a corresponding cavity.
  • Field coils 11 generate a magnetic field with the field lines 13 to align the magnetic material in the partial magnet 2, 3, which is a main direction 4 have the magnetizability, along which the length 12 of the partial magnet, shown dotted, aligned, which forms a geometric axis of symmetry of the body of the partial magnet 2, 3.
  • the material of the partial magnet 2, 3 is pressed by means of stamp 10. Since the magnetic field 13 has less field density in the upper region 6 of the partial magnet than in the lower region 5, a strong pole 5 of the partial magnet is formed in the lower region and a weak pole 6 in the upper region.
  • a radial angle error is additionally produced by a radial or orthogonal component of the magnetic field 13 which is generated by the field coils 11 for aligning the magnetic particles or the magnetic material.
  • This orthogonal or radial component 14 results in a magnetic field having an angular offset ⁇ to the main direction of the magnetization and the geometric axis of symmetry of the partial magnet 2, 3 and to its length or longitudinal axis 12.
  • the partial magnet 2, 3 now has a north-south fault because of the different field density at its top, and bottom 6, 5 and a radial angle error.
  • FIGS. 3 a) to c) it will now be explained by way of example how, in the case of a magnet arrangement comprising a first and a second partial magnet, the north-south fault is substantially compensated, at least substantially reduced.
  • Fig. 3 a shows a magnet with north-south fault
  • the magnetizing field lines in Fig. 3 a) to c) are respectively illustrated with the arrows.
  • Fig. 3 b) are now two partial magnets 2, 3 shown, which have been produced in the same tool and each have a strong pole 5 and a weak Pol 6 in terms of their magnetizability.
  • the two partial magnets are now joined together by way of example with their weak poles 6 axially and as shown with reference to FIG. 3 c) mechanically interconnected and magnetized together.
  • the resulting magnetic field 7 of the magnet assembly detected at least in a defined minimum distance, no significant north-south fault more.
  • the magnet in FIG. 4 a) to d) exemplifies how the radial angle error in a magnet arrangement consisting of two partial magnets 2, 3 is compensated or at least substantially reduced.
  • a side view is shown at the top and a top view of the magnet or the magnet arrangement is shown below.
  • the magnet in FIG. 4 a) has a radial component M_radial of the magnetizability, as a result of which the entire direction of magnetizability M is pronounced, which has just a radial angle error.
  • the orientation direction of the magnetic particles is thus not parallel to the geometric axis of symmetry or longitudinal axis or length of the magnet.
  • FIG. 4 d) illustrates by way of example at least a minimum distance to Magnetic arrangement 1, the radial angle error is compensated or at least significantly reduced.

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Manufacturing & Machinery (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Hard Magnetic Materials (AREA)
  • Manufacturing Cores, Coils, And Magnets (AREA)

Abstract

L'invention concerne un ensemble aimant (1), comprenant au moins deux parties d'aimant (2, 3) reliées mécaniquement l'une à l'autre. La longueur (12) de chaque partie d'aimant (2, 3) s'étend dans la direction principale d'aimantation (4) de chaque partie d'aimant (2, 3) et/ou dans la direction principale (4) dans laquelle une partie d'aimant (2, 3) peut être aimantée ou dans laquelle son aimantation est prévue, et un premier côté (5) et un second côté (6) sont définis sous la forme de zones opposées aux extrémités de la partie d'aimant (2, 3) par rapport à sa longueur (12). Les deux parties d'aimant (2, 3) ou plus sont disposées l'une à la suite de l'autre par rapport à leur longueur (12) et sont reliées entre elles. En termes d'aimantation ou d'aimantabilité, les deux parties d'aimant (2, 3) ou plus sont orientées l'une par rapport à l'autre de telle façon que des écarts du sens d'aimantation et/ou d'aimantabilité d'une partie d'aimant (2) par rapport à la direction principale d'aimantation et/ou d'aimantabilité (4) minimisent et/ou compensent pratiquement les écarts de direction d'aimantation et/ou d'aimantabilité de l'autre partie d'aimant (3) ou des parties d'aimant voisines par rapport à la direction principale d'aimantation et/ou d'aimantabilité (4), en particulier par rapport à l'aimantation et/ou l'aimantabilité de l'intégralité de l'ensemble aimant.
EP13811147.1A 2012-12-07 2013-12-09 Correction des erreurs angulaires d'aimants permanents Withdrawn EP2929549A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE102012023897 2012-12-07
PCT/EP2013/075956 WO2014087012A1 (fr) 2012-12-07 2013-12-09 Correction des erreurs angulaires d'aimants permanents

Publications (1)

Publication Number Publication Date
EP2929549A1 true EP2929549A1 (fr) 2015-10-14

Family

ID=49841642

Family Applications (1)

Application Number Title Priority Date Filing Date
EP13811147.1A Withdrawn EP2929549A1 (fr) 2012-12-07 2013-12-09 Correction des erreurs angulaires d'aimants permanents

Country Status (6)

Country Link
US (1) US9601251B2 (fr)
EP (1) EP2929549A1 (fr)
KR (1) KR102102498B1 (fr)
CN (1) CN104969310B (fr)
DE (1) DE102013225291A1 (fr)
WO (1) WO2014087012A1 (fr)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112497435A (zh) * 2020-10-22 2021-03-16 横店集团东磁股份有限公司 一种永磁铁氧体外弧强磁磁瓦模具
CN113029204B (zh) * 2021-03-01 2023-06-23 歌尔微电子股份有限公司 传感器和电子设备

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DE975672C (de) 1951-01-30 1962-04-26 Magnetfabrik Gewerkschaft Wind Verfahren zur Herstellung von Dauermagneten mit uebereinstimmender Kristallorientierungs- und Magnetisierungsrichtung und danach hergestellte Dauermagnete
US2897417A (en) * 1957-10-17 1959-07-28 Bomac Lab Inc Fixture for magnetizing toroidal permanent magnets
CS213709B1 (en) * 1979-03-13 1982-04-09 Vaclav Landa Anizotropous permanent magnets
AU2002337022B2 (en) 2001-08-24 2004-10-07 Berlin Heart Gmbh Magnetically hard object and method for adjusting the direction and position of a magnetic vector
US20040189123A1 (en) * 2001-08-24 2004-09-30 Peter Nusser Magnetically hard object and method for adjusting the direction and position of a magnetic vector
WO2004044930A2 (fr) * 2002-11-07 2004-05-27 Stereotaxis, Inc Procede servant a fabriquer un aimant composite
TWI250536B (en) * 2003-02-27 2006-03-01 Mitsubishi Electric Corp Ring-shaped magnet and manufacturing method thereof
US20050158972A1 (en) 2004-01-20 2005-07-21 Nanya Technology Corporation Method for manufacturing bit line contact structure of semiconductor memory
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JP4391897B2 (ja) 2004-07-01 2009-12-24 インターメタリックス株式会社 磁気異方性希土類焼結磁石の製造方法及び製造装置
RU2423748C2 (ru) 2006-12-21 2011-07-10 Улвак, Инк. Постоянный магнит и способ его изготовления
JP4497198B2 (ja) * 2007-12-06 2010-07-07 トヨタ自動車株式会社 永久磁石とその製造方法、およびロータとｉｐｍモータ
JP4914922B2 (ja) 2007-12-25 2012-04-11 株式会社アルバック 永久磁石の製造方法
JP4636198B2 (ja) 2008-12-08 2011-02-23 日亜化学工業株式会社 円柱状ボンド磁石およびその製造方法並びに棒状磁石体
WO2012105006A1 (fr) 2011-02-02 2012-08-09 トヨタ自動車株式会社 Aimant permanent, rotor ou stator de moteur et machine dynamo-électrique

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Also Published As

Publication number Publication date
CN104969310A (zh) 2015-10-07
US9601251B2 (en) 2017-03-21
DE102013225291A1 (de) 2014-06-12
KR20150092274A (ko) 2015-08-12
WO2014087012A1 (fr) 2014-06-12
CN104969310B (zh) 2017-07-07
US20150332832A1 (en) 2015-11-19
KR102102498B1 (ko) 2020-04-20

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