• 专利附录
  • 专利说明
  • 权利要求
  • 类似技术
  • 同族专利
  • 引用文献
  • 法律状态
  • 优先权
    • 专利摘要:
    The invention first relates to an active stabilizing device (10) for primary damping of rolling movements of a watercraft including a hull (14), in particular of a ship (12), wherein the stabilizing device (10) includes at least one positioning device (18) including a drive journal (20) and including a stabilizing surface (16) attached to the drive journal (20) in the region of its root (22), wherein the stabilizing surface (16) includes a leading edge (40) and a trailing edge (42), and the stabilizing surface (16) is disposed under water (26). According to the invention it is provided that the stabilizing surface (16) having an angle of attack (y) set by the positioning device (16) is pivotable about a pivot axis (S) between a first and second position (80, 86) and is rotatable by the positioning device (18) about an axis of rotation (D). Consequently the leading edge (40) can always be oriented essentially in the direction of the pivot direction (82, 90) of the stabilizing surface (16), which stabilizing surface (16) is moving under water (26), which results in a considerable reduction of the flow resistance. A particularly energy-saving operation of the stabilizing device (10) is thereby possible. Furthermore the invention involves a method for operating the active stabilizing device (10).
    公开号:EP3693263A1
    申请号:EP20154921.9
    申请日:2020-01-31
    公开日:2020-08-12
    发明作者:Holger Spardel
    申请人:SKF Marine GmbH；
    IPC主号:B63B39-00
    专利说明:
    [0001] The invention first relates to an active stabilizing device for primary damping of rolling movements of a watercraft having a hull, in particular of a ship, wherein the stabilizing device includes at least one positioning device including a drive journal and including a stabilizing surface attached to the drive journal in the region of its root, wherein the stabilizing surface includes a leading edge and a trailing edge, and the stabilizing surface is disposed under water. In addition the invention relates to a method for operating an active stabilizing device for primary damping of rolling movements of a watercraft having a hull, in particular of a ship, that is essentially not moving through the water.
    [0002] For damping in particular undesirable rolling movements of watercraft, in particular larger motor-driven ships, it is known to use active stabilizing devices that include fin stabilizers attached to a hull of the watercraft below the waterline.
    [0003] When the watercraft moves through the water at a sufficient speed, it is sufficient to change an angle of attack, using suitable actuators, of the stabilizing fins pivoted-out into a constant working position such that the hydrodynamic forces built up from the fin stabilizers counteract the rolling movement for damping thereof.
    [0004] In the case of a watercraft not actively moving through the water, changing the angle of attack of the fin stabilizers is not sufficient, since sufficiently high hydrodynamic forces are not generatable thereby. Rather, in such a constellation it is necessary, for example, to move the fin stabilizers back and forth through the water using further actuators at sufficient speed with a slightly changed angle of attack at most in the end positions of the pivot movement in order to build up the hydrodynamic forces required for weakening the undesirable rolling movements of the hull of the watercraft. A further possibility consists, for example, in varying the angle of attack of the stabilizing surface at high speed with constant pivoting angle in order to generate by such a paddle movement the mechanical forces required for stabilizing the hull against rolling movements.
    [0005] It is disadvantageous that a leading edge of a flow profile of the stabilizing fins is flowed-against by the water in a pivoting direction as provided, but in the pivoting direction opposite thereto the trailing edge is exposed to the inflow by the water. Consequently due to the stabilizing fins periodically pivoting in opposite directions a significantly increased flow resistance arises that impairs the energetic efficiency of the entire stabilizing device.
    [0006] An object of the invention is first to increase the energetic efficiency of a stabilizing device for damping in particular of rolling movements of a watercraft, in particular of a ship. In addition, the invention includes an optimized method for operating such a stabilizing device.
    [0007] The above-mentioned object is first achieved by a stabilizing device including the characterizing features of patent claim 1, according to which the stabilizing surface, having an angle of attack specifiable by the positioning device, is pivotable by the positioning device about a pivot axis between a first and a second position, and is rotatable by the positioning device about an axis of rotation. Consequently with the active stabilizing device and watercraft not moving through the water, the stabilizing surface can be rotated about the axis of rotation such that, independently of the current direction of movement of the stabilizing surface, the leading edge is always flowed-against by the water. In this way the flow resistance of the stabilizing surface periodically pivoted back and forth when the watercraft is not moving through the water is reduced, and as a result the efficiency of the stabilizing device can be significantly increased. Here the free end of the stabilizing surface can follow, for example, a trajectory that is approximately rectangular or corresponds to an eight on its side or the infinity sign.
    [0008] Using the positioning device the stabilizing surface is rotatable by approximately / essentially half a rotation. The stabilizing surface is rotatable, in particular using the positioning device, such that the leading edge of the stabilizing surface located under water preferably always remains essentially directed in the respective current pivot direction of the stabilizing surface.
    [0009] The stabilizing surface is preferably rotatable about the axis of rotation by at least half a rotation.
    [0010] Consequently the stabilizing surface can always be turned such that the leading edge is flowed-against by water, and the flow resistance and associated energy demand of the stabilizing device is reduced.
    [0011] In the case of one refinement a radius of curvature of the leading edge is dimensioned to form an inflow nose larger than a radius of curvature of the trailing edge.
    [0012] An optimal hydrodynamic profile thereby results for the stabilizing surface.
    [0013] Preferably in the region of the drive journal a non-co-rotating inflow body is disposed at least flow-edge-side, which non-co-rotating inflow body is located between the first and second position of the stabilizing surface at least partially outside the hull. Due to the inflow body, functioning as a spoiler, the flow properties in the region of the drive journal can be optimized, since the hydrodynamic properties in the region of the drive journal are matched to those of the stabilizing surface.
    [0014] In a technically advantageous design the inflow body is oriented essentially parallel to the hull longitudinal axis.
    [0015] Consequently an increase of resistance during pivoting of the stabilizing surface can be avoided to the greatest possible extent. In addition the generation of dynamic uplift forces is counteracted by the inflow body.
    [0016] In the case of a further design a cross-sectional geometry of the inflow body in a connecting region corresponds essentially to a cross-sectional geometry of the stabilizing surface in the vicinity of the hull.
    [0017] Turbulent currents and eddies are thereby reduced in a connecting region between the inflow body and the stabilizing surface which stabilizing surface is preferably simultaneously rotatable about its axis of rotation.
    [0018] In one favorable refinement the hull includes at least one receiving pocket for preferably complete receiving of each associated stabilizing surface. Consequently when the stabilizing device is not in use, in the ideal case the at least one stabilizing surface can be completely received in the associated receiving pocket to minimize the flow resistance of the hull.
    [0019] In addition, the above-mentioned object is achieved by a method including the following characterizing steps:a) periodic pivoting of the at least one stabilizing surface, adjusted by an angle of attack specified by a positioning device, about a pivot axis up to reaching a first or a second position, and b) with reversing of a pivoting direction of the stabilizing surface, twisting of the stabilizing surface by the positioning device about an axis of rotation such that preferably the leading edge of the stabilizing surface located under water always remains essentially directed in the respective current pivoting direction of the stabilizing surface. Consequently in the case of a watercraft not moving through the water the efficiency of the stabilizing device can be significantly increased, since due to the leading edge always being oriented in the pivot direction the flow resistance of the stabilizing surface is reduced.
    [0020] In one refinement of the method it is provided that using the positioning device the at least one stabilizing surface is pivoted between the first and second position about the pivot axis by a pivot angle of up to +60 degrees.
    [0021] Due to the pivot angle of ± 60° or 120° with respect to a central position of the stabilizing surface, wherein the stabilizing surface projects approximately at right angles from the hull of the watercraft or of the ship, an optimal damping of undesirable rolling movements of the watercraft is ensured. A maximum pivot angle of the stabilizing surface about the pivot axis is up to 160° with respect to a rest position of the stabilizing surface inside the receiving pocket in the hull of the ship and a first, maximally-pivoted-out-rearward position of the stabilizing surface.
    [0022] According to one advantageous refinement of the method the angle of attack of the at least one stabilizing surface is varied using the positioning device in a range between ±60°. Due to the variation of the angle of attack of the stabilizing surface by ±60° or 120°, a further efficiency increase of the stabilizing effect can be achieved.
    [0023] In the case of a preferred further development of the method, to set a rest position in the inactive state of the stabilizing device the at least one stabilizing surface is pivoted by the positioning device so far that the stabilizing surface is preferably completely received in a receiving pocket of the hull.
    [0024] Consequently an increase of the flow resistance of the hull of the watercraft or of the ship due to the stabilizing device is avoided to the greatest possible extent. In the rest position of the stabilizing surface there is an angle of approximately 0° between the axis of rotation of the stabilizing surface and the hull longitudinal axis, i.e., they extend approximately parallel to each other. Starting from the rest position of the stabilizing surface inside the receiving pocket, the stabilizing surface can be pivoted using the positioning device by up to about 160° up to reaching the first, maximally rearward position.
    [0025] In the following a preferred exemplary embodiment of the invention is explained in more detail with reference to schematic Figures.
    [0026] Figures 1-3 show a perspective schematic view of a stabilizing surface of a stabilizing device in a first pivot direction in each of three different positions, andFigures 4-6 show a perspective schematic view of the stabilizing surface of the stabilizing device of Fig. 1 in a second pivot direction, oriented opposite the first pivot direction of Figs. 1 to 3, in each of three different positions.
    [0027] Figures 1 to 3 - which are referred to together in the further course of the description - show a perspective schematic view of a stabilizing surface of a stabilizing device in a first pivot direction in each of three different positions.
    [0028] A watercraft or a ship 12 includes a conventional hull 14. For the predominant weakening of undesirable rolling movements an active stabilizing device 10 is integrated in the hull 14. Here the stabilizing device 10 includes, for example, a stabilizing surface 16 that is approximately rectangular and fin-like. If necessary the stabilizing surface 16 can also exhibit a peripheral contour of a polygon having more than four corners., The stabilizing surface 16 is pivotable about a pivot axis S and rotatable about an axis of rotation D using a suitable, preferably powerful, hydraulic positioning device 18 including a drive journal 20. In the region of its root 22 the stabilizing surface 16 is connected to the drive journal 20, preferably in a straight-line manner. An angled attaching of the stabilizing surface 16 to the drive journal 20 by, for example, 15° or more is also possible in individual cases.
    [0029] Merely by way of example the ship 12 moves here through the water 26 in a preferred direction of the arrow 24. The stabilizing device 10 is activated when a speed v of the ship 12 through the water 26 is practically zero, or relatively low in relation to normal travel or cruising speed of the ship 12, which is synonymous with a speed v of up to 4 knots. In accordance with the preferred direction of travel through the water 26, the hull 14 of the ship 12 includes a bow 28 and a stern 30 advantageously formed in terms of fluid flow.
    [0030] The hull 14 of the ship 12 is in general configured mirror-symmetric with respect to a hull longitudinal axis 32, that is, in addition to the stabilizing device 10 only schematically depicted here the hull 14 of the ship 12 preferably includes a further starboard-side stabilizing device formed mirror-symmetric with respect to the stabilizing device 10, but not depicted in drawing. Here the term "starboard side" means rightward in the direction of travel of the ship 12, while "port side" means leftward in the direction of travel of the ship 12. In the normal operating state of the ship 12 at least the stabilizing surface 16 of the stabilizing device 10 is always located completely under water 26.
    [0031] Here the pivot axis S coincides merely by way of example with a vertical axis H (so-called yaw axis) of an orthogonal coordinate system 32 of the hull 14, the vertical axis H being oriented essentially parallel to the force of gravity FG when the hull is not heeling, i.e., is lying level in the water 26. Varying from this the pivot axis S of the stabilizing surface 16 can optionally extend at an angle (not illustrated) inclined up to 45° with respect to the vertical axis H of the rectangular coordinate system 32. The pivot movements of the stabilizing surface 16 by the positioning device 18 occur about the pivot axis S by a pivot angle +β, while if necessary rotational movements or changes of an angle of attack γ of the stabilizing surface 16 are also performed about the axis of rotation D.
    [0032] Here the axis of rotation D extends, for example, parallel with respect to a leading edge 40 and a trailing edge 42 of the stabilizing surface 16. Varying from this a non-parallel course of the axis of rotation D is possible in relation to the leading edge 40 and/or the trailing edge 42 of the stabilizing surface 16. To provide an inflow nose 44 having a suitable, fluidically optimal profiling a first radius of curvature R1 of the leading edge 40 is dimensioned significantly larger than a radius of curvature R2 of the trailing edge 42.
    [0033] A receiving pocket 50 in the hull 14 serves for preferably complete receiving of the stabilizing surface 16 when the stabilizing device 10 is inactive. In this case the stabilizing surface 16 is located in the so-called rest position wherein the axis of rotation D extends approximately parallel to the hull longitudinal axis 32.
    [0034] A flow-edge-side inflow body 60 or filling body not co-rotating with respect to the axis of rotation D is disposed in the region of the drive journal 20; the inflow body 60 or filling body is oriented essentially parallel to the hull longitudinal axis 32. A cross-sectional geometry of the inflow body 60, not shown for the sake of a better drawing overview, essentially corresponds in a connecting region 62, at least with an angle of attack γ of approximately 0°, to an also not-shown cross-sectional geometry of the stabilizing surface 16.
    [0035] A central plane 72 of the stabilizing surface 16 is defined by the leading edge 40 and the trailing edge 42. Here by way of example the angle of attack between the central plane 72 and the horizontal 70 is +γ.
    [0036] As shown in Figure 1, the stabilizing surface 16 is located in a first position 80, that is, the stabilizing surface 16 here is pivoted back about the pivot axis S by way of example as far as possible toward the stern 30 of the hull 14. Starting from the first position 80 the stabilizing surface 16 is pivoted by the positioning device 18 in a first pivot direction 82, here facing the bow 28, until the stabilizing surface 16 has assumed a central position 84 according to Figure 2 and projects from the hull 14 approximately at right angles. Here by way of example the angle of attack +γ of the stabilizing surface 16 remains unchanged, but if required can also be changed using the positioning device 18. Due to the positive angle of attack +γ a hydrodynamic lifting force FH1 acts on the pivoting stabilizing surface 16, which force FH1 is oriented opposite the force of gravity FG. Due to the hydrodynamic lifting force a (tilting) moment is caused about the hull longitudinal axis 32 of the ship 12, which (tilting) moment is used by the stabilizing device 10 for the greatest possible compensation of the rolling movements of the ship 12 occurring primarily about the hull longitudinal axis 32.
    [0037] For this purpose the stabilizing device 10 includes a complex sensor system for detecting rolling-, pitching- and yawing-movement as well as the speed and further ship-relevant parameters in the water 26 in real time, on the basis of which a not-depicted efficient digital control- and/or regulating-device of the stabilizing device 10 controls the positioning device 16 such that in particular the undesirable rolling movements of the ship about the hull longitudinal axis 32 can be reduced as effectively as possible. Here a height of the hydrodynamic lifting force FH1 varies with the pivot speed of the stabilizing surface 16 or the relative speed between the stabilizing surface 16 and the water 26, and the angle of attack γ.
    [0038] Figure 3 shows the stabilizing surface 16 in a second position 86 that is reached after a further pivoting of the stabilizing surface 16 by the pivoting device 18 about the pivot axis S by the angle +β toward the bow 28 or the first pivot direction 82.
    [0039] According to the invention the leading edge 40 of the stabilizing surface 16 is always oriented independently of the respective current pivot and incidence angle β, preferably always essentially toward the inflowing water 26, whereby the positioning device 10 is particularly energy efficient. Starting from the second position according to Figure 3, by moving further in the first pivot direction 82 the stabilizing surface 16 reaches the rest position of the stabilizing surface 16, wherein in the ideal case the stabilizing surface 16 is received completely in the receiving space and such that it is terminally flush with the hull 14. In the rest position there is thus no significant change of the hydrodynamic properties of the hull 14 and in particular no relevant increase of the flow resistance.
    [0040] When the second position 86 is reached, using a positioning device 18 a reversal of the first pivot direction 82 is effected in a second pivot direction 90 that is oriented opposite to the first pivot direction 82, wherein the stabilizing surface 16 is preferably simultaneously rotated by approximately half a rotation or by an angle of rotation α of 180° about the axis of rotation D such that the stabilizing surface 16 assumes the further positions according to Figures 4 to 6. Varying from this, larger or smaller angles of rotation α of the stabilizing surface 16 about the axis of rotation D are also possible.
    [0041] Here a free end surface 96 of the stabilizing surface 16 is provided by way of example with a rib structure oriented parallel to the center plane 72 and not shown for the sake of drawing clarity; the rib structure includes a plurality of parallel ribs for minimizing, in particular for reducing, turbulences and eddies.
    [0042] Figures 4 to 6 - which are referred to together in the further course of the description - illustrate a perspective view of the stabilizing surface of the stabilizing device in a second pivot direction, oriented opposite the first pivot direction according to Figures 1 to 3, in each of three different positions.
    [0043] The hull 14 of the ship 12 is in turn moved through the water again in the direction of the white arrow 24. In Figure 4 the stabilizing surface 16 of the stabilizing device 10 is still located in the second position 86. However, in contrast to the position of Figure 3, the stabilizing surface 16 is rotated about its axis of rotation D by approximately half a rotation or 180°, such that during subsequent further pivoting of the stabilizing surface 16 the leading edge 40 is optimally flowed-against by the surrounding water 26. This makes possible a considerable reduction of the energy demand of the stabilizing device 10.
    [0044] In addition, in contrast to Figures 1 to 3 there is, merely by way of example, an approximately constant angle of attack -γ here between the horizontal 70 and the central plane 72 of the stabilizing surface, whereby a hydrodynamic downthrust force FH2 oriented in the direction of the force of gravity FG is generated by the stabilizing surface 16 and serves for damping rolling movements of the hull 14 of the ship 12 about the hull longitudinal axis 32. The level of the hydrodynamic downthrust force FH2 is in turn dependent on the pivot speed of the stabilizing surface 16 or a relative speed resulting therefrom between the stabilizing surface and the water 26. Furthermore a speed v of the hull 14 of the ship 12 different from zero influences the downthrust force FH2 under certain circumstances. In the reversal points of the pivot movement of the stabilizing surface 16, that is, in the first and second position of the stabilizing surface 16, wherein preferably the rotation is also provided by the angle of rotation α of 180° or half the rotation about the axis of rotation D, the downthrust force FH2 can consequently become small.
    [0045] Figure 5 illustrates the central position 84 of the stabilizing surface 16, wherein it is in turn oriented essentially at right angles to the hull 14 of the ship 12. Due to the further pivoting by the positioning device 18 of the stabilizing surface 16 toward the second pivot direction 90, the stabilizing surface 16 of the stabilizing device 10 ultimately reaches the first position 80 again according to Figure 6.
    [0046] In the further course of the description the inventive method shall be briefly explained, again with reference to Figures 1 to 6.
    [0047] In a first method step a) with no heeling of the hull 14, the periodic pivoting of the at least one stabilizing surface 16, set at an angle of attack specified by a positioning device 18, is effected about the pivot axis S, essentially parallel to the force of gravity FG or the in the direction of the force of gravity, by the pivot angle of ±β up to reaching the first or the second position 80, 86. Here the central position 84 is cyclically traversed. With respect to the central position 84 of the stabilizing surface 16, the pivot angle β can be up to ±60°. A positive pivot angle +β defines a pivot movement about the pivot axis S in the clockwise direction, and a negative pivot angle -β a pivot movement about the pivot axis S in the counterclockwise direction, each as seen in plan view.
    [0048] According to the method a change of the angle of attack γ of the stabilizing surface 16 can be effected in a range of up to ±60° with respect to the horizontal 70 in the course of the oscillating pivot movements about the pivot axis S in the two pivot directions 82, 90.
    [0049] In a second method step b) during changing from the first to the second pivot direction 82, 90 and vice versa, i.e., in the respective reversal points of the pivot movement or when reaching one of the two positions 80, 86 of the stabilizing surface 16, a rotation of the stabilizing surface 16 is effected by the positioning device 18 by at least approximately half a rotation or by the angle of rotation α of 180° about the axis of rotation D of the stabilizing surface 16.
    [0050] Consequently the inflow nose 44 of the leading edge 40 is always acted upon by the surrounding water 26, whereby the energetic efficiency of the stabilizing device 10 is significantly increased in active roll-damping operation.
    [0051] According to Figures 1 to 6, according to the method, in active roll-damping operation the free end side 96 of the stabilizing surface 16, which free end side 96 is directed away from the drive journal 20 of the positioning device 18, follows a trajectory that approximately corresponds to a rectangle, or figure 8 on its side, or an infinity sign. REFERENCE NUMBER LIST
    [0052] 10Stabilizing device12Ship14Hull16Stabilizing surface18Positioning device20Drive journal22Root (stabilizing surface)24White arrow26Water28Bow30Stern32Hull longitudinal axis40Inflow edge42Outflow edge44Inflow nose50Receiving pocket60Inflow body62Connecting region70Horizontal72Central plane (stabilizing surface)80First position (stabilizing surface)82First pivot direction84Central position (stabilizing surface)86Second position (stabilizing surface)90Second pivot direction96Free end side (stabilizing surface)FH1Hydrodynamic lifting forceFH2Hydrodynamic downthrust forceFGGravitational forceHVertical axisDAxis of rotationSPivot axisαAngle of rotation (stabilizing surface)βPivot angle (stabilizing surface)γAngle of attack (stabilizing surface)R1First radius of curvatureR2Second radius of curvaturevSpeed (watercraft, ship)
    权利要求:
    Claims (11)
    [0001] Active stabilizing device (10) for the primary damping of rolling movements of a watercraft including a hull (14), in particular a ship (12), wherein the stabilizing device (10) includes at least one positioning device (18) including a drive journal (20) and a stabilizing surface attached to the drive journal (20) in the region of its root (22), wherein the stabilizing surface (16) includes a leading edge (40) and a trailing edge (42), and the stabilizing surface (16) is disposed under water (26), characterized in that the stabilizing surface (16) having an angle of attack (γ) set by the positioning device (18) is pivotable between a first and second position (80, 86) about a pivot axis (S) by the positioning device (18) and is rotatable about an axis of rotation (D) by the positioning device (18).
    [0002] Stabilizing device (10) according to patent claim 1, characterized in that the stabilizing surface (16) is rotatable about the axis of rotation (D) by at least half a rotation.
    [0003] Stabilizing device (10) according to patent claim 1 or 2, characterized in that to form an inflow nose (44) a radius of curvature (Ri) of the leading edge (40) is greater than a radius of curvature (R2) of the trailing edge (42).
    [0004] Stabilizing device (10) according to one of patent claims 1 to 3, characterized in that a non-co-rotating inflow body (60) is disposed in the region of the drive journal (20) at least flow-edge-side, which non-co-rotating inflow body (60) is located at least partially outside the hull (14) at least between the first and second position (80, 86) of the stabilizing surface (16).
    [0005] Stabilizing device (10) according to claim 4, characterized in that the inflow body (60) is oriented essentially parallel to the hull longitudinal axis (32).
    [0006] Stabilizing device (10) according to patent claim 4 or 5, characterized in that a cross-sectional geometry of the inflow body (60) in a connecting region (62) essentially corresponds to a cross-sectional geometry of the stabilizing surface (16) in the vicinity of the hull.
    [0007] Stabilizing device (10) according to one of the preceding patent claims, characterized in that the hull (14) includes at least one receiving pocket for preferably complete receiving of each associated stabilizing surface (16).
    [0008] Method for operating an active stabilizing device (10), in particular according to one of patent claims 1 to 7, for the predominant damping of rolling movements of a watercraft including a hull (14), in particular of a ship (12), essentially not moving through the water (26), comprising the following steps:
    a) periodically pivoting the at least one stabilizing surface (16) about a pivot axis (S) up to reaching a first or a second position (80,86), whereby an angle of attack (γ) is adjusted by a positioning device (18), and
    b) with reversing of a pivoting direction (82, 90) of the stabilizing surface (16), twisting the stabilizing surface (16) by the positioning device (18) about an axis of rotation (D) such that preferably the leading edge (40) of the stabilizing surface located under water (26) always remains essentially directed in the respective current pivoting direction (82, 90) of the stabilizing surface (16).
    [0009] Method according to claim 8, characterized in that the at least one stabilizing surface (16) is pivoted, using the positioning device (18), between the first and second position (80, 86) by a pivot angle (β) of up to ±60° about the pivot axis (S).
    [0010] Method according to patent claim 8 or 9, characterized in that the angle of attack (γ) of the at least one stabilizing surface (16) is changed using the positioning device (18) in a range between ±60°.
    [0011] Method according to one of claims 8 to 10, characterized in that for setting a rest position in an inactive state of the stabilizing device (10), the at least one stabilizing surface (16) is pivoted by the positioning device (18) far enough until the stabilizing surface (16) is preferably completely received in a receiving pocket (50) of the hull (14).
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    JP2020128201A|2020-08-27|
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