JP5398290B2 - Crankshaft manufacturing apparatus and manufacturing method - Google Patents

Description

  The present invention relates to a method and an apparatus for manufacturing a crankshaft, and more particularly to an improvement in technology for forming a plurality of hollow holes in a crankshaft for weight reduction.

  A crankshaft of an internal combustion engine includes a journal shaft portion. A crankpin portion parallel to the journal shaft portion is connected by an arm. The arm portion is formed with a counterweight portion, and the formation position of the counterweight portion with respect to the journal shaft portion is on the opposite side of the connecting portion of the crankpin portion. In the crankshaft, from the viewpoint of improving fuel efficiency, a hollow hole may be formed in the crankpin portion to reduce the weight. Even when the hole is formed in the crankpin portion, the rigidity of the crankshaft is hardly affected. Therefore, it is preferable to form the hole in the crankpin portion.

  For the formation of the hole in the crankpin part, it is conceivable to use a forging device having a side forming punch that moves in a direction perpendicular to the moving direction of the press ram. The drive source for the side forming punch of the forging device is simpler than servo motors or hydraulic means, does not require installation outside the die set, and linearly follows the press ram operation. A cam mechanism that enables this is often used.

  FIG. 6 is a conceptual diagram for explaining the operation of the side forming punch 20 by the cam mechanism 10. The cam mechanism 10 includes a cam 11, a cam driver 12 that drives the cam 11, and a cam holder 13 on which the members 11 and 12 are slidably supported. A side molding punch 20 is provided on the side surface of the cam 11 on the inner side of the mold, the side surface of the cam 11 on the outer side of the mold is an inclined surface, and the lower surface of the cam driver 12 is an inclined surface of the cam 11 in the initial state. The inclined surface is arranged at a predetermined interval from the surface and slides relative to the inclined surface when the cam 11 is operated. In the cam mechanism 10, when the upper plate 31 moves downward by a predetermined distance toward the lower plate 32 by a press ram (not shown), the inclined surfaces of the cam 11 and the cam driver 12 come into contact with each other. These inclined surfaces slide with each other when the upper plate 31 moves further downward, and the side molding punch 20 moves to the inside of the mold along the horizontal direction.

JP 2007-245229 A

  However, when the crankshaft is formed by the forging device, the crankshaft is placed in the mold so that its axial direction is perpendicular to the moving direction of the press ram. 20 needs to be inserted into the crankpin portion from the axial direction of the crankshaft. For this reason, when forming a hole in each crankpin portion of a crankshaft having a plurality of cylinders, the side forming punches intersect each other.

  Specifically, in the side molding using the cam mechanism 10, since the cam 11 is interlocked with the movement of the press ram, the side molding punch 20 provided on the cam 11 is at the bottom dead center of the press ram, The maximum insertion length into the crankpin portion is reached, after which the press ram moves toward top dead center and the side forming punch 20 is pulled out from the crankpin portion. For this reason, as shown in FIG. 7, for example, when the hole 44 is formed in each crankpin portion 43 of the four-cylinder crankshaft 40 having the full counterweight structure, the side forming punches 21 and 22 intersect each other. The side forming punches 23 and 24 intersect each other (portion surrounded by a broken line in the figure). For this reason, it is impossible to form a plurality of holes at positions where the side forming punches interfere with each other within one stroke from the top dead center to the bottom dead center of the press ram. In addition, the codes | symbols 41 and 42 of FIG. 7 have shown the crankshaft part and the crank arm part.

  For the above reasons, the side molding using the cam mechanism cannot be applied to forging a crankshaft having a shape such that the side molding punches interfere with each other. Therefore, it is conceivable to avoid the above-mentioned intersection by using a servo motor or hydraulic means independent of the operation of the press ram as a drive source of the side forming punch and performing independent control on the side forming punch. . However, this technology requires a large space for installation of actuators and the like, which not only decreases workability and productivity, but also expands the movable range outside the die set, resulting in a large press facility. .

  Therefore, according to the present invention, even when a cam mechanism is used as a drive source for the side molding punch, the positions where the side molding punches intersect each other within one stroke from the top dead center to the bottom dead center of the press ram. It is an object of the present invention to provide a crankshaft manufacturing apparatus and manufacturing method capable of forming a plurality of holes in the above.

The crankshaft manufacturing apparatus of the present invention includes a lower mold, an upper mold that is movable with respect to the lower mold, and a plurality of side molding punches that move in a direction perpendicular to the movement direction of the upper mold. Provided in each side molding punch, and a press ram for closing and molding the crankshaft material in the mold by moving the upper mold relative to the lower mold. A cam mechanism that moves the punch toward the inside of the mold in conjunction with the movement of the press ram and a cam mechanism that is provided on at least one of the side forming punches to prevent interference between the side forming punches. A retraction mechanism that releases the interlock with the movement of the press ram via the cam mechanism, the cam mechanism has a side forming punch and is provided so as to be movable in a direction perpendicular to the moving direction of the upper mold, Firmly to the press ram And a cam driver that drives the cam by moving in the same direction as the press ram, and the retracting mechanism includes a fixing member that fixes the cam driver of the cam mechanism on the side provided with the retracting mechanism to the press ram, It is characterized by having a retracting member that moves the cam driver in a direction opposite to the moving direction of the press ram when the fixing of the cam driver and the press ram by the member is released .

  In the crankshaft manufacturing apparatus of the present invention, the material of the crankshaft is closed and molded in the mold by the movement of the press ram, and each side molding punch is moved to the mold by a cam mechanism linked to the movement of the press ram. By moving in the inner direction, holes are formed in each part of the material.

  Here, in order to prevent the side forming punches from interfering with each other, a retraction mechanism is provided that is provided on at least one of the side forming punches and releases the interlock with the movement of the press ram via the cam mechanism. Therefore, after one side forming punch is moved toward the inside of the mold by a cam mechanism linked to the movement of the press ram, a hollow hole is formed, and then the movement of the press ram is linked by the retraction mechanism. It can be released and retracted to the outside of the mold to return to the initial position. The other side molding punch can start moving in the inner direction of the mold by a cam mechanism interlocked with the movement of the press ram. Therefore, the other side molding punch is hollow without interfering with the one side molding punch. Shaped holes can be formed.

  Specifically, when the above-described interference prevention method is applied when there are N (> 2) side forming punches at positions intersecting with each other, the first side forming punch is moved into the mold → Retraction of the first side molding punch to the outside of the mold, movement of the first side molding punch to the inside of the mold → retraction of the first side molding punch to the outside of the mold, ... .., movement into the mold by the (N-1) th side molding punch → retraction to the outside of the mold by the (N-1) th side molding punch, mold by the Nth side molding punch The movement to the inside can be executed in order.

  By using the interference prevention method as described above, a plurality of holes can be formed with a time difference in one process from the top dead center to the bottom dead center of the press ram. This load can be suppressed to about half compared to the case where a plurality of holes are simultaneously formed. As a result, it is possible to reduce the size of the press facility. In addition, as described above, a cam mechanism that can be housed in a die set can be used as a drive source for a plurality of side forming punches. A space for installing the apparatus becomes unnecessary, the press facility can be further downsized, and workability and productivity can be improved. Furthermore, since the movable range of the side forming punch can be set in the die set, there is no problem in the safety of the operator.

The crankshaft manufacturing method of the present invention includes a method of laterally forming a plurality of holes by the crankshaft manufacturing apparatus as described above. That is, the crankshaft manufacturing method of the present invention includes a lower mold, an upper mold that is movable with respect to the lower mold, and a plurality of side moldings that move in a direction perpendicular to the moving direction of the upper mold. A mold having a punch, a press ram for moving the upper mold relative to the lower mold, a cam mechanism provided in each side molding punch, and a side molding punch to prevent interference between the side molding punches. A retraction mechanism that releases the interlock with the movement of the press ram via the cam mechanism, and the cam mechanism has a side molding punch and moves in the direction of movement of the upper mold. And a cam driver that is fixed to the press ram and moves in the same direction as the press ram. The retraction mechanism is a cam of the cam mechanism on the side where the retraction mechanism is provided. Driver A fixing member for fixing to the press ram, and a retracting member for moving the cam driver in a direction opposite to the moving direction of the press ram when the fixing of the cam driver and the press ram by the fixing member is released. The crankshaft material is closed and molded in the mold, and each side forming punch is moved inward of the mold by the cam mechanism in conjunction with the movement of the press ram. The side molding punch is moved by the cam mechanism when the cam driver is moved in the same direction as the movement direction of the press ram and the cam provided with the side molding punch is driven. When forming a hole in the material with the side forming punch, if using a material having a shape that crosses the side forming punches, the side forming punches In order to prevent the one side molding punch from moving after the hole has been formed, the retraction mechanism releases the interlock with the movement of the press ram and retreats to the outside of the mold. The movement of the mold in the internal direction is started, and the retraction mechanism retracts the one side forming punch. When the fixing member is released, the cam driver moves in the direction opposite to the press ram movement direction. It is characterized by being performed .

  The crankshaft manufacturing method of the present invention can achieve the same effect as the crankshaft manufacturing apparatus of the present invention using the interference prevention method.

  According to the crankshaft manufacturing apparatus or the manufacturing method of the present invention, even when a cam mechanism is used as a drive source for a side forming punch, a plurality of press rams within a single process from the top dead center to the bottom dead center. Since the hole portion can be formed with a time difference, it is possible to obtain an effect such as miniaturization of the press facility.

It is a top view showing schematic structure of the manufacturing apparatus of the crankshaft of one Embodiment which concerns on this invention. 1 shows a schematic configuration of a crankshaft manufacturing apparatus according to an embodiment of the present invention, in which (A) is a side sectional view taken along line 2A-2A ′ of FIG. 1, and (B) is a line 2B-2B ′ of FIG. FIG. It is a graph for showing the time dependence of the stroke of the press ram of the manufacturing apparatus of the crankshaft shown in FIGS. 1 and 2, and explaining the operation of each side forming punch when the stroke changes. (A)-(C) are top views showing operation | movement of each side shaping | molding punch at the time of the change of the stroke of a press ram shown in FIG. (A)-(C) are top views showing operation | movement of each side shaping | molding punch following FIG. It is side sectional drawing showing schematic structure of the cam mechanism of the manufacturing apparatus of the conventional crankshaft. It is a top view for demonstrating the problem of the manufacturing apparatus of the conventional crankshaft.

(1) Configuration of Embodiment Hereinafter, an embodiment of the present invention will be described with reference to the drawings. 1 and 2 show a schematic configuration of a crankshaft manufacturing apparatus 100 according to an embodiment of the present invention. 1 is a schematic top view showing the overall configuration of the crankshaft manufacturing apparatus 100, FIG. 2A is a schematic side sectional view taken along line 2A-2A 'of FIG. 1, and FIG. 2B is 2B-2B of FIG. FIG. In FIGS. 1 and 2, for convenience of illustration, illustration of each part is omitted and illustration is simplified. Specifically, the press ram 104 and the load adjusting unit 105 are not shown in FIG. 1, and the upper mold 103A, the lower mold 103B, and the cam holders 113h to 116h of the mold 102 are simplified in FIG. In FIG. 1, for convenience of illustration, the relative positions of the side forming punches 111p to 118p and the cam mechanisms 111 to 118 are not strictly shown.

  The crankshaft manufacturing apparatus 100 includes, for example, a press bolster 101, and a press ram 102 is supported on the press bolster 101. A mold 103 is disposed between the press bolster 101 and the press ram 102. Reference numeral 104 in FIG. 1 indicates one surface of the bed on which the press bolster 101 is placed.

  The mold 103 includes a lower mold 103A, an upper mold 103B, and side forming punches 111p to 118p. A preform 200 is placed in the mold 103. The preformed product 200 includes a journal shaft portion 201, and the journal shaft portion 201 is provided with an arm portion 202. Adjacent arm portions 202 are connected to each other by a crankpin portion 203 arranged in parallel with the journal shaft portion 210. The crankpin portion 203 is disposed in parallel with the journal shaft portion 201. The cavity surface of the mold 103 has a shape corresponding to the crankshaft preform 200. The upper mold 103B is provided so as to be movable with respect to the lower mold 103A. Reference numeral 105 in FIG. 2 denotes a load adjusting unit (such as a hydraulic means or an air pressure means) that adjusts an initial load on the upper mold 103B.

  The side forming punches 111p to 118p are provided so as to be movable in a direction perpendicular to the moving direction of the upper mold 103B. The side forming punches 111p to 118p can be inserted into and removed from the inside of the mold 103 through punch holes (not shown) formed in the side portion of the mold 103.

  The side forming punches 111p to 118p include cam mechanisms 111 to 118 that move into the mold 103 in conjunction with the movement of the press ram 102. The cam mechanisms 111 to 118 include cams 111c to 118c, a cam driver that drives the cam, and cam holders 111h to 118h on which the cam and the cam driver are slidably supported.

  Side forming punches 111p to 118p are provided on the side surfaces of the cams 111c to 118c on the inner side of the mold 103. The side surfaces of the cams 111c to 118c on the outside of the mold 103 are inclined surfaces, and the lower surface of the cam driver is an inclined surface that slides with respect to the inclined surfaces of the cams 111c to 118c. In the cam mechanisms 111 to 118, when the upper mold 103B is moved downward by the press ram 102, the cam driver and the inclined surfaces of the cams 111c to 118c come into contact with each other. When the press ram 102 further moves downward, these inclined surfaces slide with each other, and the side molding punches 111p to 118p move toward the inside of the mold 103 along the horizontal direction.

  The cam drivers of the cam mechanisms 111 to 114 are arranged so as to be movable in the vertical direction through the passage hole 102 </ b> A of the press ram 102. In this case, each cam driver is fixed in the passage hole 102A by the following fixing member until completion of molding by the corresponding side molding punch. In this case, the fixed position of the cam driver with respect to the inclined surface of the cam is set a predetermined distance above the fixed position of the cam drivers of the cam mechanisms 111 to 114. 2A shows the cam drivers 113d and 114d and the fixing members 113v and 114v of the cam mechanisms 113 and 114, the cam mechanisms 111 and 112 also have cam drivers and fixing members having the same configuration. Have. In FIG. 2B, the cam drivers 115d and 116d of the cam mechanisms 115 and 116 are shown, but the cam mechanisms 117 and 118 also have cam drivers having the same configuration.

  The cam mechanisms 111 to 114 are provided with cam evacuation mechanisms that evacuate the side molding punches 111p to 114p to the outside of the mold 103 after completion of the side molding in the middle of the top dead center to the bottom dead center of the press ram 102. The cam retracting mechanism includes a first retracting member, a second retracting member, and the fixing member. The first retracting member is an elastic member provided on the side surface of the cams 111c to 114c on the outside of the mold 103, for example. The second retracting member is an elastic member provided on the upper surface of the cam driver, for example. The fixing member moves from the upper surface of the cam driver to the retraction hole 102B of the press ram 102 to release the interlocking between the press ram 102 and the cams 111c to 114c after the side forming punches 111p to 114p are completely formed. When the fixing member enters the retracting hole 102B of the press ram 102, the cam driver moves upward by the second retracting member, and the cam retracts to the outside of the mold 103 by the first retracting member. In FIG. 2A, the first elastic members 113s and 114 and the second elastic members 113t and 114t of the cam mechanisms 113 and 114 are shown, but the cam mechanisms 111 and 112 are also similar to the first ones. , Having a second elastic member.

  The cam mechanisms 115 to 118 are provided with a cam retracting mechanism for retracting the side forming punches 115p to 118p to the outside of the mold 103 after the side forming is completed at the bottom dead center of the press ram 102. And a first retracting member. In FIG. 2B, the first retracting members 115s and 116s of the cam mechanisms 115 and 116 are illustrated, but the cam mechanisms 117 and 118 also have the same first retracting members.

  For example, when the preform 200 is provided in an engine having a small to medium displacement, the preform 200 is preliminarily formed while suppressing deformation at the time of forming a hole in a state where the preform 200 is heated to a high temperature (for example, 1000 to 1200 ° C.). The load on the mold 103 necessary for holding the molded product 20 is, for example, about 400 t. Although the load at the time of forming the hole depends on the shape and cross-sectional area, for example, it is about 100 t because of forging. As a result, the crankshaft manufacturing apparatus 100 requires a press having a forming load capacity of about 1200 t as the total load. The mold 103 and the cam mechanisms 111 to 118 are arranged so as to fit in the press die set as described above.

(2) Operation | movement of embodiment Operation | movement of the manufacturing apparatus 100 of a crankshaft is mainly demonstrated with reference to FIGS. FIG. 4 is a graph showing the time dependence of the stroke of the press ram 102 of the crankshaft manufacturing apparatus 100 shown in FIGS. 1 and 2 and explaining the operation of the side forming punches 111p to 118p when the stroke changes. is there. 4 and 5 are schematic top views showing the operations of the side forming punches 111p to 118p when the stroke of the press ram 102 shown in FIG. 3 is changed. In this embodiment, the operations of the side molding punches 113p and 114p using the cam mechanisms 113 and 114 are the same as the operations of the side molding punches 111p and 112p using the cam mechanisms 111 and 112, respectively. The operations of the side forming punches 115p and 116p using the cam mechanisms 115 and 116 are the same as the operations of the side forming punches 117p and 118p using the cam mechanisms 117 and 118. The operation of the forming punches 111p, 112p, 117p, 118p is mainly used.

  First, a crankshaft preform 200 is placed in the mold 103. As shown in FIG. 4A, the side forming punches 111p to 118p are in a standby state outside the mold 102 in the initial state (state 4A in FIG. 3). Subsequently, when the press ram 102 starts to move downward from the top dead center, the cam drivers of the cam mechanisms 111 to 118 start to descend accordingly.

  Then, in the cam mechanisms 111 to 114, the inclined surfaces of the cam drivers (the reference numerals 113d and 114d in FIG. 2A for the cam mechanisms 113 and 114) and the inclined surfaces of the cams 111c to 114c contact each other. When the press ram 102 is further lowered, these inclined surfaces slide with each other (point P in FIG. 3), and as shown in FIG. 4B, the side forming punches 111p to 114p are along the horizontal direction. To the inside of the mold 103. As a result, the side forming punches 111p to 114p perform side forming on the crankpin portion 203 of the preform 200 to form the holes 211 to 214 (state 4B in FIG. 3). At this time, the inclined surfaces of the cam drivers of the cam mechanisms 115 to 118 (reference numerals 115d and 116d in FIG. 2B for the cam mechanisms 115 and 116) are positioned above the cam drivers of the cam mechanisms 111 to 114, and the cam drivers It is not in contact with the inclined surfaces 115c to 118c.

  Next, when the stroke length of the cams 111c to 114c is maximized (point Q in FIG. 3) and the formation of the holes 211 to 214 by the side forming punches 111p to 114p is completed, the upper surface of the cam driver is fixed. When the members (reference numerals 113v and 114v in FIG. 2A in the cam mechanisms 113 and 114) move to the retraction hole 102B of the press ram 102, the interlock between the press ram 102 and the cams 111c to 114c is released. Then, the cam driver moves upward through the passage hole 102A of the press ram 102 by the second retracting member (reference numerals 113t and 114t in FIG. 2A in the cam mechanisms 113 and 114), and the cams 111c to 114c are in the first retracting state. As shown in FIG. 4C, the members (reference numerals 113s and 114s in FIG. 2A for the cam mechanisms 113 and 114) retreat to the outside of the mold 103 (state 4C in FIG. 3).

  Next, at the same time that the cams 111c to 114c return to the initial positions, the cam mechanisms 115 to 118 have cam surfaces (indicated by reference numerals 115d and 116d in FIG. The inclined surface 118c comes into contact. When the press ram 102 is further lowered, these inclined surfaces slide with each other (point R in FIG. 3), and as shown in FIG. 5 (A), the side forming punches 115p to 118p are along the horizontal direction. To the inside of the mold 103. As a result, the side forming punches 115p to 118p perform side forming on the crankpin portion 203 of the preform 200 to form holes 215 to 218 (state 5A in FIG. 3).

  Subsequently, when the press ram 102 reaches the bottom dead center S, the stroke length of the cams 115c to 118c is maximized, and the formation of the holes 215 to 218 by the side forming punches 115p to 118p is completed. Next, when the cam driver starts to rise with the upward movement of the press ram 102, the cams 115c to 118c are the first retracting members (in the cam mechanisms 115 and 116, reference numerals 115s and 116s in FIG. 2B). Thus, as shown in FIG. 5B, the metal 103 is retracted to the outside (state 5B in FIG. 3). After the cams 115c to 118c return to the initial positions (the state 5C after the point T in FIG. 3), the release pin is actuated (the point U in FIG. 3), so that as shown in FIG. The crankshaft 200 in which the portions 211 to 218 are formed is released.

  In the present embodiment, by using the interference prevention method as described above, the time difference formation of the plurality of holes 211 to 218 can be performed within one process from the top dead center to the bottom dead center of the press ram 102. The load for forming the plurality of hole portions 211 to 218 can be suppressed to about half compared to the case where the plurality of hole portions 211 to 218 are simultaneously formed. As a result, it is possible to reduce the size of the press facility. Further, as described above, the cam mechanisms 111 to 118 that can be housed in the die set can be used as the drive sources of the plurality of side forming punches 111p to 118p, and therefore the side forming punches 111P to 118P. This eliminates the need for a space for installing an external device such as an actuator for performing independent control, further reducing the size of the press facility, and improving workability and productivity. Furthermore, since the movable range of the side forming punches 111P to 118P can be set in the die set, there is no problem in worker safety.

  DESCRIPTION OF SYMBOLS 100 ... Crankshaft manufacturing apparatus, 102 ... Press ram, 102A ... Pass-through hole, 102A ... Retraction hole, 103 ... Mold, 103A ... Lower die, 103B ... Upper die, 111-118 ... Cam mechanism, 111c-118c ... Cam, 113d , 116d, cam driver, 113s, 116s, first retracting member (retracting mechanism), 113t, 114t, second retracting member (retracting mechanism), 113v, 114v, fixing member (retracting mechanism), 111p-118p, side molding. Punch 200, preform (material), 201 crankshaft, 202 arm, 203 crankpin, 211-218 hole

Claims (2)

A mold having a lower mold, an upper mold provided so as to be movable with respect to the lower mold, and a plurality of side molding punches that move in a direction perpendicular to the moving direction of the upper mold;
A press ram that closes and molds the material of the crankshaft in the mold by moving the upper mold relative to the lower mold;
A cam mechanism that is provided on each side molding punch and moves the side molding punch toward the inside of the mold in conjunction with the movement of the press ram;
In order to prevent interference between the side forming punches, a retraction mechanism is provided on at least one of the side forming punches and releases the interlock with the movement of the press ram via the cam mechanism. ,
The cam mechanism includes the side forming punch and is provided so as to be movable in a direction perpendicular to the moving direction of the upper mold, and is fixed to the press ram and moves in the same direction as the press ram. And a cam driver for driving the cam.
The retracting mechanism includes a fixing member that fixes the cam driver of the cam mechanism on the side where the retracting mechanism is provided to the press ram, and when the fixing of the cam driver and the press ram by the fixing member is released. An apparatus for manufacturing a crankshaft , comprising: a retracting member that moves the cam driver in a direction opposite to a direction in which the press ram moves . A mold having a lower mold, an upper mold provided so as to be movable with respect to the lower mold, and a plurality of side molding punches that move in a direction perpendicular to the moving direction of the upper mold ;
A press ram for moving the upper mold relative to the lower mold;
A cam mechanism provided on each side forming punch;
In order to prevent interference between the side forming punches, a retraction mechanism is provided on at least one of the side forming punches and releases the interlock with the movement of the press ram via the cam mechanism. ,
The cam mechanism has the side forming punch and is provided so as to be movable in a direction perpendicular to the moving direction of the upper mold, and a cam fixed to the press ram and moving in the same direction as the press ram With a driver,
The retracting mechanism includes a fixing member that fixes the cam driver of the cam mechanism on the side where the retracting mechanism is provided to the press ram, and when the fixing of the cam driver and the press ram by the fixing member is released. A retracting member for moving the cam driver in a direction opposite to the moving direction of the press ram,
Moves with molding closes the material crankshaft into the mold by the movement of the press ram, the lateral molding punch, in conjunction with movement of the press ram by the cam mechanism to the inside direction of the mold Thus, a hole is formed in each part of the material, and the lateral molding punch is moved by the cam mechanism when the cam driver is moved in the same direction as the moving direction of the press ram. Is performed by driving the cam provided with a punch for,
When forming the hole in the material by the side molding punch, when using the material having a shape such that the side molding punches intersect, the side molding punches do not interfere with each other. After the formation of the hole, one side forming punch is released from the movement of the press ram by a retracting mechanism and retracted to the outside of the mold, and the other side forming punch is The movement of the press ram is started when the one side forming punch is retreated by the retraction mechanism when the mold is released from the fixing direction. A method for manufacturing a crankshaft, wherein the method is performed by moving in a direction opposite to the direction .

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