JP2014518352A - Device for operating a valve of an internal combustion engine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an apparatus for operating at least one valve slidably mounted in a support body by a cam without using hydraulic oil.
This device is mounted above a free end of a valve shaft (3a), and a tappet (8) that is displaceable relative to a support (1), and the tappet is connected to a cam (2). And a return spring means (9) for the tappet. The device further comprises an electromagnetic actuator (22) having a coil (24), preferably located outside the tappet, and the tappet and valve (3) being translated together by energizing the coil. The magnetic field from the electromagnetic actuator so as to selectively displace between a locked state coupled so that the tappet (8) can freely slide relative to the valve stem. And at least one pin (12) that receives the action of
[Selection] Figure 1

Description

  The present invention relates to the field of internal combustion engine control, particularly control of a 4-cycle internal combustion engine, and more particularly, control of intake valve decoupling of a 4-cycle internal combustion engine (eg, a gasoline engine).

  An internal combustion engine includes an engine block that defines a plurality of combustion chambers (ie, combustion cylinders). One end of each combustion chamber is closed by a cylinder head, and the other end is closed by a piston that is slidably received inside the combustion chamber. Each combustion chamber is combined with a means for injecting a mixture of air and fuel and a means for discharging burned gas. The efficiency of an internal combustion engine is significantly related to the amount of air filling the combustion chamber.

  In order to increase the efficiency of the internal combustion engine, it is desirable to operate the internal combustion engine in a region where the filling rate is maximum. When the engine load is low, the control system of the internal combustion engine may only allow as much air as necessary to handle the engine load. Therefore, hunting occurs in the internal combustion engine, and the efficiency of the engine decreases. In particular, when the internal combustion engine is operating at half load, it is known to increase the load on the operating combustion chamber by deactivating half of the combustion chamber to increase the optimum operating range. is there.

  By disabling the intake and exhaust valves of some combustion chambers, their operation can be deactivated.

  For this purpose, as disclosed in Patent Document 1, an apparatus in which at least one valve is operated by a cam is known. Such a device comprises a valve that can slide in the cylinder head and is maintained in a stable closed position by a valve spring. The valve is used to close an intake hole for supplying air to the combustion chamber, or an exhaust hole for letting combustion gas generated by the combustion escape from the combustion chamber. The valve shaft is in contact with a hydrostatic thrust bearing inserted in the sleeve. A tappet is slidably attached to the sleeve. The camshaft actuates the valve by acting on the sleeve or tappet. A coupling mode in which the sleeve is coupled to the tappet using a pin that can be displaced by the action of an actuator supplied with hydraulic oil, and a decoupling mode in which the tappet can slide relative to the sleeve. The choice between is made. This actuator using pins is supplied with pressure generated by a hydraulic pump driven by the engine from a hydraulic circuit.

  However, this device is difficult to use because it requires the use of a hydraulic circuit and a camshaft with multiple cams. Apart from the complexity of devices that move such devices in tune, the response time of actuators that utilize hydraulic pressure is too long, making it difficult to set up an effective engine management strategy. The response time of an actuator that uses hydraulic pressure depends directly on the feed pressure and temperature of the hydraulic circuit, and thus on the operating state of the engine.

US Pat. No. 5,878,705

  The present invention aims to provide a device for actuating at least one valve by means of a cam, which can eliminate at least some of the above-mentioned drawbacks.

  To achieve the above object, the present invention provides an apparatus for actuating at least one valve slidably mounted within a support by a cam. This device is adapted to be attached to the free end of the valve stem of the valve, and is adapted for a tappet that is displaceable relative to the support and a tappet adapted to press the tappet against the cam. Return spring means. The device further includes a locked state in which the tappet and valve are coupled so that they can translate together, and an unlocked state in which the tappet can freely slide relative to the valve shaft. Electromagnetic locking means adapted to selectively operate between.

  This device for actuating the valve is in particular driven directly by a cam, ie the cam is driven by contacting this device without any intermediary elements. By using the electromagnetic locking means, the response time can be shortened and the hydraulic circuit can be omitted. This makes it easy to incorporate this device for actuating the valve into a support such as a cylinder head.

  The tappet has an opening adapted to slidably receive the valve, and an electromagnetic locking means is disposed within the opening to constrain the tappet so that the tappet and valve translate together. Configured to slide at right angles to the valve between the protruding operating position and the non-operating position retracted from the opening to allow the tappet to slide freely relative to the valve shaft Preferably, the electromagnetic locking means further comprises an electromagnetic actuator for selectively displacing the pin between an operating position and a non-operating position.

  Therefore, the pin is operated remotely, that is, the pin constituting one member working in the tappet and the electromagnetic actuator are not in mechanical contact.

  For example, the electromagnetic actuator generates a magnetic field only when the electromagnetic locking means (pin) is not receiving a forcing force from the cam. Specifically, this corresponds to the case where the back surface (minimum portion) of the cam is in contact with the tappet.

  The electromagnetic actuator is preferably external to the tappet. In that case, the electromagnetic actuator does not translate with the tappet. Therefore, when the electromagnetic actuator is mounted in the tappet, there is no movable connector required in this case to supply current to the electromagnetic actuator. Movable connectors are usually fragile and run the risk of breaking after many cycles. In particular, the electromagnetic actuator is in a stationary state, and in particular is located within the support.

  The pin is preferably fully integrated in the tappet. In that case, the pin does not come into contact with the support. Therefore, this device for actuating the valve is hardly subject to friction when actuating the valve.

  The electromagnetic actuator preferably has a magnetic coil extending perpendicular to the valve so that the axial component of the generated magnetic field can displace the pin.

  In particular, the magnetic coil preferably has a coil axis substantially parallel to the displacement direction of the pin.

  Specifically, the magnetic coil is incorporated in the support body and is immobile with respect to the support body.

  In the operating position, the pin preferably abuts one end of the valve stem in order to lock the tappet to the valve.

  The electromagnetic locking means preferably has two diametrically opposed pins that can slide in opposite directions to perform or release the tappet.

  The electromagnetic actuator preferably has a magnetic coil that extends parallel to the valve so that the radial component of the generated magnetic field can displace the pin.

  In particular, the magnetic coil preferably has a coil axis that is substantially perpendicular to the direction of pin displacement.

  Each pin preferably has a flat surface adapted to be pressed against the end of the valve stem.

  This device preferably comprises two or more pins.

  Each pin is preferably combined with one electromagnetic actuator.

  The invention further provides a device for actuating at least one valve slidably mounted in a support by means of a cam. This device is adapted to be mounted above the free end of the valve stem of the valve, and is a tappet that is displaceable relative to the support and a tappet that is adapted to press the tappet against the cam. A return spring means, and preferably an electromagnetic actuator having a coil located outside the tappet, and energizing the coil so that the tappet and valve can translate together At least one subject to a magnetic field from an electromagnetic actuator to selectively displace between a coupled locked state and an unlocked state in which the tappet is free to slide relative to the valve shaft. An electromagnetic locking means having a pin is provided.

  This device may have one or more of the features described above.

  In particular, in one embodiment, the tappet has an opening adapted to slidably receive the valve, and the pin is positioned within the opening to prevent translational movement of the tappet relative to the valve. Slides at a right angle to the valve between an actuated position protruding into the valve and a non-actuated position in which the pin is retracted from the opening to allow the tappet to slide freely relative to the valve shaft The electromagnetic actuator is configured to selectively displace the pin between an operating position and a non-operating position.

  Other features and advantages of the invention will become apparent upon reading the following description of some non-limiting embodiments of the invention.

1 is a longitudinal sectional view in combined mode of a device for actuating a valve according to a first embodiment of the invention; FIG. 2 is a longitudinal sectional view showing the device of FIG. 1 in combined mode with the entire valve. FIG. 2 is a longitudinal sectional view showing the apparatus of FIG. 1 in the decoupling mode together with the entire valve. FIG. 6 is a longitudinal sectional view in a decoupling mode of a device for actuating a valve according to a second embodiment of the present invention. FIG. 5 is a longitudinal section view of the device of FIG. 4 in combined mode with the entire valve. FIG. 5 is a longitudinal sectional view showing the device of FIG.

  Reference is made to the accompanying drawings, which are given by way of non-limiting examples.

  FIG. 1 shows in detail an apparatus according to a first embodiment of the invention for use in an internal combustion engine. Since the structure of the internal combustion engine itself is known, it will not be described in detail in this specification. This device is mounted on a cylinder head 1 constituting a support. In this device, the movement of a cam 2 fixed to a rotating shaft is applied to a valve 3 (in FIG. 1, only the end 4 of the valve shaft 3a of the valve 3 is shown in the wall of the cylinder head 1). (Not shown) is selectively transmitted as a slide motion along the axis X. The valve 3 can open and close a combustion chamber, that is, a combustion cylinder (not shown). The movement of the cam 2 is transmitted directly. The whole apparatus is shown more clearly in FIGS. 2 and 3 described below.

  A spring receiver 5 is provided at the end 4 of the valve shaft 3 a of the valve 3. As is well known, the spring receiver 5 is fixed to the valve shaft 3a of the valve 3 via two fixing half-cones 6. The spring receiver 5 receives a valve spring 7 pressed against the cylinder head 1 on its first surface 5a in order to keep the valve 3 in a closed state. Such valve structures are well known to those skilled in the art and will not be described in further detail herein.

  This device is provided with a tappet 8 which is mounted in the inner wall of the cylinder head 1 and is in contact with the cam 2 so that it can slide along the same axis X as the axis of the valve 3. In order to bring the tappet 8 and the cam 2 into close contact with each other, a tappet spring 9 is disposed inside the tappet 8 by pressing against the second surface 5 b of the spring receiver 5 and the lower surface of the tappet 8. The tappet 8 is prevented from rotating relative to the cylinder head 1 by a complementary cotter 10 received in a groove 11 formed in the inner wall of the cylinder head 1. Therefore, the tappet 8 is prevented from angular movement relative to the cylinder head 1 and only translates relative to the cylinder head 1.

  A receiving groove extending along the axis X is provided in the center of the tappet 8. The receiving groove of the tappet 8 accommodates a sleeve 14 that can slide freely inside the tappet 8. The sleeve 14 includes a complementary cotter 15 that is received within a groove 16 formed in the tappet 8. Accordingly, the sleeve 14 is prevented from angular movement relative to the tappet 8 and can only perform translational movement along the axis X of the valve 3.

  In the center of the sleeve 14, a perforation is formed in contact with the end 4 of the valve shaft 3 a of the valve 3 and into which a shim 20 for absorbing clearance is inserted. The sleeve 14, the shim 20 and the valve stem 3a form a stack of rigid elements extending in the direction of the axis X, adapted to transmit the force from the sleeve 14 to the valve 3. Yes.

  As shown in FIG. 1, the sleeve 14 and the tappet 8 define a support plane for the cam 2. However, the cam 2 (in this example, a double-lobe cam) is pressed against the tappet 8 only. Since the cam 2 has a double-lobe shape, the contact area of the cam 2 with the tappet 8 is distributed on both sides of the axis X. Therefore, the force is balanced and the wear of the parts is small.

  The device further comprises electromagnetic locking means having a pin 12 made of a ferromagnetic material. The pin 12 made of a ferromagnetic material can freely slide in the hole formed in the tappet 8 along an axis Y orthogonal to the axis X of the displacement of the tappet 8.

  The sleeve 14 has a cylindrical receiving groove 17 extending in the direction of the axis Y and adapted to receive the end of the pin 12.

  The electromagnetic lock means further includes an electromagnetic actuator 22 for displacing the pin 12 between two extreme positions. The electromagnetic actuator 22 includes a main body 23 having a magnetic coil 24 and a magnetic core 25 made of a ferromagnetic material for guiding a magnetic field radiated from the magnetic coil 24 therein.

  In order to guide the magnetic field radiated from the magnetic coil 24 of the electromagnetic actuator 22 substantially along the axis of displacement of the pin 12, that is, the axis Y, the body 23 of the electromagnetic actuator 22 is aligned with the pin 12. It arrange | positions in the cylinder head 1 like this. Therefore, when a current flows through the magnetic coil 24, the pin 12 is displaced by the action of the magnetic field from the electromagnetic actuator 22. In other words, the pin 12 is displaced under the action of the magnetic force of the electromagnetic actuator 22, specifically, the axial component of the magnetic force generated by the magnetic coil 24.

  The magnetic coil 24 has a coil axis that is substantially parallel to the direction of displacement of the pin 12.

  The electromagnetic actuator 22 further includes a pin spring 26 that urges the pin 12 to move away from the main body 23 of the electromagnetic actuator 22. More precisely, the pin spring 26 tries to hold the pin 12 in a position protruding into the receiving groove 17 of the sleeve 14.

  The tappet 8, the sleeve 14, and the cylinder head 1 perform an angular motion relative to each other so that the main body 23, the pin 12, and the receiving groove 17 of the electromagnetic actuator 22 can be aligned on the same plane. Has been stopped.

  The electromagnetic actuator 22 is free from the coupling between the sleeve 14 and the tappet 8 when the pin 12 protrudes into the receiving groove 17 of the sleeve 14 so that the sleeve 14 and the tappet 8 are coupled to each other. As such, the pin 12 can be displaced between a non-actuated position in which the pin 12 is retracted from the receiving groove 17.

  FIG. 2 shows the device when the pin 12 occupies the operating position connecting the tappet 8 and the sleeve 14. The movement of the cam 2 is transmitted sequentially to the tappet 8, then to the sleeve 14, then to the shim 20 and finally to the valve 3. In this operating position, the cam 2 displaces the valve 3. Accordingly, it is possible to exchange fresh gas (intake gas) and burned gas (exhaust gas) between the inside and outside of the combustion chamber.

  FIG. 3 shows the device in the decoupled mode when the pin 12 is in the inoperative position. In this decoupled mode, the tappet 8 can slide freely relative to the cylinder head 1 and relative to the stack containing the sleeve 14, shim 20 and valve 3. Since the tappet spring 9 is softer than the valve spring 7, the movement of the cam 2 is transmitted only to the tappet 8, and the valve 3 is kept closed. Therefore, when the pin 12 is in the inoperative position, the cam 2 is disconnected from the valve 3 and the valve 3 is kept closed.

  In this embodiment, there is only one pin 12 and there is only one electromagnetic actuator 22. Of course, the device may include a plurality of electromagnetic actuators and a plurality of pins distributed around the device in the vicinity of the valve.

  The shim 20 preferably includes a hydrostatic thrust bearing to absorb the clearance caused by the wear of the parts. Such a hydrostatic thrust bearing is known per se and will not be further described in this specification.

  Several alternative embodiments of the invention are possible. FIG. 4 shows in detail an apparatus according to a second embodiment of the invention. This second embodiment has a number of parts in common with the first embodiment. Therefore, in the second embodiment, parts that are the same as or equivalent to the parts in the first embodiment are denoted by reference numerals obtained by adding 100 to the reference numerals in the first embodiment. For example, as a code for the tappet, 8 is used in the first embodiment, whereas 108 is used in the second embodiment.

  In the second embodiment, as in the first embodiment, this apparatus is mounted on the cylinder head 101 forming the support, and the movement of the cam 102 is caused by the action of the valve spring 107. The signal is selectively transmitted to the valve 103 maintained in the valve closing position. That is, the valve spring 107 applies a restoring force to the valve 103 so that the valve 103 closes the intake hole or the exhaust hole.

  The device includes a tappet 108 having a generally bell-shaped shape. The tappet 108 has a cylindrical wall that slides in a bore formed in the cylinder head, and a cover 108a against which the cam 102 is pressed.

  A sleeve 114 is provided inside the tappet 108. The sleeve 114 also has a substantially bell-like shape, is inserted into the tappet 108, and is firmly connected to the tappet 108. The sleeve 114 has a first wall 114a that is spatially separated from the cover 108a of the tappet 108 by a shim 120 for absorbing clearance. The sleeve 114 has a second wall 114b that is spatially separated from the cover 108a of the tappet 108, leaving a free space therebetween. In the center of the second wall 114b, a receiving groove is provided in which the valve shaft of the valve 3 can freely slide.

  Accordingly, the valve shaft 103a of the valve 103 can freely slide in the sleeve 114 over the height H between the first wall 114a and the second wall 114b of the sleeve 114.

  The device further comprises electromagnetic locking means 122, which are housed one by one in the two perforations of the sleeve 114 and have two pins 112a and 112b made of ferromagnetic material, which are diametrically opposed. ing. These perforations lead to the receiving groove of the sleeve 114 and extend in a direction perpendicular to the axis X along which the valve 103 slides. Each pin 112 (pin 112a or 112b) has an operating position in which the pin 112 protrudes into the region of the receiving groove and the valve shaft 103a in the sleeve 114 so as to prevent the valve shaft 103a from sliding in the sleeve 114. So that the pin 112 is retracted from the area of the receiving groove and can be slid within the bore.

  The electromagnetic locking means 122 has one pin spring 126 for each pin 112. The pin 112 is biased by the pin spring 126 so as to be kept in the operating position.

  Therefore, when the two pins 112 are in the operating position, the valve 103 is stationary with respect to the tappet 108, so that the movement of the cam 102 is transmitted to the valve 3. Thus, the valve 103 is coupled to the cam 102 (see FIG. 5).

  When the two pins 112 are in the inoperative position, the valve stem of the valve 3 is not locked by the two pins 112 and can slide in the sleeve 114 over the height H (FIGS. 4 and 6). See). Therefore, the valve 103 is decoupled from the cam 102. More precisely, the movement of the cam 102 is transmitted only to the tappet 108, and therefore the tappet 108 slides relative to the cylinder head 101 and the valve 103.

  In the sleeve 114, the displaceable height H of the valve shaft of the valve 3 is at least equal to the displacement amount given to the valve 103 by the cam 102. Therefore, in the decoupling mode, the valve 103 is never opened by the movement of the cam 102.

  The electromagnetic locking means 122 has at least one electromagnetic actuator 122 for displacing the pin 112. As shown in FIGS. 4 to 6, the electromagnetic actuator 122 includes a main body 123 that houses one annular magnetic coil 124. The magnetic coil 124 is incorporated in the cylinder head 101 and is wound around the tappet 108 in an annular shape so as to generate a magnetic field having an axis substantially coinciding with the displacement axis X of the valve 103. . Such a magnetic field can displace the pins 112a and 112b extending radially with respect to the magnetic coil 124 without stopping the angular motion of the pins 112a and 112b relative to the cylinder head 101. In the second embodiment, the tappet 108 may rotate. Since the magnetic coil 124 is wound around the tappet 108, magnetic driving is possible regardless of the angular position of the tappet 108. That is, the pin 112 is displaced by the action of the radial component of the magnetic force (specifically, generated by the magnetic coil 124) by the electromagnetic actuator 122.

  Specifically, the magnetic coil 124 has a coil axis that is substantially orthogonal to the direction of displacement of the pin 112.

  The sleeve 114 preferably includes a ferromagnetic portion for guiding the magnetic field generated by the magnetic coil 124 along the sliding axis of the pin 112.

  More preferably, each pin 112 has a flat surface 130 at its end so that it can come into contact with the end of the valve shaft 103a. In that case, the contact between the pin 112 and the valve shaft 103a is a contact between flat surfaces, and the contact pressure (also referred to as Hertz pressure) between the two portions is reduced.

  By stopping the angular movement of the pin 112 relative to the sleeve 114 so that the plane 130 can occupy a position opposite the end of the valve stem 103a, good contact between the two parts can be achieved. . The rotation of the pin 112 is stopped using a cotter, for example.

  In the second embodiment, two pins facing each other in the diametrical direction are used. However, only one pin may be used, and conversely, more than two pins may be used.

  As in the case of the first embodiment, the shim 120 for absorbing clearance may include a hydrostatic thrust bearing to absorb valve clearance. The valve clearance is set in a range of 0.05 to 0.2 mm, for example. This determination ensures that in all cases, for example, at all operating temperatures, the valve rests on its seat.

  The change from the coupling mode to the decoupling mode, and the change from the decoupling mode to the coupling mode is performed when the pins 12 and 112 are aligned with the receiving grooves 17 and 117, that is, the tappets 14 and 114 are dead. This is preferably done when at a point position, i.e. on the base circle of the cam 102. Therefore, the pins 12 and 112 must be fitted into and removed from the receiving grooves 17 and 117 in a very short time. For example, if the engine speed is 4000 rpm and one stroke spans a crankshaft angle of 240 °, when the valves 3, 103 are used, the pin 12 is used to make a transition between coupled and decoupled modes. , 112 must be made within about 20 ms.

  Of course, the invention is not limited to the embodiments described above, but encompasses any and all variants within the scope of the invention as defined by the claims.

  In particular, the electromagnetic actuators 22 and 122 may be bistable types having the pins 12 and 112 that are magnetic bodies so that the pin springs 26 and 126 can be omitted. In that case, the pins 12, 112 are displaced between a stable first operating position and a stable second non-operating position.

  Other electromagnetic actuators can also be used. For example, a rotary actuator (stepping motor type) that drives a crank connected to itself and displaces the pin 12 can be used. The rotation axis of the rotary actuator is preferably parallel to the axis X of displacement of the valve.

  Due to the above-mentioned characteristics, the device according to the invention is compact, very simple, and can be applied to a wide variety of existing cylinder heads 1, 101 by simply reopening the perforations for the tappets 8, 108. Can be incorporated. There is no need to prepare any oil core (oil nut). This device also allows the decoupling system to be independent for each valve 3, 103.

1, 101 Cylinder head 2, 102 Cam 3, 103 Valve 3a, 103a Valve shaft 4 End 5 Spring receiver 5a First surface 5b Second surface 6 Semi-conical body 7, 107 Valve spring 8, 108 Tappet 9 Tappet spring 10, 15 Cotter 11, 16 Groove 12, 112, 112a, 112b Pin 14 Sleeve 17 Receiving groove 20, 120 Shim 22 Electromagnetic actuator 23, 123 Body 24, 124 Magnetic coil 25 Magnetic core 26, 126 Pin spring 108a Cover 114a First Wall 114b Second wall 122 Electromagnetic actuator (electromagnetic locking means)
X, Y axis

Claims (11)

  Device for actuating at least one valve (3, 103) slidably mounted in a support (1, 101) by means of a cam (2, 102), said valve stem (3a) 103a) a tappet (8, 108) adapted to be mounted above the free end and displaceable relative to the support (1, 101); and the tappet (8, 108), A device comprising return spring means (9, 109) for the tappet, adapted to press against the cam (2, 102), located outside the tappet (8, 108) And the tappet (8, 108) and the valve (3, 10) by energizing the coil (24, 124) and the electromagnetic actuator (22, 122) having the coil (24, 124). ) Are coupled so that they can translate together, and the tappet (8, 108) is relatively free to slide relative to the valve stem (3a, 103a). Electromagnetic locking means comprising at least one pin (12, 112) subjected to the action of a magnetic field from the electromagnetic actuator (22, 122) so as to selectively displace between locked states. A device characterized by.   The tappet (8, 108) has an opening adapted to slidably receive the valve (3, 103), and the pin (12, 112) includes the tappet (8, 108) and the An operating position in which the pin (12, 112) protrudes into the opening to restrain the tappet (8, 108) so that the valve (3, 103) translates together; and the tappet (8, 108) in a non-actuated position in which the pins (12, 112) are retracted from the openings to allow free sliding relative to the valve stem (3a, 103a). The electromagnetic actuator (22, 122) moves the pin (12, 112) between the operating position and the non-operating position. Selective between And it is configured to displace Apparatus according to claim 1.   Device according to claim 1 or 2, wherein the pin (12, 112) is fully integrated in the tappet (8, 108).   Device according to claim 2 or 3, wherein in the operating position the pin (12) is received in a receiving groove (17) of a sleeve (14) fixed to the valve (3).   3. In the operating position, the pin (112) is pressed against one end of the valve stem (103a) to lock the tappet (108) to the valve (103). 3. The apparatus according to 3.   The device according to claim 5, wherein the pins (112a, 112b) comprise a flat surface (130) designed to be pressed against the end of the valve stem (103a).   The coil (24) of the electromagnetic actuator (22) has the valve so that the axial component of the magnetic field generated from the coil (24) of the electromagnetic actuator (22) can displace the pin (12). The apparatus according to claim 1, wherein the apparatus is configured to extend at right angles to (3).   The coil (124) of the electromagnetic actuator (122) is such that the radial component of the magnetic field generated from the coil (124) of the electromagnetic actuator (122) can displace the pins (112a, 112b) The device according to claim 1, wherein the device is configured to extend parallel to the valve (103).   The device according to claim 1, comprising two or more pins (112 a, 112 b).   The electromagnetic locking means has two diametrically opposed pins (112a, 112b) that can slide in opposite directions to perform and release the tappet (108). The apparatus of claim 9.   Device according to claim 9 or 10, wherein each of said pins (12) is associated with a respective electromagnetic actuator (22).

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