JP5831042B2 - Pneumatic tire - Google Patents

Description

  The present invention relates to a pneumatic tire, and more particularly, to a pneumatic tire that can suppress uneven wear at an edge portion of a rib.

  In the conventional pneumatic tire, in order to suppress uneven wear of the edge portion of the rib, a configuration having a sipe in the groove wall of the circumferential main groove is known. As a conventional pneumatic tire employing such a configuration, a technique described in Patent Document 1 can be given.

JP 2010-105591 A

  An object of the present invention is to provide a pneumatic tire capable of suppressing uneven wear of the edge portion of the rib.

  In order to achieve the above object, a pneumatic tire according to the present invention is formed on a pair of circumferential main grooves extending in the tire circumferential direction, ribs defined by the pair of circumferential main grooves, and the ribs. A pneumatic tire including an inclined lug groove extending while being inclined with respect to the tire circumferential direction, wherein the inclined lug groove opens into one of the circumferential main grooves defining the rib. It does not open to the other circumferential main groove (hereinafter referred to as a terminal-side circumferential main groove) and communicates with the other inclined lug groove that terminates in or adjacent to the rib, and the terminal side of the rib The tire circumferential direction of the region X in the range of 10% to 40% of the rib width WL with respect to the edge portion on the circumferential main groove side and the extending range of the inclined lug groove in the region X Excluding section A and area A from area X When defining the section B in the tire circumferential direction, the end-side circumferential main groove has a plurality of concave portions arranged periodically or continuously in the tire circumferential direction in the groove wall surface on the rib side, and the section The unit volume Va of the concave portion arranged in A and the unit volume Vb of the concave portion arranged in the section B have a relationship of Va <Vb.

  In the pneumatic tire according to the present invention, the width Wa of the recess in the section A is in the range of 0.3 [mm] ≦ Wa ≦ 1.0 [mm], and the width Wb of the recess in the section B is It is preferable to be in the range of 0.5 [mm] ≦ Wb ≦ 2.0 [mm].

In the pneumatic tire according to the present invention, the depth Ha of the recess in the section A and the depth Hb of the recess in the section B are 0.3 [mm] ≦ Ha ≦ 1.0 [mm], It is preferable to satisfy the requirements of 1.3 [mm] ≦ Hb ≦ 3.0 [mm] and Hb−Ha ≧ 1.0 [mm].

  In the pneumatic tire according to the present invention, the arrangement interval Da of the recesses in the section A and the arrangement interval Db of the recesses in the section B are in a range of 1.5 ≦ Da / Db ≦ 3.0. Is preferred.

  A pneumatic tire according to the present invention includes a pair of circumferential main grooves extending in the tire circumferential direction, ribs defined by the pair of circumferential main grooves, and formed on the ribs and around the tire circumference. A pneumatic tire comprising an inclined lug groove extending while being inclined with respect to a direction, wherein the inclined lug groove opens into one of the circumferential main grooves defining the rib and the other circumferential direction The main groove (hereinafter referred to as a terminal-side circumferential main groove) does not open but communicates with the other inclined lug groove at the end or adjacent to the rib, and the end-side circumferential main groove side of the rib A region X in the range of 10% to 40% of the rib width WL with reference to the edge portion of the tire, and a section A in the tire circumferential direction over the extending range of the inclined lug groove in the region X, Section of tire circumferential direction excluding section A from area X When defining B, the radius of curvature Ra of the rib side groove bottom of the end side circumferential main groove in section A and the curvature of the rib side groove bottom of the end side circumferential main groove in section B The radius Rb has a relationship of Ra> Rb.

In the pneumatic tire according to the present invention, the section B is divided into a central portion and left and right end portions, the tire circumferential direction length L2 of the central portion, and the left and right end portions of the tire circumferential direction. When the length L3 is within the range of 10 [mm] ≦ L2 and 3 [mm] ≦ L3 ≦ 15 [mm], the curvature radius Ra of the section A and the curvature radius Rb_ce of the central portion of the section B However, 4.5 [mm] ≦ Ra ≦ 15.0 [mm], 1.5 [mm] ≦ Rb_ce ≦ 5.0 [mm] and 3.0 [mm] ≦ Ra−Rb_ce preferable.

  In the pneumatic tire according to the present invention, in the adjacent sections A and B, the curvature radius Ra of the section A, the curvature radius Rb_ce of the central portion of the section B, the curvature radius of the end portion of the section B, and Are preferably continuous.

  A pneumatic tire according to the present invention includes a pair of circumferential main grooves extending in the tire circumferential direction, ribs defined by the pair of circumferential main grooves, and formed on the ribs and around the tire circumference. A pneumatic tire comprising an inclined lug groove extending while being inclined with respect to a direction, wherein the inclined lug groove opens into one of the circumferential main grooves defining the rib and the other circumferential direction The main groove (hereinafter referred to as a terminal-side circumferential main groove) does not open but communicates with the other inclined lug groove at the end or adjacent to the rib, and the end-side circumferential main groove side of the rib A region X in the range of 10% to 40% of the rib width WL with reference to the edge portion of the tire, and a section A in the tire circumferential direction over the extending range of the inclined lug groove in the region X, Section of tire circumferential direction excluding section A from area X When defining B, the rib-side groove wall angle θa of the end-side circumferential main groove in section A and the rib-side groove wall angle θb of the end-side circumferential main groove in section B are , Θa> θb.

  Further, the pneumatic tire according to the present invention divides the section B into a central portion and left and right end portions, the tire circumferential direction length L2 of the central portion of the section B, and the tire circumferential direction of the left and right end portions. And the groove wall angle θa of the section A and the groove at the central portion of the section B when the length L3 of the section is within the ranges of 10 [mm] ≦ L2 and 3 [mm] ≦ L3 ≦ 15 [mm] The wall angle θb_ce preferably satisfies the conditions of 15 [deg] ≦ θa ≦ 35 [deg], 5 [deg] ≦ θb_ce ≦ 10 [deg], and 10 [deg] ≦ θa−θb_ce.

  The pneumatic tire according to the present invention includes a groove wall angle θa in the section A, a groove wall angle θb_ce at the center of the section B, and a groove at the end of the section B in the adjacent sections A and B. The wall angle is preferably continuous.

  In the pneumatic tire according to the present invention, the groove depth GD and the groove width GW of the end-side circumferential main groove are 5.0 [mm] ≦ GD ≦ 12.0 [mm] and 5.0 [mm]. mm] ≦ GW ≦ 18.0 [mm] is preferably satisfied.

  In the pneumatic tire according to the present invention, the difference in rigidity of the edge portion of the rib between the section A and the section B due to the inclined lug groove is alleviated. Thereby, there exists an advantage by which the partial wear of the edge part of a rib is suppressed.

FIG. 1 is a sectional view in the tire meridian direction showing a pneumatic tire according to an embodiment of the present invention. FIG. 2 is a plan view showing a tread surface of the pneumatic tire depicted in FIG. 1. FIG. 3 is an explanatory view showing a recess of the groove wall of the circumferential main groove of the pneumatic tire shown in FIG. 2. FIG. 4 is an explanatory view showing a recess of the groove wall of the circumferential main groove of the pneumatic tire shown in FIG. 2. FIG. 5 is an explanatory view showing a recess in the groove wall of the circumferential main groove of the pneumatic tire shown in FIG. 2. FIG. 6 is an explanatory view showing a recess of the groove wall of the circumferential main groove of the pneumatic tire shown in FIG. 2. FIG. 7 is a table showing the results of the performance test of the pneumatic tire according to the embodiment of the present invention. FIG. 8 is an explanatory view showing a modified example of the pneumatic tire shown in FIG. 1. FIG. 9 is an explanatory view illustrating a modified example of the pneumatic tire depicted in FIG. 1. FIG. 10 is an explanatory view showing a modified example of the pneumatic tire shown in FIG. 1. FIG. 11 is an explanatory view showing a modified example of the pneumatic tire shown in FIG. 1. FIG. 12 is an explanatory diagram illustrating a modification of the pneumatic tire depicted in FIG. 1. FIG. 13 is an explanatory view illustrating a modified example of the pneumatic tire depicted in FIG. 1. FIG. 14 is an explanatory view showing a modified example of the pneumatic tire depicted in FIG. 1. FIG. 15 is an explanatory view showing a modified example of the pneumatic tire shown in FIG. 1. FIG. 16 is an explanatory diagram illustrating a modification of the pneumatic tire depicted in FIG. 1. FIG. 17 is an explanatory diagram illustrating a modification of the pneumatic tire depicted in FIG. 1. FIG. 18 is an explanatory diagram showing a modification of the pneumatic tire depicted in FIG. FIG. 19 is an explanatory diagram showing a modification of the pneumatic tire depicted in FIG. FIG. 20 is an explanatory diagram illustrating a modification of the pneumatic tire depicted in FIG. 1. FIG. 21 is a table showing the results of the performance test of the pneumatic tire according to the embodiment of the present invention. FIG. 22 is a table showing the results of the performance test of the pneumatic tire according to the embodiment of the present invention.

  Hereinafter, the present invention will be described in detail with reference to the drawings. Note that the present invention is not limited to the embodiments. Further, the constituent elements of this embodiment include those that can be replaced while maintaining the identity of the invention and that are obvious for replacement. In addition, a plurality of modifications described in this embodiment can be arbitrarily combined within a range obvious to those skilled in the art.

[Pneumatic tire]
FIG. 1 is a sectional view in the tire meridian direction showing a pneumatic tire according to an embodiment of the present invention. The figure shows a radial tire for a passenger car.

  The pneumatic tire 1 includes a pair of bead cores 11, 11, a pair of bead fillers 12, 12, a carcass layer 13, a belt layer 14, a tread rubber 15, and a pair of sidewall rubbers 16, 16. (See FIG. 1). The pair of bead cores 11 and 11 has an annular structure and constitutes the core of the left and right bead portions. The pair of bead fillers 12 and 12 are disposed on the tire radial direction outer periphery of the pair of bead cores 11 and 11 to reinforce the bead portion. The carcass layer 13 is bridged in a toroidal shape between the left and right bead cores 11 and 11 to form a tire skeleton. Further, both end portions of the carcass layer 13 are wound and locked outward in the tire width direction so as to wrap the bead core 11 and the bead filler 12. The belt layer 14 includes a pair of stacked belt plies 141 and 142, and is disposed on the outer periphery in the tire radial direction of the carcass layer 13. These belt plies 141 and 142 are formed by arranging and rolling a plurality of belt cords made of steel material or organic fiber material, and by crossing the belt cords in different directions in the tire circumferential direction, Configure the structure. The tread rubber 15 is disposed on the outer circumference in the tire radial direction of the carcass layer 13 and the belt layer 14 to constitute a tread portion of the tire. The pair of side wall rubbers 16 and 16 are respectively arranged on the outer side in the tire width direction of the carcass layer 13 to constitute left and right side wall portions.

[Inclined lug groove]
FIG. 2 is a plan view showing a tread surface of the pneumatic tire depicted in FIG. 1. The figure shows an example of a tread pattern.

  The pneumatic tire 1 includes a plurality of circumferential main grooves 2 extending in the tire circumferential direction and a plurality of land portions 31 and 32 partitioned by the circumferential main grooves 2 in the tread portion (FIG. 2). reference). For example, in this embodiment, three ribs 31 are partitioned into a tread portion center region by four circumferential main grooves 2, and a pair of left and right land portions 32 are partitioned into a tread portion shoulder region. . Thereby, the tread pattern based on the rib is formed.

  Further, the rib 31 in the tread portion center region has the inclined lug groove 4. The inclined lug groove 4 is a lug groove extending while being inclined with respect to the tire circumferential direction, and has an arbitrary shape such as an arc shape, a bent shape, or a linear shape. In this embodiment, the inclined lug groove 4 has an arc shape. A plurality of inclined lug grooves 4 are periodically arranged in the tire circumferential direction with a predetermined pitch therebetween. In addition, the inclined lug groove 4 has a semi-closed structure, opens at one end in the circumferential main groove 2 defining the rib 31 at one end, and the other circumferential main at the other end. It terminates inside the rib 31 without opening in the groove 2.

  In this embodiment, of the pair of circumferential main grooves 2 and 2 that define the rib 31, the circumferential main groove 2 on the side where the inclined lug groove 4 opens is referred to as an opening-side circumferential main groove. 2_OP is attached. The other circumferential main groove 2 is called a terminal-side circumferential main groove, and is denoted by reference numeral 2_CL.

[Concavity of groove wall of circumferential main groove]
FIG. 3 is an explanatory view showing a recess of the groove wall of the circumferential main groove of the pneumatic tire shown in FIG. 2. 4 to 6 are enlarged views showing the recesses of the groove wall of the circumferential main groove shown in FIG. In these drawings, FIG. 3 shows the arrangement of the recesses in the groove wall, FIG. 4 shows a plan view of the recesses, and FIGS. 5 and 6 show sectional views of the recesses in the depth direction. Moreover, in FIG. 3 and FIG. 4, the recessed part is hatched.

  In the configuration in which the inclined lug groove has a semi-closed structure, the rigidity of the edge portion of the rib on the end side circumferential main groove side (the side where the inclined lug groove does not open) becomes uneven in the tire circumferential direction. Specifically, the rigidity of the section A in the vicinity of the inclined lug groove is lower than the rigidity of the other sections B. For this reason, the section B having high rigidity is likely to be worn, and uneven wear is likely to occur at the edge portion of the rib.

  Therefore, the pneumatic tire 1 employs the following configuration in order to suppress uneven wear of the rib having the semi-closed inclined lug groove (see FIG. 3).

  First, a region X is defined that is within a range of 10% to 40% of the rib width WL with reference to the edge portion of the rib 31 on the end-side circumferential main groove 2_CL side. The range of the region X is a range for appropriately determining the influence of the inclined lug groove 4 on the rigidity of the edge portions of the ribs 31 and 32. Further, a section A in the tire circumferential direction over the extending range of the inclined lug groove 4 in the region X and a section B in the tire circumferential direction excluding the section A from the region X are defined. The edge portion of the rib 31 on the terminal end side circumferential main groove 2_CL side includes the section A and the section B.

  At this time, the terminal end side circumferential main groove 2_CL has a plurality of recesses 5A and 5B on the groove wall surface on the rib 31 side. These recesses 5A and 5B are, for example, serrations or knurls, and are arranged periodically or continuously in the tire circumferential direction to form a repeated pattern. In addition, the recesses 5A and 5B can have any planar shape such as a linear shape, a zigzag shape, a wave shape, or a curved shape inclined in a predetermined direction (not shown).

  Further, the unit volume Va of the recess 5A disposed in the section A and the unit volume Vb of the recess 5B disposed in the section B have a relationship of Va <Vb. The unit volumes Va and Vb are the volumes of the recesses 5A and 5B per unit pitch. In addition, the recesses 5A and 5B may have an arbitrary cross-sectional shape such as a rectangular shape, a V shape, or a U shape.

  For example, in this embodiment, the recesses 5A and 5B are linear inclined narrow grooves inclined with respect to the tire circumferential direction, and have the same length and the same width as each other (see FIGS. 3 and 4). The plurality of recesses 5A and 5B are periodically arranged at predetermined intervals in the tire circumferential direction to form a serration. Moreover, these recessed parts 5A and 5B have mutually different shapes in the depth direction, and the depth Hb of the recessed part 5B in the section B is deeper than the depth Ha of the recessed part 5A in the section A (FIGS. 5 and 6). reference). Specifically, the depth Hb of the recess 5B in the section B is shallow on the groove opening side of the terminal-side circumferential main groove 2_CL (same as the recess 5A in the section A) and deep on the groove bottom side. Therefore, the unit volume Vb of the recess 5B in the section B is larger than the unit volume Va of the recess 5A in the section A (Va <Vb). Further, by arranging these recesses 5A and 5B in the sections A and B, the rigidity of the edge part in the section B is set smaller than the rigidity of the edge part in the section A.

  In this pneumatic tire 1, since the inclined lug groove 4 has a semi-closed structure, the rigidity of the section A in the vicinity of the inclined lug groove 4 is set at the edge portion on the terminal side circumferential main groove 2_CL side of the rib 31. It becomes lower than the rigidity of B. On the other hand, since the unit volume Va of the recess 5A in the section A is smaller than the unit volume Vb of the recess 5B in the section B (Va <Vb), the rigidity of the section A increases more than the rigidity of the section B. Therefore, the rigidity of the section A and the rigidity of the section B at the edge part of the rib 31 are made uniform, and uneven wear of the edge part is suppressed.

  In the pneumatic tire 1, the unit volume Va of the recess 5A in the section A and the unit volume Vb of the recess 5B in the section B are appropriately set so that the rigidity of the section A and the rigidity of the section B are uniform. The These unit volumes Va and Vb can be arbitrarily adjusted by, for example, the depths Ha and Hb, the widths Wa and Wb, and the lengths La and Lb of the recesses 5A and 5B.

  At this time, the length La of the recess 5A in the section A is in the range of 4.0 [mm] ≦ La ≦ 10.0 [mm], and the length Lb of the recess 5B in the section B is 6.0 [mm]. ≦ Lb ≦ 12.0 [mm] is preferable (see FIG. 4). Thereby, the lengths La and Lb of the recesses 5A and 5B are optimized.

  Further, the width Wa of the recess 5A in the section A is in the range of 0.3 [mm] ≦ Wa ≦ 1.0 [mm], and the width Wb of the recess 5B in the section B is 0.5 [mm] ≦ Wb ≦ It is preferably within the range of 2.0 [mm] (see FIG. 4). Thereby, the widths Wa and Wb of the recesses 5A and 5B are optimized. The widths Wa and Wb of the recesses 5A and 5B are measured as the maximum values in the entire area of the recesses 5A and 5B.

Further, the depth Ha of the recess 5A in the section A and the depth Hb of the recess 5B in the section B are 0.3 [mm] ≦ Ha ≦ 1.0 [mm], 1.3 [mm] ≦ Hb ≦ It is preferable to satisfy the requirements of 3.0 [mm] and Hb−Ha ≧ 1.0 [mm] (see FIGS. 5 and 6). Thereby, the depths Ha and Hb of the recesses 5A and 5B are optimized. The depths Ha and Hb of the recesses 5A and 5B are measured with reference to the groove wall surface of the end-side circumferential main groove 2_CL. The depths Ha and Hb of the recesses 5A and 5B are measured as maximum values in the entire area of the recesses 5A and 5B.

  In this embodiment, the recess 5A in the section A and the recess 5B in the section B have a linear shape with the same length (La = Lb) and the same width (Wa = Wb) in plan view ( (See FIG. 4). Further, the depth Ha of the recess 5A in the section A is constant, and the depth Hb of the recess 5B in the section B increases as it goes toward the bottom of the terminal-side circumferential main groove 2_CL (see FIG. 5 and FIG. 5). (See FIG. 6). The difference between the depths Ha and Hb forms a difference between the unit volume Va of the recess 5A in the section A and the unit volume Vb of the recess 5B in the section B. Thereby, the rigidity of the section A and the rigidity of the section B are made uniform.

  In this embodiment, the arrangement interval Da of the recesses 5A in the section A and the arrangement interval Db of the recesses 5B in the section B are set to be constant (Da = Db) (see FIG. 4). For this reason, only the unit volumes Va and Vb of the recesses 5A and 5B are adjusted, and the rigidity of the section A and the rigidity of the section B are made uniform.

  In the above configuration, the arrangement interval Da of the recesses 5A in the section A and the arrangement interval Db of the recesses 5B in the section B preferably have a relationship of 1.5 ≦ Da / Db ≦ 3.0. In addition, the arrangement interval Da is preferably 2.5 [mm] ≦ Da ≦ 5.0 [mm], and the arrangement interval Db is preferably 1.5 [mm] ≦ Db ≦ 3.0 [mm].

[Curve radius of groove bottom of circumferential main groove]
8-10 is explanatory drawing which shows the modification of the pneumatic tire 1 described in FIG. 8 and 9 show sectional views in the tire meridian direction of the end-side circumferential main groove 2_CL, and FIG. 10 shows the curvature radii Ra and Rb of the groove bottom of the end-side circumferential main groove 2_CL. It shows a change. In these drawings, the same components as those of the pneumatic tire 1 of FIGS. 1 to 6 are denoted by the same reference numerals, and the description thereof is omitted.

  In the configuration of FIG. 2, the terminal-side circumferential main groove 2_CL has a plurality of recesses 5A and 5B on the groove wall surface on the rib 31 side (see FIG. 3), and the unit volume Va of the recess 5A in the section A and the section B Since the unit volume Vb of the recess 5B has a relationship of Va <Vb (see FIG. 5 and FIG. 6), the rigidity difference of the edge portion of the rib 31 between the section A and the section B caused by the inclined lug groove 4 Has been relaxed.

  8 and 9, the radius of curvature Ra of the groove bottom on the rib 31 side of the terminal-side circumferential main groove 2_CL in the section A and the rib 31 of the terminal-side circumferential main groove 2_CL in the section B are provided. The curvature radius Rb of the groove bottom on the side has a relationship of Ra> Rb. Even with this configuration, the difference in rigidity of the edge portion of the rib 31 between the section A and the section B is alleviated.

  Here, the radius of curvature of the groove bottom refers to the radius of curvature of the connecting portion between the maximum depth position of the groove bottom and the groove wall of the rib in a cross-sectional view perpendicular to the groove length direction.

  In addition, it is preferable that the length L1 of the tire circumferential direction of the area A exists in the range of 10 [mm] <= L1. In the configuration satisfying 10 [mm] ≦ L1, the rigidity of the edge portion of the rib 31 in the section A is likely to be lowered due to the inclined lug groove 4. Therefore, by applying the above configuration to such a configuration, the difference in rigidity of the edge portion of the rib 31 between the section A and the section B is effectively reduced. The upper limit of L1 is restricted by the length of the inclined lug groove 4 in the tire circumferential direction.

Further, the section B is divided into a central portion and left and right end portions. Further, the length L2 in the tire circumferential direction of the center portion and the length L3 in the tire circumferential direction of the left and right end portions are within a range of 10 [mm] ≦ L2 and 3 [mm] ≦ L3 ≦ 15 [mm]. (See FIG. 10). At this time, the curvature radius Ra of the section A and the curvature radius Rb_ce at the center of the section B are 4.5 [mm] ≦ Ra ≦ 15.0 [mm], 1.5 [mm] ≦ Rb_ce ≦ 5. The conditions of 0 [mm] and 3.0 [mm] ≦ Ra−Rb_ce are satisfied. In addition, the upper limit of L2 is restricted by the arrangement interval of the inclined lug grooves 4.

  In such a configuration, by setting 2.0 [mm] ≦ Ra, the rigidity of the rib 31 is appropriately ensured, and by setting Ra ≦ 15.0 [mm], the drainage of the terminal-side circumferential main groove 2_CL. Is properly secured. Further, by setting 1.5 [mm] ≦ Rb_ce, the occurrence of cracks at the groove bottom is suppressed, and by setting Rb_ce ≦ 5.0 [mm], the rib 31 between the section A and the section B The rigidity balance of the edge part is optimized. Moreover, the rigidity difference of the edge part of the rib 31 between the area A and the area B is optimized by setting it as 3.0 [mm] <= Ra-Rb_ce.

  In the adjacent sections A and B, the curvature radius Ra of the section A, the curvature radius Rb_ce at the center of the section B, and the curvature radius at the end of the section B are continuous (see FIG. 10). That is, as described above, the curvature radius Ra of the section A and the curvature radius Rb_ce of the central portion of the section B have different ranges. Therefore, the radius of curvature of the groove bottom is smoothly changed so that no step is generated at the groove bottom of the end-side circumferential main groove 2_CL. Thereby, the rigidity of the edge part of the rib 31 can be changed smoothly in the connection part of the area A and the area B. FIG.

  As the above configuration, for example, as shown in FIG. 10, the radius of curvature Ra of the groove bottom is constant in the section A, and the radius of curvature Rb of the groove bottom is the minimum value Rb_ce in the center of the section B. The radius of curvature of the groove bottom monotonously increases or decreases monotonously at both ends of the section B (from the position where the radius of curvature Rb takes the minimum value Rb_ce to the boundary position between the sections A and A on the left and right of the section B). The structure to do is mentioned.

  Note that the continuity of the radius of curvature refers to mathematical continuity.

  Moreover, in this pneumatic tire 1, the structure of FIG. 2 and the structure of FIG. 8 and FIG. 9 may be used together, and only the structure of FIG. 8 and FIG. 9 may be used independently.

[Groove wall angle of circumferential main groove]
FIGS. 11-15 is explanatory drawing which shows the modification of the pneumatic tire 1 described in FIG. In these drawings, FIGS. 11 and 12 show sectional views in the tire meridian direction of the end-side circumferential main groove 2_CL, and FIG. 13 shows changes in the groove wall angles θa and θb of the end-side circumferential main groove 2_CL. Show. 14 shows a configuration in which the rib 31 has a chamfered portion at the edge portion, and FIG. 15 shows a configuration in which the groove wall has a multistage structure. In these drawings, the same components as those of the pneumatic tire 1 of FIGS. 1 to 6 are denoted by the same reference numerals, and the description thereof is omitted.

  11 and 12, the groove wall angle θa on the rib 31 side of the terminal-side circumferential main groove 2_CL in the section A and the groove wall angle θb on the rib 31 side of the terminal-side circumferential main groove 2_CL in the section B Have a relationship of θa> θb. Even with this configuration, the difference in rigidity of the edge portion of the rib 31 between the section A and the section B is alleviated.

  Here, the groove wall angle is measured as an angle formed by a straight line passing through the edge portion of the rib and perpendicular to the tread surface of the rib and the groove wall surface in a cross-sectional view in the tire meridian direction. As shown in FIG. 14, when the rib 31 has a chamfered portion at the edge portion, an imaginary line extending the tread surface of the rib 31 and an imaginary line extending the groove wall surface are taken, and this intersection point is determined. The angle between the straight line perpendicular to the tread of the street rib and the groove wall surface is the groove wall angle. In addition, as shown in FIG. 15, in the configuration in which the groove wall has a multi-stage structure in which the inclination angle is changed in the groove depth direction, the groove wall angle of the groove wall portion closest to the groove opening is used.

  In addition, it is preferable that the length L1 of the tire circumferential direction of the area A exists in the range of 10 [mm] <= L1.

  Further, the section B is divided into a central portion and left and right end portions. Further, the length L2 in the tire circumferential direction of the center portion and the length L3 in the tire circumferential direction of the left and right end portions are within a range of 10 [mm] ≦ L2 and 3 [mm] ≦ L3 ≦ 15 [mm]. (See FIG. 13). At this time, the groove wall angle θa of the section A and the groove wall angle θb_ce at the center of the section B are 15 [deg] ≦ θa ≦ 35 [deg], 5 [deg] ≦ θb_ce ≦ 10 [deg] and 10 [Deg] ≦ θa−θb_ce is satisfied. In addition, the upper limit of L2 is restricted by the arrangement interval of the inclined lug grooves 4.

  In such a configuration, by setting 15 [deg] ≦ θa, the rigidity of the rib 31 is appropriately ensured, and by setting θa ≦ 35 [deg], the drainage performance of the terminal-side circumferential main groove 2_CL is appropriately ensured. Is done. Further, by setting 5 [deg] ≦ θb_ce, the occurrence of cracks at the groove bottom is suppressed, and by setting θb_ce ≦ 10 [deg], the rigidity of the edge portion of the rib 31 between the section A and the section B is set. Balance is optimized. Further, by setting 10 [deg] ≦ θa−θb_ce, the rigidity difference of the edge portion of the rib 31 between the section A and the section B is optimized.

  In adjacent sections A and B, the groove wall angle θa of section A, the groove wall angle θb_ce at the center of section B, and the groove wall angle at the end of section B are continuous (see FIG. 13). . That is, as described above, the groove wall angle θa of the section A and the groove wall angle θb_ce at the center of the section B have different ranges. Therefore, the groove wall angle is smoothly changed so that no step is generated at the groove bottom of the terminal end side circumferential main groove 2_CL. Thereby, the rigidity of the edge part of the rib 31 can be changed smoothly in the connection part of the area A and the area B. FIG.

  For example, as shown in FIG. 13, the groove wall angle θa is constant in the section A, and the groove wall angle θb takes the minimum value θb_ce in the center of the section B, as shown in FIG. The groove wall angle monotonously increases or decreases monotonously at both ends (the portion from the position where the groove wall angle θb takes the minimum value θb_ce to the boundary position between the section B and the left and right sections A, A). .

  In addition, the continuation of groove wall angle shall mean a mathematical continuation.

  Moreover, in this pneumatic tire 1, the structure of FIG. 2 and the structure of FIG. 11 and FIG. 12 may be used together, and only the structure of FIG. 11 and FIG. 12 may be used independently. Further, the configuration of FIG. 2, the configurations of FIGS. 8 and 9, and the configurations of FIGS. 11 and 12 may be used in combination.

[Application example]
FIGS. 16-20 is explanatory drawing which shows the modification of the pneumatic tire 1 described in FIG. In these drawings, FIG. 16 shows an example of a tread pattern having an inclined lug groove 4 different from that in FIG. 2, and FIG. 17 shows a region X and sections A and B. 18-20 has shown an example of the inclined lug groove 4 different from FIG.

  In the configuration of FIG. 2, the inclined lug groove 4 opens in one circumferential main groove 2 </ b> _OP that defines the rib 31, and terminates in the rib 31 without opening in the other terminal side circumferential main groove 2 </ b> _CL. (See FIG. 3).

  On the other hand, in the tread pattern of FIG. 16, the inclined lug groove 4 opens in one circumferential main groove 2 </ b> _OP that defines the rib 31 and is adjacent to the other terminal side circumferential main groove 2 </ b> _CL without opening. It communicates with other matching inclined lug grooves 4. Specifically, one rib 31 has a plurality of inclined lug grooves 4 having an arc shape, and these inclined lug grooves 4 are continuously arranged with their directions aligned in the tire circumferential direction. In addition, the inclined lug groove 4 opens into one circumferential main groove 2_OP, extends in the rib 31 while being curved in an arc shape in the tire circumferential direction, and is adjacent to the other adjacent inclined lug groove 4 in the rib 31. Open at. Thereby, the inclined lug grooves 4 and 4 adjacent to each other in the tire circumferential direction communicate with each other. The pneumatic tire 1 may have such a tread pattern.

  Also in the tread pattern of FIG. 16, the region X and the sections A and B are defined by the same definition as the configuration of FIG. 2 (see FIG. 17).

  In the tread pattern of FIG. 2, the inclined lug groove 4 has an arc shape, opens at one end to the circumferential main groove 2 </ b> _OP, and terminates within the rib 31 at the other end. .

  However, the present invention is not limited to this, and in the tread pattern of FIG. 2, the inclined lug groove 4 may have a bent shape (see FIGS. 18 and 19), or may have a wave shape or a meander shape (see FIG. 20).

  Further, in the pneumatic tire 1, in the tread pattern of FIGS. 2 and 16, the groove depth GD and the groove width GW of the terminal-side circumferential main groove 2_CL are 5.0 [mm] ≦ GD ≦ 12.0. It is preferable that the conditions of [mm] and 5.0 [mm] ≦ GW ≦ 18.0 [mm] are satisfied. In such a terminal side circumferential main groove 2_CL, due to the inclined lug groove 4, the rigidity of the edge portion of the rib 31 in the section A is likely to decrease. Therefore, in such a configuration, by applying the configuration of FIG. 2, the configuration of FIG. 8 and FIG. 9, the configuration of FIG. 11 and FIG. 12, or the combination thereof, the sections A and B The difference in rigidity of the edge portion of the rib 31 between is effectively mitigated.

[effect]
As described above, the pneumatic tire 1 includes a pair of circumferential main grooves 2 and 2 that extend in the tire circumferential direction, ribs 31 that are divided into the circumferential main grooves 2 and 2, and ribs. And an inclined lug groove 4 that is formed at 31 and extends while inclining with respect to the tire circumferential direction (see FIG. 2). Further, the inclined lug groove 4 opens in one circumferential main groove 2_OP that defines the rib 31, and terminates in the rib 31 without opening in the other circumferential main groove (terminal side circumferential main groove) 2_CL. (Refer to FIG. 3) Or, it communicates with another adjacent inclined lug groove 4 (see FIG. 17). Further, the terminal end circumferential main groove 2_CL has a plurality of recesses 5A and 5B arranged periodically or continuously in the tire circumferential direction on the groove wall surface on the rib 31 side. Further, the unit volume Va of the recess 5A disposed in the section A and the unit volume Vb of the recess 5B disposed in the section B have a relationship of Va <Vb (see FIGS. 5 and 6).

  In such a configuration, since the unit volume Vb of the recess 5B in the section B is larger than the unit volume Va of the recess 5A in the section A (Va <Vb), the rib between the section A and the section B caused by the inclined lug groove 4 The rigidity difference between the 31 edge portions is alleviated. Thereby, there exists an advantage by which the partial wear of the edge part of the rib 31 is suppressed.

  In the pneumatic tire 1, the width Wa of the recess 5A in the section A is in the range of 0.3 [mm] ≦ Wa ≦ 1.0 [mm], and the width Wb of the recess 5B in the section B is 0.00. It is in the range of 5 [mm] ≦ Wb ≦ 2.0 [mm] (see FIG. 4). Thereby, the widths Wa and Wb of the recesses 5A and 5B are optimized. For example, when Wa <0.3 [mm], the heat dissipation effect by the recess 5A cannot be obtained, and when 1.0 [mm] <Wa, the rigidity of the rib 31 becomes too low, which is not preferable. Further, when Wb <0.5 [mm], the rigidity of the edge portion of the rib 31 in the section A cannot be reduced, and when 2.0 [mm] <Wb, cracks are easily generated in the groove wall, which is preferable. Absent.

In the pneumatic tire 1, the depth Ha of the recess 5A of the section A, and a depth Hb of the concave portion 5B of the section B, 0.3 [mm] ≦ Ha ≦ 1.0 [mm], 1. 3 [mm] ≦ Hb ≦ 3.0 [mm] and Hb−Ha ≧ 1.0 [mm] are satisfied (see FIGS. 5 and 6). Thereby, the depths Ha and Hb of the recesses 5A and 5B are optimized. For example, if Ha <0.3 [mm], the heat dissipation effect by the recess 5A cannot be obtained, and if 1.0 [mm] <Ha, the rigidity of the rib 31 becomes too low, which is not preferable. Further, when Hb <1.0 [mm], the rigidity of the edge portion of the rib 31 in the section A cannot be reduced, and when 3.0 [mm] <Hb, cracks are easily generated in the groove wall, which is preferable. Absent. Further, when Hb−Ha <1.0 [mm], it is difficult to equalize the rigidity difference between the edge portions in the sections A and B, which is not preferable.

  Further, in this pneumatic tire 1, the arrangement interval Da of the recesses 5A in the section A and the arrangement interval Db of the recesses 5B in the section B are in the range of 1.5 ≦ Da / Db ≦ 3.0 (FIG. 4). reference). Thereby, the rigidity of the edge part in the area B reduces, and there exists an advantage by which the rigidity difference of the edge part between the area A and the area B is relieve | moderated.

  Further, in this pneumatic tire 1, the radius of curvature Ra of the groove 31 side of the end-side circumferential main groove 2_CL in the section A and the groove bottom of the end-side circumferential main groove 2_CL in the section B on the rib 31 side. The curvature radius Rb has a relationship of Ra> Rb (see FIGS. 8 and 9). Thereby, the rigidity difference of the edge part of the rib 31 between the area A and the area B is relieved, and there exists an advantage by which the partial wear of the edge part of the rib 31 is suppressed.

Moreover, in this pneumatic tire 1, the curvature radius Ra of the section A and the curvature radius Rb_ce at the center of the section B are 4.5 [mm] ≦ Ra ≦ 15.0 [mm], 1.5 [mm]. ] ≦ Rb_ce ≦ 5.0 [mm] and 3.0 [mm] ≦ Ra−Rb_ce are satisfied (see FIG. 10). Thereby, the relationship between the curvature radius Ra of the section A and the curvature radius Rb of the section B is optimized, and there is an advantage that uneven wear of the edge portion of the rib 31 is suppressed.

  Moreover, in this pneumatic tire 1, in the adjacent sections A and B, the curvature radius Ra of the section A, the curvature radius Rb_ce of the central portion of the section B, and the curvature radius of the end portion of the section B are continuous. (See FIG. 10). Thereby, since the rigidity of the edge part of the rib 31 can be changed smoothly in the connection part of the area A and the area B, there exists an advantage by which the partial wear of the edge part of the rib 31 is suppressed.

  Further, in the pneumatic tire 1, the groove wall angle θa on the rib 31 side of the end-side circumferential main groove 2_CL in the section A, and the groove wall angle θb on the rib 31 side of the end-side circumferential main groove 2_CL in the section B However, it has the relationship of groove wall angle (theta) a> (theta) b (refer FIG. 11 and FIG. 12). Thereby, the rigidity difference of the edge part of the rib 31 between the area A and the area B is relieved, and there exists an advantage by which the partial wear of the edge part of the rib 31 is suppressed.

  Further, in this pneumatic tire 1, the groove wall angle θa in the section A and the groove wall angle θb_ce in the central part of the section B are 15 [deg] ≦ θa ≦ 35 [deg], 5 [deg] ≦ θb_ce ≦. The conditions of 10 [deg] and 10 [deg] ≦ θa−θb_ce are satisfied (see FIG. 13). Thereby, the relationship between the groove wall angle θa of the section A and the groove wall angle θb of the section B is optimized, and there is an advantage that uneven wear of the edge portion of the rib 31 is suppressed.

  Further, in this pneumatic tire 1, in adjacent sections A and B, the groove wall angle θa of section A, the groove wall angle θb_ce at the center of section B, and the groove wall angle of the end of section B are Are continuous (see FIG. 13). Thereby, since the rigidity of the edge part of the rib 31 can be changed smoothly in the connection part of the area A and the area B, there exists an advantage by which the partial wear of the edge part of the rib 31 is suppressed.

  Moreover, in this pneumatic tire 1, the groove depth GD and the groove width GW of the end-side circumferential main groove 2_CL are 5.0 [mm] ≦ GD ≦ 12.0 [mm] and 5.0 [mm]. The condition of ≦ GW ≦ 18.0 [mm] is satisfied (see FIGS. 3 and 17). By adopting such a configuration, there is an advantage that the effect of suppressing uneven wear of the edge portion of the rib 31 can be effectively obtained.

  FIG. 7 is a table showing the results of the performance test of the pneumatic tire according to the embodiment of the present invention.

  In this example, evaluation about uneven wear resistance was performed for a plurality of different pneumatic tires (see FIG. 7). In these performance tests, a pneumatic tire having a tire size of 205 / 55R16 is assembled to a rim having a rim size of 16 × 6.5 J, and an air pressure of 230 kPa and a load capacity specified by JATMA are given to the pneumatic tire. Further, a front wheel drive vehicle having a displacement of 1.4 [L] is used as a test vehicle.

  In addition, the test vehicle travels 10,000 km on a predetermined travel path, and then the deviation generated at the edge portion on the end-side circumferential main groove (the circumferential main groove on the side where the inclined lug groove does not open) side of the rib is generated. Wear is observed. And based on this observation result, evaluation by a 5-point method is performed. In this evaluation, the higher the score, the less uneven wear is preferable. Moreover, if evaluation is 4 or more, it will be recognized that there exists an advantage.

  Further, in this example, evaluation regarding steering stability performance was performed for a plurality of different pneumatic tires (see FIG. 7). In this evaluation, the test vehicle travels on a circuit of 2 [km] per lap, and a specialized test driver performs a feeling evaluation regarding lane change performance and cornering performance. This evaluation is performed by a 5-point method, and the larger the value, the better. Moreover, if evaluation is 4 or more, it will be recognized that there exists an advantage.

  The pneumatic tires 1 of Examples 1 to 6 include the inclined lug grooves 4 having a semi-closed structure (see FIGS. 2 and 3). Further, the terminal-side circumferential main groove 2_CL has a plurality of concave portions 5A and 5B arranged in a knurled shape on the groove wall surface on the rib 31 side (see FIG. 4). Further, the unit volume Va of the recess 5A in the section A and the unit volume Vb of the recess 5B in the section B have a relationship of Va <Vb (see FIGS. 5 and 6). Thereby, the rigidity difference of the edge part of the rib 31 between the area A and the area B is equalized.

  In the pneumatic tire 1 of Comparative Example 1, the unit volumes Va and Vb of the recesses 5A and 5B in the sections A and B are equal (Va = Vb) in the pneumatic tire 1 of Example 1. In the pneumatic tire of Comparative Example 2, the unit volume Va of the recess 5A in the section A and the unit volume Vb of the recess 5B in the section B have a relationship Va> Vb.

  As shown in the test results, in the pneumatic tires 1 of Examples 1 to 6, it is understood that the uneven wear resistance performance of the tire is improved (see FIG. 7). Further, comparing Examples 1 and 2, it can be seen that the same effect can be obtained even if the unit volumes Va and Vb of the recesses 5A and 5B are adjusted while maintaining the relationship Va <Vb. Further, in Examples 3 to 5, the unit volumes Va and Vb of the recesses 5A and 5B are determined by the widths Wa and Wb, the depths Ha and Hb of the recesses 5A and 5B of the sections A and B, and the arrangement intervals Da and Db. It can be seen that the relationship (Va <Vb) can be adjusted. Similarly, in Example 6, the relationship between the unit volumes Va and Vb of the recesses 5A and 5B (Va <Vb) is obtained only by the unit volumes Va and Vb of the recesses 5A and 5B in the sections A and B (Example 6). ) Can be adjusted.

  Moreover, in the pneumatic tire 1 of Examples 1-6, it turns out that the steering stability performance of a tire improves (refer FIG. 7).

  21 and 22 are tables showing the results of the performance test of the pneumatic tire according to the embodiment of the present invention.

  In this performance test, evaluations regarding uneven wear resistance performance and steering stability performance were performed for a plurality of different pneumatic tires (see FIGS. 21 and 22). Since these evaluation methods are the same as those in Example 1, the description thereof is omitted.

  The pneumatic tires 1 of Examples 7 to 12 have the tread pattern of FIG. However, the terminal-side circumferential main groove 2_CL has the configuration described in FIGS. 8 and 9 instead of the recesses 5A and 5B (see FIGS. 5 and 6). Further, a length L1 in the tire circumferential direction of the section A and a length L2 in the tire circumferential direction of the central portion of the section B are set to L1 = 20 [mm] and L2 = 15 [mm]. Further, the radius of curvature of the groove bottom at the end of the section B monotonously increases or decreases monotonously, so that the radius of curvature Ra of the groove bottom of the section A and the radius of curvature Rb_ce of the groove bottom of the center of the section B are continuous. They are connected smoothly (see FIG. 10).

  The pneumatic tires 1 of Examples 13 to 18 have the tread pattern of FIG. However, the terminal-side circumferential main groove 2_CL has the configuration described in FIGS. 11 and 12 instead of the recesses 5A and 5B (see FIGS. 5 and 6). Further, the length L1 in the tire circumferential direction of the section A and the length L2 in the tire circumferential direction of the central portion of the section B are set to L1 = 20 [mm] and L2 = 10 [mm]. Further, the groove wall angle θa of the section A and the groove wall angle θb_ce of the central part of the section B are continuously and smoothly connected by monotonously increasing or monotonously decreasing the groove wall angle at the end of the section B. (See FIG. 13).

  As shown in the test results, it can be seen that in the pneumatic tires 1 of Examples 7 to 18, the uneven wear resistance performance and steering stability performance of the tire are improved (see FIGS. 21 and 22).

  DESCRIPTION OF SYMBOLS 1 Pneumatic tire, 2_OP opening side circumferential main groove, 2_CL terminal side circumferential main groove, 31 center land part (rib), 32 shoulder land part, 4 inclined lug groove, 5A, 5B recessed part, 11 bead core, 12 bead filler , 13 carcass layer, 14 belt layer, 141, 142 belt ply, 15 tread rubber, 16 sidewall rubber

Claims (11)

A pair of circumferential main grooves extending in the tire circumferential direction, a rib formed by the pair of circumferential main grooves, and an inclination formed on the rib and extending while being inclined with respect to the tire circumferential direction A pneumatic tire comprising a lug groove,
The inclined lug groove opens in one of the circumferential main grooves defining the rib and does not open in the other circumferential main groove (hereinafter referred to as a terminal-side circumferential main groove). Communicated with the other end of the inclined lug groove, or
A region X in the range of 10% to 40% of the rib width WL with reference to the edge portion of the rib on the end side circumferential direction main groove side, and the extension of the inclined lug groove in the region X When defining a section A in the tire circumferential direction related to the range and a section B in the tire circumferential direction excluding the section A from the region X,
The terminal-side circumferential main groove has a plurality of recesses arranged periodically or continuously in the tire circumferential direction on the rib-side groove wall surface, and the unit volume Va of the recesses disposed in the section A; A pneumatic tire characterized by having a relationship of Va <Vb with a unit volume Vb of the concave portion arranged in the section B.   The width Wa of the recess in the section A is in the range of 0.3 [mm] ≦ Wa ≦ 1.0 [mm], and the width Wb of the recess in the section B is 0.5 [mm] ≦ Wb ≦ 2. The pneumatic tire according to claim 1, which is in a range of 0 [mm]. The depth Ha of the recess in the section A and the depth Hb of the recess in the section B are 0.3 [mm] ≦ Ha ≦ 1.0 [mm], 1.3 [mm] ≦ Hb ≦ 3. The pneumatic tire according to claim 1, wherein the pneumatic tire satisfies the requirements of 0 [mm] and Hb−Ha ≧ 1.0 [mm].   The arrangement interval Da of the recesses in the section A and the arrangement interval Db of the recesses in the section B are in the range of 1.5 ≦ Da / Db ≦ 3.0. Pneumatic tires. A pair of circumferential main grooves extending in the tire circumferential direction, a rib formed by the pair of circumferential main grooves, and an inclination formed on the rib and extending while being inclined with respect to the tire circumferential direction A pneumatic tire comprising a lug groove,
The inclined lug groove opens in one of the circumferential main grooves defining the rib and does not open in the other circumferential main groove (hereinafter referred to as a terminal-side circumferential main groove). Communicated with the other end of the inclined lug groove, or
A region X in the range of 10% to 40% of the rib width WL with reference to the edge portion of the rib on the end side circumferential direction main groove side, and the extension of the inclined lug groove in the region X When defining a section A in the tire circumferential direction related to the range and a section B in the tire circumferential direction excluding the section A from the region X,
The radius of curvature Ra of the rib-side groove bottom of the terminal-side circumferential main groove in the section A and the radius of curvature Rb of the rib-side groove of the terminal-side circumferential main groove in the section B are Ra> Rb. A pneumatic tire characterized by having the following relationship: The section B is divided into a center portion and left and right end portions, and the length L2 in the tire circumferential direction of the center portion and the length L3 in the tire circumferential direction of the left and right end portions are 10 [mm] ≦ L2. And 3 [mm] ≦ L3 ≦ 15 [mm]
The curvature radius Ra of the section A and the curvature radius Rb_ce at the central portion of the section B are 4.5 [mm] ≦ Ra ≦ 15.0 [mm], 1.5 [mm] ≦ Rb_ce ≦ 5.0 [ The pneumatic tire according to claim 5 , wherein the conditions of mm] and 3.0 [mm] ≦ Ra−Rb_ce are satisfied. The air according to claim 6 , wherein in adjacent sections A and B, a curvature radius Ra of section A, a curvature radius Rb_ce of the central portion of section B, and a curvature radius of the end portion of section B are continuous. tire. A pair of circumferential main grooves extending in the tire circumferential direction, a rib formed by the pair of circumferential main grooves, and an inclination formed on the rib and extending while being inclined with respect to the tire circumferential direction A pneumatic tire comprising a lug groove,
The inclined lug groove opens in one of the circumferential main grooves defining the rib and does not open in the other circumferential main groove (hereinafter referred to as a terminal-side circumferential main groove). Communicated with the other end of the inclined lug groove, or
A region X in the range of 10% to 40% of the rib width WL with reference to the edge portion of the rib on the end side circumferential direction main groove side, and the extension of the inclined lug groove in the region X When defining a section A in the tire circumferential direction related to the range and a section B in the tire circumferential direction excluding the section A from the region X,
The groove wall angle θa on the rib side of the end-side circumferential main groove in section A and the groove wall angle θb on the rib side of the end-side circumferential main groove in section B have a relationship of θa> θb. A pneumatic tire characterized by that. The section B is divided into a central portion and left and right end portions, and the length L2 in the tire circumferential direction of the central portion of the section B and the length L3 in the tire circumferential direction of the left and right ends are 10 [mm]. When it is within the range of ≦ L2 and 3 [mm] ≦ L3 ≦ 15 [mm]
The groove wall angle θa of the section A and the groove wall angle θb_ce at the center of the section B are 15 [deg] ≦ θa ≦ 35 [deg], 5 [deg] ≦ θb_ce ≦ 10 [deg] and 10 [deg]. The pneumatic tire according to claim 8 , wherein the condition of ≦ θa−θb_ce is satisfied. Adjacent section A, in B, according to claim 9, and groove wall angle θa of the section A, the groove wall angle θb_ce of the central portion of the section B, and a groove wall angle of the end portion of the section B successively Pneumatic tires. The groove depth GD and the groove width GW of the end-side circumferential main groove are 5.0 [mm] ≦ GD ≦ 12.0 [mm] and 5.0 [mm] ≦ GW ≦ 18.0 [mm]. The pneumatic tire according to any one of claims 1 to 10 , which satisfies the following condition.

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