Patent Publication Number: US-2021187634-A1

Title: Cutting insert, cutting tool, and method for manufacturing machined product

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a national stage entry according to 35 U.S.C. 371 of PCT Application No. PCT/JP2019/021959, filed on Jun. 3, 2019, which claims priority to Japanese Application No. 2018-106134, filed on Jun. 1, 2018, which are entirely incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclose generally relates to cutting inserts for use in a cutting process. Specifically, the present disclose relates to cutting inserts for use in a milling process. 
     BACKGROUND 
     For example, a cutting insert is discussed in WO 2004/050283 (Patent Document 1) as a cutting insert for use in a cutting process of a workpiece, such as metal. The cutting insert discussed in Patent Document 1 may include two end surfaces, a peripheral lateral surface and a cutting edge. The two end surfaces may have a rectangular shape and may be opposed to each other. The peripheral lateral surface may be extended between these end surfaces. The cutting edge may be formed on an intersecting part of the end surfaces and the peripheral lateral surface. A land surface may be located on a region in each of the end surfaces which is extended along the cutting edge. 
     SUMMARY 
     A cutting insert in non-limiting aspects of the present disclosure may include a first surface, a second surface, a third surface and a cutting edge. The first surface may include a first side, a second side and a first corner. The first corner may be located between the first side and the second side. The second surface may be located on a side opposite to the first surface. The third surface may be located between the first surface and the second surface. The cutting edge may be located on at least a part of a ridgeline where the first surface intersects with the third surface. 
     An imaginary straight line passing through a center of the first surface and a center of the second surface may be a central axis. An imaginary flat surface which is located between the first surface and the second surface and which is orthogonal to the central axis may be a reference plane. The first surface may further include a land surface and an inclined surface. The land surface may be located along the first side, the second side and the first corner. The inclined surface may be located along the land surface and may become closer to the reference plane as going away from the land surface. The land surface may include a first land surface, a second land surface and a corner land surface. The first land surface may be located along the first side. The second land surface may be located along the second side. The corner land surface may be located along the first corner. 
     An inclination angle of the first land surface relative to the reference plane may be a first land angle. An inclination angle of the second land surface relative to the reference plane may be a second land angle. An inclination angle of the corner land surface relative to the reference plane may be a corner land angle. The first land surface may include a part thereof where the first land angle increases as going away from the first corner. The corner land surface may include a part thereof where the corner land angle increases as going away from the first side. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view illustrating a cutting insert in non-limiting aspects of the present disclosure; 
         FIG. 2  is a plan view of a first surface in the cutting insert illustrated in  FIG. 1 ; 
         FIG. 3  is a side view of the cutting insert illustrated in  FIG. 2  as viewed from a B 1  direction; 
         FIG. 4  is a side view of the cutting insert illustrated in  FIG. 2  as viewed from a B 2  direction; 
         FIG. 5  is an enlarged view of a region A 1  illustrated in  FIG. 1 ; 
         FIG. 6  is an enlarged view of a region A 2  illustrated in  FIG. 2 ; 
         FIG. 7  is a plan view identical to that of the cutting insert illustrated in  FIG. 2 ; 
         FIG. 8  is a cross-sectional view taken along the line VIII-VIII in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 9  is a cross-sectional view taken along the line IX-IX in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 10  is a cross-sectional view taken along the line X-X in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 11  is a cross-sectional view taken along the line XI-XI in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 12  is a cross-sectional view taken along the line XII-XII in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 13  is a cross-sectional view taken along the line XIII-XIII in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 14  is a cross-sectional view taken along the line XIV-XIV in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 15  is a cross-sectional view taken along the line XV-XV in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 16  is a cross-sectional view taken along the line XVI-XVI in the cutting insert illustrated in  FIG. 7 ; 
         FIG. 17  is a perspective view illustrating a cutting tool in non-limiting aspects of the present disclosure; 
         FIG. 18  is an enlarged view of a region A 3  illustrated in  FIG. 17 ; 
         FIG. 19  is a schematic diagram illustrating one of steps in a method for manufacturing a machined product in non-limiting aspects of the present disclosure; 
         FIG. 20  is a schematic diagram illustrating one of the steps in the method for manufacturing a machined product in the non-limiting aspects of the present disclosure; and 
         FIG. 21  is a schematic diagram illustrating one of the steps in the method for manufacturing a machined product in the non-limiting aspects of the present disclosure. 
     
    
    
     EMBODIMENTS 
     In general, a cutting edge may have high strength if an inclination angle of a land surface is small, and good cutting performance may be obtainable if the inclination angle of the land surface is large. During a cutting process of a workpiece for manufacturing a machined product, a principal force may be applied in a direction orthogonal to the land surface. Accordingly, if the inclination angle of the land surface is large, such a load as to push the cutting insert outward may tend to be applied. Consequently, machining accuracy may deteriorate due to dislocation of the cutting insert. 
     The cutting inserts  1  in non-limiting embodiments may be described in detail below with reference to the drawings. For the sake of description, the drawings referred to in the following may illustrate, in simplified form, only main members necessary for describing the non-limiting embodiments. The cutting inserts  1  disclosed in the following may therefore be capable of including any arbitrary structural member not illustrated in the drawings referred to. Dimensions of the members in each of the drawings faithfully may represent neither dimensions of actual structural members nor dimensional ratios of these members. 
     &lt;Inserts&gt; 
     The cutting insert  1  (hereinafter also referred to simply as “the insert  1 ”) in non-limiting aspects of the present disclosure may include, for example, a first surface  3 , a second surface  5 , a third surface  7  and a cutting edge  9 . The first surface  3  may have a polygonal shape including corners and sides as illustrated in  FIG. 2 . The first surface  3  may have an approximately rectangular shape as in a non-limiting embodiment illustrated in  FIG. 2 . The second surface  5  may be located on a side opposite to the first surface  3 . Similarly to the first surface  3 , the second surface  5  may have a polygonal shape including corners and sides. Similarly to the first surface  3 , the second surface  5  may have an approximately rectangular shape. The insert  1  may have a quadrangular plate shape as illustrated in  FIG. 1 . 
     The term “polygonal shape” may not denote a strict polygonal shape. For example, the four corners of the first surface  3  may be slightly curved in a plan view of the first surface  3 , instead of being a strict straight line. The four corners of the first surface  3  may not be individually a strict corner. 
     The first surface  3  may have a rectangular shape and may include four corners and four sides as illustrated in  FIG. 2 . One of the sides in the first surface  3  may be a first side  11 . One of long sides of the first surface  3  may be the first side  11  as illustrated in  FIG. 2 . One of short sides of the first surface  3  may be a second side  13  as illustrated in  FIG. 2 . 
     A corner located between the first side  11  and the second side  13  on the first surface  3  may be a first corner  15 . In other words, the first side  11  and the second side  13  may be individually extended from the first corner  15 . Because the first surface  3  is the rectangular shape in the non-limiting embodiment illustrated in  FIG. 2 , an angle formed by an extension line of the first side  11  and an extension line of the second side  13  may be approximately 90° in a plan view of the first surface  3 . 
     An imaginary straight line passing through a center of the first surface  3  and a center of the second surface  5  may be a central axis O 1 . An imaginary flat surface that is located between the first surface  3  and the second surface  5  and is orthogonal to the central axis O 1  may be a reference plane S 1 . An intersection of diagonals on the first surface  3  may be the center of the first surface  3  as illustrated in  FIG. 1 . An intersecting part of extension lines of the individual sides constituting the rectangular shape may serve as a starting point of the diagonals. 
     Similarly, an intersection of diagonals on the second surface  5  may be the center of the second surface  5 . If the first surface  3  does not have a rectangular shape, the center of the first surface  3  may be determined by, for example, a position of a center of gravity of the first surface  3  in the plan view of the first surface  3 . 
     The four corners and the four sides of the first surface  3  may have 180° rotational symmetry around the central axis O 1  in the plan view of the first surface  3 . The second surface  5  may have 180° rotational symmetry around the central axis O 1  in the plan view. 
     Shapes of the first surface  3  and the second surface  5  are not limited to the above shape. The shape of the first surface  3  may be an approximately quadrangular shape. The first surface  3  and the second surface  5  may have, for example, a triangular shape, pentagonal shape, hexagonal shape or octagonal shape. 
     The third surface  7  may be located between the first surface  3  and the second surface  5  in non-limiting aspects of the present disclosure. Hereinafter, the third surface may be referred to as a lateral surface  7 . The lateral surface  7  may connect to the first surface  3  and the second surface  5  as illustrated in  FIGS. 3 and 4 . The lateral surface  7  may include a first lateral surface  17 , a second lateral surface  19  and a first corner lateral surface  21  as illustrated in  FIGS. 3 and 4 . The first lateral surface  17  may be located along the first side  11 . The second lateral surface  19  may be located along the second side  13 . The first corner lateral surface  21  may be located along the first corner  15 . 
     A maximum width of the first surface  3  in the plan view thereof may be, for example, 6-25 mm. A height from the first surface  3  to the second surface  5  may be, for example, 5-20 mm. The term “the height from the first surface  3  to the second surface  5 ” may denote a maximum value of a space between the first surface  3  and the second surface  5  in a direction parallel to the central axis O 1 , in other words, a width of the lateral surface  7  in a direction along the central axis O 1 . 
     The insert  1  may include a cutting edge  9  located on at least a part of a ridgeline where the first surface  3  intersects with the lateral surface  7  in non-limiting aspects of the present disclosure. The cutting edge  9  may be usable for cutting a workpiece during the time that a machined product is manufactured using the insert  1 . The cutting edge  9  may be located on the whole or a part of the ridgeline. Alternatively, the insert  1  may further include other cutting edge located on at least a part of a ridgeline where the second surface  5  intersects with the lateral surface  7 . 
     If the cutting edge  9  is located on at least the part of the ridgeline, one of the first surface  3  and the lateral surface  7  may include a rake surface region. If the cutting edge is located on at least the part of the ridgeline, the other of the first surface  3  and the lateral surface  7  may include a flank surface region. The first surface  3  may include the rake surface region and the lateral surface  7  may include the flank surface region as illustrated in  FIG. 1 . 
     The cutting edge  9  may include a first cutting edge  23 , a second cutting edge  25  and a corner cutting edge  27  as illustrated in  FIGS. 5 and 6 . The first cutting edge  23  may be located at the first side  11 . The second cutting edge  25  may be located at the second side  13 . The corner cutting edge  27  may be located at the first corner  15 . The corner cutting edge  27  may be located on the whole or a part of the first corner  15 . The corner cutting edge  27  may be located on the whole of the first corner  15  as illustrated in  FIGS. 5 and 6 . 
     The first cutting edge  23  may be located on the whole or a part of the first side  11 . As illustrated in  FIG. 1 , the first cutting edge  23  may be extended from an end portion of the first side  11  which is located at a side of the first corner  15 , toward an end portion thereof located at a side away from the first corner  15 . The second cutting edge  25  may be located on the whole or a part of the second side  13 . As illustrated in  FIG. 1 , the second cutting edge  25  may be extended from an end portion of the second side  13  which is located at a side of the first corner  15 , toward an end portion thereof located at a side away from the first corner  15 . 
     For example, the second cutting edge  25  may be usable as a bottom cutting edge located along a machined surface (finished surface) of a workpiece during a cutting process of the workpiece by using the insert  1  in non-limiting aspects of the present disclosure. Alternatively, the first cutting edge  23  may be used as an outer peripheral cutting edge. In cases where the second cutting edge  25  is used as the bottom cutting edge and the first cutting edge  23  is used as the outer peripheral cutting edge as described above, the first cutting edge  23  may mainly contribute to the cutting process. The first cutting edge  23  may therefore be referred to as a main cutting edge in some cases. 
     The first surface  3  may include a land surface  29  and an inclined surface  31  as illustrated in  FIGS. 5 and 6 . The land surface  29  may be located along the first side  11 , the second side  13  and the first corner  15 . In other words, the land surface  29  may be located along the first cutting edge  23 , the second cutting edge  25  and the corner cutting edge  27 . If the first surface  3  includes the land surface  29 , the cutting edge  9  may have enhanced durability. 
     The inclined surface  31  may be located along the land surface  29 . The inclined surface  31  may be located more inside the first surface  3  than the land surface  29 . The inclined surface  31  may become closer to the reference plane S 1  as going away from the land surface  29 . The inclined surface  31  of the first surface  3  may be the rake surface region described above. 
     If the first surface  3  includes the inclined surface  31  servable as the rake surface, it may be easy to control a flow direction of chips generated by the cutting edge  9  during the cutting process. This may lead to enhanced chip discharge performance. An inclination angle of the inclined surface  31  may be larger than an inclination angle of the land surface  29 . The term “inclination angle” of the land surface  29  and the inclined surface  31  may denote an inclination angle relative to the reference plane S 1 . 
     The land surface  29  may include a first land surface  33 , a second land surface  35  and a corner land surface  37  as in a non-limiting embodiment illustrated in  FIGS. 5 and 6 . The first land surface  33  may be located along the first side  11 . The second land surface  35  may be located along the second side  13 . The corner land surface  37  may be located along the first corner  15 . As illustrated in  FIGS. 8 to 10 , an inclination angle of the first land surface  33  relative to the reference plane S 1  may be a first land angle ψ 1 . As illustrated in  FIGS. 11 to 13 , an inclination angle of the second land surface  35  relative to the reference plane S 1  may be a second land angle ψ 2 . As illustrated in  FIGS. 14 to 16 , an inclination angle of the corner land surface  37  relative to the reference plane S 1  may be a corner land angle ψ 3 . 
     The first land angle ψ 1  and the corner land angle ψ 3  may be kept constant or changed. For example, the first land surface may include a part thereof where the first land angle ψ 1  increases as going away from the first corner  15 . The corner land surface  37  may include a part thereof where the corner land angle ψ 3  increases as going away from the first side  11 . 
     A large cutting load may tend to be applied in the vicinity of a boundary between the first cutting edge  23  and the corner cutting edge  27  during the cutting process of the workpiece. If the land surface  33  includes the part thereof where the first land angle ψ 1  increases as going away from the first corner  15 , the first land angle ψ 1  may tend to become relatively small at a part of the first land surface  33  which is located in the vicinity of the first corner  15 . 
     Accordingly, even if the large cutting load is applied in the vicinity of the boundary between the first cutting edge  23  and the corner cutting edge  27 , it may be less susceptible to a force in a direction to push the insert  1  outward (a rightward direction in  FIG. 2 ). It may therefore be possible to reduce the dislocation of the insert  1  relative to a holder. This may lead to the highly accurate cutting process. 
     If the first land surface  33  includes the part thereof where the first land angle ψ 41  increases as going away from the first corner  15 , the first land angle ψ 41  may tend to become relatively large at a part of the first land surface  33  which is located away from the first corner  15 . It may therefore be possible to reduce a cutting load in at least the part of the first land surface  33  which is located away from the first corner  15 . Accordingly, the cutting load applied to the whole of the insert  1  can be minimized, and consequently the insert  1  satisfying the above configuration may have enhanced durability. 
     The corner land surface  37  may include the part thereof where the corner land angle ψ 3  increases as going away from the first side  11 , the corner land angle ψ 43  may tend to become relatively small at a part of the corner land surface  37  which is located in the vicinity of the first side  11 . 
     Accordingly, even if the large cutting load is applied in the vicinity of the boundary between the first cutting edge  23  and the corner cutting edge  27 , it may be less susceptible to the force in the direction to push the insert  1  outward (a lower right direction in  FIG. 2 ). It may therefore be possible to reduce the dislocation of the insert  1  relative to the holder. This may lead to the highly accurate cutting process. 
     If the corner land surface  37  includes a part thereof where the corner land angle ψ 3  increases as going away from the first side  11 , the corner land angle ψ 3  at a part of the corner land surface  37  which is located away from the first side  11  may tend to become relatively large. It may therefore be possible to reduce the cutting load in at least the part of the corner land surface  37  which is located away from the first side  11 . Accordingly, the cutting load applied to the whole of the insert  1  can be minimized, and consequently the insert  1  satisfying the above configuration may have enhanced durability. 
     The first land angle ψ 1 , the second land angle ψ 2  and the third land angle ψ 3  are not individually limited to a specific value. A value of the first land angle ψ 1  may be settable to, for example, 0-10°. A value of the second land angle ψ 2  may be settable to, for example, 0-5°. A value of the third land angle ψ 3  may be settable to, for example, 0-15°. 
     As illustrated in  FIGS. 8 to 10 , the first land surface  33  may include a part thereof where the first land angle ψ 1  increases as going away from the first corner  15 . A difference  41  between a maximum value and a minimum value of the first land angle ψ 41  may be, for example, 5° or more. If the  41  is 5° or more, it may be easy to suitably obtain both a reduction in dislocation of the insert  1  and the enhanced durability of the insert  1 . A difference  43  between a maximum value and a minimum value of the corner land angle ψ 43  may be, for example, 5° or more. If the  43  is 5° or more, the dislocation of the insert  1  can be reduced, and the insert  1  may have the enhanced durability. 
     A maximum value of the second land angle ψ 2  may be larger than a maximum value of the first land angle ψ 41 . For example, if the maximum value of the second land angle ψ 2  is larger than the maximum value of the first land angle ψ 1  when using the second cutting edge  25  as a bottom cutting edge, a machined surface of a workpiece may have enhanced surface accuracy. 
     During use of the second cutting edge  25  as the bottom cutting edge, chips generated by the second cutting edge  25  may be thin, and a smaller load may be applied to the second cutting edge  25  than to the first cutting edge  23  and the first corner cutting edge  27 . The insert  1  may therefore be less susceptible to dislocation even if the maximum value of the second land angle ψ 2  is relatively large. 
     The second land angle ψ 42  may be kept constant or changed. For example, the second land surface  35  may include a part thereof where the second land angle ψ 2  increases as going away from the first corner  15  as illustrated in  FIGS. 11 to 13 . 
     A large cutting load may tend to be applied in the vicinity of the boundary between the first cutting edge  23  and the corner cutting edge  27  during the cutting process of the workpiece. If the second land surface  35  includes the part thereof where the second land angle ψ 2  increases as going away from the first corner  15 , the second land angle ψ 42  at a part of the second land surface  35  which is located in the vicinity of the first corner  15  may tend to become relatively small. 
     Hence, even if the large cutting load is applied in the vicinity of the boundary between the first cutting edge  23  and the corner cutting edge  27 , it may be less susceptible to the force in the direction to push the insert  1  outward (a downward direction in  FIG. 2 ). It may therefore be possible to reduce the dislocation of the insert  1  relative to the holder. This may lead to the highly accurate cutting process. 
     If the second land surface  35  includes a part thereof where the second land angle ψ 2  increases as going away from the first corner  15 , the second land angle ψ 42  at a part of the second land surface  35  which is located away from the first corner  15  may tend to become relatively large. It may therefore be possible to reduce a cutting load in at least the part of the second land surface  35  which is located away from the first corner  15 . Accordingly, the cutting load applied to the whole of the insert  1  can be minimized, and consequently the insert  1  satisfying the above configuration may have enhanced durability. 
     As stated earlier, in the non-limiting embodiment illustrated in  FIG. 2 , one of the long sides of the first surface  3  may be the first side  11 , and one of the short sides of the first surface  3  may be the second side  13 . Specifically, the first surface  3  may have a rectangular shape, the first side  11  may be the long side and the second side  13  may be the short side in a plan view of the first surface  3 . 
     If the first surface  3  has the above configuration, the following configuration may be particularly effective. That is, the first land surface  33  may include the part thereof where the first land angle ψ 41  increases as going away from the first corner  15  in the insert  1  of a non-limiting embodiment illustrated in  FIGS. 8 to 10 . 
     If the first side  11  is the long side, the first cutting edge  23  may tend to become longer than each of the second cutting edge  25  and the corner cutting edge  27 , and a length in a direction along the first side  11  on the first land surface  33  located along the first cutting edge  23  also may tend to become longer. In cases where the above length on the first land surface  33  is large, it may be difficult to accomplish both the highly accurate cutting process and the enhanced durability of the insert  1  if the first land angle ψ 1  is kept constant. However, if the first land surface  33  includes the part thereof where the first land angle ψ 41  increases as going away from the first corner  15 , the insert  1  satisfying this configuration may be capable of offering the highly accurate cutting process and the enhanced durability. 
     Widths of the first land surface  33 , the second land surface  35  and the corner land surface  37  in the plan view of the first surface  3  are not individually limited to a specific value. The widths of the first land surface  33 , the second land surface  35  and the corner land surface  37  may be kept constant or changed. 
     For example, the second land surface  35  may include a part thereof whose width decreases as going away from the corner land surface  37  in the plan view of the first surface  3 . If the second land surface  35  has the above configuration, the insert  1  satisfying this configuration may achieve high surface accuracy of a finished surface. 
     The width of the second land surface  35  may denote a length of the second land surface  35  in a direction orthogonal to a part of the second side  13  which is extended along a measurement target region on the second land surface  35 . The width of the first land surface  33  and the width of the corner land surface  37  may be evaluated in a similar manner. 
     The width of the second land surface  35  may be measured at five points located at equal intervals in a direction along the second side  13  on the second land surface  35 . If measured widths decrease as going away from the corner land surface  37 , it may be regarded that the width of the second land surface  35  decreases as going away from the corner land surface  37 . 
     As in a non-limiting embodiment illustrated in  FIG. 3 , the first cutting edge  23  located on at least a part of the first side  11  may include a part thereof that becomes closer to the reference plane S 1  as going away from the first corner  15 . For example, a height of the first cutting edge  23  from the reference plane S 1  may be denoted by h 11  as illustrated in  FIG. 8 . A height of the first cutting edge  23  from the reference plane S 1  may be denoted by h 12  as illustrated in  FIG. 9 . A height of the first cutting edge  23  from the reference plane S 1  may be denoted by h 13  as illustrated in  FIG. 10 . These heights may have a relationship of h 11 &gt;h 12 &gt;h 13  as illustrated in  FIGS. 8 to 10 . 
     If the first cutting edge  23  has the above configuration, the first cutting edge  23  may be subjected to a small cutting load. Accordingly, it may be less susceptible to the force in the direction to push the insert  1  outward (the rightward direction in  FIG. 2 ) which is due to a cutting load applied to the first cutting edge  23 . It may therefore be possible to reduce the dislocation of the insert  1  relative to the holder. 
     The phrase that “the first cutting edge  23  becomes closer to the reference plane S 1  as going away from the first corner  15 ” may denote that at least the first cutting edge  23  is not located further away from the reference plane S 1  as going away from the first corner  15 . Hence, the first cutting edge  23  may partially include a part thereof whose height from the reference plane S 1  is kept constant. 
     In cases where, instead of the configuration that the first cutting edge  23  partially includes the part thereof whose height from the reference plane S 1  is kept constant, the configuration that the whole of the first cutting edge  23  becomes closer to the reference plane S 1  as going away from the first corner  15 , it may be much less susceptible to the force in the direction to push the insert  1  outward (the rightward direction in  FIG. 2 ). It may therefore be possible to further reduce the dislocation of the insert  1  relative to the holder. 
     The second cutting edge  25  located on at least a part of the second side  13  may include a part thereof that becomes closer to the reference plane S 1  as going away from the first corner  15  as in a non-limiting embodiment illustrated in  FIG. 4 . A height of the second cutting edge  25  from the reference plane S 1  may be denoted by h 21  as illustrated in  FIG. 11 . A height of the second cutting edge  25  from the reference plane S 1  may be denoted by h 22  as illustrated in  FIG. 12 . A height of the second cutting edge  25  from the reference plane S 1  may be denoted by h 23  as illustrated in  FIG. 13 . These heights may have a relationship of h 21 &gt;h 22 &gt;h 23  as illustrated in  FIGS. 11 to 13 . 
     If the second cutting edge  25  has the above configuration, the second cutting edge  25  may be subjected to a small cutting load. Accordingly, it may be less susceptible to the force in the direction to push the insert  1  outward (the downward direction in  FIG. 2 ) which is due to a cutting load applied to the second cutting edge  25 . It may therefore be possible to reduce the dislocation of the insert  1  relative to the holder. 
     The phrase that “the second cutting edge  25  becomes closer to the reference plane S 1  as going away from the first corner  15 ” may denote that at least the second cutting edge  25  is not located further away from the reference plane S 1  as going away from the first corner  15 . Hence, the second cutting edge  25  may partially include a part thereof whose height from the reference plane S 1  is kept constant. 
     With the configuration that the whole of the second cutting edge  25  becomes closer to the reference plane S 1  as going away from the first corner  15 , it may be much less susceptible to the force in the direction to push the insert  1  outward (the downward direction in  FIG. 2 ). It may therefore be possible to further reduce the dislocation of the insert  1  relative to the holder. 
     The first corner  15  may not be a strict corner formed by an intersection of the first side  11  with the second side  13 . For example, the first corner  15  may have a convex curvilinear shape that is protruded outward in the plan view of the first surface  3 . Alternatively, the first corner  15  may be formed by combining a straight line and a curved line as in a non-limiting embodiment illustrated in  FIG. 6 . 
     The first corner  15  may be formed by a curvilinear part. The first corner  15  may be formed by a first curvilinear part  39 , a second curvilinear part  41  and a connection part  43  in the plan view of the first surface  3  as illustrated in  FIG. 6 . The first curvilinear part  39  may be located at a part of the first corner  15  which is located closer to the first side  11  and may have a convex curvilinear shape protruded outward. The second curvilinear part  41  may be located at a part of the first corner  15  which is located closer to the second side  13  and may have a convex curvilinear shape protruded outward. The connection part  43  may connect to the first curvilinear part  39  and the second curvilinear part  41 , and may have a straight line shape. 
     If the first corner  15  includes the connection part  43 , a cutting load applied to the corner cutting edge  27  can be reduced, thus leading to enhanced durability of the corner cutting edge  27 . If the first corner  15  includes the first curvilinear part  39 , a cutting load may be less likely to be accumulated in the vicinity of a boundary between the first corner  15  and the first side  11 . If the first corner  15  includes the second curvilinear part  41 , a cutting load may be less likely to be accumulated in the vicinity of a boundary between the first corner  15  and the second side  13 . 
     A shape of the first curvilinear part  39  and a shape of the second curvilinear part  41  in the plan view of the first surface  3  are not particularly limited as long as both have the convex curvilinear shape. The first curvilinear part  39  and the second curvilinear part  41  may have a circular arc shape as illustrated in  FIG. 6 . 
     In cases where the first corner  15  includes the first curvilinear part  39  and the second curvilinear part  41  each having the circular arc shape, a radius of curvature of the first curvilinear part  39  and that of the second curvilinear part  41  are not limited to a specific value. For example, the radius of curvature of the first curvilinear part  39  may be larger than that of the second curvilinear part  41 . 
     For example, if the first cutting edge  23  is used as an outer peripheral cutting edge and the second cutting edge  25  is used as a bottom cutting edge, a large cutting load may tend to applied in the vicinity of a boundary between the first corner and the first side  11  than in the vicinity of a boundary between the first corner  15  and the second side  13 . 
     If the radius of curvature of the first curvilinear part  39  is larger than that of the second curvilinear part  41 , the first curvilinear part  39  may have higher durability than the second curvilinear part  41 . Therefore, even if a relatively large cutting load is applied in the vicinity of the boundary between the first corner  15  and the first side  11 , the insert  1  may have enhanced durability. The insert  1  may be highly versatile because the first cutting edge  23  is usable as the excellent outer peripheral cutting edge, and the second cutting edge  25  is usable as the excellent bottom cutting edge. 
     If the radius of curvature of the second curvilinear part is smaller than that of the first curvilinear part  39 , the second cutting edge  25  may be subjected to a small cutting load during a cutting process. This may lead to improved surface accuracy of a machined surface. 
     An angle formed by an imaginary line extended from the first side  11  and an imaginary line extended from the connection part  43  in the plan view of the first surface  3  may be a first imaginary angle ϕ 1 . An angle formed by an imaginary line extended from the second side  13  and an imaginary line extended from the connection part  43  may be a second imaginary angle ϕ 2 . 
     For example, the first imaginary angle ϕ 1  may be smaller than the second imaginary angle ϕ 2  as in a non-limiting embodiment illustrated in  FIG. 6 . In this case, the first corner  15  may be subjected to a small cutting load. Accordingly, it may be less susceptible to a force in a direction to push the insert  1  outward (a lower right direction in  FIG. 2 ). It may therefore be possible to further reduce the dislocation of the insert  1  relative to the holder. 
     The connection part  43  may be located further away from the reference plane S 1  as going from a side of the first curvilinear part  39  toward a side of the second curvilinear part  41  as in the non-limiting embodiment illustrated in  FIG. 4 . The connection part  43  may be inclined so as to extend upward as going from the side of the first curvilinear part  39  toward the side of the second curvilinear part  41  as in the non-limiting embodiment illustrated in  FIG. 4 . 
     With the connection part  43  having the above configuration, the connection part  43  may be susceptible to a cutting load in a leftward direction in  FIG. 2 . This may be offset by the force to push the insert  1  outward (the rightward direction in  FIG. 2 ), thereby further reducing the dislocation of the insert  1  relative to the holder. 
     The first curvilinear part  39  may have a curvilinear shape recessed in a direction becoming closer to the reference plane S 1  in a side view. The first curvilinear part  39  having the above configuration may facilitate a smooth connection of the connection part  43  and the first side  11 . A large cutting load may therefore be less likely to be applied in the vicinity of a boundary between the first cutting edge  23  and the corner cutting edge  27 . 
     The second curvilinear part  41  may have a curvilinear shape protruded in a direction away from the reference plane S 1  in the side view. If the connection part  43  is inclined as described, the second curvilinear part  41  located between the connection part  43  and the second side  13  may be protruded upward. In this case, the second curvilinear part  41  may tend to become a portion for biting a workpiece during the cutting process, and a large cutting load may tend to be applied to the second curvilinear part  41 . With the second curvilinear part  41  having the above configuration, the insert  1  may have enhanced durability because of high strength of the second curvilinear part  41 . 
     The inclined surface  31  may include a first inclined surface  45 , a second inclined surface  47  and a corner inclined surface  49  as in a non-limiting embodiment illustrated in  FIGS. 5 and 6 . The first inclined surface  45  may be located along the first side  11 . The second inclined surface  47  may be located along the second side  13 . The corner inclined surface  49  may be located along the first corner  15 . If the inclined surface  31  includes the first inclined surface  45 , the second inclined surface  47  and the corner inclined surface  49 , it may be easy to control a flow direction of chips generated by the first cutting edge  23 , the second cutting edge  25  and the corner cutting edge  27 . 
     The first inclined surface  45 , the second inclined surface  47  and the corner inclined surface  49  may be individually formed by one or a plurality of surface regions. For example, the first inclined surface  45 , the second inclined surface  47  and the corner inclined surface  49  may be individually formed by two surface regions as illustrated in  FIGS. 5 and 6 . 
     The first inclined surface  45  may include a first outer inclined surface  45   a  and a first inner inclined surface  45   b  as illustrated in  FIGS. 5 and 6 . The first outer inclined surface  45   a  may be located along the first land surface  33 . The first inner inclined surface  45   b  may be located along the first outer inclined surface  45   a . An inclination angle of the first inner inclined surface  45   b  may be larger than that of the first outer inclined surface  45   a  as illustrated in  FIGS. 8 to 10 . 
     If an inclination angle θ 11  of the first outer inclined surface  45   a  is relatively small, the first cutting edge  23  may have high strength. If an inclination angle θ 12  of the first inner inclined surface  45   b  is relatively large, the first inclined surface  45  may be less subjected to contact with chips. A ridgeline may be located on a boundary part between the first outer inclined surface  45   a  and the first inner inclined surface  45   b  as in a non-limiting embodiment illustrated in  FIGS. 5 and 6 . 
     The second inclined surface  47  may include a second outer inclined surface  47   a  and a second inner inclined surface  47   b  as in the non-limiting embodiment illustrated in  FIGS. 5 and 6 . The second outer inclined surface  47   a  may be located along the second land surface  35 . The second inner inclined surface  47   b  may be located along the second outer inclined surface  47   a . An inclination angle of the second inner inclined surface  47   b  may be larger than that of the second outer inclined surface  47   a  as illustrated in  FIGS. 11 to 13 . 
     If an inclination angle θ 21  of the second outer inclined surface  47   a  is relatively small, the second cutting edge  25  may have high strength. If an inclination angle θ 22  of the second inner inclined surface  47   b  is relatively large, the second inclined surface  47  may be less subjected to contact with chips. A ridgeline may be located on a boundary part between the second outer inclined surface  47   a  and the second inner inclined surface  47   b  as in a non-limiting embodiment illustrated in  FIGS. 5 and 6 . 
     The corner inclined surface  49  may include a corner outer inclined surface  49   a  and a corner inner inclined surface  49   b  as in the non-limiting embodiment illustrated in  FIGS. 5 and 6 . The corner outer inclined surface  49   a  may be located along the corner land surface  37 . The corner inner inclined surface  49   b  may be located along the corner outer inclined surface  49   a . An inclination angle of the corner inner inclined surface  49   b  may be larger than that of the corner outer inclined surface  49   a  as illustrated in  FIGS. 14 to 16 . 
     If an inclination angle θ 31  of the corner outer inclined surface  49   a  is relatively small, the corner cutting edge  27  may have high strength. If an inclination angle θ 32  of the corner inner inclined surface  49   b  is relatively large, the corner inclined surface  49  may be less subjected to contact with chips. A ridgeline may be located on a boundary part between the corner outer inclined surface  49   a  and the corner inner inclined surface  49   b  as in the non-limiting embodiment illustrated in  FIGS. 5 and 6 . 
     The first outer inclined surface  45   a , the first inner inclined surface  45   b , the second outer inclined surface  47   a , the second inner inclined surface  47   b , the corner outer inclined surface  49   a  and the corner inner inclined surface  49   b  may be individually a flat surface or curved surface. If the inclined surface  31  is the curved surface and indicated by a curved line in a specific cross section, a maximum value of an angle relative to the reference plane S 1  may be an inclination angle. For example, the maximum value of the angle relative to the reference plane S 1  on the corner outer inclined surface  49   a  having the concave curvilinear shape may be denoted by an inclination angle θ 31  in cross sections illustrated in  FIGS. 14 to 16 . 
     The inclination angle θ 11  of the first outer inclined surface  45   a , the inclination angle θ 12  of the first inner inclined surface  45   b , the inclination angle θ 21  of the second outer inclined surface  47   a , the inclination angle θ 22  of the second inner inclined surface  47   b , the inclination angle θ 31  of the corner outer inclined surface  49   a  and the inclination angle θ 32  of the corner inner inclined surface  49   b  are not individually limited to a specific value. 
     A value of the inclination angle θ 11  may be settable to, for example, 5-35°. A value of the inclination angle θ 12  may be settable to, for example, 15-65°. A value of the inclination angle θ 21  may be settable to, for example, 10-40°. A value of the inclination angle θ 22  may be settable to, for example, 15-65°. A value of the inclination angle θ 31  may be settable to, for example, 15-45°. A value of the inclination angle θ 32  may be settable to, for example, 15-65°. 
     As illustrated in  FIGS. 8 and 9 , the first outer inclined surface  45   a  may include a part thereof where the inclination angle θ 11  decreases as going away from the first corner  15 . In cases where the first land surface  33  includes a part thereof where the first land angle ψ 41  increases as going away from the first corner  15  and the inclination angle θ 11  of the first outer inclined surface  45   a  is in the above state, the durability of the first cutting edge  23  may be less likely to deteriorate. The above configuration may therefore be effective if the durability is needed for the first cutting edge  23 . 
     As illustrated in  FIGS. 9 and 10 , the first outer inclined surface  45   a  may include a part thereof where the inclination angle ψ 11  increases as going away from the first corner  15 . In cases where the first land surface  33  includes a part thereof where the first land angle ψ 41  increases as going away from the first corner  15  and the inclination angle ψ 11  of the first outer inclined surface  45   a  is in the above state, the first cutting edge  23  offers high cutting performance. The above configuration may therefore be effective if the cutting performance is needed for the first cutting edge  23 . 
     As in a non-limiting embodiment illustrated in  FIGS. 8 to 10 , the first outer inclined surface  45   a  may include a part thereof where the inclination angle θ 11  decreases as going away from the first corner  15 , and a part thereof where the inclination angle θ 11  increases as going away from the first corner  15 . In the non-limiting embodiment illustrated in  FIGS. 8 to 10 , the first inclined surface  45  may have these two parts, and the first outer inclined surface  45   a  may have a convex shape in a direction along the first cutting edge  23 . This may lead to a stable flow direction of chips generated by the first cutting edge  23 . 
     The first inner inclined surface  45   b  may include a part thereof where the inclination angle θ 12  decreases as going away from the first corner  15  as in the non-limiting embodiment illustrated in  FIGS. 8 to 10 . In other words, the first inner inclined surface  45   b  may include a part thereof where the inclination angle θ 12  increases as becoming closer to the first corner  15 . 
     In addition to chips generated by the first cutting edge  23 , chips generated by the corner cutting edge  27  and the second cutting edge  25  may flow to a region in the first inner inclined surface  45   b  which is located close to the first corner  15 . If the first inner inclined surface  45   b  includes the part thereof where the inclination angle θ 12  increases as becoming closer to the first corner  15 , it may be easy to ensure a chip flow space in the region in the inner inclined surface  45   b  located close to the first corner  15 . Consequently, chip clogging may be less likely to occur. 
     The second outer inclined surface  47   a  and the second inner inclined surface  47   b  may respectively include parts thereof where the inclination angles θ 21  and  022  decrease as going away from the first corner  15 . Alternatively, the second outer inclined surface  47   a  and the second inner inclined surface  47   b  may respectively include parts thereof where the inclination angles θ 21  and  022  increase as going away from the first corner  15 . Still alternatively, the inclination angle θ 21  of the second outer inclined surface  47   a  and the inclination angle θ 22  of the second inner inclined surface  47   b  may be kept constant. 
     For example, if the second cutting edge  25  is used as a bottom cutting edge, chips generated by the second cutting edge  25  may tend to have a small thickness. If the inclination angle θ 21  of the second outer inclined surface  47   a  and the inclination angle θ 22  of the second inner inclined surface  47   b  are kept constant, a flow direction of chips generated by the second cutting edge  25  may tend to become stable. Thus, with the insert  1  in a non-limiting embodiment illustrated in  FIGS. 11 to 13 , the second cutting edge  25  may be usable as an excellent bottom cutting edge. 
     The phrase that “the inclination angle θ 21  of the second outer inclined surface  47   a  and the inclination angle θ 22  of the second inner inclined surface  47   b  are kept constant” may not denote that these inclination angles θ 21  and  022  are kept strictly constant. There is no problem if the inclination angle θ 21  of the second outer inclined surface  47   a  and the inclination angle θ 22  of the second inner inclined surface  47   b  are evaluated as being constant even if the inclination angles θ 21  and  022  have variations of approximately 2-3°. 
     The corner outer inclined surface  49   a  may include a part thereof where the inclination angle θ 31  decreases as becoming closer to the first side  11  as in a non-limiting embodiment illustrated in  FIGS. 14 to 16 . As stated earlier, the large cutting load may tend to be applied in the vicinity of the boundary between the first corner  15  and the first side  11 . If the corner outer inclined surface  49   a  includes the part thereof where the inclination angle θ 31  decreases as becoming closer to the first side  11 , it may be easy to ensure a thickness of the corner cutting edge  27  in a region in the corner outer inclined surface  49   a  which corresponds to a portion susceptible to a large cutting load. Therefore, the insert  1  having the above configuration may have enhanced durability. 
     For a similar reason, the corner inner inclined surface  49   b  may include a part thereof where the inclination angle θ 32  decreases as becoming closer to the first side  11 . 
     The insert  1  may include a through hole  51  that opens into regions located on opposite sides in the lateral surface  7  as in the non-limiting embodiment illustrated in  FIG. 1 . A central axis of the through hole  51  may be inclined relative to the central axis O 1  of the insert  1  or may be orthogonal to the central axis O 1 . 
     The through hole  51  may be usable for inserting, for example, a screw when fixing the insert  1  to the holder. Instead of the screw, for example, a clamping member may be used to fix the insert  1  to the holder. Although the through hole  51  opens into the regions located on the opposite sides in the lateral surface  7 , the through hole  51  is not limited to the above configuration. For example, the through hole  51  may be formed from the center of the first surface  3  toward the center of second surface  5 . 
     The first surface  3  may include a surface region other than the land surface  29  and the inclined surface  31  described above. For example, the first surface  3  may include a surface region  3   a  located so as to surround an opening of the through hole  51 . The second surface  5  may include a flat surface region corresponding to the flat surface region in the first surface  3 . If the second surface  5  includes the above surface region, the insert  1  may be stably fixable to the holder. 
     The above surface region in the second surface  5  may be orthogonal to the central axis O 1 . If the surface region is orthogonal to the central axis O 1 , the insert  1  may be more stably fixable to the holder. 
     The flat surface region is not limited to a strict flat surface. The surface region may be approximately flat and may have a slight curve or slight irregularities to the extent that the curve or irregularities cannot be observed in a general view of the insert  1 . Specifically, for example, the flat surface  39  may have slight irregularities of approximately several tens of μm. 
     For example, cemented carbide and cermet may be usable as a material of the insert  1 . Examples of composition of the cemented carbide may include WC—Co, WC—TiC—Co and WC—TiC—TaC—Co. WC, TiC and TaC may be hard particles, and Co may be a binding phase. 
     The cermet may be a sintered composite material obtainable by compositing metal into a ceramic component. Examples of the cermet may include titanium compounds composed mainly of titanium carbide (TiC) or titanium nitride (TiN). The material of the insert  1  is not limited to the above composition. 
     A surface of the insert  1  may be coated with a coating film by using chemical vapor deposition (CVD) method or physical vapor deposition (PVD) method. Examples of composition of the coating film may include titanium carbide (TiC), titanium nitride (TiN), titanium carbonitride (TiCN) and alumina (Al 2 O 3 ). 
     &lt;Cutting Tools&gt; 
     A cutting tool  101  in non-limiting aspects of the present disclosure may be described below with reference to  FIGS. 17 and 18 .  FIGS. 17 and 18  may illustrate a state where the insert  1  illustrated in  FIG. 1  is attached to a pocket  105  of a holder  103  by a screw  107 . A rotation axis Y 1  of the cutting tool  101  may be indicated by a two-dot chain line in  FIG. 17  or the like. 
     The cutting tool  101  in the non-limiting aspects of the present disclosure may be usable for a milling process. The cutting tool  101  may include the holder  103  and the insert  1  as illustrated in  FIG. 17 . The holder  103  may have a columnar shape extended from a first end to a second end along a rotation axis Y 1 . The holder  103  may include a pocket  105  located at a side of the first end. The insert  1  may be located in the pocket  105 . 
     The holder  103  may include only one pocket  105 , or alternatively, a plurality of pockets  105  as in a non-limiting embodiment illustrated in  FIG. 17 . If the holder  103  includes the pockets  105 , the cutting tool  101  may include the inserts  1 , and the inserts  1  may be respectively located in the pockets  105 . 
     The pocket  105  may open into an outer peripheral surface of the holder  103  and an end surface at a side of the first end. In cases where the holder  103  includes the pockets  105 , these pockets  105  may be located at equal intervals or unequal intervals around the rotation axis Y 1 . As apparent from, for example, the fact that the holder  103  includes the pockets  105 , the holder  103  may not be a strict columnar shape. 
     The insert  1  may be attached to the pocket  105  so that at least a part of the cutting edge is protruded from the holder  103 . Specifically, the insert  1  of the non-limiting aspects of the present disclosure may be attached to the holder  103  so that the first cutting edge is located more outward than the outer peripheral surface in the holder  103  and the second cutting edge is protruded from the holder  103  toward a workpiece. 
     At least the second surface, the flat surface region on the second surface and the lateral surface in the insert  1  may be in contact with the holder  103  in the cutting tool  101  in the non-limiting aspects of the present disclosure. 
     The insert  1  may be attached to the pocket  105  by a screw  107 . Specifically, the insert  1  may be attached to the holder  103  by inserting the screw  107  into a screw hole of the insert  1 , and by inserting a front end of the screw  107  into a screw hole formed in the pocket  105  so as to fix the screw  107  to the screw hole. For example, steel or cast iron may be usable for the holder  103 . Of these materials, the use of steel may particularly contribute to enhancing toughness of the holder  103 . 
     &lt;Method for Manufacturing Machined Product&gt; 
     A method for manufacturing a machined product in non-limiting aspects of the present disclosure may be described below with reference to  FIGS. 19 to 21 .  FIGS. 19 to 21  may illustrate a method for manufacturing a machined product in a cutting process using the above cutting tool. The rotation axis Y 1  of the cutting tool  101  may be indicated by a two-dot chain line in  FIGS. 19 to 21 . The machined product  203  may be manufacturable by carrying out the cutting process of the workpiece  201 . The manufacturing method in the non-limiting aspects of the present disclosure may include the following steps: 
     (1) rotating the cutting tool  101  represented by the foregoing aspects; 
     (2) bringing the cutting tool  101  being rotated into contact with the workpiece  201 ; and 
     (3) moving the cutting tool  101  away from the workpiece  201 . 
     More specifically, firstly, the cutting tool  101  may be relatively brought near the workpiece  201  while rotating the cutting tool  101  in Y 2  direction around the rotation axis Y 1  as illustrated in  FIG. 19 . The workpiece  201  may be then cut out by bringing the cutting edge in the cutting tool  101  into contact with the workpiece  201  as illustrated in  FIG. 20 . Thereafter, the cutting tool  101  may be relatively moved away from the workpiece  201  as illustrated in  FIG. 21 . 
     In the non-limiting aspects of the present disclosure, the workpiece  201  may be fixed and the cutting tool  101  may be brought near the workpiece  201 . The workpiece  201  may be fixed and the cutting tool  101  may be rotated around the rotation axis Y 1  in  FIGS. 19 to 21 . The workpiece  201  may be fixed and the cutting tool  101  may be moved away in  FIG. 21 . During the cutting process with the manufacturing method in the non-limiting aspects of the present disclosure, the workpiece  201  may be fixed and the cutting tool  101  may be moved in each of the steps. However, it is not intended to limit to these non-limiting aspects. 
     For example, the workpiece  201  may be brought near the cutting tool  101  in the step (1). Similarly, the workpiece  201  may be moved away from the cutting tool  101  in the step (3). If desired to continue the cutting process, the step of bringing the cutting edge in the insert into contact with different portions of the workpiece  201  may be repeated while keeping the cutting tool  101  rotated. 
     Representative examples of material of the workpiece  201  may include carbon steel, alloy steel, stainless steel, cast iron and nonferrous metals. 
     DESCRIPTION OF THE REFERENCE NUMERAL 
     
         
         
           
               1  cutting insert (insert) 
               3  first surface 
               5  second surface 
               7  third surface (lateral surface) 
               9  cutting edge 
               11  first side 
               13  second side 
               15  first corner 
               17  first lateral surface 
               19  second lateral surface 
               21  corner lateral surface 
               23  first cutting edge 
               25  second cutting edge 
               27  corner cutting edge 
               29  land surface 
               31  inclined surface 
               33  first land surface 
               35  second land surface 
               37  corner land surface 
               39  first curvilinear part 
               41  second curvilinear part 
               43  connection part 
               45  first inclined surface 
               45   a  first outer inclined surface 
               45   b  first inner inclined surface 
               47  second inclined surface 
               47   a  second outer inclined surface 
               47   b  second inner inclined surface 
               49  corner inclined surface 
               49   a  corner outer inclined surface 
               49   b  corner inner inclined surface 
               51  through hole 
               101  cutting tool 
               103  holder 
               105  pocket 
               107  screw 
               201  workpiece 
               203  machined product 
             O 1  central axis