Cutting tool and round double sided cutting insert therefor

Abstract

A cutting insert for retention in a rotating cutting tool having an axis of rotation has two opposing end surfaces and a peripheral surface extending therebetween, each end surface having a mutual first axis of symmetry passing through the end surfaces about which each end surface has N-fold rotational symmetry for some value of N where N is chosen from the group consisting of 2, 3 and 4. A peripheral cutting edge is formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge having N curved cutting edges merging with N straight cutting edges which extend between the curved cutting edges at extremities thereof. The curved cutting edges of the two end surfaces are not aligned in an end view of the cutting insert along the first axis of symmetry.

What is claimed is: 
     
       1. A double-sided cutting insert ( 18 ,  118 ) for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces ( 28 ,  128 ) and a peripheral surface ( 26 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2, 3 and 4; 
 a peripheral cutting edge ( 66 ,  166 ) formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) merging with N straight cutting edges ( 44 ,  50 ;  144 ,  150 ) which extend between the curved cutting edges at extremities thereof; wherein: 
 the curved cutting edges of the two end surfaces are not aligned, as seen in an end view of the cutting insert: and 
 each of the N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) lies on a torus and extends along an angle equal to or larger than 120°, as seen along the first axis of symmetry (B). 
 
     
     
       2. The cutting insert ( 18 ,  118 ) according to  claim 1 , wherein:
 N cutting edge pivot axes (C), located in a mid portion ( 35 ) of each of the N curved cutting edges, extend parallel to the first axis of symmetry (B), and 
 each of the N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) of one of the end surfaces ( 28 ,  128 ) is rotated about its associated cutting edge pivot axis (C) relative to an opposite curved cutting edge ( 34 ′,  32 ′) of the other end surface, as seen in an end view of the cutting insert. 
 
     
     
       3. A double-sided cutting insert ( 18 ,  118 ) for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces ( 28 ,  128 ) and a peripheral surface ( 26 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2, 3 and 4; 
 a peripheral cutting edge ( 66 ,  166 ) formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) merging with N straight cutting edges ( 44 ,  50 ;  144 ,  150 ) which extend between the curved cutting edges at extremities thereof; wherein: 
 the curved cutting edges of the two end surfaces are not aligned, as seen in an end view of the cutting insert; 
 the two end surfaces ( 28 ,  128 ) are identical; 
 a major angular portion (MP 11 , MP 12 ) of each of the curved cutting edges extends along an angle equal to or larger than 120° as seen in an end view of the cutting insert. 
 
     
     
       4. The cutting insert ( 118 ) according to  claim 1 , wherein:
 one extremity ( 136 ,  140 ) of any given curved cutting edge ( 132 ,  134 ) is located further from a median plane (M) of the cutting insert than the other extremity ( 138 ,  142 ) of the given curved cutting edge, the median plane being located midway between the end surfaces. 
 
     
     
       5. A double-sided cutting insert ( 18 ,  118 ) for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces ( 28 ,  128 ) and a peripheral surface ( 26 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2, 3 and 4; 
 a peripheral cutting edge ( 66 ,  166 ) formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) merging with N straight cutting edges ( 44 ,  50 ;  144 ,  150 ) which extend between the curved cutting edges at extremities thereof; wherein: 
 the curved cutting edges of the two end surfaces are not aligned, as seen in an end view of the cutting insert; and 
 each of the N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) extends along an angle equal to or larger than 120°, as seen along the first axis of symmetry (B). 
 
     
     
       6. The cutting insert ( 18 ) according to  claim 1 , wherein:
 the curved cutting edges ( 32 ,  34 ) associated with one of the end surfaces ( 28 ) are located in a first reference plane (P 1 ) and the curved cutting edges ( 32 ′,  34 ′) associated with the other end surface are located in a second reference plane (P 2 ), 
 the first and second reference planes being parallel to each other and located equidistant from and on either side of a median plane (M) of the cutting insert, the median plane being located midway between the end surfaces. 
 
     
     
       7. The cutting insert ( 18 ,  118 ) according to  claim 1 , wherein:
 the two end surfaces ( 28 ,  128 ) are identical. 
 
     
     
       8. The cutting insert according to  claim 7 , wherein:
 a major angular portion (MP 11 , MP 12 ) of each of the curved cutting edges extends along an angle equal to or larger than 120° as seen in an end view of the cutting insert. 
 
     
     
       9. The cutting insert ( 18 ,  118 ) according to  claim 8 , wherein:
 the first main cutting edge ( 32 ,  132 ) and the second main cutting edge ( 34 ,  134 ) follow a major first radius of curvature (MR 11 , MR 12 ) along the major angular portion (MP 11 , MP 12 ) thereof and a minor second radius of curvature (MR 21 , MR 22 ) along a minor angular portion (MP 21 , MP 22 ) thereof. 
 
     
     
       10. A double-sided cutting insert ( 18 ,  118 ) for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces ( 28 ,  128 ) and a peripheral surface ( 26 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2, 3 and 4 2 and 4; 
 a peripheral cutting edge ( 66 ,  166 ) formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) merging with N straight cutting edges ( 44 ,  50 ;  144 ,  150 ) which extend between the curved cutting edges at extremities thereof; wherein: 
 the curved cutting edges of the two end surfaces are not aligned, as seen in an end view of the cutting insert; 
 the cutting insert comprises a through bore ( 30 ), having a through bore axis (B) constituting the first axis of symmetry, that extends between the two end surfaces ( 28 ); and 
 the peripheral surface ( 26 ) comprises first ( 58 ), second ( 60 ), third ( 62 ) and fourth ( 64 ) pairs of side abutment surfaces, each pair of side abutment surfaces having 180° rotational symmetry around the through bore axis (B). 
 
     
     
       11. The cutting insert according to  claim 10 , wherein:
 a first end surface of the two opposing end surfaces ( 28 ,  128 ) constituting an upper surface ( 22 ,  122 ) defining a first reference plane (P 1 ), a second end surface of the two opposing end surfaces constituting a lower surface ( 24 ,  124 ) defining a second reference plane (P 2 ) parallel to the first reference plane; 
 the curved cutting edges comprise a first main cutting edge ( 32 ,  132 ) and a second main cutting edge ( 34 ,  134 ); 
 in an end view of the cutting insert the first main cutting edge ( 32 ,  132 ) has a first radius of curvature (R 1 ) with respect to a first cutting edge axis (A 1 ) and the second main cutting edge ( 34 ,  134 ) has a second radius of curvature (R 2 ) with respect to a second cutting edge axis (A 2 ), 
 the first cutting edge axis (A 1 ) and the second cutting edge axis (A 2 ) are parallel to the through bore axis (B) and located at opposite sides thereof; 
 the first cutting edge axis (A 1 ) is located a first distance (D 1 ) from the second main cutting edge ( 34 ,  134 ), the through bore axis (B) is located a second distance (D 2 ) from the second main cutting edge ( 34 ,  134 ), and the first distance (D 1 ) is smaller than the second distance (D 2 ). 
 
     
     
       12. The cutting insert ( 18 ,  118 ) according to  claim 11 , wherein:
 the cutting insert has 180° rotational symmetry around a second symmetry axis (S), the second symmetry axis lies on a median plane (M) between the first and the second reference planes (P 1 , P 2 ), and intersects the peripheral surface ( 26 ) at two median insert symmetry points ( 56 ); 
 each of the median insert symmetry points is formed at the intersection of a first reference line (L 1 ) with a second reference line (L 2 ), as seen in a first side view of the cutting insert that is perpendicular to a given secondary cutting edge; 
 the first reference line (L 1 ) connects the leading end ( 36 ,  136 ) of a first main cutting edge ( 32 ,  132 ) of a given end surface ( 28 ,  128 ) with the leading end ( 36 ,  136 ) of a first main cutting edge ( 32 ,  132 ) of an opposite end surface ( 28 ,  128 ); and 
 the second reference line (L 2 ) connects the trailing end ( 42 ,  142 ) of a second main cutting edge ( 34 ,  134 ) of a given end surface ( 28 ) with the trailing end ( 42 ,  142 ) of a second main cutting edge ( 34 ,  134 ) of an opposite end surface ( 28 ). 
 
     
     
       13. The cutting insert ( 18 ,  118 ) according to  claim 12 , wherein the first cutting edge axis (A 1 ) and the second cutting edge axis (A 2 ) are located at opposite sides of an imaginary plane (N) that is perpendicular to a symmetry plane (SP) that contains the first axis of symmetry (B) and the second symmetry axis (S). 
     
     
       14. The cutting insert ( 18 , 118 ) according to  claim 13 , wherein:
 each side abutment surface of the first pair of side abutment surfaces ( 58 ) converges towards each other in a direction toward the upper surface ( 22 ,  122 ); 
 each side abutment surface of the second pair of side abutment surfaces ( 60 ) converges towards each other in a direction toward the lower surface ( 24 ,  124 ); 
 each side abutment surface of the third pair of side abutment surfaces ( 62 ) converges towards each other in a direction toward the upper surface ( 22 ,  122 ); and 
 each side abutment surface of the fourth pair of side abutment surfaces ( 64 ) converges towards each other in a direction toward the lower surface ( 24 ,  124 ). 
 
     
     
       15. The cutting insert ( 18 ,  118 ) according to  claim 14 , wherein:
 the third pair of side abutment surfaces ( 62 ) has 180° rotational symmetry with the fourth pair of side abutment surfaces ( 64 ) around the symmetry axis (S). 
 
     
     
       16. The cutting insert ( 18 ,  118 ) according to  claim 15 , wherein:
 the first pair of side abutment surfaces ( 58 ) converge towards each other in a direction toward the upper surface ( 22 ,  122 ) as viewed in a cross-section taken in a first section plane (P 3 ), 
 the first section plane contains the through bore axis (B) and is obliquely disposed, as seen in an end view of the cutting insert, with respect to a symmetry plane (SP) containing the through bore axis (B) and the symmetry axis (S). 
 
     
     
       17. The cutting insert ( 18 ,  118 ) according to  claim 16 , wherein:
 the second pair of side abutment surfaces ( 60 ) converge towards each other in a direction toward the lower surface ( 24 ,  124 ) as viewed in a cross-section taken in a second section plane (P 4 ), 
 the second section plane (P 4 ) contains the through bore axis (B) and is obliquely disposed at a plane angle (φ), as seen in a top view of the cutting insert, with respect to the symmetry plane (SP) and with respect to the first section plane (P 3 ). 
 
     
     
       18. The cutting insert ( 18 ,  118 ) according to  claim 17 , wherein:
 the plane angle (φ) is 80°. 
 
     
     
       19. The cutting insert ( 18 ,  118 ) according to  claim 17 , wherein:
 the peripheral surface ( 26 ) forms with the first reference plane (P 1 ) and with the second reference plane (P 2 ) an obtuse first internal included angle (α), as seen in a first side view of the cutting insert that is perpendicular to a secondary cutting edge ( 44 ,  50 ,  144 ,  150 ); and 
 the peripheral surface ( 26 ) forms with the first reference plane (P 1 ) and with the second reference plane (P 2 ) an acute second internal included angle (β), as seen in a second side view of the cutting insert that is perpendicular to the first side view. 
 
     
     
       20. A cutting insert ( 218 ) for retention in a rotating cutting tool ( 10 ) having an axis of rotation (A), the cutting insert comprising:
 two opposing end surfaces ( 228 ) and a peripheral surface ( 226 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has 180° rotational symmetry; 
 a peripheral cutting edge ( 266 ) formed at the junction between a first end surface, constituting an upper surface ( 222 ), and the peripheral surface, the peripheral cutting edge comprising two curved cutting edges ( 232 ,  234 ) merging with two straight cutting edges which extend between the curved cutting edges at extremities thereof; 
 a continuously extending rake surface ( 268 ) extends inwardly from the peripheral cutting edge, the rake surface is slanted at a rake slant angle (λ) with respect to a second end surface, constituting a lower surface ( 224 ); 
 the upper surface comprises a rake inner extremity ( 92 ) at the innermost extremity of the rake surface and a bore upper end ( 96 ) at the uppermost end of a through bore ( 30 ) that extends between the end surfaces, a length between a given point ( 98 ) on the peripheral cutting edge and the rake inner extremity comprises a first rake length (H 1 ) and a length between the given point and the bore upper end comprises a second rake length (H 2 ), the first rake length and the second rake length taken in a plane parallel to the lower surface; wherein: 
 the rake slant angle is equal to or greater than 25°; 
 a rake extension ratio (E), defined as a ratio between the first rake length (H 1 ) and the second rake length (H 2 ), is smaller than 1 and equal to or greater than 0.8; and 
 a major angular portion (MP 11 , MP 12 ) of each of the curved cutting edges lies on a torus and extends along an angle equal to or larger than 120° as seen along the first axis of symmetry (B). 
 
     
     
       21. The cutting insert ( 218 ) according to  claim 20 , wherein the peripheral surface comprises:
 a first ( 258 ) pair of side abutment surfaces that converge towards each other in a direction toward the upper surface; and 
 a third ( 262 ) pair of side abutment surfaces that converge towards each other in a direction toward the upper surface. 
 
     
     
       22. A cutting tool ( 10 ) having a longitudinal axis of rotation (A) and comprising:
 a tool body ( 12 ) having at least one insert pocket ( 14 ) formed in a front end ( 16 ) of the tool body and a cutting insert ( 18 ,  118 ) retained in the at least one insert pocket, wherein: 
 the at least one insert pocket comprises:
 a pocket base abutment surface ( 74 ); 
 a threaded bore ( 76 ) extending tangentially rearwardly from the pocket base abutment surface; 
 pocket side walls ( 78 ) extending upwardly from the pocket base abutment surface and comprising a first pocket abutment surface ( 80 ) forming an acute first pocket internal angle (γ) with the pocket base abutment surface, and a second pocket abutment surface ( 82 ) forming an acute second pocket internal angle (δ) with the pocket base abutment surface, the first and second pocket abutment surfaces being spaced apart from one another; and 
 
 the cutting insert ( 18 ,  118 ) comprises:
 two opposing end surfaces ( 28 ,  128 ) and a peripheral surface ( 26 ) extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry for some value of N where N is a number from the group consisting of 2, 3 and 4; 
 a peripheral cutting edge ( 66 ,  166 ) formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges ( 32 ,  34 ;  132 ,  134 ) merging with N straight cutting edges ( 44 ,  50 ;  144 ,  150 ) which extend between the curved cutting edges at extremities thereof, wherein the curved cutting edges of the two end surfaces are not aligned, as seen in an end view of the cutting insert. 
 
 
     
     
       23. The cutting tool according to  claim 22 , wherein:
 the cutting insert further comprises first ( 58 ), second ( 60 ), third ( 62 ) and fourth ( 64 ) pairs of side abutment surfaces, each pair of the side abutment surfaces having 180° rotational symmetry around the through bore axis (B), wherein:
 the first pair of side abutment surfaces ( 58 ) converge towards each other in a direction toward the upper surface ( 22 ,  122 ), 
 the second pair of side abutment surfaces ( 60 ) converge towards each other in a direction toward the lower surface ( 24 ,  124 ), 
 the third pair of side abutment surfaces ( 62 ) converge towards each other in a direction toward the upper surface ( 22 ,  122 ), 
 the fourth pair of side abutment surfaces ( 64 ) converge towards each other in a direction toward the lower surface ( 24 ,  124 ), 
 the third pair has 180° rotational symmetry with the fourth pair around a second symmetry axis (S) that passes between the third pair and the fourth pair, 
 
 the upper surface defines a first reference plane (P 1 ) and the lower surface defines a second reference plane (P 2 ), the first and second reference planes are parallel to a median plane (M) that is located midway between the upper surface and the lower surface; 
 the peripheral surface ( 26 ) forms with the first reference plane (P 1 ) and with the second reference plane (P 2 ) an obtuse first internal included angle (a), as seen in a first side view of the cutting insert that is perpendicular to a given secondary cutting edge; 
 the peripheral surface ( 26 ) forms with the first reference plane (P 1 ) and with the second reference plane (P 2 ) an acute second internal included angle (β), as seen in a second side view of the cutting insert that is perpendicular to the first side view: 
 the upper surface ( 22 ,  122 ) is provided with a planar upper central abutment surface ( 70 ,  170 ), constituting an insert upper base abutment surface, that extends inwardly from an associated rake surface ( 68 ,  168 ) toward the through bore ( 30 ); and 
 the lower surface ( 24 ,  124 ) is provided with a planar lower central abutment surface ( 72 ), constituting an insert lower base abutment surface, that extends inwardly from the associated rake surface ( 68 ,  168 ) toward the through bore ( 30 ); 
 wherein, in a retained position of the cutting insert ( 18 ,  118 ):
 the insert lower base abutment surface ( 72 ) abuts the pocket base abutment surface ( 74 ); 
 one abutment surface of the insert first pair of side abutment surfaces ( 58 ) abuts the first pocket abutment surface ( 80 ); 
 one abutment surface of the insert third pair of side abutment surfaces ( 62 ) abuts the second pocket abutment surface ( 82 ); and 
 a clamping screw ( 20 ) passes through the through bore ( 30 ) of the cutting insert and threadingly engages the threaded bore ( 76 ) of the insert pocket. 
 
 
     
     
       24. The cutting tool ( 10 ) according to  claim 23 , wherein:
 the at least one insert pocket ( 14 ) is provided with a pocket abutment relief surface ( 84 ) that is located above the second pocket abutment surface ( 82 ), the pocket abutment relief surface being relieved from the adjacent abutment surface of the insert fourth pair of side abutment surfaces ( 64 ) in a retained position of the cutting insert. 
 
     
     
       25. The cutting tool ( 10 ) according to  claim 22 , wherein:
 the cutting insert ( 18 ,  118 ) is four times indexable within the at least one insert pocket ( 14 ). 
 
     
     
       26. The cutting tool ( 10 ) according to  claim 22 , wherein:
 the first pocket abutment surface ( 80 ) forms with the second pocket abutment surface ( 82 ) an acute pocket angle (θ) as seen in a top view of the at least one insert pocket ( 14 ). 
 
     
     
       27. The cutting tool ( 10 ) according to  claim 22 , wherein:
 the at least one insert pocket ( 14 ) is provided with a pocket relief channel ( 86 ) located between the pocket side walls ( 78 ) and the pocket base abutment surface ( 74 ). 
 
     
     
       28. A double-sided cutting insert for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces and a peripheral surface extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2 and 4;   a peripheral cutting edge formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges merging with N straight cutting edges which extend between the curved cutting edges at extremities thereof; wherein:   the curved cutting edges of the two end surfaces are not aligned, in a direction along the first axis of symmetry (B);   the cutting insert comprises a through bore, having a through bore axis (B) constituting the first axis of symmetry, that extends between the two end surfaces; and   the peripheral surface comprises first, second, third and fourth pairs of side abutment surfaces, each pair of side abutment surfaces having 180° rotational symmetry around the through bore axis (B).    
     
     
       29. The cutting insert according to claim 28, wherein:
 in a top view of the cutting insert, the curved cutting edges are longer than the straight cutting edges.    
     
     
       30. The cutting insert according to claim 29, wherein:
 N=4 and the cutting insert has eight curved cutting edges.    
     
     
       31. The cutting insert according to claim 29, wherein:
 one extremity of any given curved cutting edge is located further from a median plane of the cutting insert than the other extremity of the given curved cutting edge, the median plane being located midway between the end surfaces.    
     
     
       32. The cutting insert according to claim 31, wherein:
 the curved cutting edges associated with one of the end surfaces define a first reference plane and the curved cutting edges associated with the other end surface define a second reference plane, with the entire cutting insert being located between the first reference plane and the second reference plane; and   the first and second reference planes are parallel to each other and located equidistant from and on either side of the median plane of the cutting insert.    
     
     
       33. The cutting insert according to claim 32, wherein:
 at each end surface, the N curved cutting edges and the N straight cutting edges form a continuously extending peripheral cutting edge that is associated with a rake surface that extends continuously along the entire circumference of that end surface;   the rake surface merges with a central abutment surface; and   the entire central abutment surface is located closer to the median plane than the reference plane associated with that end surface.    
     
     
       34. The cutting insert according to claim 33, wherein:
 at said each end surface, the rake surface merges with the upper central abutment surface through an undercut.    
     
     
       35. The cutting insert according to claim 32, wherein:
 the cutting insert has 180° rotational symmetry around a second symmetry axis (S), the second symmetry axis lies on the median plane between the first and the second reference planes and intersects the peripheral surface at two median insert symmetry points.    
     
     
       36. The cutting insert according to claim 29, wherein:
 the curved cutting edges associated with one of the end surfaces are located in a first reference plane and the curved cutting edges associated with the other end surface are located in a second reference plane, with the entire cutting insert being located between the first reference plane and the second reference plane; and   the first and second reference planes are parallel to each other and located equidistant from and on either side of a median plane of the cutting insert, the median plane being located midway between the end surfaces.    
     
     
       37. The cutting insert according to claim 36, wherein:
 at each end surface, the N curved cutting edges and the N straight cutting edges form a continuously extending peripheral cutting edge that is associated with a rake surface that extends continuously along the entire circumference of that end surface;   the rake surface merges with a central abutment surface; and   the entire central abutment surface is located closer to the median plane than the reference plane associated with that end surface.    
     
     
       38. The cutting insert according to claim 37, wherein:
 at said each end surface, the rake surface merges with the upper central abutment surface through an undercut.    
     
     
       39. The cutting insert according to claim 36, wherein:
 the cutting insert has 180° rotational symmetry around a second symmetry axis (S), the second symmetry axis lies on the median plane between the first and the second reference planes and intersects the peripheral surface at two median insert symmetry points.    
     
     
       40. A cutting tool having a longitudinal axis of rotation (A) and comprising:
 a tool body having at least one insert pocket formed in a front end of the tool body and a cutting insert in accordance with claim 28 retained in the at least one insert pocket, wherein:   the at least one insert pocket comprises:
 a pocket base abutment surface; and 
 a threaded bore extending tangentially rearwardly from the pocket base abutment surface.  
   
     
     
       41. The cutting insert according to claim 28, wherein:
 a section plane containing the through bore axis (B) and any point on any one of the straight cutting edges intersects an adjacent side abutment surface which slopes inwardly with respect to the through bore axis (B), in an axial direction away from an associated end surface and towards the opposite end surface.    
     
     
       42. A double-sided cutting insert for retention in a rotating cutting tool having an axis of rotation, the cutting insert comprising:
 two opposing end surfaces and a peripheral surface extending therebetween, each end surface having a mutual first axis of symmetry (B) passing through the end surfaces about which each end surface has N-fold rotational symmetry, where N is a number from the group consisting of 2 and 4;   a peripheral cutting edge formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge comprising N curved cutting edges merging with N straight cutting edges which extend between the curved cutting edges at extremities thereof; wherein:   in a top view of the cutting insert, the curved cutting edges are longer than the straight cutting edges;   a median plane of the cutting insert is located midway between the end surfaces;   one extremity of any given curved cutting edge is located further from the median plane than the other extremity of the given curved cutting edge;   the cutting insert comprises a through bore, having a through bore axis (B) constituting the first axis of symmetry, that extends between the two end surfaces; and   the peripheral surface comprises first, second, third and fourth pairs of side abutment surfaces, each pair of side abutment surfaces having 180° rotational symmetry around the through bore axis (B).    
     
     
       43. The cutting insert according to claim 42, wherein:
 N=4 and the cutting insert has eight curved cutting edges.    
     
     
       44. The cutting insert according to claim 42, wherein:
 the curved cutting edges associated with one of the end surfaces define a first reference plane and the curved cutting edges associated with the other end surface define a second reference plane, with the entire cutting insert being located between the first reference plane and the second reference plane; and   the first and second reference planes are parallel to each other and located equidistant from and on either side of the median plane of the cutting insert.    
     
     
       45. The cutting insert according to claim 44, wherein:
 at each end surface, the N curved cutting edges and the N straight cutting edges form a continuously extending peripheral cutting edge that is associated with a rake surface that extends continuously along the entire circumference of that end surface;   the rake surface merges with a central abutment surface; and   the entire central abutment surface is located closer to the median plane than the reference plane associated with that end surface.    
     
     
       46. The cutting insert according to claim 45, wherein:
 at said each end surface, the rake surface merges with the upper central abutment surface through an undercut.    
     
     
       47. The cutting insert according to claim 42, wherein:
 the cutting insert has 180° rotational symmetry around a second symmetry axis (S), the second symmetry axis lies on the median plane between the first and the second reference planes and intersects the peripheral surface at two median insert symmetry points.    
     
     
       48. The cutting insert according to claim 42, wherein:
 a section plane containing the through bore axis (B) and any point on any one of the straight cutting edges intersects an adjacent side abutment surface which slopes inwardly with respect to the through bore axis (B), in an axial direction away from an associated end surface and towards the opposite end surface.