Title of Invention: Method For Operating Continuous Casting Machine Technical Field [0001] This invention relates to a method for operating a continuous casting machine used for continuous casting, and specifically, related to a method for operating a continuous casting machine of oscillating a rnold. Background Art [0002] Continuous casting of steel is carried out in such a way that: molten steel is poured from a ladle via a tundish into a mold; and after a solidified shell forms in the mold, a slab including an unsolidif,ied area is withdrawn downward underneath the mold. 'When a continuous casting machine is operated, especially when molten steel is cast at high speed, there is a case where part of the solidified shell is constrained from being withdrawn by stick on an inner wall of the mold and this constrained part functions as a hindrance to fonnation of a normal solidified shell. kr this case, not only various faults but also breakout might occur in products. [0003] Conventionally, powder to be put into molten steel in a mold is selected to deal with this problem. Molten powder floats and spreads over the surface of the molten steel, is supplied to a space between the mold and the solidified shell, and functions as a lubricant reducing frictional force between them. Whereby, stick of the solidified shell on the inner wall of the mold can be suppressed in some degree. [0004] However, in recent years, operation of continuous casting has been applied for various kinds of steel grades, and carried out under various casting conditions. 10 15 20 10 Therefore, there is a limit if physical properties of powder are changed to deal with such various situations. Thus, such-a method is tried that a mold is oscillated at the same time when powder is put. Proper oscillation of the mold makes it possible to suppress stick in the mold. [0005] Patent Literature 1 discloses applying, to a casting mold, vertical oscillation, having a deviated sine waveform that is deviated from a sine waveform. Patent Literature I gives the following formula (X) as a specific deviated sine waveform: Z: a1sin}nft r a2sin4nfr. * a3sin6nft + ... (X) where Z is displacement of the mold (mm), à1, ã2, ã3, ... àrÈ arnplitude (mm), f is oscillation frequency of the mold (cycles/s) and t is time(s). [0006] According to Patent Literature 1, oscillation having the waveform represented by the above formula (X) is controlled so that: (i) the maximum descending speed of the mold during negative strip time is fast; (ii) the maximum ascending speed of the mold during positive strip time is slow; (iii) the negative strip time is short; and (iv) the positive strip time is long, compared to the case where the oscillation waveform is a sine wave. [0007] The negative strip time is time when the descending speed of the mold is faster than the withdrawal rate of an unsolidified slab. The positive strip time is time when the speed of the mold is slower than the withdrawal rate of the unsolidified slab. According to Patent Literature 1, meeting the requirements of the above (i) to (iv) makes it possible to increase the inflow of molten powder into a space between the mold and the solidified shell and to suppress occurrence of breakout. 15 20. 25 ffii [0008] Howeve¡ in the method of Patent Literature 1, the movement of the mold suddenly changes from the ascent to the descent upon the oscillation of the mold. At this time, molten powder adhered in the vicinity of meniscus in the mold and unmolten powder are involved in molten steel. Whereby, the surface quality of a slab deteriorates and/or troubles on the operation occur depending on a type ofpowder used. t0009] Conventionally, an oscillator including an electric motor and an eccentric cam is used for oscillating a mold. A desired oscillation wavefonn is obtained according to a shape of an eccentric cam. In this case, an eccentric cam coresponding to an oscillation waveform has to be prepared for changing the oscillation wavefonn. In recent years, an electro-hydraulic oscillator has been used for oscillating a mold, which has made it easy to change parameters when a rnold is oscillated with complex waveforms as disclosed in Patent Literature 1 and Patent Literature 2 below. t0010] Patent Literature 2 discloses the method for operating a continuous casting machine comprising vertically vibrating a mold with the waveform expressed by the formula (Y) below: Z: A(sinZnft + bcos4ruft + c) ... (Y) where Z is displacement of the mold (mm), Ais Il2 of a vibration stroke S of the mold (mm); b is strain constant, c is strain constant, f is vibration frequency of the mold (Hzl60) and t is time (s). [0011] According to Patent Literature 2, employment of such a vibration waveform makes it possible that abrupt change in the mold frorr an ascent to a descent does not occur, and molten and unmolten powder are not involved in molten steel. [0012] When such a vibration waveform is employed, a neutral position of the oscillation shifts to either upper or lower side. In this case, symmetry of the oscillation is secured in vertical type continuous casting, in which a path where an unsolidified slab 10 15 20 25 travels in a mold is in a perpendicular direction. On the contrary, in curved type continuous c,asting, in which u p:rh where an unsolidified slab travels in a rnold curves, symmetry of oscillation is broken, and such a problem tends to be arose like poor lubrication in the mold and involvement of powder into molten steel. [0013] If the above vibration waveform in Patent Literature 2 is employed, the displacement Z atlhetime t: 0 is not 0 but SC/2. h this case, a mold cannot oscillate with a predetermined oscillation waveform at the start of operation of an oscillator that oscillates the mold, and the mold is displaced step by step as time passes, for example. This disables a dummy bar, which seals an opening in the bottom side of the mold at the start of casting, to seal an opening enough, and molten steel might leak out of the mold. Citation List Patent Literature [0014] Patent Literature 1: Japanese Examined Patent Application Publication No. 15 H4-79744 Patent Literature 2: Japanese Patent No. 3651447 Summary of Invention Technical Problem t00151 An object of this invention is to provide a method for operating a continuous casting machine with which poor lubrication and involvement of powder into molten steel due to the above problems of the prior arts, especially due to the shift of a neutral position in curved type continuous castingcan be prevented. Another object of this invention is to provide a method for operating a continuous casting machine with which troubles at the initial stage of casting (like seal 10 20 i-. ¡*. i: ii: 25 leakage) can be prevented, and with which a mold can oscillate with a predetermined oscillation waveform since the start of operation of an oscillator. Solution to Problem [0016] Tlre essentials of this invention include the following method for operating a continuous casting machine: A method for operating a continuous casting machine where withdrawn from a mold for continuous casting while the mold is oscillated in direction, the method comprising: oscillating the mold so as to satisfy the following formula (2) oscillation waveforrn represented by the following formula (l): r(t) : (S/2){sin(cot + q) + bcos2(ot + q) + b} ... (l) [Math. 1] a slab is a vertical with an / = ttan-'{ wherein r(t) is displacement of the mold (mm), S is an oscillation stroke of the mold S (mrn), rrr is angular velocity (: 2nÐ (rad/s), f is oscillation frequency of the mold (Hz), t is time (s),

0) ... (4) 100291 Since lsingl < 1, the following formula (5) is obtained if sing is made ro be the subject of the formula (4): sing: {1 - (1 + t6ú>u2}/4b ... (5) [0030] If g is made to be the subject of the formula (5) using the formulae of a trigonometlic function, tang = sing/cosrp and cosg = +(1 - .irrq)trr, the above formula (2) is obtained. [0031] That is, satisfaction of the formula (2) makes the displacement of the mold r(0) 0 when the time t : 0. Therefore, it becomes possible to oscillate the mold with a predetermined oscillation waveform since the start of operation of the oscillator that oscillates the rnold, and to well seal the opening of the mold with a dummy bar. [0032] Two values of g are determined by the formula (2). If a direction of the rnovement of the mold at the start of oscillation is upward, rp that satisfies cosq > 0 may be employed since dr(O)/dt > O. [0033] A non-sine coeffrcient b is any value within the range of 0 < b s 0.25. "b" is a coefücient of cos2(cot + p) in the term of bcos2(ot + g), and determines magnitude of the term of bcos2(rrit + rp) to the term of sin(cot + g). Ír a case of 0.25 < b, the term of bcos Z(at +p) is too large compared to the term of sin(ot + tp), whiclr arises a problem that the mold descends when r¡t + g: n(llT+ 2n) (n is 0 or a positive integer), where the mold should ascend most. Thus, b < 0.25. For your reference, Fig. 2 shows the waveforms when b : 0.4 and the initial phase e : 33.66". As shown in Fig. 2,inthe case of b:0.4 that satisf,res 0.25 < b, the mold descends when cot + q : n(112 + 2n) (n is 0 or a positive integer), where the mold should ascend most. Therefore, in this invention, b < 0.25. [0034] On the other hand when b is 0, the waveform of the displacement of the 10 20 Í li t 25 l0 -F¿FSirffi""" ' ;i ii; iÌ mold r(t) shows simple harmonic motion. In this case, compared with the case of 0 < b, the inflow of the molten powder into a space between the mold and the solidified shell caffiot be increased. Thus, in this invention,0 < b. Preferably 0.15 < b in this invention in order to increase the inflow of the molten powder enough compared with the case of the simple harmonic motion. [0035] Table 1 shows values of the initial phase tp determined by the formula (2) in each case where the non-sine coefficient b is 0.15,0.20 and 0.25. It makes r(0): g possible that a value of the initial phase rp that satisfies the formula (2) is employed according to a value of the non-sine coeffrcient b. [0036] fTable l] Non-sine Coefficient (b) o.15 0.20 0.2s Initial Phase (p) 16.08 20.535 24.46 [0037] Figs. 3 to 5 show waveforms based on the formula (1) (relation between the time t and the displacement of the mold r(t)) when the combination shown in Table 1, thatis,(b:0.15,abs(z1 )>abs(z2), and the pair of first and/or second back contact surfaces (130a,b; 140a,b) extends between the points (x1 , z1 ) and (x2, z2), wherein abs(z3)-abs(z1 )> 0.03 x Wl. 21. A tooth in accordance with claim 20, wherein abs(z3)-abs(z1 ) <0.6 x W. 22. A tooth in accordance with any one of the previous claims, wherein, in the front portion, the first and/or second inner wall (106, 107) comprises a pair of essentially planar first and/or second front contact surfaces (1 10a,b, 120a, b), being symmetrical about, and facing away from, the plane spanned by the Z and Y axes, so as to form an angle (delta, epsilon) with the plane spanned by the X and Y axes being less than 35 degrees. 23. A tooth in accordance with claim 22, wherein the angle delta and/or the angle epsilon less than 25 degrees, preferably 10 to 20 degrees, preferably 12 to 17 degrees, most preferred about 15 degrees, preferably the angle delta is substantially equal to the angle beta, and the angle epsilon is substantially equal to the angle gamma. 24. A tooth in accordance with any one of the claims 22-23, wherein, in the front portion, there is at least a divided portion wherein at least one, preferably both, of the pairs of first and second front contact surfaces (1 10a, b; 120a, b) is separated by a first or second front divider region (1 12, 122) where the inner first or second wall (106,107) extend beyond the pair of first or second front contact surfaces (1 10a, b; 120a, b) in the Z direction away from the XY plane. 25. A tooth in accordance with any one of the claims 22-24, wherein, in the front portion, there is at least an interconnected portion wherein at least one, preferably both, of the pairs of first or second front contact surfaces (1 10a, b; 120a, b) are connected by a first or second front connecting region (1 13, 123) where the inner first/second wall (106,107) extends in the Z direction along or towards the plane spanned by the X and Y axes. 26. A tooth in accordance with claims 24 and 25, wherein said connected portion is located closer to the bottom end (105) of the cavity than said divided portion. 27. A tooth in accordance with any one of the previous claims, wherein the second inner wall (107) of the stepped portion forms a slope (160a,b) approaching the plane spanned by the X and Y axes while extending towards the bottom wall (105), interconnecting said second back contact surfaces (140a,b) and said second front contact surface (120a,b). 28. A tooth in accordance with any one of the previous claims, wherein, in the stepped portion, the first and/or second inner wall (106, 107) merges with the first and/or second back contact surfaces (130a, b, 140a,b), the first and/or second back divider region (132, 142), and with the first and/or second front contact surfaces (1 10a, b, 130 a,b), forming said slope(s) (150a,b, 160 a,b) at least between the first and/or second back contact surfaces (130a,b; 140 a,b) and the first and/or second front contact surfaces (1 10a, b, 120a,b). 29. A tooth in accordance with claim 28, wherein said slope (150a,b; 160 a,b) is curved, preferably forming an S-shape. 30. A tooth in accordance with any one of the preceding claims, wherein said first and/or second front and back contact surfaces (1 10a, b, 130a, b; 120a, b, 140a, b)), being connected by said slope (150a,b, 160a,b), are arranged such that, if they were interconnected by a straight line, such a line would from an angle of more than 10 degrees, preferably more than 20 degrees with the plane spanned by the X and Y axes. 31. A tooth in accordance with any one of the previous claims, wherein, in the stepped portion, the first and/or second inner wall (106, 107) forms a pair of sloping first surfaces (150a, b; 160a,b)), being symmetrical about the plane spanned by the Z and Y axes, extending between and merging with the first and/or second back contact surfaces (130a, b) and the corresponding first and/or second front contact surfaces (1 10 a, b). 32. A tooth in accordance with claim 30 and claim 24, wherein, in the stepped portion, the first and/or second inner wall (106, 107) forms an intermediate divider region (152; 162), extending between the intermediate first or second back surfaces (150a,b, 160a,b), and moreover extending between and merging with the first or second back divider region (132,142) and the first or second front divider region (1 12, 122). 33. A tooth in accordance with any one of the claims 27 to 32, wherein first and/or second the back divider region (132, 142), and the corresponding intermediate divider region (152, 162) , form a continuous divider region, the maximum extension of which in the Z direction away from the XY plane is diminishing from a maximum adjacent the open end (104) of the cavity along the Y axis towards the bottom end of the cavity (105). 34. A tooth in accordance with any one of the previous claims, wherein, at least in the back portion, the opposing side surfaces (108) comprises opposing, essentially planar, back side contact surfaces (170a,b) and, at least in the front portion, the opposing side surfaces (108) comprises opposing, essentially planar front side contact surfaces (180a,b), the back side contact surfaces (170a,b) and the front side contact surfaces (180a,b) being located in different planes. 35. A tooth in accordance with claim 34, wherein the entire front side contact surfaces (180a,b) are located closer to the plane spanned by the Z and Y axes than the entire back side contact surfaces (170a,b). 36. A tooth in accordance with claim 34 or 35, wherein the opposing front side contact surfaces (180a,b) extend substantially from the bottom end (105) of the cavity. 37. A tooth in accordance with any one of the claims 34 to 36, wherein the opposing back side contact surfaces (170a,b) extend at least from the plane spanned by the X and Z axes, in a direction towards the open end (105) of the cavity along the Y axis, over a distance r, preferably 2r, where r is the maximum radius of the through holes (109). 38. A tooth in accordance with any one of the claims 34 to 37, wherein the opposing back side contact surfaces (170a,b)) extend at least from the plane spanned by the X and Z axes, in a direction towards the bottom end (104) of the cavity along the Y axis, at least over a distance r, where r is the maximum radius of the through holes (109). 39. A tooth in accordance with any one of the claims 34 to 38, wherein the opposing side surfaces (108) defines opposing sloping side surfaces (190) interconnecting the opposing back side contact surfaces (170) and the front side contact surfaces (180) 40. A tooth in accordance with claim 39, wherein the sloping side surfaces (190) comprises curved surfaces. 41. A tooth in accordance with any one of the claims 34 to 40, wherein the pair of front side surfaces and the pair of back side surfaces form an angle with the plane spanned by the Y and Z axes being less than 5 degrees, preferably less than 2 degrees. 42. A tooth in accordance with any one of the claims 34 to 41 , wherein the back side contact surfaces (170a,b) extend over a distance in the direction of the Z axis corresponding to at least 3r, where r is the maximum radius of the through holes (109). 43. A tooth in accordance with any one of the previous claims, wherein the bottom end (104) of the cavity comprises an inner bottom wall. 44. A tooth in accordance with any one of the previous claims, wherein the angle alfa is between 0.5 and 5 degrees, most preferred between 1 and 3 degrees. 45. A tooth (1 ) in accordance with claim 20 or 21 , wherein at least one out of (x1 , abs(z1 )), (x2, abs(z2)), and (x3, abs(z3)) differs between the first inner wall (106) and the second inner wall (107). 46. An adaptor (2) for attachment of a tooth to the lip of a bucket of a working machine, such as an excavator or loader, the adaptor (2) comprising a connector portion (22) for arrangement to or at a bucket, and a nose portion (203) for arrangement in a corresponding cavity of a tooth (1 ), the nose portion (203) having a width in a horizontal direction (H), intended to extend along the lip of bucket, and having a length extending in a longitudinal direction (L) from a connector end (204) adjacent the connector portion (22) of the adaptor, to a free end (205), and having an outer wall (202), the outer wall (202) comprising a first outer wall (206) and an externally opposed second outer wall (207), and externally opposing side walls (208), interconnecting said first and second outer walls (206, 207), the nose portion (203) delimiting a through hole (209,) extending between said opposing side walls (208), for receiving a pin extending through the nose portion (203) for attachment of the tooth (1 ) to the adaptor (2), a first axis X being defined extending through the centre of through hole (209), a second axis Y extending along the nose portion (203) from the connector end (204) of the nose portion towards the free end (205) of the nose portion, and a third axis Z being orthogonal to said first and second axes X, Y, the three axes X, Y, Z thereby forming an orthogonal axes system, meeting at an origo, whereby each point of the outer wall (202) may be defined by Cartesian coordinates (x, y, z), characterised by the nose portion (203) defining a back portion (BP) extending along the Y axis, the back portion being at least partially located between the plane spanned by the X and Z axes and the connector end (204) of the nose portion, a front portion (FP) extending along the Y axis, the front portion being located between the plane spanned by the X and Z axes and the free end (205) of the nose portion (203); and a stepped portion (SP), interconnecting the back portion (BP) and the front portion (FP); in the back portion, the first and second outer walls (206, 207), each comprises a pair of essentially planar back contact surfaces (230a, b; 240a,b), each pair of back contact surfaces being symmetrical about, and facing towards, the plane spanned by the Z and Y axes, so as to form an angle (beta, gamma) with the plane spanned by the X and Y axes being less than 35 degrees, each pair of back contact surfaces (230a, b; 240 a,b) being separated by a back divider region (232, 242), extending beyond the pair of first contact surfaces (230a, b) in the Z direction away from the XY plane; in the front portion, the first and second outer wall (206, 207) each comprises the each comprises a pair of essentially planar front contact surfaces (210a,b, 220a, b), being symmetrical about the plane spanned by the Z and Y axes, all contact surfaces forming an angle (alfa) less than 5 degrees with the Y axis, as seen in any plane parallel to the plane spanned by the Z and Y axes, the first and/or second front contact surfaces (210a,b; 220a, b) being located closer to the plane spanned by the X and Y axes than the corresponding back contact surfaces (230a, b, 240 a,b), and in the stepped portion, the first and/or second outer wall (206, 207) forming a slope (250a, b) wherein at least a portion of the outer wall approaches the XY plane towards the bottom wall (205), interconnecting said first and/or second back contact surfaces (230a, b, 240a, b) and the corresponding first and/or second front contact surface (210a,b; 220a, b), wherein a first stepped distance (D1 ) along the Z axis is bridged by the first outer wall (206) along the stepped portion (SP), between the first back contact surfaces and the first front contact surfaces; and wherein a second stepped distance (D2) along the Z axis is bridged by the second outer wall (207) along the stepped portion (SP), between the second back contact surfaces and the second front contact surfaces; wherein 0<=D2<=0.80 D1. 47. An adaptor in accordance with claim 46, wherein the angle (beta, gamma) is less than 25 degrees, preferably 10 to 20 degrees, preferably 12 to 17 degrees, most preferred about 15 degrees. 48. An adaptor in accordance with claim any one of the claims 46 to 47, wherein the angle gamma of the second outer wall (207) is less than the angle beta of the first outer wall (206), preferably gamma is 5 to 15 degrees and beta is 10 to 20 degrees. 49. An adaptor in accordance with any one of claims 46 to 48, wherein the pairs of first and/or second back contact surfaces (230a, b; 240 a, b) extend substantially from the opposing side walls (208), and preferably substantially to the respective back divider region (232, 242). 50. An adaptor in accordance with any one of the claims 46 to 49, wherein the back portion, comprising the first and second back contact surfaces (230a, b; 240a, b) extends at least from the plane spanned by the Z and X axes, and over a distance along the Y axis, in a direction towards the connector end (204), corresponding to at least the greatest radius (r) of the opposing through hole (209), preferably at least 2r. 51. An adaptor in accordance with any one of the claims 46 to 50, wherein the back portion, comprising the first and second back contact surfaces (230a, b; 240a, b) extends also in front of the plane spanned by the Z and X axes and preferably over a distance along the Y axis, in a direction towards the free end 205, corresponding to at least the greatest radius (r) of the through hole (209). 52. An adaptor in accordance with any one of the claims 46 to 51 , wherein each one out of the pair of the first and/or second back contact surfaces (230a, b; 240a, b) extends at least over a distance along the X axis of 0.2 x Wl, where Wl is the extension of the first/second outer wall (206, 207) along the X axis. 53. An adaptor in accordance with any one of the claims 46 to 52, wherein, throughout a majority of the back portion, the extension along the X axis of the first back contact surfaces (230a, b) is less than the extension along the X axis of the opposing second back contact surfaces (240a, b). 54. An adaptor in accordance with any one of the claims 46 to 53, wherein the first and/or second back divider region (232, 242) comprises a pair of divider side surfaces (234, 244), being symmetrical about, and facing away from, the ZY plane. 55. An adaptor in accordance with claim 54, wherein the pair of divider side surfaces (234, 244) of the first and/or second back divider region (232, 242) extend substantially from the first and/or second back contact surfaces (230a, b, 240a, b), respectively. 56. An adaptor in accordance with claim 55, wherein the extension of the first and/or second back divider region (232, 242) in the Z direction away from the XY plane is determined by the extension of the corresponding pair of divider side surfaces (234, 244) in said direction. 57. An adaptor in accordance with any one of the claims 54 to 56, wherein, through a majority of the back portion of the nose portion, the extension of the first back divider region (232) in the Z direction away from the XY plane is greater than the extension of the second back divider region (242) in the Z direction away from the XY plane. 58. An adaptor in accordance with any one of the claims 46 to 57, wherein the extension of the first and/or second back divider region (232, 242) in the Z direction away from the XY plane has a maximum adjacent the connector end (204) of the nose portion and is diminishing along the Y axis towards the free end of the nose portion (205). 59. An adaptor in accordance with any one of the claims 54 to 58, wherein, for the first and/or second back divider region, each one of the pair of divider side surfaces (234, 244) comprises a steeper region (234', 244') wherein a tangent to the side surface in the XZ plane forms an angle of more than 45 degrees with the X axis, followed by a flatter region (234'. 244"') wherein a tangent to the side surface in the XZ plane forms an angle of less than 45 degrees with the X axis. 60. An adaptor in accordance with claim 59, wherein said steeper region (234', 244') of each one of the pair of divider side surfaces (234, 244) has a greater extension along the Z axis than along the X axis. 61. An adaptor in accordance with claim 59,60, wherein, for the first and/or second back divider region, along a majority of the steeper region's (234', 234') length along the X axis, a tangent to the side surface in the XZ plane forms an angle of more than 45 degrees and less than 80 degrees with the X axis towards the Z axis. 62. An adaptor in accordance with any one of the claims 59 to 61 , wherein, for the first and/or second back divider region, along a majority of the flatter region's (234", 244") length along the X axis, a tangent to the divider side surface in the XZ plane forms an angle of less the 5 degrees with the X axis towards the Z axis. 63. An adaptor in accordance with any one of the claims 54 to 62, wherein, for the first and/or second back divider region, a pair of essentially planar secondary first and/or second back contact surfaces (236a, b; 246a, b), extend from the divider side surfaces towards the YZ plane, the secondary first/second back contact surfaces (236a, b; 246a, b) being symmetrical about, and facing towards, the plane spanned by the Z and Y axes, so as to form an angle (eta, theta) with the plane spanned by the X and Y axes being less than 35 degrees. 64. An adaptor in accordance with claim 63, wherein the essentially planar secondary first/second back contact surfaces (236a, b; 246a, b) are substantially parallel to the respective first/second back contact surfaces (230a, b; 240 a, b). 65. An adaptor in accordance with any one of the claims 46 to 64, wherein, in the back portion, the first and/or second outer wall (206, 207) displays a contour formed by points (x, z), the contour being symmetrical about the Z axis and having a width Wl along the X axis, the contour being defined by the following: in peripheral portions at abs(x) greater than or equal to 0.9 x WI/2, a first maximum abs(z) is defined in a pair of points (x1 , z1 ), for abs(x) less than abs(x1 ): abs(z) is diminishing until a minimum abs (z) is defined at a pair of points (x2, z2), and for abs(x) less than abs(x2): abs(z) is increasing until a maximum abs(z) is defined at a pair of points (x3, z3), wherein abs(z3)>abs(z1 )>abs(z2), and the pair of first and/or second back contact surfaces (130a,b; 140a,b) extends between the points (x1 , z1 ) and (x2, z2), wherein abs(z3)-abs(z1 )> 0.03 x Wl. 66. An adaptor in accordance with claim 65, wherein abs(z3)-abs(z1 ) <0.6 x Wl. 67. An adaptor in accordance with any one of the claims 46 to 66, wherein, in the front portion, the first and/or second outer wall (206,207) comprises a pair of essentially planar first and/or second front contact surfaces (210a, b, 220a, b)) , being symmetrical about, and facing towards, the plane spanned by the Z and Y axes, so as to form an angle (delta) with the plane spanned by the X and Y axes being less than 35 degrees. 68. An adaptor in accordance with any one of the claims 46 to 67, wherein, in the front portion region (FP), the second outer wall (207) comprises a pair of essentially planar second front contact surfaces (220a, b), being symmetrical about, and facing away from, the plane spanned by the Z and Y axes, so as to form an angle (epsilon) with the plane spanned by the X and Y axes being less than 35 degrees. 69. An adaptor in accordance with claim 67 or 68, wherein the angle delta and/or the angle epsilon is less than 25 degrees, preferably 10 to 20 degrees, preferably 12 to 17 degrees, most preferred about 15 degrees, preferably the angle delta = angle beta, and angle epsilon= angle gamma. 70. An adaptor in accordance with any one of the claims 68-69, wherein, in the front portion, there is at least a divided portion wherein at least one, preferably both, of the pair of first and second front contact surfaces (210a, b; 220a, b) is separated by a first or second front divider region (212, 222) where the outer first or second wall (206,207) extends beyond the pair of first or second front contact surfaces (210a, b; 220a, b) in the Z direction away from the XY plane. 71. An adaptor in accordance with any one of the claims 68-70, wherein, in the front portion, there is at least an interconnected portion wherein at least one, preferably both, of the pairs of first or second front contact surfaces (210a, b; 220a, b) are connected by a first or second front connecting region (213, 223) where the outer first/second wall (206,207) extend in the Z direction along or towards the XY plane. 72. An adaptor in accordance with claims 70 and 71 , wherein said connected portion is located closer to the free end (205) of the nose portion than said divided portion. 73. An adaptor in accordance with any one of the claims 46 to 72 wherein the second outer wall (207) in the stepped portion forms a slope (260a, b) approaching the plane spanned by the X and Y axes while extending towards the free end (205), interconnecting said second back contact surfaces (240a, b) and said second front contact surface (220a, b). 74. An adaptor in accordance with any one of the claims 46 to 73, wherein, in the stepped portion, the first and/or second outer wall (206, 207) merges with the first and/or second back contact surfaces (230a, b, 240a, b), the first and/or second back divider region (232,242), and with the first and/or second front contact surfaces (210a, b, 230a, b)), forming said slope(s) (250a, b, 260a, b) at least between the first and/or second back contact surfaces(230a,b; 240a, b) and the first and/or second front contact surfaces (210a, b, 220a, b). 75. An adaptor in accordance with claim 74, wherein said slope is curved, preferably forming an S-shape. 76. An adaptor in accordance with any one of the claims 46 to 75, wherein said first front and back contact surfaces (210a,b, 230a, b; 220a, b; 240 a,b), being connected by said slope(250a,b; 260a, b) , are arranged such that, if they were interconnected by a straight line, such a line would from an angle of more than 10 degrees, preferably more than 20 degrees with the plane spanned by the X and Y axes. 77. An adaptor in accordance with any one of claims 46 to 76, wherein, in the stepped portion, the first and/or second outer wall (206, 207) forms a pair of sloping first surfaces (250a, b; 260 a,b), being symmetrical about the plane spanned by the Z and Y axes, extending between and merging with the first and/or second back contact surfaces (230a, b; 240 a,b) and the corresponding first and/or second front contact surfaces (210 a, b, 220 a,b). 78. An adaptor in accordance with claim 76 and claim 70, wherein, in the stepped portion, the first and/or second outer wall (206, 207) forms an intermediate divider region (252; 262), extending between the first or second sloping back surfaces (250a, b), and moreover extending between and merging with the first or second back divider region (232, 242) and the first or second front divider region (212,222) 79. An adaptor in accordance with any one of the claims 73 to 78, wherein the first and/or second back divider region (232, 142), and the corresponding intermediate divider region (252,262) , form a continuous divider region, the maximum extension of which in the Z direction away from the XY plane is diminishing from a maximum adjacent the connector end (204) of the nose portion along the Y axis towards the free end of the nose portion (205). 80. An adaptor in accordance with any one of the claims 46 to 79, wherein, at least in the back portion, the opposing side surfaces (208) comprises opposing, essentially planar, back side contact surfaces (270a, b), and at least in the front portion, the opposing side surfaces (208) comprises opposing, essentially planar front side contact surfaces (280a, b), the back side contact surfaces (270a, b) and the front side contact surfaces (280a, b) being located in different planes. 81. An adaptor in accordance with claim 80, wherein the entire front side contact surfaces (280a, b) are located closer to the plane spanned by the Z and Y axes than the entire back side contact surfaces (270a, b). 82. An adaptor in accordance with claim 80 or 81 , wherein the opposing front side contact surfaces (280a, b) extend substantially from the free end (205) of the nose portion. 83. An adaptor in accordance with any one of the claims 80 to 82„ wherein the opposing back side contact surfaces (270a, b) extend at least from the plane spanned by the X and Z axes, in a direction towards the connector end (205) of the nose portion along the Y axis, over a distance r, preferably 2r, where r is the maximum radius of the throughhole (209). 84. An adaptor in accordance with any one of the claims 80 to 83, wherein the opposing back side contact surfaces (270a, b)) extend at least from the plane spanned by the X and Z axes, in a direction towards the free end (204) of the nose portion along the Y axis, at least over a distance r, where r is the maximum radius of the through holes (209). 85. An adaptor in accordance with any one of the claims 79 to 84, wherein the opposing side surfaces (208) defines opposing sloping side surfaces (290a, b) interconnecting the opposing back side contact surfaces (270a, b) and the front side contact surfaces (280a, b). 86. An adaptor in accordance with claim 85, wherein the sloping side surfaces (290a, b) comprises curved surfaces. 87. An adaptor in accordance with any one of the claims 79 to 86, wherein the pair of front side surfaces (280) and the pair of back side surfaces (270) form an angle with the YZ plane being less than 5 degrees, preferably less than 2 degrees. 88. An adaptor in accordance with any one of the claims 79 to 87, wherein the back side contact surfaces (270a, b) extend over a distance in the direction of the Z axis corresponding to at least 3 r, where r is the maximum radius of the through hole (209). 89. An adaptor in accordance with any one of the claims 46 to 88, wherein the free end (205) of the nose portion comprises an outer end wall. 90. An adaptor in accordance with any one of the claims 46 to 89, wherein the angle alfa is between 0.5 and 5 degrees, most preferred between 1 and 3 degrees. 91. An adaptor (2) in accordance with claim 65 or 66, wherein at least one out of (x1 , abs(z1 )), (x2, abs(z2)), and (x3, abs(z3)) differs between the first outer wall (206) and the second outer wall (207). 92. A tooth having a cavity designed so as to fit with an adaptor as described in any one of the claims 46 to 91. 93. A vehicle comprising a bucket to which an adaptor as described in any one of the claims 46 to 91 is arranged. 94. A bucket formed integrally with at least one adaptor in accordance with any one of the claims 46 to 91.