INTERFACE BETWEEN AN OUTER END OF A WING AND A MOVEABLE WING TIP DEVICE
20170355439 · 2017-12-14
Inventors
Cpc classification
Y02T50/10
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
B64C23/072
PERFORMING OPERATIONS; TRANSPORTING
B64C3/56
PERFORMING OPERATIONS; TRANSPORTING
B64F5/00
PERFORMING OPERATIONS; TRANSPORTING
International classification
B64C3/56
PERFORMING OPERATIONS; TRANSPORTING
F16J15/10
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
An aircraft (102) including a wing (101), having a fixed wing (105) with a wing tip device (103) moveably mounted at the outer end thereof. The wing tip device (103) is moveable between: a flight configuration; and a ground configuration. The wing tip device (103) and the fixed wing (105) are separated along an oblique primary cut plane (113). The wing tip device (103) and the fixed wing (105) meet along an interfacing cut line (135). The interfacing cut line (135) comprises a first length (137) offset from the primary cut plane (113) in a first direction; a second length (141) offset from the primary cut plane (113) in a second direction, opposite to the first direction; and a transition section (139) over which the interfacing cut line (135) transitions from the first length to the second length.
Claims
1. An aircraft comprising a wing, the wing having a fixed wing with a wing tip device moveably mounted at the outer end thereof, the wing tip device being moveable between: (a) a flight configuration for use during flight; and (b) a ground configuration for use during ground-based operations, in which ground configuration the wing tip device is moved away from the flight configuration such that the span of the aircraft wing is reduced, wherein the wing tip device and the fixed wing are separated along a primary cut plane, the primary cut plane being obliquely orientated, and the wing tip device being rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, and wherein when the wing tip device is in the flight configuration, the outer end of the fixed wing and the inner end of the wing tip device meet along an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, the interfacing cut line comprising: (i) a first length, formed by a cut through the outer surface, but offset from the primary cut plane in a first direction; (ii) a second length, formed by a cut through the outer surface but offset from the primary cut plane in a second direction, opposite to the first direction; and (iii) a transition section over which the interfacing cut line transitions from the first length to the second length.
2. The aircraft according to claim 1, wherein the interfacing cut line is arranged such that when the wing tip device rotates from the flight configuration to the ground configuration, the wing tip device contacts the fixed wing at a sliding contact along the transition section, but the wing tip device separates away from the fixed wing along the first length and second length.
3. The aircraft according to claim 2, wherein at least part of the transition section lies along a plane that is parallel to the primary cut plane, and the sliding contact occurs along that part of the transition section.
4. The aircraft according to claim 2, wherein the separating movement along the first and second lengths is in opposite directions.
5. The aircraft according to claim 1, wherein the first length is in a first plane that is parallel to the primary cut plane but offset from the primary cut plane in the first direction, and wherein the second length is in a second plane that is parallel to the primary cut plane but offset from the primary cut plane in the second direction.
6. The aircraft according to claim 1, wherein the wing comprises a sealing assembly for sealing between the fixed wing and the wing tip device when the wing tip device is in the flight configuration.
7. The aircraft according to claim 6, wherein the sealing assembly comprises a sliding seal for making/breaking a seal under a relative sliding action between the fixed wing and the wing tip device, and a compression seal for making/breaking a seal under a relative coming together/separation of the fixed wing and wing tip device, and wherein the sliding seal is associated with the transition section and the compression seal is associated with the first and second lengths.
8. The aircraft according to claim 6, wherein the wing comprises a first seal support structure, the first seal support structure being located below the outer surface of the wing and extending beyond the first length of the interfacing cut line and towards the primary cut plane, and the first seal support structure being located below the first length of the interfacing cut line, such that it under-laps the interfacing cut line.
9. The aircraft according to claim 8, wherein the wing comprises a second seal support structure, the second seal support structure being located below the outer surface of the wing and extending beyond the second length of the interfacing cut line and towards the primary cut plane, and the second seal support structure being located below the second length of the interfacing cut line, such that it under-laps the interfacing cut line.
10. The aircraft according to claim 8, wherein the first and/or second seal support surfaces extend substantially up to the primary cut plane.
11. The aircraft according to claim 8, wherein the seal support structure supports a compression seal that is compressed in the region of under-lap when the wing tip device is in the flight configuration.
12. The aircraft according to claim 9, wherein the outer end of the fixed wing terminates at an outer rib, and the inner end of the wing tip device terminates at an inner rib, such that when the wing tip device is in the flight configuration, the outer and inner ribs are located on opposing sides of the interface between the fixed wing and the wing tip device, and wherein the first seal support structure is part of the outer rib and the second seal support structure is part of the inner rib.
13. The aircraft according to claim 1, wherein the wing comprises an upper surface extending from the leading edge, over the wing, to the trailing edge, and the wing comprises a lower surface extending from the leading edge, under the wing, to the trailing edge, and wherein the first and second lengths are both along one of the upper surface or the lower surface of the wing.
14. The aircraft according to claim 1, wherein the interfacing cut line further comprises: (i) a third length, formed by cut through the outer surface but offset from the primary cut plane in the first direction; (ii) a fourth length, formed by a cut through the outer surface but offset from the primary cut plane in the second direction; and (iii) a further transition section over which the interfacing cut line transitions from the third length to the fourth length.
15. The aircraft according to claim 14, wherein the interfacing cut line comprises further transition sections between the first and third lengths, and the fourth and second lengths, such that the interfacing cut line is made up of the first to fourth lengths, each length transitioning into the adjacent length by a respective transition section.
16. The aircraft according to claim 14, wherein the third and fourth lengths are both along the other one of the upper surface or the lower surface of the wing.
17. The aircraft according to claim 1, wherein the first length is located aft of the axis of rotation and the second length is located fore of the axis of rotation.
18. The aircraft according to claim 17, wherein, the third length is located aft of the axis of rotation and the fourth length is located fore of the axis of rotation.
19. The aircraft according to claim 1, wherein the transition section comprises a first portion in a plane that is parallel to the primary cut plane, and a second portion at which the interfacing cut-line moves directly from that plane over to the second length of the interfacing cut line.
20. The aircraft according to claim 1, wherein the wing comprises an inspection panel associated with at least one transition section, through which the transition section may be accessed.
21. The aircraft according to claim 20, wherein the inspection panel comprises a moveable panel operable from a closed configuration in which it forms a smooth surface of the wing, and an open configuration in which the transition section may be accessed.
22. The aircraft according to claim 20, in which the inspection panel is removeable.
23. The aircraft wing for use as the wing of claim 1, the wing having a fixed wing with a wing tip device moveably mounted at the outer end thereof, the wing tip device being moveable between: (a) a flight configuration for use during flight; and (b) a ground configuration for use during ground-based operations, in which ground configuration the wing tip device is moved away from the flight configuration such that the span of the aircraft wing is reduced, wherein the wing tip device and the fixed wing are separated along a primary cut plane, the primary cut plane being obliquely orientated, and the wing tip device being rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, and wherein when the wing tip device is in the flight configuration, the outer end of the fixed wing and the inner end of the wing tip device meet along an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, the interfacing cut line comprising: (i) a first length, formed by a cut through the outer surface, but offset from the primary cut plane in a first direction; (ii) a second length, formed by a cut through the outer surface, but offset from the primary cut plane in a second direction, opposite to the first direction; and (iii) a transition section in which the interfacing cut line transitions from the first length to the second length.
24. A fixed wing, for use as the fixed wing in claim 1, the fixed wing being configured to receive a wing tip device that is separated along a primary cut plane, the primary cut plane being obliquely orientated, such that the wing tip device may be rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, and wherein the outer end of the fixed wing is shaped such that it would meet the inner end of the wing tip device meet along an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, the interfacing cut line comprising: (i) a first length, formed by a cut through the outer surface, but offset from the primary cut plane in a first direction; (ii) a second length, formed by a cut through the outer surface, but offset from the primary cut plane in a second direction, opposite to the first direction; and (iii) a transition section in which the interfacing cut line transitions from the first length to the second length.
25. A wing tip device for use as the wing tip device in claim 1, the wing tip device being configured to be received on a fixed wing that is separated along a primary cut plane, the primary cut plane being obliquely orientated, such that the wing tip device may be rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, and wherein the inner end of the wing tip device is shaped such that it would meet the outer end of the fixed wing along an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, the interfacing cut line comprising: (i) a first length, formed by a cut through the outer surface, but offset from the primary cut plane in a first direction; (ii) a second length, formed by a cut through the outer surface but offset from the primary cut plane in a second direction, opposite to the first direction; and (iii) a transition section in which the interfacing cut line transitions from the first length to the second length.
26. A method of designing an interface between the outer end of a fixed wing and the inner end of a wing tip device for an aircraft, the wing tip device being moveable between: (i) a flight configuration for use during flight; and (ii) a ground configuration for use during ground-based operations, in which ground configuration the wing tip device is moved away from the flight configuration such that the span of the aircraft wing is reduced, wherein the method comprises: separating the wing tip device and the fixed wing along a primary cut plane, the primary cut plane being obliquely orientated, and the wing tip device being rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, defining an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, by defining (i) a first length, formed by cut through the outer surface but offset from the primary cut plane in a first direction; (ii) a second length, formed by a cut through the outer surface but offset from the primary cut plane in a second direction, opposite to the first direction; and (iii) a transition section in which the interfacing cut line transitions from the first length to the second length.
27. The method according to claim 26 in which the wing tip device is then manufactured to that design.
28. An aircraft comprising a wing, the wing having a fixed wing with a wing tip device moveably mounted at the outer end thereof, the wing tip device being moveable between: (a) a flight configuration for use during flight; and (b) a ground configuration for use during ground-based operations, in which ground configuration the wing tip device is moved away from the flight configuration such that the span of the aircraft wing is reduced, wherein the wing tip device and the fixed wing are separated along an oblique primary cut plane, and the wing tip device being rotatable between the flight and ground configurations, about an axis of rotation orientated normal to the primary cut plane, and wherein the outer end of the fixed wing and the inner end of the wing tip device meet along an interfacing cut line that separates the outer surfaces of the fixed wing and the wing tip device, the interfacing cut line comprising: (i) a first section, formed by a cut through the outer surface, that is offset from the primary cut plane in one of an inboard or an outboard direction; (ii) a second section, formed by a cut through the outer surface but offset from the primary cut plane in the other of the inboard or outboard direction; and (iii) a transition section over which the interfacing cut line transitions from the first length to the second length. such that when the wing tip device rotates from the flight configuration to the ground configuration, the wing tip device contacts the fixed wing at a sliding contact along the transition section, but the wing tip device separates away from the fixed wing along the first section and second section.
Description
DESCRIPTION OF THE DRAWINGS
[0047] Embodiments of the present invention will now be described by way of example only with reference to the accompanying schematic drawings of which:
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DETAILED DESCRIPTION
[0070]
[0071] The wing tip device 3 is placed in the flight configuration for flight. In the flight configuration, the wing tip device 3 thus increases the span of the aircraft (thereby providing beneficial aerodynamic effects, for example, reducing the component of induced drag and increasing the lift). In principle, it would be desirable to maintain this large span at all times and simply have a large fixed wing. However, the maximum aircraft span is effectively limited by airport operating rules which govern various clearances required when manoeuvring around the airport (such as the span and/or ground clearance required for gate entry and safe taxiway usage). Thus, in the first embodiment of the invention, the wing tip device 3 is moveable to a ground configuration for use when on the ground.
[0072] In the ground configuration (
[0073] The movement of the wing tip devices is determined by the type of joint about which the wing tip device rotates relative to the fixed wing. To achieve the above-mentioned movement, the wing tip device 3 and the fixed wing 5 are separated along an oblique cut plane 13 passing through the upper and lower surfaces of the wing. The wing tip device 3 is rotatable about the axis 11 that extends in a direction perpendicular to the oblique cut plane 13. The axis 11 is orientated at an acute angle to all three mutually perpendicular axes X, Y and Z (i.e. chordwise, spanwise and vertical).
[0074] Small gaps, steps or other mismatch at the interface between the outer end of the fixed wing and the inner end of the wing tip device, when the moveable wing tip device is in the flight configuration, can create aerodynamic penalties (e.g. drag and pressure leakage). In some moveable wing tip arrangements, such as the one described above with reference to
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[0077] The nature of the movement is also illustrated in
[0078] The first embodiment of the invention has a particular layout of interfacing cut line 135 between the fixed wing and the wing tip device, as is described below with reference to
The Interfacing Cut Line
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[0080] The primary cut plane 113 is indicated in
[0081] Referring to
[0082] The interfacing cut line 135 comprises a first length 137 (see
[0083] The interfacing cut line 135 also comprises a second length 141 extending from the leading edge, over the upper-fore quadrant (UF) to the other end of the transition section 139. As is most clearly shown in
[0084] It will be appreciated from above, that the first and second lengths 137, 141 thus both lie in oblique planes parallel to the primary cut plane 113, but in planes that are offset from that primary cut plane in opposite directions.
[0085] Between the first 137 and second lengths 141 is a transition section 139. The transition section 139 comprises a first section 139a that lies in the same plane 113a as the first length 137 and a second section 139b at which the interfacing cut jumps across from the first plane 113a to the second plane 113b. The transition section 139 thus transitions the interfacing cut line 135 from the first 137 to the second 141 lengths.
[0086] The interfacing cut line 135 is arranged such that when the wing tip device 103 rotates from the flight configuration to the ground configuration, specific types of relative movement occur between the outer end of the fixed wing 105 and the inner end of the wing tip device 103. This is most readily understood with reference to
[0087] As can be seen from the top image in
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[0090] The first section 139a of the transition section 139 extends to a fore-most location that reflects the fore-most location of the sliding contact point (e.g. at its position when the wing tip device 103 is in the ground configuration taking into account some leeway for further movement). At this point, it is necessary for the transition section 139 to move to the second length of the interfacing cut line 141. Accordingly, the second part 139b of the transition section 139 comprises a short length, in an outboard direction, that jumps from the inboard cut plane 113a, across the primary cut plane 113 and to the outboard cut plane 113b, to meet the second length 141. This second length 139b is not visible in
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[0092] In a similar manner to that described with reference to the upper surface shown in
[0093] On the lower surface 133 of the wing, the interfacing cut line 135 also comprises a further transition region 149 at the trailing edge. This further (third) transition section 149 links from the third length to the first length and thus traverses from the outboard cut plane 113b on which the third length lies, to the inboard cut plane 113a on which the first length lies.
[0094] Since this further transition section 149 is relatively far away from the axis of rotation 111, and since the curvature of the trailing edge is very tight, there tends to be negligible sliding contact at this further transition region 149. Instead, this third transition section 149 undergoes a separation, as shown in the close-up views in
[0095] Referring now to
[0096] It will be appreciated from the above-description that the interfacing cut line 135 is thus divided into 4 notional lengths 137, 141, 143, 145 each separated by transition sections 139, 147, 149, 151. Each of the lengths 137, 141, 143, 145 of the interfacing cut line is adjacent, but linked by a transition section 139, 147, 149, 151 to another length 137, 141, 143, 145 that is offset in the opposing cut plane 113a, 113b. The pairs of lengths of cut line that are on opposing sides of the axis of rotation (i.e. the first and second lengths 137, 141, and the third and fourth lengths 143, 145) are each, respectively, split by a transition region 139, 147 in which there is a sliding contact as the wing tip device 103 rotates between the flight and the ground configurations. In contrast, the pairs of lengths 137, 141, 143, 145 of the interfacing cut line 135 undergo a translational separating movement as the wing tip device 103 rotates between the flight and the ground configurations.
[0097] The above-mentioned arrangement has been found to be especially beneficial with respect to the sealing between the fixed wing 105 and the wing tip device 103. More specifically, it enables the use of a compression seal (i.e. an arrangement that forms a seal under a compressive movement) along the first to fourth lengths 137, 141, 143, 145 of the interfacing cut line 135, but a sliding seal only along the first and second transition regions 139, 147. The compression seal is arranged to seal under the action of the wing tip device 103 and the fixed wing 105 coming together under a local translational movement. Such a compression seal tends to provide an effective seal, yet is not subject to particularly high wear because there tends not to be any relative sliding across the seal. The sliding seal provides a seal when the wing tip device 103 is in the flight configuration, yet it is designed to withstand the wear from the sliding contact that moves along the seal as the wing tip device 103 rotates. By offsetting the lengths 137, 141, 143, 145 of the interfacing cut line 135 in opposing planes 113a, 113b, either side of the axis of rotation 111, the first embodiment of the invention maximises the length of the compression seal, but minimises the length of the sliding seals.
[0098] Part of the sealing arrangement in the first embodiment of the invention is shown in
[0099] The sealing arrangement in
The Construction of the Interface
[0100] As mentioned above, the first embodiment of the invention has a particular construction of interface between the fixed wing and the wing tip device. This will now be described below with reference to
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[0102] At the section shown, the interfacing cut line 135 on the upper surface lies in the inboard cut plane 113a and the interfacing cut line 135 on the lower surface lies in the outboard cut plane 113b (see description above with reference to the “Interfacing cut line”).
[0103] The wing includes a slew-ring bearing 112 linking the outer rib 115 to the inner rib 117. The rotational axis of the slew ring is coaxial with the axis of rotation 111. The rotational movement of the wing tip device is effected by an actuator (not shown).
[0104] The fixed wing 105 comprises a fixed wing-skin 119 forming the outer surface of the fixed wing, and the wing tip device comprises a wing tip device-skin 121 forming the outer surface of the wing tip device 103. In a manner akin to known rib/skin assemblies, the fixed wing-skin 119 is fastened to rib feet 123 on the outer rib 115 and the wing tip device skin 121 is fastener to rib feet 125 on the inner rib 117. An oblique webbing (only part of which is visible in
[0105] In contrast to known rib/skin assemblies, the fixed wing-skin 119 terminates before (i.e. inwardly of) the interface 135. The outer rib 115 comprises a surface-forming portion 127, that creates an extension of the fixed wing-skin 119 towards the interface 135. Likewise, the wing tip device-skin 121 terminates outwardly of the interface 135. The inner rib 117 comprises a surface-forming portion 129, that creates an extension of the wing tip device-skin 121 towards the interface 135.
[0106] Providing an arrangement in which the skins (i.e. the fixed wing-skin 119 and the wing tip device-skin 121) both terminate before the interface, enables the wing surface in the vicinity of the interface to instead be provided by the surface-forming portions 127, 129 of the ribs 115, 117. This has been found to be advantageous because it enables the tolerances at the interface to be more readily, and/or more accurately, controlled. For example, the surface-forming portions need not necessarily be of the same material or construction as the skin. This may facilitate tighter control of tolerances at the interface 135.
[0107] In the first embodiment of the invention, this is exemplified by the use of composite skins 119, 121 and metallic ribs 115, 117. If the composite skins were to extend up to the interface, it would be hard to ensure the sufficient tolerances are achieved because composite is difficult to machine and/or deflect to the required shape. In contrast, by providing metallic surface forming portions 129, 127 the outer surface layer can be machined to the correct tolerance (described in more detail with respect to
[0108] The outer and inner rib arrangement described above also has advantages with respect to how the ribs may be manufactured. This aspect is described separately below—see “Manufacture of the inner and outer ribs”.
Sealing Arrangement
[0109] The above-mentioned ribs provide an improved structure on which a seal can be provided. Specifically, each rib comprises a secondary surface for supporting a compression seal. On the outer rib 115, the secondary surface 153 is below the outer surface of the wing but extends in a direction substantially parallel to the outer surface such that it under-laps the surface-forming portion 129 on the opposing rib 117. Likewise, on the inner rib 117, the secondary surface 155 is below the outer surface of the wing but extends in a direction substantially parallel to the outer surface such that it under-laps the surface-forming portion 127 on the opposing rib 115. In the first embodiment of the invention, the secondary surfaces extend substantially up to the primary cut plane 113.
[0110] As a result of the local translational movement that occurs along the first to fourth lengths of the interfacing cut line (upon rotation of the wing tip device (see description above)), a rubber element 157 is compressed between the underside of the surface-forming portion 127, 129 of one rib, and the secondary surface 153, 155 of the other rib, when the wing tip device is brought into the flight configuration. This compression seal acts to inhibit leakage flow from the lower to upper surfaces of the wing. The first embodiment of the invention also comprises a secondary noise seal 159 in the form of an embedded rubber strip in one of the ribs, directly below the interface 135.
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Manufacture of the Inner and Outer Ribs
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[0115] Since the ribs are single piece metallic forgings, it is possible to machine the surface-forming portions with the tow ribs in situ. More specifically, by holding the ribs in their correct relative positions for flight, it is possible to precision machine the surface-forming portions to the precise outer mould line (OML) required.
Other Embodiments of the Invention
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[0117] The wing tip device 203 is rotatably mounted on the outer end of the fixed wing 205. The wing tip device is separated from the fixed wing 205 along a notional oblique cut plane (not explicitly illustrated in
[0118] In the flight configuration, the outer end of the fixed wing 205 and the inner end of the wing tip device 203 meet along an interfacing cut line 235, which is itself formed from four lengths in the upper aft (UA), upper-fore (UF), lower-aft (LA) and lower-fore (LF) quadrants respectively of the aerofoil. Only the first and second lengths 237 and 241 are visible in
[0119] The first length 237 is formed by a cut through the outer surface of the wing in an inboard plane, parallel to the primary cut plane, but located inboard thereof. The second length 237 is formed by a cut through the outer surface of the wing in an outboard plane, parallel to the primary cut plane, but located outboard thereof. The first and second lengths 237, 239 are joined by a transition section 239 (formed itself by two section 239a (which lies in the inboard cut plane) and 239b (which moves directly from the inboard to the outboard cut plane)). As the wing tip device rotates away from the flight configuration, towards the ground configuration, the wing tip device separates (‘upwardly’) away from the outer end of the fixed wing along the first length 237 of the interfacing cut line 235 and the wing tip device separates (‘downwardly’) away from the outer end of the fixed wing along the second length 241 of the interfacing cut line 235. In the transition section 239 there is a sliding contact, that moves fore-aft along section 239a as the wing tip rotates along a sliding seal.
[0120] The above-mentioned features broadly reflect those in the first embodiment of the invention. In the second embodiment however, the interfacing cut is deeper and instead of providing a compression seal on a secondary surface 153, 155, that runs parallel to the outer surface of the wing, a secondary surface 253, 255 is instead provided (on the fixed wing 205) in a vertical plane running through the mid-chord depth. Opposing surfaces on the wing tip device are also provided, and those surfaces are shown in dotted lines in
[0121] The second embodiment of the invention recognises that the local translational movement (suitable for using a compression seal) can be provided a different location within the wing. In that respect, the secondary surfaces are provided with compression seal elements (not shown) that are compressed to form a seal when the wing tip device is in the flight configuration. The second embodiment continues to recognise that offsetting the lengths of the interfacing cut lines from the primary cut plane, is advantageous in limiting the length of the (transition) regions in which there is a sliding contact.
[0122] Whilst the present invention has been described and illustrated with reference to particular embodiments, it will be appreciated by those of ordinary skill in the art that the invention lends itself to many different variations not specifically illustrated herein. By way of example only, certain possible variations will now be described.
[0123] Where in the foregoing description, integers or elements are mentioned which have known, obvious or foreseeable equivalents, then such equivalents are herein incorporated as if individually set forth. Reference should be made to the claims for determining the true scope of the present invention, which should be construed so as to encompass any such equivalents. It will also be appreciated by the reader that integers or features of the invention that are described as preferable, advantageous, convenient or the like are optional and do not limit the scope of the independent claims. Moreover, it is to be understood that such optional integers or features, whilst of possible benefit in some embodiments of the invention, may not be desirable, and may therefore be absent, in other embodiments.