HOLE FORMING TOOL WITH AT LEAST ONE ROTATABLE CUTTING MEMBER

Abstract

The invention relates to hole forming tools suitable for use in subterranean drilling operations, operable with two non-parallel rotational motions for forming a hole of substantially circular cross section in a material, the tool comprising a rotatable drill body (17) having a proximal end (19) for attachment to a drive mechanism and a distal end (21) on which is disposed at least one rotatable cutting member (23), wherein the or each rotatable cutting member (23) independently extends away from said distal end (21); the or each rotatable cutting member (23) independently being substantially concentric with and supported by a cantilever shaft (35); wherein on the or each rotatable cutting member (23) is disposed at least one cutting structure (24), the or each cutting structure (24) independently having a cutting face with a continuous cutting edge which is substantially concentric with the axis of rotation of said rotatable cutting member (23).

Description

The present invention relates to a tool for forming a hole. More particularly, the invention relates to a tool operable with two non-parallel rotational motions for forming a hole of substantially circular cross section in a material.

Hole-making, hole forming or drilling by the removal of material is often an expensive and time-consuming process due to the wear of cutting edges and the necessity for replacement of the hole forming tool so as to maintain productivity and or the quality of the formed hole. Despite substantial improvements in the geometry and construction of drilling tools and the hard materials comprising the cutting edges, there is an ever-increasing desire to further improve such tools so as to provide for longer tool life whilst maintaining productivity and or the quality of the hole. One requirement of hole forming tools is that they possess sufficient strength and toughness so as to withstand high forces and often a dynamic load component arising from drilling vibrations or heterogeneity within the material being cut.

It is known in the art that prolonged continuous contact between a cutting edge and the material being cut is deleterious in terms of cutting edge wear and several approaches have been developed to address this issue. For rotationally symmetric cutting tools, one such approach is to permit the tool to rotate freely or in a regulated manner about its own axis, e.g. as disclosed in US 2014/0186127 A1. Although such self-propelled rotary turning tools have been known in the art for several decades, industrial use is rare. In the field of subterranean drilling, tools incorporating cutting edges permitted to rotate about an axis substantially perpendicular to the axis of primary rotation were a popular approach about one century ago in the form of ‘disc cutters’. With reference to FIGS. 1 and 2, disc cutters 2 are disposed on journal bearings 4, each supported on each end by pairs of elements 3 extending from the tool body 1. Numerous embodiments have been disclosed in U.S. Pat. No. 1,721,921, U.S. Pat. No. 1,533,078, U.S. Pat. No. 1,769,956, U.S. Pat. No. 1,574,731, U.S. Pat. No. 1,026,886, U.S. Pat. No. 1,646,620, U.S. Pat. No. 2,713,993, U.S. Pat. No. 1,843,096, U.S. Pat. No. 2,951,683 and U.S. Pat. No. 1,582,332. Disc cutters may have specific preparations of their peripheral cutting regions as claimed in U.S. Pat. No. 1,176,965, U.S. Pat. No. 4,846,290 and U.S. Pat. No. 1,523,912. GB 2167107 claim a drilling tool similar to disc cutters, but where the periphery of the advancing face of each disc is covered with a plurality of small circular diamond cutters. US 2013/126246 and US 2013/126247 describe drill bits utilising at least one rotatable member on which is disposed a plurality of cutters of the type used conventionally on PDC shear bits. U.S. Pat. No. 4,553,615 discloses a drill bit on which are fixed a plurality of ‘insert cutters’, each such insert cutter comprising a mounting block or a pair of mounting blocks fitted into the drill body. The mounting blocks house a conical bearing which supports a rotatable cutter on whose working face are fixed a plurality of diamond bodies of a variety of forms. The arrangement of journal bearings in such are subject to the ingress of abrasive particulate matter.

Certain subterranean drill bits comprise a plurality of cylindrical polycrystalline diamond cutters, commonly ranging in diameter from ½-¾ inch (12.7-19 millimetres), and arranged on a plurality of blades on the drill body. Such tools are generally referred to in the art as “shear bits” or “drag bits”, as exemplified in U.S. Pat. No. 8,327,956, US 2010/0089648, US 2014/0097028, WO 2011/090618A1 and WO 2014/028152. U.S. Pat. No. 4,511,006 discloses a shear bit for mining as shown in FIG. 3; the bit comprising a single rotatably mounted cutter 6 of a first diameter; said cutter made rotatable by a smaller shaft of a second diameter which extends into a suitably sized bore of an adjacent body 7 whose external diameter is comparable to the first diameter. This adjacent body is bonded to the drill body 5. U.S. Pat. No. 4,553,615 claim a subterranean drill on which the same rotatable cutters are employed.

Another class of drilling tools, known in the field as “roller cones” (IPC E21B10/08), exert a crushing action on the material to be removed. With reference to FIG. 4, such crushing action occurs under hard pyramidal, conical or similar-shaped indenters 11 which are positioned around the periphery of generally conical rotatable members 10 whose axis of rotation is substantially parallel to radial lines of the tool body when viewed in a traverse plane of the tool body. The art interchangeably refers to both the individual indenters and the rotatable member assembled with the indentors as “cutters”, though it will be evident that such articles impart a different mode of material removal to the “cutters” described in the art relating to shearing of work materials—the latter belonging to IPC E21B10/42. Numerous embodiments of roller cone drills are known in the art: U.S. Pat. No. 3,134,447, U.S. Pat. No. 5,289,889, US 2008/0099252, US 2014/0202772, US 2014/0196956, US 2013/0192898 including combinations of roller cones with shear cutters as in US 2012/0031671, WO 2011/084944A2 and U.S. Pat. No. 5,805,665. Shear cutters 13 are mounted on blade-like protrusions 12 on the drill body 9. FIG. 4 depicts a prior art ‘hybrid’ bit, comprised roller cones and shear cutters.

WO 1999/18326 describes a drill bit with rolling ‘disc cutters’. WO 1999/11900 describes a drill employing multiple discs disposed on rotatable members. CN 102747960, WO 2015/178908 and WO 1985/02223 describe other hybrid drill bits of similar function. Disc-like rolling structures appear not to have been widely successful.

All drilling tools intended for subterranean drilling applications have a threaded element 8 for attachment to the drive mechanism, nozzles 15 for delivery of cutting fluid and hard, abrasion resistant, non-cutting elements 14 disposed on regions of the drill body which are otherwise vulnerable to excessive wear.

As a result of the limitations of the prior art, there is a need for an improved hole forming tool so as to provide improved tool life, drilling productivity and/or improved hole quality, especially during subterranean drilling operations.

SUMMARY

The present invention provides hole forming tools suitable for subterranean drilling and is particularly defined in the appended claim which are incorporated into this description by reference and for the purposes of economy of presentation are not reproduced verbatim in the description.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention will now be described with reference to the accompanying drawings, FIGS. 5 to 21 of which show, by way of example only, embodiments of a hole forming tool according to the invention.

In the drawings:

FIGS. 1 to 4 show prior art subterranean drilling tools.

FIGS. 5 and 6 show preferred hole forming tools with rotatable cutting members in accordance with the invention and suitable for subterranean use.

FIG. 7 shows an alternative preferred hole forming tool with rotatable cutting members in accordance with the invention.

FIGS. 8A and 8B show cross sections of preferred rotatable cutting members in accordance with the invention.

FIGS. 9A, 9B, 10A-10D, 11A and 11B illustrate aspects of the geometry of preferred rotatable cutting members and cutting structures of the hole forming tools according to the invention.

FIG. 12 shows a cross section view of a preferred cutting structure and analytically-derived stresses occurring at distinct regions on the cutting structure.

FIG. 13 illustrate aspects of the geometry of preferred cutting structures of the hole forming tools according to the invention.

FIGS. 14 and 15 show a series of charts displaying angular quantities relevant to the realisation of working embodiments of the invention.

FIGS. 16 to 20 each illustrate the projection of multiple preferred cutting structures of the hole forming tools according to the invention onto a radial plane of the drill body of the tool.

In one aspect, embodiments disclosed herein relate to hole forming tools with defined cutting structures which are rotatable and therefore have greater resistance to wear; said cutting structures being disposed to shear rather than crush the material to be cut. The cutting structures extend from the distal end of the drill body which is the working face of the hole forming tool and are disposed on, preferably attached rigidly, to rotatable cutting members which in turn are supported on and permitted to rotate on bearings disposed on cantilever shafts. Each cantilever shaft extends from the tool body. While it has long been known, particularly in the art of metal cutting lathe tooling, that cutting elements of a larger diameter are inherently more robust and resistant to impact loading than those of a smaller diameter, prior art drills which permit cutting structure rotation fail to combine sizeable cutting structures with robust, mechanically sound bearing arrangements and those prior art drills that do provide for sizeable rotatable cutting elements, fail to provide a robust and stiff cutting structure which is resistant to bending, breakage and or vibration. The hole forming tools of the invention address these shortcomings and additionally provide for the incorporation of several cutting structures on a compact but rigid rotatable cutting member and the exposure of each cutting structure to a share of the applied load so as to limit the maximum load applied to any one cutting structure, thereby significantly reducing the likelihood of fracture in use.

Referring to the drawings, FIGS. 1 to 4 relate to prior art drilling tools discussed in the background section hereinabove. FIGS. 1 and 2 show a prior art drill bit as described in U.S. Pat. No. 1,646,620. FIG. 3 shows a drill bit design as described in U.S. Pat. No. 4,511,006. FIG. 4 shows a drill bit as described in US 2011/0162893.

FIG. 5 discloses a preferred embodiment of the present invention in which a hole forming tool, indicated generally by reference numeral 16 comprises a drill body 17 with openings or ‘flutes’ 18 running along the length of the drill body. On the proximal end 19 of the drill body there is an attachment means, such as a threaded member 20, for directly or indirectly attaching the hole forming tool 16 to a drive mechanism. On or near the opposing distal end 21 of the drill body are several drill body elements 22, each of which supports a rotatable cutting member 23 by means of a cantilever shaft (not shown in FIG. 5) extending between the drill body element and the rotatable cutting member. There is an inner arrangement of rotatable cutting members and an outer arrangement of rotatable cutting members. Each of the rotatable cutting members 23 may contain two cutting structures 24, each of which is concentric with the rotatable cutting member and extends in a continuous, uninterrupted manner around the periphery of the rotatable cutting member. The cutting structure 24 distal its associated drill body element 22 will be termed the ‘leading’ cutting structure and that proximal the drill body element, the ‘lagging’ cutting structure. The embodiment disclosed in FIG. 5 contains an inner arrangement of three smaller rotatable cutting members and an outer arrangement of three larger rotatable cutting members, though each arrangement may independently be variable in number. By the term ‘continuous’ as used in relation to the cutting edge of cutting structures in accordance with the present disclosure, is meant the absence of joints which would otherwise exist on cutting edges formed from separate and distinct bodies of cutting materials. In other words, the cutting material comprising a cutting edge has been sintered as a unitary body. The elements 22 may be integral with the drill body 17 or joined to the drill body 17 by mechanical or thermal means.

So as to provide a sufficiently robust design with sufficient space to permit the evacuation of cuttings, it may be preferable to incorporate reliefs 25 within the drill body elements. It will also be appreciated that it is desirable to have a degree of overlap between any inner arrangement of cutting structures and any outer arrangement of cutting structures—such overlap being apparent when the cutting edges of inner and outer cutting structures are rotationally projected about the axis of the drill body onto a radial plane of the drill body. Advantageously therefore, the angular position of the drill body elements 22 supporting the inner and outer rotatable cutting members 24 are preferably staggered. Where an inner and outer arrangement of drill body elements is adopted, the drill body elements and hence cutting structures 24 are preferably positioned at equal angular intervals or alternatively positioned at unequal angular intervals. Without being bound by theory, this positioning of the cutting structures 24 is considered to be helpful in counteracting regenerative vibration. A similar effect may also be achieved in embodiments of the present invention by providing differing angles of inclination of the cantilever shafts relative to radials of the drill body when viewed in a transverse plane of the drill body.

In addition to the distinct arrangement of inner and outer rotatable cutting members 23 or more generally, distinct groups of rotatable cutting members 23 positioned along substantially distinct circles of rotation about the drill body axis, in an alternative embodiment, each rotatable cutting member is positioned on a unique circle of rotation about the drill body axis. It will be noted that any arrangement of rotatable cutting members 23 and their cutting structures 24 must provide for a balanced hole forming tool such that any forces acting normal to the axis of rotation of the drill body 17 during use are minimal. This is provided by the invention.

Flutes 18 are preferably located adjacent the outermost drill body elements 22 such that cuttings exiting the associated cutting structures 24 have free passage into the flutes 18. The flutes 18 also reduce the area of contact between the drill body 17 and the hole being formed and thus serve to reduce frictional heating and wear. Preferably, innermost drill body elements 22 and associated rotatable cutting members 23 and cutting structures 24 lie at an angular position on the drill body which provides for easy flow of cuttings into the flutes 18.

In other preferred embodiments of the current invention, rotatable cutting members 23 with cutting structures 24 disposed thereon and with associated supporting cantilever shafts, may only be disposed on certain annular or segmental regions of the working face (distal end) of the hole forming tool, with remaining regions of the working face provided with non-rotatable fixed cutting structures.

Referring to FIG. 6, there is shown an alternative embodiment of the hole forming tool according to the invention, indicated generally by the reference numeral 26, and having an inner arrangement of fixed cutting structures 27 and an outer arrangement of rotatable cutting members 23. Like features of tool 26 are indicated by like reference numerals indicated above for tool 16.

In the preferred embodiment shown in FIG. 6, in the outer annular region of the working face of the hole forming tool 26, there are several drill body elements 22 supporting rotatable cutting members 23, on each of which is disposed cutting structures 24, and in the inner working region of the drill body 17, there are multiple fixed cutting structures 27 disposed on blade-like protrusions 28 from the drill body.

Referring to FIG. 7, there is shown a further alternative embodiment of the hole forming tool according to the invention, indicated generally by the reference numeral 29 and having an inner twist drill point 30 and an outer arrangement of rotatable cutting members 23. Like features of tool 29 are indicated by like reference numerals indicated above for tools 16 and 26.

As shown in FIG. 7, hole forming tool 29 comprises a drill body 17 with longitudinally orientated flutes 18 and a central region on the distal end 21 constituted by a conventional twist drill point 30 configuration comprising cutting edges 31, clearance faces 32 and web-thinning notches 33 adjacent a central chisel point 34. Also shown are two rotatable cutting members 23, each containing a single cutting structure 24 which extends in a continuous, uninterrupted manner around the entire periphery of the rotatable cutting member 23. In the embodiment shown, rotatable cutting members 23 are supported on bearings secured within the drill body 17.

While the embodiments illustrated include either two cutting structures 24 disposed on each rotatable cutting member 23 as shown in FIGS. 5 and 6 or one cutting structure disposed on each rotatable cutting member as shown in FIG. 7, any number of cutting structures 24 may be disposed on each rotatable cutting member 23. For example, on larger drill bodies, more than one or two cutting structures may be disposed on each rotatable cutting member, whereas on smaller drill bodies, manufacturing considerations may advise against more than one or two cutting structures on each rotatable cutting member. The number of rotatable cutting members disposed on the working face of the hole forming tool according to the invention may also be varied. Larger tools will favour generally larger and or more numerous rotatable cutting members. It should be noted that more numerous rotatable cutting members are in particular convenient where the maximum size of the rotatable cutting member is limited by the availability of the highly specialised materials from which cutting structures are manufactured.

With reference to FIG. 8a, a preferred example of the construction of a rotatable cutting member 23 is shown. It is generally preferable to position the cutting structures 24 as close to the origin of the cantilever shaft 35 as other design and manufacturing considerations permit so as to limit the bending moment acting on the cantilever shaft. A longer cantilever shaft provides for both a more precise rotation of the rotatable cutting member 23 and a more rigid assembly less susceptible to wear and vibration. FIG. 8a also depicts a journal bearing 36, a thrust bearing 37 and retaining balls 38 secured in the ball-tracks in the cantilever shaft 35 and at an internal diameter of the rotatable cutting member 23. The preferred embodiment in FIG. 8a also contains sealing means 39 which, by way of example, may comprise an O-ring and or flange-type seal which are preferably energised; a pressure equilibration device combining lubricant reservoir 40 and pressure regulating diaphragm 41 with perforated retaining disc 42 and internal diameter spring clip 43; said reservoir 40 connecting to the bearing cavity through supply channel 44. The pressure equilibration device, which may alternatively consist of a piston arrangement, for example, serves to maintain substantially equal pressure across the seal(s) during use, where pressures external to the bearing cavity would otherwise be sufficient to promote ingress of abrasive matter. As an alternative to plain bearings, roller-element bearings may be used, as may alternative sealing arrangements. The cutting structures 24 may be brazed to the rotatable cutting member 23 and may consist of, for example, a sintered diamond material 45 integrally bonded to a carbide backing layer 46; the cutting edge of which may be provided with a bevel 47 or radius 48 or multiples or combinations of both. The side face of the cutting structures 24 is preferably provided with a clearance angle 49 providing an approximately conical form. In particularly preferred embodiments this same form is applied to the adjacent supporting portion 50 of the rotatable cutting member.

Referring to FIG. 8b, a preferred alternatively constructed embodiment of a rotatable cutting member 23 is shown. In this case, the rotatable cutting member 23 has a diameter substantially larger than its length and accordingly, a potentially more robust and thus preferred design has the cantilever shaft 35 integral to the rotatable cutting member 23 where this shaft 35 extends into a suitably sized bore in the drill body element 22. This optional arrangement may also be preferred depending on available manufacturing processes. The embodiment in FIG. 8b benefits from the arrangement of bearings 36, 37, seals 39, retaining balls 38 and pressure equilibration device components 40-44. Other preferred embodiments may have cutting structures 24 which have a clearance angle 49 over their side face with additional clearance 51 provided over the adjacent supporting portion 50 of the rotatable cutting member 23, providing, for example, easier evacuation of cuttings. Where excessive wear of the rotatable cutting member 23 adjacent cutting structures 24 is experienced, it may be preferable to incorporate a more wear resistant sleeve 52 provided with clearance angles, whether the same or different to the clearance angle 49 imparted on the cutting structure 24. The position of the cutting structures 24 along the axis of the preferred rotatable cutting member 23 shown in FIG. 8b is in part determined by the dimensions d1, T1, d12, T2 and d2 in this Figure. Further reference herein to any clearance angles 49 disposed on a cutting structure 24 or any clearance angles arising from a particular configuration of a cutting structure on a drill body 17 should be taken to also apply to any adjacent region 50 of the rotatable cutting member supporting that cutting structure and/or wear resistant sleeves 52 optionally associated with that cutting structure. In a preferred embodiment, the hole forming tool according to the invention has one or more cutting structures 24 such as those depicted in FIGS. 8a and 8b which extend along a fraction of the dimensions d1 and d12. In an alternative preferred embodiment, the hole forming tool has one or more cutting structures 24 which extend along the entirety of the dimensions d1 and d12.

Aspects of embodiments of the present invention depicted in one Figure may be interchangeable or combined with aspects of embodiments depicted in other Figures. Features on one cutting structure or on one location of a rotatable cutting member may be applied to other cutting structures and other locations of rotatable cutting members. Aspects illustrated in FIGS. 8a and 8b may differ in form and location without deviating from the disclosure. For example, lubricant reservoir 40 may be located more distal the rotatable cutting member 23, e.g., within a more central region of the drill body 17 adjacent the flutes 18 or any internal channels in the drill body which serve to direct fluids to the working face of the hole forming tool.

Embodiments of the present invention may differ also at least in terms of the angles of inclination of, the position of, and the construction of the cantilever shafts relative to the drill body axis; the configuration of the rotatable cutting members and their respective cutting structures; the cutting edge and clearance face geometry of the cutting structures; the geometry of the drill body and drill body elements; bearings, sealing elements and the construction of pressure equilibration devices and any methods used to realise articles in accordance with the present disclosure. Features such as gage pads and flushing nozzles, as are used on prior art shear drills and roller cone drills are preferably also incorporated in the hole forming tools of the invention.

With regard to the direction of rotation of a rotatable cutting member; FIG. 9a depicts a plan view of a rotatable cutting member 23 whose axis lies in a transverse plane of the drill body 17 (i.e., the plane of the page); said axis being coincident with the line defined by points a and c. At each of points a, b and c, the face of a cutting structure is disposed, each visible in this plan view as a line. The axis of the rotatable cutting member is inclined at an angle αa to the reference radial 53 of the drill body passing through point a. The inclination of the faces of the cutting structures located at b and c, relative to other radials of the drill body extending through their centre-points, differs from angle αa and beyond a minimum distance between these points and point a, these angles are in the opposite sense to αa. If the coordinate system employed considers angle αa as positive, angles αb and αc, as depicted in FIG. 9a, is negative.

FIG. 9b shows a slightly oblique side view of three discs representing the cutting faces of the cutting structures 24 in FIG. 9a. Force vector F lying in the transverse plane is tangent to a circle of radius R_bc centred on the drill body axis of rotation and said force vector F applied to the lowest point on the cutting face c. Other force vectors are similarly constructed for cutting faces a and b. Under the influence of their respective force vector, the preferred direction of rotation of each cutting structure 24 is as shown in FIG. 9b. The resultant direction of rotation of the rotatable cutting member 23 is therefore influenced by the angle of inclination of the rotatable cutting member axis, the distance between cutting structures along the length of the rotatable cutting member and the magnitude of each torque component ω1, ω2 and ω3.

In FIG. 9a, the angle ψ denotes the angular position of the rotatable cutting member on which a, c and c are disposed relative to the rotatable cutting member at point d.

In turn, the torque on each cutting structure will depend in part on the un-deformed cross-sectional area of cut to which that cutting structure is exposed and hence, the drill translation rate and the degree of overlap between adjacent cutting structures. The degree of overlap is illustrated in FIG. 9a by the annular region of width ‘0’ which is shared between the smaller rotatable cutting member and cutting structures at ‘d’ and the larger rotatable cutting member and cutting structures at points a-c. The magnitude of the force component on each cutting structure will also be influenced by any bevels, radii or combination of same provided on the periphery of the cutting face of that cutting structure and the frictional conditions on the cutting face. For each rotatable cutting member to be ‘self-propelled’, the applied torque must overcome the friction within its bearings; such frictional conditions will vary as a function of drill operating temperature and the degree of wear and lubrication of the bearings; in addition to the cutting characteristics of the material to be drilled, of which there are numerous types such as but not limited to sandstone and shale.

There is a necessary minimum clearance angle γ_min, required on each cutting structure so as to avoid contact between it and the just-formed surface of the hole being drilled. Such clearance should not be excessively large so as to compromise the strength of the cutting edge. Generally, the cutting structures have substantially conical clearance surfaces. Such conical forms incur virtually no compromise in terms of performance, compared to more complex forms constructed for example, by using the helical trajectory or approximation thereof, of a point of interest P on the cutting edge as a generatrix about the axis of the rotatable cutting member.

FIG. 10a shows an edge of an idealised isolated cutting structure, represented by the circle C of radius r_c, which is normal to the axis A of a rotatable cutting member. A lies in a longitudinal plane S1 parallel to the axis of rotation of the drill body and inclined to the normal of a reference radial 53 of the drill body by an angle α1. The centre of the circle C, point Oc, is positioned at a distance d from the point of intersection I of the axis A and the reference radial of the drill body, with said point of intersection I at a distance R_b from the axis of rotation of the drill body which is coincident with the Z-axis. The axis of rotation of the rotatable cutting member is also inclined downwards at an angle α2 relative to a transverse plane S2 of the drill body, which is parallel to the XY plane in FIG. 10a. The angle α2 may be expressed relative to any transverse plane of the drill body including a first transverse plane at the proximal end of the drill body. The geometric quantities in FIG. 10a and FIG. 10b, are depicted such that the intended direction of translation of the hole forming tool is from the top to the bottom of the page.

With reference to FIG. 10b, the minimum necessary clearance angle which must be provided on the peripheral side surface of a cutting structure may be most conveniently expressed relative to the axis of rotation A. For the purpose of illustration and employing for the present, certain simplifying assumptions, this may be approximated by the maximum of the interference angles ϕ1 & ϕ2, which are subtended between the following vectors:

• • Vectors through points P1 and P2, each parallel to the axis A (note in FIG. 10b, all lines parallel to the axis A are marked “=”) and,
  • The tangents, Tn1 and Tn2, to the helices H1 and H2, passing through the points of interest on the circle C, said helices defined by:
    • The diameter of the respective circle of rotation through each point of interest P, about the axis of rotation of the drill body; the projection of said circles onto the XY plane shown as Cy1 and Cy2 in FIG. 10b; and
    • The translation per revolution of the drill body.

Depending on the position and inclination of the cutting structure and absent any overlapping cutting structures, the minimum necessary clearance angle γ_min is determined at one or other of the positions P1 or P2. In FIG. 9a for example, the necessary minimum clearance angles are represented as ϕa, ϕb & ϕc (ignoring the overlap region ‘O’). The interference angles may be positive or negative quantities; being negative where the tangent to the helix passing through the point of interest P extends away from the axis of rotation A as it extends from the point of interest on the cutting edge in the direction of the point I. In FIG. 10b, ϕ2 is positive while ϕ1 is negative. Where the angle of interference is negative around the entire engagement region of a cutting edge, the side surface of a cylindrical cutting structure will not interfere with the newly formed surface of the hole.

Where one or more adjacent cutting structures are positioned such that points equivalent to either or both P1 or P2 will not engage the material to be drilled—in effect being shielded by one or more adjacent overlapping cutting structures—the minimum necessary clearance angle γ_min should be determined at one or other of the points on the cutting edge denoting the extremities of the engagement region on that edge. By the term “engagement region” is meant that part of the cutting edge of a cutting structure which at any given instant during use of the hole forming tool engages the material in which a hole is to be formed. Identical cutting structures disposed on two or more identically sized rotatable cutting members which are positioned in an identical manner on the drill body but for the angular position of their respective reference radials, are not considered to ‘overlap’ in accordance with the use of the term in the present disclosure. In such cases, the engagement region of each cutting structure is practically identical to an arrangement where only one such rotatable cutting member is disposed on the drill body. The term ‘overlap’ relates here to adjacent cutting structures, each of which shields a portion of the other so as to effectively reduce the engagement region on one or both cutting edges. By nature of being rotatable, every part of the cutting edge of a cutting structure in accordance with the present invention is for some period within an engagement region.

The cutting structure and any supporting region of the rotatable cutting member has a finite thickness T along the axis of the rotatable cutting member. The minimum necessary clearance angle γ_min determined at the cutting face may not in all cases be sufficient to ensure clearance at the rear face of that cutting structure (the rear face being that which opposes the cutting face and positioned at a distance T from the cutting face). The methodology noted above for both the cutting face and the rear face indicates at which location the interference angle is greatest (in a positive sense). The face at which the maximum interference angle occurs is the determinant of the minimum necessary clearance angle.

It is, in some cases, possible to provide a conical surface whose apex angle is less than twice the maximum interference angle at the rear face, yet still maintain clearance on the cutting structure during use.

FIG. 10c shows a plan view of a cylindrical cutting structure on which a minimum necessary clearance angle γ_min must be provided and which for simplicity is not inclined to the transverse plane (i.e. the rotatable cutting member axis lies in the plane of the page). Focussing for the present on the right side of the Y axis in FIG. 10c, the angles ϕ3 and ϕ4 denote the interference angles at the cutting face 54 and rear face 55 respectively; the latter angle in this case being the greatest. A clearance angle of ϕ4 imparted to the cutting structure provides clearance, though depending on the magnitude of such, it may adversely weaken the cutting edge. The angle ϕ5 also provides adequate clearance and results in a more robust cutting edge. Angle ϕ5 is determined by the thickness T of the cutting structure (including any supporting region of the rotatable cutting member) and the location of the intersection of the helix H (visible as a circle in this plan view) with the rear face; said helix H having a radius defined by the point of interest P on the cutting edge and a pitch defined by the translation per revolution of the drill body. The radius r_r extending on the rear face 55 from its centre ‘Or’ to the point of intersection of the helix is used when calculating the angle ϕ5.

FIG. 10d shows an example where the interference angle at the cutting face 54 is greater than at the rear face 55. While the depictions in FIGS. 10c and 10d are two-dimensional, the rational outlined here is readily and necessarily applicable to the three dimensions in which embodiments of the present disclosure are realised.

The conical or similar form of the clearance face of a cutting structure, being concentric with the axis of rotation of the rotatable cutting member, ensures the clearance angle relative to the axis of the rotatable cutting member is constant at all points on the circumference of that cutting structure. With respect to the presentation of the cutting structure to the material in which a hole is to be formed, the effective clearance angle varies along the engagement region of the cutting edge. By way of illustration and with reference to FIG. 10b, with the axis of the rotatable cutting member inclined only downwardly in the z-direction by the angle α2 (i.e., α1≈0), the largest effective clearance angle, ϕ3 in FIG. 10b, is in the vicinity of point P3 on the cutting edge which is most distal the drill body. The effective clearance angle at this point is the sum of the minimum necessary clearance angle on the cutting structure and the angle of downward inclination α2; i.e., ϕ3≈max(ϕ1, ϕ2)+α2.

More generally, determination of the maximum effective clearance angle, hereafter denoted γ_{eff max}, employs the minimum interference angle over the entire engagement region of the cutting edge, rather than α2 as in the simplified case above. Therefore (and omitting for the present, the possible refinement noted above concerning a maximum interference angle at the rear face of the cutting structure), γ_{eff max} is the difference between the maximum and the minimum angles of interference (ϕmax and ϕmin respectively); i.e., γ_{eff max}=ϕmax−ϕmin. Generally, ϕmin is a negative quantity in accordance the convention adopted in this disclosure.

Where there is a multiple m of engagement regions on a cutting structure, m being a whole number greater than one, γ_{eff max} within each engagement region is determined using the maximum of the m minimum necessary clearance angles, each of the m minimum necessary clearance angles is determined for each engagement region. Part of the cutting edge comprising one instantaneous engagement region at a first position relative to the drill body will at other times comprise part of another instantaneous engagement region at a second position relative to the drill body. γ_{eff max} within an engagement region is determined using the minimum angle of interference for that engagement region.

Conditions 1 and 2 and the Equations 1-13 hereinbelow summarise the considerations outlined above with regard to determining γ_{eff max}. These equations define the maximum effective clearance angle γ_{eff max} on an engagement region of a cutting structure which is provided with a minimum necessary clearance angle γ_min. The ‘Max’ terms in Equations 1 and 2 represent the minimum necessary clearance angle. The ‘Min’ terms in Equations 1 and 2 represent the minimum (most negative) angle of interference. Each of these angular quantities are independently dependent on the parameters α1, α2, d, T, R_b, r_c and also the hole forming tool translation per revolution f which determines the pitch of the helical path followed by each point on the engagement region of the cutting edge of interest.

FIG. 11a illustrates the geometry relating to Equations 1-13. The parameter r_r in Equations 2 and 10 is as depicted in FIGS. 10c and 10d. Where Condition 2 holds true, Equation 2 applies and the minimum necessary clearance angle is determined at the rear face of the cutting structure.

The position of each point of interest on an engagement region is given with respect to the rotatable cutting member by the coordinates λ and t. λ lies in the interval [λ1, λ2], where λ1 and λ2 are cutting face angular coordinates denoting the extremities of the engagement region of interest. The ‘Min’ terms in Equations 1 and 2 are evaluated over the interval [λ1, λ2]. Where there is more than one engagement region on a cutting structure, the ‘Max’ terms are evaluated over each angular interval relating to each engagement region on the cutting structure of interest. That is to say, the ‘Max’ terms are evaluated over the entire set Γ, where Γ comprises at least one sub-set, each sub-set being the angular interval [λ1, λ2] for each engagement region on the cutting structure of interest. The determination of the coordinates λ1 and λ2 is described below; but by way of illustration, where for an isolated cutting structure, the hole forming tool translation per revolution f is negligible in magnitude relative to the cutting structure radius r_c, λ1 and λ2 are about 0° and 180°, respectively.

In FIG. 11a, λ is expressed relative to a reference radial 56 of the cutting face which lies in a second transverse plane of the drill body and extends inwards with respect to the axis of rotation of the drill body (the latter coincident with the Z axis in FIG. 11a). Where two or more separate engagement regions exist on a cutting face, the maximum value of the minimum necessary clearance angle in each region applies to all other regions.

The parameter t is either 0 or T. The quantity (d−t) is referenced from the point of intersection I of the axis of the rotatable cutting member and the reference radial 53 of the drill body, which in FIG. 11a is coincident with the X-axis. The transformation from the rotatable cutting member coordinate system (cX-cY-cZ) to the coordinate system of the drill body (X-Y-Z) is contained within Equations (7)-(9) hereinbelow. The Z coordinate, z_i, is expressed relative to the point I.

By the term “point of interest P” is meant any one of the numerous points on the cutting structure (in the prescribed range of values for λ and t), all of which must be considered in the solution to the system of equations. According to the convention adopted here, the angles α1 and α2 as shown in FIG. 11 are in the positive sense. Caution is to be exercised concerning the calculation of both the magnitude and sense of the angle subtended between the vectors {right arrow over (A)} and {right arrow over (Tn)}. At any point (x_i, y_i, z_i) on the cutting edge, χ has a value of +1 if {right arrow over (Tn)} at that point extends inwardly with respect to the rotatable cutting member axis and χ has a value of −1 if {right arrow over (Tn)} extends outwardly with respect to the rotatable cutting member axis. Each of the parameters α1, α2, d, T, R_b and r_c may be set to a single defined value for a given solution to the Equations 1-13.

$\begin{array}{cc}\left(\underset{\lambda \in \Gamma ;t=0}{\mathrm{Max}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)\ge \left(\underset{\lambda \in \Gamma ;t=T}{\mathrm{Max}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)& \mathrm{Condition}1\\ {\gamma }_{\mathrm{eff}\max }=\left(\underset{\lambda \in \Gamma ;t=0}{\mathrm{Max}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)-\left(\underset{\lambda \in \left[\lambda 1,\mathrm{\lambda 2}\right];t=0}{\mathrm{Min}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)& \mathrm{Eqn}.1\\ \left(\underset{\lambda \in \Gamma ;t=0}{\mathrm{Max}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)<\left(\underset{\lambda \in \Gamma ;t=T}{\mathrm{Max}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)& \mathrm{Condition}2\\ {\gamma }_{\mathrm{eff}\max }=\left(\underset{\lambda \in \Gamma ;t=T}{\mathrm{Max}}\left(A\tan \left(\frac{r_c-r_r}{T}\right)\right)\right)-\left(\underset{\lambda \in \left[\lambda 1,\mathrm{\lambda 2}\right];t=0}{\mathrm{Min}}\left(\chi ·A\cos \left(\frac{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}{\overrightarrow{\mathrm{Tn}}·\overrightarrow{A}}\right)\right)\right)& \mathrm{Eqn}.2\end{array}$

wherein {right arrow over (A)} represents the direction vector of the rotatable cutting member axis and is given by:

{right arrow over (A)}=−sin(α1)·cos(α2),−cos(α1)·cos(α2), sin(α2)  Eqn. 3

wherein {right arrow over (Tn)} represents the tangent to the helix passing through the point of interest Pt_i, on the cutting structure with coordinates (x_i, y_i, z_i); the direction vector for {right arrow over (Tn)} being given by:

$\begin{array}{cc}\overrightarrow{\mathrm{Tn}}=〈\sin \left({\theta }_i\right),-\cos \left({\theta }_i\right),\left(\frac{f}{2·\pi ·r_i}\right)〉& \mathrm{Eqn}.4\end{array}$

wherein the parameters r_i and θ_i represent the polar coordinates of the point of the interest relative to the drill body axis of rotation, r_i being the radius of the circle of rotation for that point, whereby r_i and θ_i are given by:

$\begin{array}{cc}{r}_i=\sqrt{x_i^2+y_i^2}& \mathrm{Eqn}.5\\ {\theta }_i=A\tan \left(\frac{y_i}{x_i}\right)& \mathrm{Eqn}.6\end{array}$

The coordinates of the point of interest Pt_i, are given by:

x_i=−R_b+sin(α1)·cos(α2)·(d−t)+r_c·cos(λ)·cos(α1)−r_c·sin(α2)·sin(λ)·sin(α1)   Eqn. 7

y_i=cos(α1)·cos(α2)·(d−t)−r_c·sin(α2)·sin(λ)·cos(α1)−r_c·cos(λ)·sin(α1)   Eqn. 8

z_i=−r_c·sin(λ)·cos(α2)·sin(α2)·(d−)  Eqn. 9

and for where condition 2 is true; r_r is given by:

r_r=r_c−√{square root over ((x_i−x_r)²+(y_i−y_r)²+(z_i−z_r)²)}  Eqn. 10

wherein x_r, y_r, z_r are the coordinates of the centre of the rear face of the cutting structure and are given by:

x_r=−R_b+sin(α1)·cos(α2)·(d−T)  Eqn. 11

y_r=cos(α1)·cos(α2)·(d−T)  Eqn. 12

z_r=−sin(α2)·(d−T)  Eqn. 13

The parameter f, representing the hole forming tool translation per revolution during use, is limited by the available drilling torque and/or the maximum permissible loads and drilling speeds for the hole forming tool. Where more than one cutting structure bears a portion of the cutting load on a given circle of rotation about the axis of the drill body, the maximum depth of engagement of each cutting structure is some fraction of the translation per revolution and this should not generally exceed the radius of the cutting structure. More preferably, it does not exceed about half the radius of the cutting structure, so as to ensure the integrity of the rotatable cutting member and associated journal or roller element bearings. Furthermore, in those embodiments of the invention wherein cutting structures are bonded to rotatable cutting members by means of a braze layer or where the materials from which cutting structures are composed have limited thermal stability, the maximum depth of engagement of a cutting structure may be further limited. The maximum operating temperature is proportional to the product of hole forming tool rotational speed and torque. Torque in turn is proportional to the cross sectional area of cut, the hole forming tool translation per revolution and the hardness of the material being drilled. When forming holes in very hard materials and or at high rotational speed, the maximum depth of engagement for cutting structures is preferably limited to r_c/3 or even r_c/4. Several cutting structures may engage the material in which a hole is to be formed at any given circle of rotation. The hole forming tool translation per revolution is preferably limited such that it does not substantially exceed r_c/2 or at most does not exceed r_c. In practice, the majority of hole forming operations are limited by available drilling torque such that f is typically seldom greater than about 6 or 7 mm.

For the or each engagement region on a cutting structure, γ_{eff max} will preferably be less than a maximum value so as to result in robust cutting structures and this maximum value is discussed below. The configuration of the cutting structures and the resulting overlap guides the selection of a specific combination of the parameters α1, α2, d, T, R_b and r_c. More particularly, the degree of overlap between cutting structures may be varied so as to avoid excessively large minimum necessary clearance angles and consequently, excessively large maximum effective clearance angles γ_{eff max}.

Certain combinations of the parameters α1, α2, d, T, R_b and r_c result in an identical cutting structure geometry as certain other combinations of these parameters. With reference to FIG. 11b, the combination whose parameters α1, R_b and d are post-scripted with ‘a’, differ from the combination whose parameters are post-scripted with ‘b’, yet both are an equivalent geometry in terms of the presentation of the cutting structure to the material in which a hole is to be formed. The equivalence in such cases is described in Equation 14 (where the subscripts ‘a’ and denote any two different combinations of the relevant parameters).

R_ba+d_a²·R_ba·d_a·sin(α_1a)=R_bb²−2·R_bb·d_b·sin(α_1b)  Eqn. 14

Most hard cutting tool materials tend to be relatively weak in tension and vulnerable to fracture where a cutting edge is provided with an excessively large clearance angle. Cutting materials of different mechanical properties may permit smaller or larger clearance angles and hence, a greater range of permissible angles of inclination.

FIG. 12a shows a simplified two-dimensional cross-section representation of a region of a cutting structure in which the angle β is equivalent to the minimum interference angle, while γ is equivalent to the quantity γ_min. The effective clearance angle γ_eff is the sum of these two angles. Both a smaller clearance angle and a smaller effective clearance angle provide for a stronger cutting edge. The angle of inclination of the cutting face 57, corresponding to the angle β, has a strong influence on the forces acting on the cutting structure—the forces typically increasing 2 to 4 times or more where the angle of inclination β increases from 0° to 50°. In FIG. 12a, the region 58 is where the maximum normal compressive stress exists on the cutting face. The region 59 is where the maximum tensile stress exists within the cutting face.

FIG. 12b shows the maximum tensile stress on the cutting face of a circular cutting structure of 25 mm radius, where the depth of engagement is 2 mm. The stresses are determined analytically from specific cutting pressures known in the art; specifically, the values range from 150 MPa to 450 MPa for cutting face inclination angles of 0° to 50°; the relationship approximated as being linear in nature. Young's modulus and poisons ratio of the cutting tool material are E=600 GPa and ρ=0.21. These values of specific cutting pressure are representative for example, for sedimentary rock being deformed under hydrostatic pressures of about 20 MPa and many non-ferrous alloys cut under atmospheric pressure. FIG. 12b serves solely to demonstrate the influence of the three angular quantities (in FIG. 12a) on the maximum tensile stress on the cutting face. In practice, thermal stresses, residual stresses within the cutting material and impact loading for example, will generally serve to increase the maximum tensile stresses occurring on the cutting face, while lower forces may result when cutting softer materials in the absence of drilling vibration and impact loading.

Hard cutting tool materials may exhibit tensile strengths as low as 1200-1500 MPa and relatively low Weibull moduli. Preferably, a margin of safety of, for example 2 to 3, is used such that cutting structures configured on the hole forming tool and using cutting materials known in the art have a maximum effective clearance angle of not more than about 45° over the majority of each engagement region of the cutting edge. Insofar as it represents the majority of cases, this limit for γ_{eff max} forms the basis of subsequent disclosure. Where it is necessary to form holes in extremely hard materials and/or with impact loading, the maximum effective clearance angle γ_{eff max} is preferably about 35°.

This criteria concerning γ_{eff max} may be subject to a certain allowance where the depth of engagement is small relative to the size of any bevels, radii or combinations of same disposed at the cutting edge. By the term ‘cutting edge’ is meant the outermost aspect of the cutting face of a cutting structure relative the axis of the rotatable cutting member; the cutting face including any bevels or radii disposed at the cutting edge. Edge bevels and radii are preferably limited in size to a fraction of the anticipated depth of engagement, as very high cutting forces will otherwise result. The effective depth of engagement varies along the engagement region of a cutting structure, decreasing towards the innermost and outermost extremities of the engagement region.

This point is illustrated in FIG. 13a which depicts an isolated circular cutting structure cs, which has a bevel of width Won its cutting face. The broken (discontinuous) line in FIG. 13a shows a semi-circular profile, also of radius R, but with its centre displaced by an amount fin the Z+ direction. The crescent-shaped region enclosed between the broken line and the heavier solid (continuous) line represents the shape of the un-deformed cross-sectional area of cut, resulting from the translation of the cutting structure by a distance f per revolution. The parameter L_a in FIG. 13a depicts the projected engagement length L, which is equivalent to the span of the engagement region of a cutting edge along a radial of the drill body; as is determined by first projecting the engagement region of the cutting edge onto a radial plane of the drill body, and subsequently projecting this first projection onto a radial of the drill body. By the term ‘projected edge length’ is meant the same projection, but of the entire cutting edge as distinct to only the engagement region. For example, the projected edge length shown as L_b in FIG. 13b is greater than L_a2 which is the corresponding projected engagement length.

At the position marked x-x in FIG. 13a, the depth of engagement is maximal. For example, taking the values R=25 mm, f=2 mm and W=1 mm; at the cutting face radials bounding the 124° sector, the depth of engagement h, is approximately half the maximal value. If a similar sector of 110° were constructed, its radials would denote the positions where the depth of engagement was approximately 60% of the maximal value. A less tensile or a substantially compressive stress state may exist at these positions, relative to where the depth of engagement is greater than the width of the bevel. As such, the maximum effective clearance angle γ_{eff max} may be permitted to exceed a limit to otherwise hold over the majority of the engagement region of the cutting edge where the depth of engagement is large relative to the size of edge chamfers and or radii. The dimension L_ae in FIG. 13a depicts the portion of the projected engagement length defined by a 124° sector and in this case, L_ae is 85% of L_a. For a sector of 110°, the dimension L_ae will be 78% of L_a.

With reference to FIG. 13b, where two cutting structures of the same radius R overlap, the maximum possible projected engagement lengths for each cutting structure L_a1 and L_a2 are less than the corresponding dimension L_a for an isolated cutting structure of the same radius. The extremities of the engagement region of a cutting edge of an overlapped cutting structure are dependent also on the dimension f. Noting the drill body axis of rotation B-B; for the cutting structure cs_1, the innermost, with respect to B-B, extremity of its engagement region is indicated by reference numeral 60 and the outermost possible extremity of its engagement region by reference numeral 62. For cs_2, the innermost possible extremity of its engagement region is indicated by reference numeral 61 and the outermost extremity of its engagement region by reference numeral 63. The relative angular position of cutting structures about the axis of the drill body and the dimension f determine the precise location of the points 61 and 62 and the precise values for L_a1 and L_a2. For example, in no case can L_a2 be less than L_a2_min or greater than L_a2_max.

Preferably, the majority of cutting structures disposed on the drill body each overlap with at least one other cutting structure, said other cutting structure being rotatable in accordance with the present disclosure or in accordance with prior art cutting structures, and the values for λ1 and λ2 which denote the extremities of the engagement region are determined accordingly. While the maximum permissible effective clearance angle criterion applies over a majority of the each projected engagement length independently, the minimum necessary clearance angle must be determined over the entire interval [λ1, λ2] and where multiple engagement regions exist on a cutting structure, over the entire set Γ, Γ comprising multiple sub-sets, each sub-set being the interval [λ1, λ2] for each engagement region.

FIG. 13c depicts the projection of the edges of two cutting structures cs_3 and cs_4, onto a radial plane of a drill body which has an axis of rotation B-B. Each cutting structure is shown as a bold continuous line. cs_3 and cs_4 have radii R₃ and R₄ respectively. For the purposes of simplified illustration, the axis of the cutting structures extend normal to the page, thereby not being inclined relative to the plane normal to axis B-B, nor to a radial of the drill body; i.e., both α1 and α2 are 0°. The cutting face centres 64 and 65 are separated in the X direction by a distance lx. Shown also are broken partial profiles of circles, cs_3 (n−1) and cs_4 (n−1), of radii R₃ and R₄ respectively, whose centres are displaced in the +Z direction by an amount f. The profiles cs_3 and cs_4 represent the position of the cutting edges at drill body revolution n while cs_3 (n−1) and cs_4 (n−1) represent the position of the same profiles on drill body revolution n−1; f representing the drill body translation per revolution. The areas enclosed between the profiles cs_3 (n−1) and cs_3, 66, and cs_4 (n−1) and cs_4, 67, are the un-deformed cross-sectional areas of cut on each cutting structure. The region where these areas overlap 68 is effectively shared between the two cutting structures in a manner dependent on the relative angular position of the cutting structures about the drill body axis B-B. cs_3 is not overlapped at its innermost (relative to the axis B-B) region and cs_4 is not overlapped at its outermost region. In FIG. 13c, several points relating to the determination of the values λ1 and λ2 are identified:

• • Point 69 is the innermost possible position of the innermost extremity of the engagement region on cs_4
  • Point 70 is the outermost possible position of the outermost extremity of the engagement region on cs_3
  • Point 71 is both the innermost possible position of the outermost extremity of the engagement region on cs_3 and the outermost possible position of the innermost extremity of the engagement region on cs_4
  • Point 72 is the innermost extremity of the engagement region on cs_3
  • Point 73 is the innermost extremity of the engagement region on cs_4

For the purposes of determining the angles λ1 and λ2, point 69 is preferably the innermost extremity of the engagement region on cs_4 and point 70 preferably the outermost extremity of the engagement region on cs_3. Adopting points 69 and 70 as the extremities of the engagement regions avoids otherwise more complex calculations which would incorporate the relative angular positions of the cutting structures about the drill body axis of rotation, such complexities providing little practical benefit. This approach provides a slightly more conservative estimate for the minimum necessary clearance angle and the maximum effective clearance angle; both quantities will be over-estimated by no more than several degrees in the worst case.

FIG. 13d shows an enlarged view of the points in FIG. 13c, with angles subtended between lines jointing certain of these points.

λ1 and λ2 for cs_3 are denoted λ1₃ and λ2₃. λ1 and λ2 for cs_4 are denoted λ1₄ and λ2₄. Each of λ1₃, λ2₃, λ1₄ and λ2₄ are the sum of two angular quantities as given by Equations 15-18, where λ1_3a and λ2_4a are 0° and 180°, respectively, by definition and the other quantities are as depicted in FIGS. 13c and 13d. The postscripts 3 and 4 employed in the Equations and Figures relate to the arbitrary cutting structure number.

λ1₃=λ1_3a−λ1_3b=−A sin(f/2·R₃)  Eqn. 15

λ2₃=λ2_3a+λ2_3b  Eqn. 16

λ1₄=λ1_4aλ1_4b  Eqn. 17

λ2₄=λ2_4a−λ2_4b=180°+A sin(f/2·R₄)  Eqn. 18

The angular quantities in Equations 16 and 17 are determined from the parameters, R₃, R₄, IX and f. A similar methodology, as presented here for cs_3 and cs_4 is readily extended to any arrangement of cutting structures whose axes are inclined relative to a transverse plane of the drill body and or to reference radials of the drill body and where the cutting face centres may lie in different transverse planes of the drill body.

With regard to FIG. 13c, it is noted that in conservatively adopting the points 69 and 70 as extremities of the engagement regions of cs_4 and cs_3 respectively, the engagement region may be approximately defined in terms of the parameter f relative to three transverse planes of the drill body. Where the cutting structures are disposed at a distal end of the drill body, the first transverse plane visible as a line 74 is towards the proximal end of the drill body. A third transverse plane visible as a line 75, is positioned at a distance f from the first transverse plane, this third transverse plane being more distal the distal end of the drill body than the first transverse plane is distal the distal end of the drill body. A fourth transverse plane, partly visible as lines 76 is at a distance f/2 from the cutting face centre of interest and lies between the cutting face centre of interest and the first transverse plane. The fourth transverse plane has a distal side 77 towards the distal end of the drill body and a proximal side 78 towards the proximal end of the drill body. The engagement region(s) of a cutting edge of a cutting structure of interest can thus be adequately approximated as that part of the cutting edge which lies on the distal side of the fourth transverse plane where each of any remaining part or parts of the cutting edge which lie on the distal side of the fourth transverse plane represent an overlapped region. Within said overlapped region, any first point which lies on the cutting edge shares a circle of rotation with at least one second point, said second point which lies on a cutting edge of any other cutting structure disposed on the rotatable drill body; wherein said first point is less distal the third transverse plane than said second point is distal the first transverse plane.

The precise conditions of use of the hole forming tool, including the translation per revolution f, and hence the precise values for λ1 and λ2 are rarely known in advance and in many applications may vary over the lifetime of the hole forming tool. It is, however, generally preferable that γ_{eff max} is not substantially greater than about 45° over at least about 80% of the projected engagement length of each cutting edge of each rotatable cutting member on the drill body. The following examples illustrate the influence of the parameters α1, α2, R_b, d and T on the minimum necessary clearance angle and the resulting maximum effective clearance angle on isolated cutting structures. Subsequent examples deal with overlapping cutting structures.

FIGS. 14 and 15 each contain 12 charts, in each of which is shown the variation in γ_{eff max} and γ_min on the engagement region of cutting structures as a function of distance along a radial of the drill body. Each chart is for a specific combination of α1 and α2. The cutting structure radius r_c, is expressed as a fraction of the R_b dimension which is set to unity. Within each chart, there are γ_{eff max} and γ_min curves for each of three values of the cutting structure radius, r_c=0.3·R_b, 0.6·R_b and 0.9·R_b. The cutting structure thickness T and distance d from the point I on the drill body reference radial are expressed as a fraction of the cutting structure radius; T=d=r_c/3 in FIG. 14 and T=d=r_c/2 in FIG. 15. For all charts, the translation per revolution is set as 0.015·R_b. γ_{eff max} is shown by continuous curves and γ_min by broken curves. Where r_c=0.9·R_b, it spans a greater length of the drill body radial and accordingly, the curve has the greatest span across the horizontal axis of the chart (horizontal meaning in the direction of the width of the page). The span of a cutting structure along the drill body radial is, in the case of non-overlapping cutting structures, equivalent to its projected engagement length. Each of the 12 charts in each of FIGS. 14 and 15 share the same axis ranges: −30° to +60° on the vertical axis and 0 to 2 on the horizontal axis. In certain cases, for the purposes of clarity, only parts of some curves are visible; the occluded parts representing very large (>+60°) or very small (<−30°) quantities.

Concerning the format and significance of the data, reference is now made to the upper right chart in FIG. 14, wherein α2=25°, α1=−5° and d=T=r_c/3. The centremost curve (i) in this chart displays the γ_{eff max} values for a cutting structure of r_c=0.3·R_b; curve (ii) relates to r_c=0.6·R_b and curve (iii) relates to r_c=0.9·R_b. For r_c=0.3·R_b, the largest effective clearance angle is approximately 35° and occurs at a drill body radial position of approximately 1.0, while the extremities of the cutting structure are located at drill body radial values of approximately 0.7 and 1.3. The smallest effective clearance angle (0°) occurs at the innermost aspect of the cutting edge, where the minimum necessary clearance angle is greatest (about 12°). In relation to curves (ii) and (iii) in the upper right chart of FIG. 14, γ_{eff max} increases as the cutting structure radius increases. As may be ascertained from the corresponding curves for the minimum necessary clearance angle, the reason for this is the increasing values of γ_min at the innermost aspect of the cutting structure. Generally, the larger the re value, the larger γ_{eff max}. This is most evident where the radius of the cutting structure extends closer to the axis of rotation of the drill body (towards the drill body radial position of zero). As the angle α1 is increased, the innermost and outmost aspect of the cutting structure extends closer to the drill body radial position of zero. Referring to the rightmost column of charts in FIG. 14 and the curves for the larger cutting structure as α1 is increased from −5° to 25°, the outermost aspect of the cutting structure similarly moves inwards with respect to the drill body axis. A more inwardly inclined rotatable cutting member axis, with all other parameters constant, results in a smaller diameter drilled hole. In the rightmost column of charts in FIG. 14, the outermost point on the cutting structure decreases from 1.93 to 1.81 as the angle α1 is increased from −5° to +25°. Where d is larger, this effect is more pronounced; in FIG. 15, where d is 50% larger than in FIG. 14, the outermost point on the cutting structure decreases from 1.96 to 1.80 as the angle α1 is increased from −5° to +25°. Such relationships will apply in designing hole forming tools to drill holes of specific diameter.

Certain combinations of the angles of inclination α1 and α2 and parameters d and T in FIGS. 14 and 15 provide for smaller maximum effective clearance angles due primarily to the smaller minimum necessary clearance angles. In FIG. 14, the combination of α1=5° and α2=5° result in a γ_{eff max} of about 7° where r_c=0.3·R_b. Where r_c=0.6·R_b, the maximum effective clearance angle is about 20°, and the effective clearance angle exceeds 15° for about 80% of the projected engagement length. The effective clearance angle for the cutting structure with r_c=0.9·R_b exceeds 45° over the majority of its projected engagement length and this will result in a relatively weak cutting edge vulnerable to fracture. The excessively high effective clearance angles for r_c=0.9·R_b relate to the very large (positive) values for the minimum necessary clearance angle, which exhibit a pronounced increase beyond 15° for drill body radial positions less than about 0.4. It is useful also to note that as the angle of inclination α2 increases, the minimum necessary clearance angle decreases.

Not all combinations of the parameters α1, α2, d, T and R_b permit a relatively large cutting structure radius of r_c=0.9·R_b, such that the maximum effective clearance angle γ_{eff max} is not substantially larger than about 45° over about 85% of the projected engagement length L. Examples of such are found in the third row of charts in FIG. 14. Many more combinations of these parameters are permissible where the cutting structure radius are r_c=0.6·R_b, and more again where the cutting structure radius are r_c=0.3·R_b. In those exceptional cases where the cutting structures on a hole forming tool are configured so as not to overlap and the cutting structure radius must be as large as 0.9·R_b, these combinations of parameters (found in the third row of charts in FIG. 14) are examples of preferred embodiments of the present invention. More generally, on hole forming tools in accordance with the of the present invention and absent overlapping cutting structures, the combinations of the parameters α1, α2, R_b, r_c, d and T relating at least to those curves in FIGS. 14 and 15 for which the maximum effective clearance angle γ_{eff max} does not substantially exceed about 45° over at least about 80% of the projected engagement length L are also examples of preferred embodiments of the present invention. Many other combinations of the parameters α1, α2, R_b, r_c, d and T are possible and subject to these combinations of parameters satisfying Equations 1-13 over at least about 80% of their projected engagement length L, such combinations of parameters are also preferred embodiments of the present invention.

With regard to curve (iv) in FIG. 14, if it were desirable to use such a relatively ‘larger’ cutting structure (large relative to the R_b value; i.e., r_c=0.9·R_b) with the related combination of parameters α1, α2, d and T, it would be necessary to shield the innermost aspect of this cutting structure with another overlapping cutting structure. Where the innermost region of the larger cutting structure is shielded, for example to a drill body radial position of approximately 0.5, the minimum necessary clearance angle is reduced to about 5° (from a maximum value of 60° when un-shielded). γ_{eff max} for the unshielded cutting structure is about 67° (beyond the scale in the chart), shielding the innermost portion of this reduces eff max to v about 12° (i.e., 67°−(60°−5°)). Therefore, where rotatable cutting members are configured so as to provide overlap between adjacent cutting structures, the combination of the parameters α1, α2, d, T, R_b and r_c which provide preferred embodiments is greatly increased.

For hole forming tools which comprise multiple cutting structures, the cutting structures are preferably configured such that their cutting edges overlap when projected about the axis of drill rotation onto a radial plane of the drill body. The degree of overlap is expressed as that which results in a certain percentage reduction in the projected engagement length L of the cutting structure of interest. Two cases are considered hereinbelow: firstly, where the projected engagement length L of the cutting edge of a cutting structure of interest is reduced by 15% at its innermost aspect (more proximal the drill body axis) and secondly, where the projected engagement length L is reduced at the outermost aspect of the cutting structure.

Tables 1 and 2 detail several geometrical parameters of hole forming tools in accordance with the present disclosure, all such parameters being dependent on α1, α2, d, T, and R_b. Each of Tables 1 and 2 comprise 20 sub-tables arranged in four rows and five columns. Within each sub-table, α1 varies from −20° to 40° and α2 varies from 0° to 50°. The sub-tables in different rows differ in the relative values for d, T and r_c, all expressed as a fraction of R_b. For example, in row (a), d=T=r_c/3. All other length dimensions are expressed as fractions or multiples of R_b which is set to unity.

The first column in each of Tables 1 and 2 notes the maximum permissible cutting structure radius for the stated values of α1, α2, R_b, d and T so as to ensure the maximum effective clearance angle γ_{eff max} is 45° or less where that cutting structure is not overlapped by an adjacent cutting structure. The second column in Table 1, labelled ‘2.a)’, notes the maximum permissible cutting structure radius r_c, for the stated values of α1, α2, R_b, d and T so as to ensure the maximum effective clearance angle γ_{eff max} does not exceed 45° where the outermost 15% of the projected edge length is shielded by another adjacent overlapping cutting structure. The second column in Table 2, labelled ‘2.a)’, notes the maximum permissible cutting structure radius r_c for the stated values of α1, α2, R_b, d and T so as to ensure the maximum effective clearance angle γ_{eff max} does not exceed 45° where the innermost 15% of the projected edge length is shielded. The third column in each of Tables 1 and 2, labelled ‘2.b)’, shows the minimum necessary clearance angle, which must be provided on an otherwise cylindrical cutting structure so as to avoid interference between the side surface of that cutting structure and the surface of the formed hole. These values for the minimum necessary clearance angle are determined where the stated degree of overlap exists (and not for the isolated cutting structure referenced in column 1). While 15% overlap is relatively small—in practice, it often being 50% or greater—it better serves to demonstrate the effect of cutting structure overlap on the permissible combinations of the parameters α1, α2, d, T, R_b and r_c. A larger degree of overlap would permit a broader range of parameter combinations as will be determinable following the present disclosure.

Concerning the format and significance of the data in Tables 1 and 2, it is useful to consider three examples in more detail. For an isolated cutting structure, where the angles α1 and α2 are each independently 20° and where d=T=r_c/3 (row a of Table 1), the maximum permissible cutting structure radius is 0.6·R_b so as to ensure the maximum effective clearance angle γ_{eff max} is 45° or less. For a cutting structure with the same parameters α1, α2, R_b, d and T which is overlapped at its outmost region by an adjacent cutting structure, the maximum permissible cutting structure radius is 0.8·R_b so as to ensure γ_{eff max} is 45° or less (Table 1, column 2.a). The minimum necessary clearance angle on is 0° (Table 1, column, 2.b). For an isolated cutting structure where the angles α1 and α2 are each independently 20° and where d=T=r_c/3 (row a of Table 2), the maximum permissible cutting structure radius is 0.6·R_b so as to ensure the maximum effective clearance angle γ_{eff max} is 45° or less. For a cutting structure with the same parameters which is overlapped at its innermost region, the maximum permissible cutting structure radius is 0.7·R_b so as to ensure γ_{eff max} is necessary 45° or less. The minimum clearance angle in this case is 8°. For an isolated cutting structure where the angles α1 and α2 are both 40° and where d/2=T=r_c/2 (row c of Table 1), it is not possible to achieve a maximum effective clearance angle γ_{eff max} of 45° or less; i.e., the maximum permissible cutting structure radius is 0 (or at least no greater than 0.05 considering the resolution of the data). For a cutting structure with the same parameters which is overlapped at its outermost region the maximum permissible cutting structure radius is 0.6·R_b to ensure γ_{eff max} is 45° or less. This cutting structure may be of cylindrical form; i.e., the minimum necessary clearance angle is 0°.

Some general relationships may be observed in Tables 1 and 2. The maximum permissible cutting structure radius for a given combination of α1, α2, R_b, d and T is more strongly influenced by shielding the innermost region of its cutting edge, in comparison to shielding its outermost region of its cutting edge. Providing overlap at the outermost aspect of a cutting structure has less benefit in terms of reducing the minimum necessary clearance angle, compared to providing the same degree of overlap at the innermost aspect of that same cutting structure. Increasing the angle of inclination α2 generally results in a decrease the minimum necessary clearance angle.

The resolution in Tables 1 and 2 for the maximum permissible cutting structure radius r_c, is limited to +1-0.05·R_b (in the worst case) and the minimum necessary clearance angles are rounded to the nearest degree. Greater precision may be derived following Equations 1-13. Alternatively, intermediate or other values may be adopted for each parameter without deviating from the present disclosure, as may alternate combinations of the parameters d, T and r_c; as for example described by Equation 14. Furthermore, adopting different and or varying degrees of overlap are obvious extensions of the methodology disclosed here, as is configuring cutting structures which may be overlapped at their innermost, outmost and or more central regions (and Table 3 outlines several such scenarios). Similarly, alternately structured relationships will convey substantially the same meaning; whereby for example, one may determine the maximum permissible values for the parameter α1 where the parameters r_c, α2, R_b, d and T are specified and where the maximum effective clearance angle may or may not be substantially greater than a value other than 45° or 35° or any other limit defined on the basis of a specific application.

Referring again to FIGS. 10c and 10d, the left side of each depicts a plan view of a cutting structure at a particular orientation to the reference radial of the drill body. FIG. 10c represents a case where the minimum necessary clearance angle is determined by the maximum interference angle subtended at the rear face 55 of the cutting structure and in 10d, where the maximum interference angle is subtended at the cutting face 54 of the cutting structure. The left side of FIGS. 10c and 10d depict cutting structures of the same orientation and thickness T as on the right side of each Figure, but which have been provided with the minimum necessary clearance angles and which for clarity, have been rotated 180° about the axis of the drill body.

Superimposed on each of these cutting structures are two triangles, which represent cones in three dimensions. The base radius of the cones is equal to the dimension r_r—i.e., the radius of the rear face of the cutting structure after the minimum necessary clearance angle has been provided. It is reiterated here that reference to ‘cutting structure’ incorporates any adjacent, supporting region of the rotatable cutting member, which too is provided with the minimum necessary clearance angle. The height of the first cone in each case in FIGS. 10c and 10d, which overlays the cutting structure, has a dimension Lsa, which in this case is equal to the thickness T. More generally, where multiple cutting structures are disposed on a rotatable cutting member, Lsa represents the sum of the thickness values for each cutting structure. The height of the other cone in each case in FIGS. 10c and 10d, denoted Lsb, is dependent on the angle of inclination of the rotatable cutting member and the minimum necessary clearance angle.

These cones (depicted as triangles in FIGS. 10c and 10d) reasonably represent the physical space available in which to house the components necessary to securely retain the rotatable cutting member to the drill body and to permit its rotation. Where the dimension Lsb is greater than Lsa, it may be more preferable to configure the rotatable cutting member and associated bearings, seals and retaining mechanisms as depicted in FIG. 8b. Where Lsb is less than Lsa, it may be more preferable to adopt the configuration depicted in FIG. 8a. The dimension r_r and the maximum value of the parameters Lsa and Lsb must be greater than some minimum; the value of which is at least dependent on the anticipated conditions of use of the hole forming tool and the characteristics of the bearings and sealing elements.

In the most general sense, the r_r dimension is preferably not substantially less than about 0.5·r_c as otherwise, it will generally be found that there is insufficient space available for sealing elements and bearings of adequate size. The bearings must resist the forces acting on the cutting face of the cutting structures disposed on the rotatable cutting member and these forces generally act over a longer moment arm to that which can exist within the bearings. Furthermore, said bearings must reside within the annular region occupied by the seal elements. Consequently, it is preferable that the minimum value for r_r is 0.7·r_c. Regarding the maximum of the dimensions Lsa and Lsb, it is preferable that this at least equals the r_r dimension and more preferably about twice the r_r dimension. The construction of the shaft within the available volume is preferably subject to the known art in terms of optimising the ratio of shaft diameter to length, including for example, using stepped cantilever shafts. Where a sufficient volume of material is available for the construction of a sturdy bearing housing in the drill body, it is also necessary to ensure an adequate cross sectional area for the cantilever shaft where it adjoins the rotatable cutting member. Similarly, where a sufficient volume of material is available for the construction of a sturdy bearing housing in the rotatable cutting member, it is also necessary to ensure an adequate cross sectional area for the cantilever shaft where it adjoins the drill body.

Columns 2.c and 2.d in each of Tables 1 and 2 show the dimensions r_r and Lsb respectively. Lsb is determined on the basis of the maximum effective clearance angle γ_{eff max} being 45° or less and 15% overlap at the indicated location on the cutting structure. The parameters r_r is expressed as a fraction of r_c, and Lsb, as a multiple of r_c. According to the convention adopted here, the Lsa values are equal to the cutting structure thickness T and in the present examples therefore, always less than the Lsb values. r_r is between 0.8·R_b-1.0·R_b, while Lsb is generally equal to or greater than 1.4 (it being slightly less than 1.4 in only five instances in Table 1 and in only four instances in Table 2). Where multiple cutting structures are disposed on a rotatable cutting member, the Lsa parameter may be greater in value, with a corresponding reduction in the value of the parameter Lsb.

The characteristics of the un-deformed cross sectional area of cut on the or each cutting structure is an important aspect of realising in accordance with the present disclosure optimum combinations of at least, the angles of inclination, cutting structure radius and the position of cutting structures along the rotatable cutting member.

TABLE 1
Parameters providing a maximum effective clearance angle no greater than 45°; overlap at outer aspect of cutting structure.
	2.) 15% of Outer Region of Projected Edge Length of Cutting Structure Shielded
	1.) Isolated Cutting		2.b) Minimum
	Structure - No Shielding		Neccesary
	Maximum rc:	2.a) Maximum rc:	Clearance Angle,	2.c) Dimension rr	2.d) Dimension Lsb
	(fraction of Rb)	(fraction of Rb)	γ_min (Degrees)	(fraction of rc)	(multiple of rc)
	α2 (degrees)	α2 (degrees)	α2 (degrees)	α2 (degrees)	α2 (degrees)
	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50
Row (a)	α1 (degrees)	−20	0.1	0.1	0	0	0	0	0.2	0.1	0	0	0	0	29	23					0.8	0.9					5.4	9.3
d = T = (rc/3)		−10	0.4	0.4	0.4	0.1	0	0	0.5	0.4	0.4	0.1	0	0	35	26	21	13			0.8	0.8	0.9	0.9			2.3	2.7	2.8	6.5
		0	0.7	0.7	0.7	0.6	0	0	0.7	0.7	0.7	0.6	0	0	37	33	25	13			0.7	0.8	0.8	0.9			1.6	1.7	1.8	2.0
		10	0.8	0.8	0.8	0.8	0	0	0.8	0.8	0.8	0.8	0.4	0	27	23	15	6	1		0.8	0.9	0.9	1.0	1.0		1.5	1.5	1.6	1.6	2.1
		20	0.9	0.8	0.6	0	0	0	0.9	0.8	0.8	0.7	0.7	0	4	1	0	0	0		1.0	1.0	1.0	1.0	1.0		1.5	1.5	1.5	1.6	1.6
		30	0	0	0	0	0	0	0	0	0.3	0.3	0.4	0.1			6	0	0	0			1.0	1.0	1.0	1.0			1.6	1.6	1.6	1.8
		40	0	0	0	0	0	0	0	0	0	0	0	0.1						0						1.0						1.5
Row (b)	α1 (degrees)	−20	0	0	0	0	0	0	0.1	0.1	0	0	0	0	25	24					0.8	0.8					9.1	9.2
d = T = (rc/2)		−10	0.3	0.3	0.3	0	0	0	0.4	0.3	0.3	0	0	0	32	24	20				0.7	0.8	0.8				2.5	3.1	3.1
		0	0.5	0.5	0.5	0.5	0	0	0.6	0.5	0.5	0.5	0	0	36	24	19	15			0.6	0.8	0.8	0.9			1.6	1.9	2.0	2.0
		10	0.7	0.7	0.7	0.7	0	0	0.7	0.7	0.7	0.7	0.2	0	32	28	20	12	2		0.7	0.7	0.8	0.9	1.0		1.3	1.4	1.5	1.6	2.5
		20	0.8	0.8	0.8	0	0	0	0.8	0.8	0.8	0.7	0.6	0	30	23	11	0	0		0.7	0.8	0.9	1.0	1.0		1.2	1.3	1.4	1.6	1.6
		30	0.8	0.7	0	0	0	0	0.8	0.8	0.6	0.4	0.3	0.1	6	3	2	0	0	0	0.9	1.0	1.0	1.0	1.0	1.0	1.4	1.4	1.5	1.6	1.6	1.8
		40	0	0	0	0	0	0	0	0	0	0	0	0
Row (c)	α1 (degrees)	−20	0	0	0	0	0	0	0.1	0	0	0	0	0	28						0.7						10
(d/2) = T = (rc/2)		−10	0.2	0.2	0.1	0	0	0	0.2	0.2	0.1	0	0	0	25	24	16				0.8	0.8	0.9				4.6	4.6	7.0
		0	0.3	0.3	0.3	0.2	0	0	0.4	0.3	0.3	0.2	0	0	33	21	18	12			0.7	0.8	0.8	0.9			2.5	3.0	3.0	3.6
		10	0.4	0.4	0.5	0.4	0	0	0.5	0.4	0.5	0.4	0.1	0	34	19	24	12	3		0.7	0.8	0.8	0.9	1.0		1.9	2.3	2.1	2.3	3.4
		20	0.5	0.5	0.5	0.5	0	0	0.5	0.5	0.5	0.5	0.4	0	23	21	15	9	3		0.8	0.8	0.9	0.9	1.0		1.8	1.8	1.9	1.9	2.0
		30	0.6	0.6	0.6	0.6	0	0	0.6	0.6	0.6	0.6	0.5	0.1	35	31	22	10	0	0	0.6	0.7	0.8	0.9	1.0	1.0	1.4	1.5	1.6	1.7	1.8	1.9
		40	0.5	0.6	0.6	0.6	0	0	0.6	0.6	0.6	0.6	0.6	0	40	34	21	6	0		0.6	0.7	0.8	0.9	1.0		1.2	1.3	1.5	1.7	1.7
Row (d)	α1 (degrees)	−20	0	0	0	0	0	0	0	0	0	0	0	0
(d/3) = T = (rc/2)		−10	0.1	0.1	0.1	0	0	0	0.1	0.1	0.1	0	0	0	20	19	19				0.8	0.8	0.8				7.8	7.8	7.7
		0	0.2	0.2	0.2	0.1	0	0	0.2	0.2	0.2	0.1	0	0	20	19	16	10			0.8	0.8	0.9	0.9			4.1	4.1	4.1	5.3
		10	0.3	0.3	0.3	0.3	0	0	0.3	0.3	0.3	0.3	0	0	22	20	16	15			0.8	0.8	0.8	0.9			2.9	2.9	2.9	2.9
		20	0.4	0.4	0.4	0.4	0	0	0.4	0.4	0.4	0.4	0.2	0	28	26	21	15	3		0.7	0.8	0.8	0.9	1.0		2.3	2.3	2.3	2.3	2.5
		30	0.4	0.4	0.4	0.4	0.4	0	0.4	0.4	0.4	0.4	0.4	0	22	20	15	8	5		0.8	0.8	0.9	0.9	1.0		2.1	2.1	2.1	2.1	2.1
		40	0.4	0.4	0.4	0.4	0.5	0	0.4	0.4	0.4	0.4	0.5	0	20	18	11	4	10		0.8	0.8	0.9	1.0	0.9		1.9	1.9	1.9	2.0	1.9

TABLE 2
Parameters providing a maximum effective clearance angle no greater than 45°; overlap at inner aspect of cutting structure.
	2.) 15% of Inner Region of Projected Edge Length of Cutting Structure Shielded
	1.) Isolated Cutting		2.b) Minimum
	Structure - No Shielding		Neccesary
	Maximum rc:	2.a) Maximum rc:	Clearance Angle,	2.c) Dimension rr	2.d) Dimension Lsb
	(fraction of Rb)	(fraction of Rb)	γ_min (Degrees)	(fraction of rc)	(multiple of rc)
	α2 (degrees)	α2 (degrees)	α2 (degrees)	α2 (degrees)	α2 (degrees)
	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50	0	10	20	30	40	50
Row (a)	α1 (degrees)	−20	0.1	0.1	0	0	0	0	0.5	1.0	1.0	1.0	1.0	1.0	25	8	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.9	2.1	2.2	2.2	2.2	2.2
d = T = (rc/3)		−10	0.4	0.4	0.4	0.1	0	0	1.0	1.0	1.0	1.0	1.0	0	24	4	0	0	0		0.9	1.0	1.0	1.0	1.0		1.8	1.9	1.9	1.9	1.9
		0	0.7	0.7	0.7	0.6	0	0	0.9	0.9	0.9	0.9	0.8	0	18	1	0	0	0		0.9	1.0	1.0	1.0	1.0		1.7	1.8	1.8	1.8	1.9
		10	0.8	0.8	0.8	0.8	0	0	0.9	0.9	0.9	0.8	0	0	12	0	1	4			0.9	1.0	1.0	1.0			1.5	1.6	1.6	1.7
		20	0.9	0.8	0.6	0	0	0	0.9	0.9	0.7	0	0	0	5	5	8				1.0	1.0	1.0				1.5	1.5	1.5
		30	0	0	0	0	0	0	0.9	0.9	0	0	0	0	9	10					0.9	0.9					1.4	1.4
		40	0	0	0	0	0	0	1.0	1.0	0	0	0	0	12	12					0.9	0.9					1.3	1.3
Row (b)	α1 (degrees)	−20	0	0	0	0	0	0	0.2	0.9	1.0	1.0	1.0	1.0	21	20	0	0	0	0	0.8	0.8	1.0	1.0	1.0	1.0	5.4	2.1	2.2	2.2	2.2	2.2
d = T = (rc/2)		−10	0.3	0.3	0.3	0	0	0	0.7	1.0	1.0	1.0	1.0	1.0	23	8	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.0	1.8	1.9	1.9	1.9	1.9
		0	0.5	0.5	0.5	0.5	0	0	0.9	0.9	0.9	0.9	0.9	0	20	4	0	0	0		0.8	1.0	1.0	1.0	1.0		1.6	1.7	1.8	1.8	1.8
		10	0.7	0.7	0.7	0.7	0	0	0.9	0.9	0.9	0.9	0	0	17	1	0	0			0.8	1.0	1.0	1.0			1.4	1.6	1.6	1.6
		20	0.8	0.8	0.8	0	0	0	0.9	0.9	0.9	0	0	0	12	3	4				0.9	1.0	1.0				1.4	1.5	1.5
		30	0.8	0.7	0	0	0	0	0.8	0.8	0	0	0	0	8	8					0.9	0.9					1.4	1.4
		40	0	0	0	0	0	0	0.9	0.9	0	0	0	0	9	10					0.9	0.9					1.3	1.3
Row (c)	α1 (degrees)	−20	0	0	0	0	0	0	0.1	0.2	1.0	1.0	1.0	1.0	20	17	0	0	0	0	0.8	0.8	1.0	1.0	1.0	1.0	10	6.3	2.9	2.8	2.7	2.6
(d/2) = T = (rc/2)		−10	0.2	0.2	0.1	0	0	0	0.3	1.0	1.0	1.0	1.0	1.0	20	12	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	3.8	2.4	2.5	2.5	2.4	2.3
		0	0.3	0.3	0.3	0.2	0	0	0.5	0.8	0.9	0.9	0.9	0.9	25	18	0	0	0	0	0.8	0.8	1.0	1.0	1.0	1.0	2.5	2.2	2.3	2.3	2.2	2.1
		10	0.4	0.4	0.5	0.4	0	0	0.7	0.8	0.8	0.8	0.8	0.9	23	11	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.0	2.1	2.2	2.1	2.1	1.9
		20	0.5	0.5	0.5	0.5	0.4	0	0.7	0.7	0.7	0.8	0.8	0	24	7	0	0	0		0.8	0.9	1.0	1.0	1.0		1.7	2.0	2.0	2.0	1.9
		30	0.6	0.6	0.6	0.6	0	0	0.7	0.7	0.7	0.7	0.8	0	20	6	0	0	0		0.8	0.9	1.0	1.0	1.0		1.7	1.8	1.9	1.9	1.8
		40	0.5	0.6	0.6	0.6	0	0	0.7	0.7	0.7	0.7	0	0	20	6	0	0			0.8	0.9	1.0	1.0			1.6	1.8	1.8	1.8
Row (d)	α1 (degrees)	−20	0	0	0	0	0	0	0	0.1	1.0	1.0	1.0	1.0		15	0	0	0	0		0.9	1.0	1.0	1.0	1.0		11	3.6	3.5	3.3	3.1
(d/3) = T = (rc/2)		−10	0.1	0.1	0.1	0	0	0	0.2	0.2	1.0	1.0	1.0	1.0	21	12	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	5.4	5.5	3.2	3.1	2.9	2.8
		0	0.2	0.2	0.2	0.1	0	0	0.3	0.4	0.9	0.9	0.9	0.9	19	16	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	3.7	3.4	3.0	2.9	2.7	2.5
		10	0.3	0.3	0.3	0.3	0	0	0.4	0.5	0.8	0.8	0.8	0.8	20	14	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.8	2.8	2.8	2.7	2.5	2.4
		20	0.4	0.4	0.4	0.4	0	0	0.5	0.6	0.7	0.7	0.7	0.7	25	16	1	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.3	2.5	2.6	2.5	2.4	2.2
		30	0.4	0.4	0.4	0.4	0.4	0	0.5	0.6	0.6	0.6	0.6	0.7	20	15	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	2.1	2.3	2.4	2.3	2.2	2.1
		40	0.4	0.4	0.4	0.4	0.5	0	0.5	0.5	0.5	0.6	0.6	0.7	24	9	0	0	0	0	0.8	0.9	1.0	1.0	1.0	1.0	1.9	2.1	2.2	2.2	2.1	2.0

Table 3 provides non-limiting examples of the present invention in which there are inner and outer arrangements of rotatable cutting members, each positioned at a distance R_b from the drill body axis of rotation. In Examples 1 to 3 of Table 3, two cutting structures are disposed on each of the inner and outer rotatable cutting members. In Examples 4 to 6, three cutting structures are disposed on the outer rotatable cutting member with one cutting structure on the inner rotatable cutting member. In each of Examples 1 to 6 and solely for the purposes of illustration, the diameter of the hole produced by the disclosed embodiments is approximately 240 mm. Example 7 shows three rotatable cutting members positioned on different circles of rotation, the first positioned more inwardly with respect to the tool body axis, the third, positioned more outwardly with respect to the tool body axis and the second, in an intermediate position. The angles α1 and α2 are as described above and as depicted in FIG. 10a.

In Table 3, the radius of the cutting structures is denoted by the r_c values which are subscripted by the cutting structure number each refers to. The dimension T in Table 3 denotes the thickness of the first cutting structure disposed on the proximal end (with respect to the drill body) of each rotatable cutting member. The dimension d for this first cutting structure on each rotatable cutting member is zero. Where a second cutting structure is disposed on the same rotatable cutting member, this is positioned such that the plane containing the cutting edge of said structure is positioned at a distance ‘d_12’ from the face of the first cutting structure. A third cutting structure disposed on the same rotatable cutting member as cutting structures C1 and C2 is positioned at a distance ‘d_23’ from the face of the second cutting structure and in this case, cutting structure C3 is leading cutting structure C2 in the sense of hole forming tool rotation, and cutting structure C2 is leading cutting structure C1. If cutting structures C1 and C2 are disposed on a first rotatable cutting member and cutting structures C3 and C4 are disposed a second rotatable cutting member, the d_23 parameter is not applicable. If cutting structures C2, C3 and C4 are disposed on the same rotatable cutting member, the parameter d_12 is not applicable.

In each example non-limiting and solely for the purposes of illustration, the hole forming tool translation per revolution is 3 mm. For simplicity, the hole forming tool in Examples 1 to 6 comprises only two rotatable cutting members and in Example 7, only three rotatable cutting members. Hence, the maximal possible depth of engagement on any cutting structure is 3 mm, though as will become apparent, only certain cutting structures experience this maximal value. It will usually be the case that multiple cutting structures engage the material in which a hole is to be formed at any particular circle of rotation and the depth of engagement is reduced in proportion to the number of cutting structures.

The γ_min_n values in Table 3 represent the minimum necessary clearance angle for cutting structure Cn. A negative angle indicates that there is no interference arising on a cutting structure of cylindrical form. Where a positive minimum necessary clearance angle is indicated, the cutting structure is of substantially conical form, the apex angle of the cone being at least twice the stated value so as to avoid interference. An additional amount of clearance is desirable to the minimum necessary angle determined from geometrical considerations—which, not wishing to bound by way of illustration and depending on the properties of the cutting structure material, is within the range of from less than 5° to as great as 20°.

The angle denoted γ_{eff max n} represents the maximum effective clearance angle subtended between the clearance face of cutting structure Cn which has been provided with the minimum necessary clearance, and the newly formed surface of the hole. The values for the maximum effective clearance angle cited in Table 3 include five degrees additional clearance beyond the minimum necessary values. Where γ_min is 0° or less the clearance angle relative to the rotatable cutting member axis of rotation is 5°. This additional five degrees clearance provides more space for the evacuation of cuttings. Further clearance may be provided for example in the form of a second concentric conical surface of a larger apex angle.

FIGS. 16-20 show the projection of the edges of the cutting structures of Examples in Table 3 onto a radial plane of the drill body. FIG. 16 relates to Example 1, FIG. 17 relates to Example 4, FIG. 18 relates to 5 FIG. 19 relates to Example 6 and FIG. 20 relates to Example 7. Cutting structures are labelled C1, C2 . . . Cn, where n represents the cutting structure number. Those cutting structures most proximal the drill body (e.g., C1 and C3 in FIG. 16) are showed as broken lines, with the more distal cutting structures shown as continuous lines.

TABLE 3
Examples of embodiments in accordance with the present invention
	Example
	1	2	3	4	5	6	7
	Rotatable cutting member
	In.	Out.	In.	Out.	In.	Out.	In.	Out.	In.	Out.	In.	Out.	In.	Cen.	Out.
α1 (°)	5	5	20	5	20	5	10	5	10	20	10	15	12	6	8
α2 (°)	20	12	20	12	20	12	10	15	10	20	10	12	15	12	6
rc1 (mm)	32	—	32	—	32	—	20	—	20	—	20	—	32	—	—
rc2 (mm)	28	—	28	—	30	—	—	40	—	45	—	38	—	40	—
rc3 (mm)	—	40	—	40	—	40	—	35	—	35	—	36	—	38	—
rc4 (mm)	—	38	—	38	—	38	—	30	—	32	—	32	—	—	40
rc5 (mm)	—	—	—	—	—	—	—	—	—	—	—	—	—	—	38
Rb (mm)	40	80	40	80	35	80	30	80	30	80	30	83	35	77	120
T (mm)	12	15	12	15	12	15	12	15	12	15	12	15	15	15	15
d12 (mm)	12	—	12	—	12	—	—	—	—	—	—	—	—	—	—
d23 (mm)	—	—	—	—	—	—	—	20	—	15	—	13	—	15	—
d34 (mm)	—	15	—	15	—	15	—	20	—	15	—	17	—	—	—
d45 (mm)	—	—	—	—	—	—	—	—	—	—	—	—	—	—	30
γmin—1 (°)	−8.7	—	−2.4	—	1.3	—	7.7	—	7.5		9.6		0.8	—	—
γmin—2 (°)	6.1	—	−7.2	—	0.8	—	—	6.9	—	16.4	—	13.9	—	−2.4	—
γmin—3 (°)	—	6.9	—	6.9	—	6.9	—	−4.7	—	—	—	−5.9	—	−5.9	—
γmin—4 (°)	—	−5.2	—	−5.5	—	−4.6	—	−10.5	—	−1.3	—	−6.0	—	—	8.5
γmin—5 (°)									—	—	—	—	—	—	−0.9
γeff max 1 (°)	34.1	—	17.6	—	11.7	—	42.8	—	42.5	—	44.6	—	75.8	—	—
γeff max 2 (°)	24.1	—	26.6	—	42.9	—	—	32.2	—	45.6	—	26.3	—	8.2	—
γeff max 3 (°)	—	17.3	—	17.5	—	17.5	—	14.2	—	—	—	16.2	—	10.0	—
γeff max 4 (°)	—	10.7	—	10.4	—	11.3	—	14.6	—	22.6	—	8.3	—	—	14.4
γeff max 5 (°)	—	—	—	—	—	—	—		—	—	—	—	—	—	10.9
In. = Inner;
Out. = Outer;
Cen. -= Centre

In Example 1 of Table 3, cutting structure C2 on the inner rotatable cutting member is required to have a minimal clearance angle of 6.1°. Including five degrees of additional clearance, this results in a maximum effective clearance angle γ_{eff max} of 24°. For cutting structures C1 and C4, the minimum necessary clearance angle is negative; the minimum effective clearance angle subtended on the side face of cylindrical cutting structures is 8.7° and 5.2°, respectively.

FIG. 16 shows the projection of the edges of the cutting structures of Example 1 onto a radial plane of the drill body. In the case of cutting structure C4, the innermost 12% of its projected edge length is shielded due to the overlap by cutting structure C1 and the outmost approximately 30% of cutting structure C1 is shielded by cutting structures C4 and C3. Cutting structure C4 is shielded over two thirds of its innermost projected edge length by cutting structure C3 such that it engages the material in which a hole is to be formed only at its outermost approximately 25% of its projected edge length. Cutting structure C3 is shielded over its outermost region by cutting structure C4 and at its innermost region by cutting structures C1 and C2 and will engage the material in which a hole is to be formed only over about 60% of its projected edge length. The values indicated adjacent the curves in FIG. 16 indicate the maximum engagement depth on each section of each cutting structure, as measured along radials of the cutting face. For example, cutting structure C3 has a maximum engagement depth of 0.9 mm—the label in the chart reads ‘0.9-C3’. Cutting structures C2 and C4 experience the full depth of engagement of 3.0 mm and bear the majority of the cutting load. Cutting structure C1 has two engagement regions, at drill body radial positions of 10-15 mm and at 42-53 mm. The engagement depth on each cutting structure is an important consequence of the configuration of the rotatable cutting members and influences the ease of removal of cuttings.

In Example 2 of Table 3, α1 for the inner rotatable cutting member is 20°, which represents a more inwardly orientated inclination of the rotatable cutting member axis relative to Example 1. This reduces the minimum necessary clearance angle on cutting structure number 2 such that with a cylindrical cutting structure, the minimum effective clearance angle is 7.2°. The maximum effective clearance angle γ_{eff max} on cutting structure C1 is thus reduced significantly relative to the same cutting structure in Example 1, while for cutting structure C2, it is increased slightly. This arises because in Example 2, the innermost aspect of cutting structure C1 is shielded by cutting structure C2, whereas in Example 1, the innermost aspect of cutting structure C2 is shielded by cutting structure C1.

In Example 3 of Table 3, the inner rotatable cutting member is 5 mm closer to drill body axis compared to Example 2. This increases the minimum necessary clearance angles for both cutting structures C1 and C2. It also significantly increases γ_{eff max} for cutting structure number C2. For cutting structures C3 and C4 in Examples 1-3, the configuration of the rotatable cutting member on which these are disposed is constant. The changes in the respective values for the minimum necessary and maximum effective clearance angles arise from the variation in the degree of overlap with cutting structures C1 and C2.

With regard to Example 4 in Table 3, the particular angles of inclination of the outer rotatable cutting member provides for negative minimum necessary clearance angles for cutting structures C3 and C4. For cutting structure C1, while the minimum necessary clearance angle is only 7.7°, the maximum effective clearance angle γ_{eff max} is 42.8°. Though large, this occurs only near the innermost aspect of the cutting structure. Over the outermost 75% of this cutting structures projected edge length, the effective clearance angle is 30° or less. The variation in the effective clearance angle as a function of drill body radial position for cutting structure C1 is similar to the curve for r_c=0.6·R_b in the lower left chart in FIG. 14.

FIG. 17 shows the effective depth of engagement on each of the cutting structures in Example 4. Profile P5 is the boundary formed by the intersection of the face of cutting structure C3 with the conical clearance face of cutting structure C4. The apparent lack of symmetry between P5 and the edge of cutting structure C4 derives from the inclination of the axis of the rotatable cutting member and the rotational projection about the drill body axis onto a radial plane of the drill body. The region bounded by P5 and cutting structure C4 illustrates the space available for the evacuation of cuttings generated by cutting structure C3. The distance between P5 and the cutting edge of cutting structure C3 reflects the width of the cutting face for cutting structure C3. The shaded region enclosed between cutting structures C3 and C4 is the cross-sectional area of cut on cutting structure C3. The maximum effective depth of engagement (3 mm) is approximately one quarter of the width of the cutting face on cutting structure C3. Cutting structure C2 is engaged at two distinct regions on its cutting edge, while the leading cutting structure C4 is engaged over the central region of its cutting edge, bearing a substantial portion of the overall cutting load acting on this rotatable cutting member. Configuring the rotatable cutting members and their cutting structures in such a manner provides for easier evacuation of cuttings.

With regard to Example 5 in Table 3, the angle α2 for the outer rotatable cutting member has increased to 20°, thereby increasing the minimum necessary clearance angles for cutting structures C2 and C4. The maximum effective clearance angles are also significantly larger; cutting structure C2 for example now has a maximum effective clearance angle γ_{eff max} of 45.6°. If, by way of illustration, cutting structure C2 were not shielded by other cutting structures, γ_{eff max} would be about 64°. With reference to FIG. 18, cutting structure C4 bears the majority of the cutting load at drill body radial positions 43 mm to 90 mm, which is favourable in terms of the evacuation of cuttings. Cutting structure C4 shields the outermost approximately 15% of cutting structure C1, while cutting structure C1 shields only a very small portion of cutting structure C4. Cutting structure C3 is entirely shielded by cutting structure C4 such that it will serve solely as a backup cutting structure.

With reference to Example 6 in Table 3, in comparison to the maximum depth of engagement for cutting structure C2 of 2.7 mm in Example 5, the corresponding value in Example 6 is 1.8 mm—illustrated by the shaded region at right in FIG. 19. This is beneficial for the flow of cuttings within the spaces between cutting structures. Optionally, annuli of various cross-sectional profiles which are known in the art to function as ‘chip breakers’ are provided on the cutting structures. Cutting structure C3 in Example 6 engages the material in which a hole is to be formed. Profile P5 in FIG. 19 is the edge formed by the intersection of the face of cutting structure C2 with the conical clearance face of cutting structure C3. Profile P6 denotes the equivalent aspect of cutting structure C3 and the shaded region centre FIG. 19, the chip load acting thereon. Selection of more than 5° clearance beyond the minimum necessary provides for a wider width of cutting face and greater space for the evacuation of cuttings. In Example 6, despite the configuration of the inner rotatable cutting member being identical to that of Example 5, the minimum necessary clearance angle is 2° larger. This arises from the more proximal (with respect to the drill body axis) overlap between cutting structure C1 and the cutting structures on the outer rotatable cutting member; compare FIGS. 18 and 19. The configuration of the outer rotatable cutting member in Example 6 also provides for a significantly smaller γ_{eff max} on cutting structure C2 relative to the same cutting structure in Examples 4 and 5, despite a relatively small difference in the minimum necessary clearance angles.

With reference to FIG. 20, relating to Example 7 in Table 3, this shows the projection of the edges of cutting structures disposed on rotatable cutting members positioned on three distinct circles of rotation. The leading cutting structure on centre rotatable cutting member C3 bears almost the entire cross-sectional area of cut in this region of the working face of the hole forming tool with the lagging cutting structure functioning largely as a backup cutting structure. On the outermost rotatable cutting member, leading cutting structure C5 bears the majority of the cross-sectional area of cut, with lagging cutting structure C4 bearing only a small portion of the overall load and only on the outermost aspect. The minimum necessary and maximum effective clearance angles in Example 7 for all but innermost cutting structure C1 are small relative to the values in other Examples. This is partly due to the smaller cutting structure radii relative to R_b. γ_{eff max} on the innermost cutting structure is 76°, but only over the innermost 14% of the projected edge length is γ_{eff max} greater than 45°. The variation in γ_{eff max} as a function of drill body radial position is very similar to the curve for r_c=0.6·R_b in the bottom centre chart in FIG. 14. In more severe hole forming operations, the situation may be addressed through one or more of several approaches: increasing the R_b value, reducing the angle α1 and/or increasing the angle α2. Alternatively, placement of a fixed cutting structure so as to shield the innermost approximately 10 mm of the projected edge length of cutting structure C1 will reduce γ_{eff max} to less than 45°.

The distribution of rotatable cutting members, according to the configurations in Table 3, on the working face of the hole forming tool may be varied. The number and relative angular positioning of the rotatable cutting members on their respective circles of rotation may be uniform or non-uniform. With regard to both aspects, numerous differing permutations are possible. In all the above non-limiting examples, one or more of the rotatable cutting members may be replaced with non-rotatable or are rotatable prior art cutting structures.

It is to be understood that the invention is not limited to the specific details described herein which are given by way of example only and that various modifications and alterations are possible without departing from the scope of the invention as defined in the appended claim.

Claims

1. A hole forming tool (16, 26, 29) operable with a translation per revolution f and comprising a rotatable drill body (17) having γ eff   max = ( Max λϵΓ; t = 0  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) ) - ( Min λϵ  [ λ   1, λ   2 ]; t = 0  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) )    applicable   where  ( Max λϵΓ; t = 0  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) ) ≥ ( Max λϵΓ; t = T  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) ) Equation   ( 1 ) γ eff   max = ( Max λϵΓ; t = T  ( A   tan  ( r c - r r T ) ) ) - ( Min λϵ  [ λ   1, λ   2 ]; t = 0  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) )    applicable   where  ( Max λϵΓ; t = 0  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) ) < ( Max λϵΓ; t = T  ( χ · A   cos  ( Tn → · A →  Tn →  ·  A →  ) ) ) Equation   ( 2 ) Tn → = 〈 sin  ( θ i ), - cos  ( θ i ), ( f 2 · π · r i ) 〉; r i = x i 2 + y i 2   and θ i = A   tan  ( y i x i );

a proximal end (19) for attachment to a drive mechanism and a distal end (21);

a drill body axis of rotation defining a Z axis;

mutually orthogonal axes X and Y, both X and Y axes intersecting at and orthogonal to the Z axis;

whereby on the distal end (21) of the rotatable drill body (17) is disposed at least one rotatable cutting member (23), the or each rotatable cutting member (23) independently being substantially concentric with and supported by a cantilever shaft (35) and independently having

a radial plane in which the Z axis lies;

a first transverse plane (S2, 74) normal to the Z axis, with a proximal side towards the proximal end (19) of the rotatable drill body (17);

a third transverse plane (75) towards the proximal side of the first transverse plane, the third transverse plane normal to the Z axis and at a distance f from the first transverse plane;

a reference radial (53) defined by the intersection of the radial plane and the first transverse plane (S2, 74);

a longitudinal plane (S1) parallel to the Z axis and subtending an angle α1 with a normal to the radial plane;

an axis of rotation (A) lying in the longitudinal plane (S1), subtending an angle α2 to the first transverse plane and extending through an intersection point I; the intersection point I at the intersection of the radial plane and the first transverse plane and at a distance Rb from the Z axis;

wherein on the or each rotatable cutting member (23) is disposed at least one cutting structure (24), the or each cutting structure independently having

a cutting face centre (Oc, 64, 65) a distance d along the axis of rotation (A) from the intersection point I;

a cutting face (54) of radius rc;

a continuous cutting edge (C, cs_3, cs_4) which is substantially concentric with the axis of rotation (A);

a thickness T extending from the cutting face centre (Oc, 64, 65) towards the intersection point I in the direction of the axis of rotation (A);

a second transverse plane normal to the Z axis, through the cutting face centre (Oc, 64, 65) and having a proximal side towards the proximal end (19) of said rotatable drill body (17);

a cutting face reference radial (56) defined by the intersection of the cutting face (54) and the second transverse plane; the cutting face reference radial (56) extending from the cutting face centre (Oc, 64, 65) towards the Z axis;

a fourth transverse plane (76) normal to the Z axis, towards the proximal side of the second transverse plane and at a distance from the second transverse plane of one half of said translation per revolution f; the fourth transverse plane having a proximal side (78) and a distal side (77);

a distal region of the continuous cutting edge (C, cs_3, cs_4) on the distal side (77) of the fourth transverse plane;

wherein the distal region of the continuous cutting edge of a first of said the or each cutting structure independently has at least one engagement region, the or each engagement region having a first edge point (Pti) with coordinates xi, yi, zi on the X, Y and Z axes respectively, xi and yi defining a radius ri of a first circle of rotation about the Z axis;

whereby on the distal region of a cutting edge of any second of said at least one cutting structure, a second edge point (Pti), having a circle of rotation about the Z axis of equal radius to said first circle of rotation about the Z axis, is less distal the first transverse plane (74) than the first edge point (Pti) is distal the third transverse plane (75);

wherein the or each engagement region independently has

an innermost extremity (72, 69) with respect to the Z axis;

an outermost extremity (70, 73) with respect to the Z axis;

a first cutting face radial extending from the cutting face centre (Oc, 64, 65) to the innermost extremity (72, 69);

a second cutting face radial extending from the cutting face centre (Oc, 64, 65) to the outermost extremity (70, 73);

a first cutting face angular coordinate λ1 subtended between the first cutting face radial and the cutting face reference radial (56);

a second cutting face angular coordinate λ2 subtended between the second cutting face radial and the cutting face reference radial (56);

wherein for the or each cutting face independently, Γ is a set comprising the angular intervals λ1, λ2 for the or each engagement region of said cutting face;

and wherein the or each engagement region independently has a projected engagement length L (L_a1, L_a2), the or each projected engagement length L independently determined by firstly rotationally projecting the engagement region about the Z axis onto the radial plane to form a first projection and secondly thereafter, projecting said first projection parallel to the Z axis onto said reference radial (53);

such that that the maximum effective clearance angle γeff max of the or each engagement region as defined by Equations (1) or (2) hereinbelow is independently not greater than 45° over at least 80% of the projected engagement length L of the or each engagement region:

wherein {right arrow over (A)} is the rotatable cutting member axis direction vector and is given by: {right arrow over (A)}=−sin(α1)·cos(α2),−cos(α1)·cos(α2), sin(α2),

and wherein {right arrow over (Tn)} is a vector given by:

wherein 0≤f≤rc;

wherein ri and θi are given by:

wherein χ has a value of +1 if {right arrow over (Tn)} extends inwardly with respect to the rotatable cutting member axis of rotation and χ has a value of −1 if {right arrow over (Tn)} extends outwardly with respect to the rotatable cutting member axis of rotation and xi=−Rb+sin(α1)·cos(α2)·(d−t)+rc·cos(λ)·cos(α1)−rc·sin(α2)·sin(λ)·sin(α1), yi=cos(α1)·cos(α2)·(d−t)−rc·sin(α2)·sin(λ)·cos(α1)−rc·cos(λ)·sin(α1) and zi=−rc·sin(λ)·cos(α2)−sin(α2)·(d−);

wherein the subscript i denotes a parameter determinable for any value of λ∈Γ;

wherein rr is given by: rr=rc−√{square root over ((xi−xr)2+(yi−yr)2+(zi−zr)2)}

wherein xr, yr, zr are given by: xr=−Rb+sin(α1)·cos(α2)·(d−T), yr=cos(α1)·cos(α2)·(d−T) and zr=−sin(α2)·(d−T).

2. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the maximum effective clearance angle γeff max is not greater than 45° over the projected engagement length L of the or each engagement region and wherein 0≤f≤rc/2.

3. A hole forming tool (16, 26, 29) as claimed in claim 2, wherein the maximum effective clearance angle γeff max is not greater than 35° over the projected engagement length L of the or each engagement region.

4. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein on the periphery of at least one of the or each rotatable cutting member (23) is disposed at least one cutting structure (24).

5. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein at least one of the or each cutting structure (24) is formed independently of and bonded to the rotatable cutting member (23) on which it is disposed.

6. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the rotatable drill body (17) has a direction of rotation about the Z axis and comprises a plurality of rotatable cutting members (23), the intersection point I of each of said plurality of rotatable cutting members (23) sharing a circle of revolution about the Z axis and wherein the angular position (ψ) of the reference radial (53) of a first rotatable cutting member relative to the reference radial (53) of a second rotatable cutting member is not equal to the angular position (ψ) of the reference radial (53) of the second rotatable cutting member relative to the reference radial (53) of the first rotatable cutting member, whereby all angular positions (ψ) are measured in the direction of rotation of the rotatable drill body (17).

7. A hole forming tool (16, 26, 29) as claimed in claim 1; wherein the rotatable drill body (17) comprises a plurality of rotatable cutting members (23); wherein the intersection point I of a first rotatable cutting member (23) lies on a first circle of rotation about the Z axis; wherein the intersection point I of a second rotatable cutting member (23) lies on a second circle of rotation about the Z axis; the diameter of said first circle of rotation being different to the diameter of said second circle of rotation.

8. A hole forming tool (16, 26, 29) as claimed in claim 1; wherein the rotatable drill body (17) comprises a plurality of rotatable cutting members (23); wherein;

the angle α1 of a first rotatable cutting member (23) is different to the angle α1 of a second rotatable cutting member (23), and or;

the angle α2 of a first rotatable cutting member (23) is different to the angle α2 of a second rotatable cutting member (23).

9. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the rotatable drill body (17) comprises a plurality of cutting structures (24) and wherein the cutting face (54) radius rc of at least one of said one or more cutting structures is different to the cutting face radius rc of another of said one or more other cutting structure (54).

10. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein at least one rotatable cutting member (23) is integral with its cantilever shaft (35), and wherein said cantilever shaft (35) is received within a bore in the distal end (21) of the rotatable drill body (17).

11. A hole forming tool (16, 26, 29) as claimed in claim 1, further comprising at least one rotatable crushing member (10) wherein a plurality of indenter elements (11) is disposed on the surface of the or each rotatable crushing member (10).

12. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the or each cutting edge (C) is provided with at least one bevel (47) and or at least one radius (48).

13. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the cutting face (54) of the or each cutting structure (24) is polycrystalline in nature and includes diamond.

14. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the rotatable drill body (17) comprises flutes (18) and or reliefs (25) for conveying cuttings away from the distal end (21) of the rotatable drill body, preferably wherein said cut-outs are substantially longitudinal, substantially helical or a combination of linear and helical.

15. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the or each rotatable cutting member (23) is independently permitted to rotate relative to the rotatable drill body (17) by means of a roller element or journal bearing (36, 37) arrangement disposed on the cantilever shaft (35) associated therewith.

16. A hole forming tool (16, 26, 29) as claimed in claim 15, wherein the or each roller element or journal bearing (36, 37) arrangement is lubricated by a lubricant reservoir (40).

17. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein the rotatable drill body (17) is of an integral construction.

18. A hole forming tool (16, 26, 29) as claimed in claim 15, wherein the rotatable drill body (17) includes a plurality of retaining balls (38).

19. A hole forming tool (16, 26, 29) as claimed in claim 1, wherein rc is not substantially greater than about 0.9·Rb.

20. A hole forming tool (16, 26, 29) as claimed in claim 19, wherein rc is not substantially less than about 0.3·Rb.