EP3580004A1

EP3580004A1 - Saw beads with reduced flattening behavior and a saw cord comprising such beads

Info

Publication number: EP3580004A1
Application number: EP18701500.3A
Authority: EP
Inventors: Jan Vaneecke; Tom Baekelandt
Original assignee: Bekaert NV SA
Current assignee: Bekaert NV SA
Priority date: 2017-02-08
Filing date: 2018-02-01
Publication date: 2019-12-18
Also published as: WO2018145980A1; CN110366468A

Abstract

A recurring problem in the use of saw cords for sawing natural or man-made stone-like materials, such as marble, granite, brick, concrete and the like, is that during the use of the saw cord the beads may develop a flat face inhibiting the rotation of the saw cord and hence leading to a preferred wear at one side of the saw cord. As only one side of the saw cord beads is eroded away the saw cords have to be discarded prematurely. The inventors have found that in order to overcome this flattening problem it is beneficial that the average working length, that is the average axial length of the bead that contacts the workpiece, must increase monotonically with decreasing diameter. In this way the loss in contact area between the bead and the workpiece due to the reduced diameter of the bead is compensated by an increased working length. As a result the contact pressure on the bead remains about constant throughout the useful life of the bead which is not the case for prior art beads. In prior art beads the contact pressure on the bead increases as the contact area diminishes with decreasing diameter.

Description

Title: Saw beads with reduced flattening behavior and a saw cord

comprising such beads

Description

Technical Field

[0001 ] The invention relates to saw beads as they are used in saw cords. Saw cords are used to cut natural or manmade stone-like materials such as marble, granite, brick, concrete and like materials. The invention extends also to saw cords using the inventive beads.

Background Art

[0002] Saw cords are increasingly being used on saw machines for slabbing

large blocks of natural or manmade stone. In such machine multiple loops of saw cords, sometimes as many as 50 or more, are driven by large sheaves and sunk into the block of stone to be sawn. The saw cords run at high speed (120 km/h). Coolant is sprayed on the saw cords for cooling and evacuation of the swarf. In one single operation the whole block is cut into slabs at saw speeds of about 30 cm per hour.

[0003] Saw cords are made of a carrier rope - that is usually a steel rope - whereon saw beads are threaded. The carrier rope is closed by means of a splice into a loop - for example as described in WO 2016/188978 A1 of the current applicant - and thereafter polymer is injection moulded between the beads as for example described in WO 2013/102542 A1 of the current applicant. The beads comprise a small, cylindrical metal sleeve whereon a circumferential abrasive layer is attached. Currently the abrasive layer is made by metal powder metallurgy (as already described in US 2,679,839) wherein abrasive particles - usually diamond grit - are mixed with metal powders and an optional organic wax. The mixture is pressed into an annular shape and thereafter sintered at high temperature and/or high pressure. The formed annular beads are then soldered to the metal sleeve.

[0004] Recently laser cladded beads have been devised whereby the abrasive layer is directly formed on the metal sleeve from a gas driven flow of metal powder and abrasive particles that is heated by a laser beam. See for example WO 2012/1 19947 A1 of the current applicant. [0005] One of the main problems encountered during sawing is the 'flattening of the beads'. It is the phenomenon whereby the wear of the abrasive layer on the bead is not circumferentially uniform. It is a self-amplifying process: once a slight flattening occurs the saw cord is hampered in its rotation and the side of the beads that is most worn will contact the stony material even more. Those beads will therefore wear faster at one side resulting in a bead of which one side of the bead is worn and flattened while the opposite side is barely used. As this affects the saw behaviour of the complete loop this results in a discarding of the whole loop.

[0006] One way to overcome this problem is to twist up the steel cord before

closure of the loop. This makes the cord stiffer in torsion and allows inducing rotation into the running saw cord loop by for example putting pulleys under angle into the trajectory of the loop. But even then it may occur that beads start to flatten.

[0007] The inventors have sought alternative ways to overcome the 'flattening bead' problem;

Disclosure of Invention

[0008] It is therefore a prime objective of the invention to overcome the flattening bead problem. It is a further objective to define those geometries of beads that will overcome the flattening bead problem. It is a further objective of the invention to provide a saw cord that is free flattening beads.

[0009] According the first aspect of the invention a saw bead is provided.

The saw bead comprises a metal sleeve. The metal sleeve has an axis of symmetry. The metal sleeve has an outer sleeve diameter of 'Dmin'. On the outer surface of the metal sleeve an abrasive layer is provided. The abrasive layer is attached to the outer circumference of the metal sleeve. The abrasive layer extends radially up to a maximum diameter of 'Dmax'.

[0010] For every diameter 'D' between Dmin and Dmax a 'working area A(D)' within the abrasive layer can be identified. The 'working area' at diameter D is equal to the area of intersection between an imaginary cylinder and the abrasive layer. The imaginary cylinder is concentric to the axis of symmetry and has a diameter D. The working area on its turn defines an 'average working length L(D)' that is equal to the working area divided by the circumference of the cylinder. Alternatively worded: the working area is equal to the product of the average working length and the circumference πϋ of the cylinder.

[001 1 ] Characteristic about the invention is now that this average working length of the abrasive layer must increase monotonically with decreasing diameter D.

[0012] The characteristic can also be expressed more formally as follows:

Let A(D) express the working area that is equal to the area of intersection between the abrasive layer and an imaginary cylinder with diameter D that is concentric to the axis of the metal sleeve. 'D' decreases from Dmax towards Dmin. The average working length L(D) is then equal to A(D)/ πϋ. Now for every D1 and D2 between Dmin and Dmax (limits included) wherein D2 is strictly larger than D1 , L(D1 ) is larger than or equal to L(D2) i.e. for every D1 , D2 for which Dmin≤D1 <D2≤Dmax, then L(D1 )≥L(D2).

[0013] The metal sleeve may comprise a closure as described in WO 201 1

061 166 A1 of the current applicant. Such metallic sleeve is normally made of low to medium carbon steels. More preferred is if the sleeve is made by metal injection moulding as described in WO 2014/082870 A1 of the current applicant. Then metal sleeve compositions are preferably iron nickel steels, stainless steels such as austenitic steels, precipitation hardenable steels and the like. Using metal injection moulding allows a large degree of freedom to make internal screwthreads to the inner side of the sleeve as described in WO 2015/180947 A1 of the current applicant. This is important to ensure a good fixture of the saw bead to the carrier steel cord by means of the polymer injection into the space between metal sleeve and steel cord. Current metal sleeves have an outer diameter - corresponding to Dmin - of 7 or 5 mm while in the future even smaller sleeves of 4 mm are considered. Metal sleeves are typically 10 to 12 mm long.

[0014] The abrasive layer comprises abrasive particles that are held in a metal matrix material. Possible abrasive particles are made of diamond, cubic boron nitride, silicon carbide, aluminium oxide, silicon nitride, tungsten carbide, titanium carbide or mixtures thereof but predominantly diamond, in particular manmade diamond is preferred.

[0015] The metal matrix materials are usually an alloy of many metals forming complex intermetallic phases. When the metal powder metallurgical route is followed, the following compositions are popular (the numbers between brackets are the percentages by weight):

- Fe(46), Co(12), Cu(31 ), supplemented with Ag, Zn, P;

- Cu(49); Ni(34), W(1 1 ), supplemented with Fe, P;

- Cu(49), Fe(34), Co(9), Ag (7), supplemented with P;

- Co(77), W(23);

The abrasive layer is formed into an annular shape by compressing the metal powder wherein the abrasive particles are mixed at high pressure followed or combined with a high temperature treatment in order to consolidate the mixture. Thereafter the formed bead ring is brazed to the metal sleeve.

[0016] Particularly preferred is if the abrasive layer is formed by laser cladding directly onto the metal sleeve. In this way the brazing can be omitted and in addition the abrasive layer is present down to the surface of the metal sleeve. In particular the metal matrix compositions as disclosed in WO 2016/050508 A1 of the current applicant are preferred. Such metal matrices comprise at least 60 percent by weight 'wt%' of copper and between 0.5 to 10 wt% of one or more metals out of the group consisting of nickel, iron, cobalt and manganese. Additionally, between 7 and 20 wt% of an element out of the group consisting of tin, zinc, silver, bismuth, antimony, indium, lead, and phosphorous and between 5 and 15 wt% of metals out of the group consisting of chromium, titanium, vanadium, tungsten, zirconium, niobium, molybdenum, tantalum and hafnium can be added.

[0017] Typically the diameter of the saw bead inclusive the abrasive layer, i.e.

Dmax, is up to 9 to 1 1 mm on 5 mm outer diameter metallic sleeves or up to a Dmax of 7 to 8 mm on 4 mm outer diameter metallic sleeves. The abrasive layer covers about 8 to 10 mm axial length on the surface of the metallic sleeve. [0018] In a first preferred embodiment the average working length increases strictly monotonically with decreasing diameter. This means that for every D1 and D2 between Dmin and Dmax (limits included) wherein D2 is larger than D1 , L(D1 ) is larger than L(D2) i.e. for every D1 , D2 for which

Dmin≤D1 <D2<Dmax, then L(D1 )>L(D2).

[0019] Prior art beads have a substantially annular abrasive layer of which the ends are planar and perpendicular to the axis of the metal sleeve. This means that the length 'L' of the abrasive layer remains constant during the use of the saw bead. During use the diameter 'D' of the bead must diminish. This is needed as the abrasive particles are worn out during sawing and must be constantly replenished with fresh abrasive particles that are revealed from the abrasive layer as the erosion progresses. The contacting surface of the bead that abrades the stone is then half the working area. As the diameter diminished and the length 'L' remains constant it follows that the pressure on this contacting surface area will increase during use as the downward force on the bead remains constant while the working area diminishes (provided the bow curvature and bow tension are kept constant). The rate of decrease of the contacting surface with the decreasing diameter is equal to πχ|_/2. This increasing pressure on the bead will lead to an increased wear rate of the bead as the bead diminishes in diameter.

[0020] According the inventors the reason why prior art saw beads have a

tendency to flatten is the following:

As long as the bead is rotating during use, the abrasion of the bead will go uniformly over the complete circumference of the bead. If - due to one or another reason - the bead momentarily stops rotating a flat will form on a series of beads on the saw cord. A flat is a part of the mantle of the bead that has a higher radius of curvature than the remaining mantle. As the flat is pressed towards the cut by the tension in the bow, it will hamper the rotation of the saw cord. As the flat has a smaller contacting surface compared to the remainder of the bead the contact pressure is increased. Consequently the bead will be worn even more at the flat i.e. the process is self-amplifying. As a result the complete loop will lock into a preferred angular position wherein one side of the loop is constantly cutting the work piece, while the diametrically opposite side rarely gets toward the work piece and hence is not sawing.

[0021 ] The inventors conjecture - without being bound by this working hypothesis - that the working of the inventive bead is as follows:

In the inventive bead the average working length L(D) of the bead monotonically increases while the bead is being used. Consequently the rate of decrease of the working area of the bead that contacts the workpiece is always lower than that of a prior art bead that has constant length. If now - by one or another reason - the saw cord is prevented from rotation, the contacting surface will locally increase - due to the increasing average working length - at the flat leading to a lower working pressure and hence less wear at that flat area. As a consequence the self- amplifying mechanism is broken and the saw cord will not lock on this position.

[0022] The inventors have found that by changing the shape of the abrasive layer of the saw bead the working area during the use of the saw bead can be adapted. These limitations are expressed in the characterising portion of claim 1 . When the average working length increases monotonically with decreasing diameter less flattening is observed. Even better is if the working length increases strictly monotonically with decreasing diameter.

[0023] The fact that in the inventive beads the working area diminishes less fast or even remains constant compared to prior art beads during the lifetime of the bead has also another unexpected advantage. As the diameter of the bead decreases during use, less material must be eroded away: the width of the cut diminishes as it progresses. Hence, the cut will progress faster through the workpiece all other factors like cord speed and tension being kept constant. In prior art beads this leads to a faster wear rate of the beads as less total working area becomes available at the same contacting force. In the inventive beads this wear rate remains more constant as the decrease of working area is much less if at all decreasing compared to prior art beads. The inventive beads therefore have a more constant wear rate.

[0024] After extensive testing the inventors found the following preferred limits to result in saw beads that do not suffer from flattening: Let us define Lmax as the average working length at the minimum diameter Dmin: Lmax=L(Dmin). In practise Lmax is equal to the axial length of the abrasive layer at the metal sleeve diameter Dmin. The ratio (Lmax/Dmin) is a convenient measure to scale the rate of increase of the average working length with decreasing diameter. During the use of the saw bead the average working length will increase with an amount AL for every AD of diameter decrease. Note that for the prior art beads AL is zero as the length of the bead does not change during use.

[0025] In order to prevent flattening the inventors found that the rate of average working length increase over diameter decrease AL/AD must at least be one third of (Lmax Dmin) or higher. If the value is less, there is a likelihood that flattening will occur. For prior art beads this rate is zero.

[0026] At the other extreme the rate of average working length increase over diameter decrease AL/AD must not be larger than or is at the most Lmax/Dmin. If the rate AL/AD becomes larger than Lmax/Dmin, there is not enough abrasive layer material available. Compared to a prior art bead with Lmax of 9 mm, Dmax of 7.6 mm and a Dmin of 5 mm only about 72% of the abrasive material remains.

[0027] A particularly preferred embodiment is if the rate of average working

length increase over diameter decrease AL/AD is about Lmax/Dmax. With 'about' is meant that the value of AL/AD remains within +/- 5% of

Lmax/Dmax. At that value the initial working area of the bead - when the bead diameter is Dmax - is equal to the end working area when the bead approaches its' end-of-life and has a diameter of Dmin. During use the working area remains about constant.

[0028] The increase of average working length with decreasing diameter can also be numerically expressed for the specific bead having an 'Lmax' of between 8 mm to 9 mm at Dmin and wherein Dmin is between 4.5 to 5.5 mm. By preference the average working length increases with at least 50 micrometer per 100 micrometer of decreasing diameter. If the increase of the average working length is less than 50 micrometer per 100 micrometer the working area decreases too fast and the risk for flattening increases.

[0029] At the other extreme the average working length should not increase more than 170 micrometer per 100 micrometer of decreasing diameter. If this becomes the case it becomes difficult to have sufficient reserve in the abrasive layer to be able to reach an acceptable lifetime of the bead.

[0030] Even more preferred is the average working length increases with at least 75 micrometer and not more than 120 micrometer per 100 micrometer of decreasing diameter. For a bead with a Dmax of 8 mm and an Lmax of 8 mm an average working length increase of 100 micrometer per 100 micrometer of decreasing diameter is best as then the working area remains about constant during the use of the bead.

[0031 ] In a further preferred embodiment the working area remains at any time during the use of the sawing bead - except when the bead is completely worn out i.e. at Dmin - smaller than that of a prior art sawing bead with a constant length equal to the working length at Dmin. So the working area of the bead remains at any working diameter 'D' of the bead smaller than the product of the circumference of the cylinder at that working diameter and the average working length at the outer sleeve diameter Dmin and this for any diameter D strictly larger than Dmin and smaller or equal to the maximum diameter Dmax.

Formally: A(D) < nDLmax for any Dmin<D≤Dmax.

Best is if the working area increases or remains substantially constant with decreasing diameter i.e. A(D) « nxDminxLmax during the use of the saw bead.

[0032] A preferred embodiment is when the abrasive particles that are held by a metal matrix in the abrasive layer are protruding from the outer surface of the abrasive layer already prior to the first sawing with the saw bead. Of course during use buried abrasive particles will gradually be revealed and will protrude from the working surface. However, specific is that already prior to use, when the beads are in their virgin, unused state, the abrasive particles are protruding. In this way the saw bead will immediately start to saw and no dressing steps are required.

[0033] In another preferred embodiment the abrasive layer comprises abrasive particles held in a metal matrix that shows a dendritic metallographic structure. Such structure is particularly preferred because it has a higher hardness than alloys having a globular structure. A globular structure is obtained when the abrasive sawing layer goes through thermal quasi- equilibrium processes i.e. processes wherein the cooling or heating is relatively slow to the melting and solidification processes. Examples of such quasi-equilibrium processes are the known ways to manufacture beads through the metal powder route.

[0034] The dendritic metallographic structures are obtained in non-equilibrium processes wherein the cooling and heating is fast compared to the melting and solidification of the metals forming the metal matrix. An exemplary process is laser cladding wherein locally molten metal alloys are cooled extremely fast and result in very fine dendritic structures. Moreover - when properly performed - the surface of such a laser cladded bead will have an outer surface that - prior to first sawing, in their unused, virgin state - has abrasive particles that protrude out of the surrounding surface. I.e. such beads do not need to be post-processed in order to reveal abrasive particles before first sawing nor do they need a special initial treatment to liberate the first abrasive diamonds from the outer surface.

[0035] According a second aspect of the invention a saw cord is claimed. The saw cord comprises a carrier cord - that is preferably a steel cord - and saw beads threaded thereon. The saw beads have the features of at least claim 1 and possibly other features from the claims depending from claim 1 . The saw beads are separated from one another by a polymer sleeve. Preferably a polyurethane polymer sleeve is used.

[0036] A preferred embodiment of the saw cord is that the saw beads are firmly attached to the carrier cord by means of the polymer. It is particularly important that the beads are rotationally fixed to the carrier cord in order to prevent that they start to rotate.

Brief Description of Figures in the Drawings

[0037] FIGURE 1 a shows a cross section of a prior art bead with different

degrees of flattening through a plane perpendicular to the axis of the bead;

[0038] FIGURE 1 b shows a cross section of a prior art bead with different

degrees of flattening through a plane that comprises the axis of the bead;

[0039] FIGURE 2 shows a cross section of an inventive bead through a plane that comprises the axis of the bead; [0040] FIGURE 3 shows explains the definitions of working area and average working length on the contacting surface of an inventive bead;

[0041 ] FIGURE 4a and 4b respectively show the average working length and the working area of a prior art bead;

[0042] FIGURE 5a and 5b respectively show the average working length and the working area of different preferred embodiments of the inventive bead [0043] Reference numbers to parts having identical function or meaning have equal units and tens across the figures while the hundred digit refer to the number of the figure.

Mode(s) for Carrying Out the Invention

[0044] FIGURE 1 a and 1 b illustrate a prior art bead 100. The bead consists of a metal sleeve 102 on top of which an abrasive layer 104 is attached. The metal sleeve 102 has an axis of symmetry 1 12 and an outer sleeve diameter Dmin. The abrasive layer 104 consists of abrasive particles 108 that are held in metal matrix 106. The abrasive layer extends from Dmin up to Dmax which is the radial outermost diameter. Lmax is the average working length at Dmin. In the case of the prior art bead L(D) remains equal to this Lmax.

[0045] During use a force 'F' with its' point of action at the centre 'C of the bead pushes the bead into the workpiece. The force is equal to the longitudinal tension on the wire divided by the radius of curvature of the bow times the length of the bead. As long as the bead is round there is nothing hampering the rotation of the bead in its interaction with the workpiece.

[0046] However, if due to one or another reason, the bead is temporarily blocked a flat 1 10 will form. At the flat the distance between the supporting surface 1 10 and the point of action 'C of the force 'F' is shortest hence a moment is needed to turn the bead out of this position. Alternatively worded: the state of lowest energy is attained when the flat is oriented towards the work piece. At the flat the contact pressure between bead and workpiece increases as the surface over which the downward force 'F' is distributed diminishes. As the contact pressure increases the wear of the bead in that segment will increase. As the wear increases the region at the flat is preferentially eroded thereby leading to an expansion of the flat 1 10'. As the bead is now locked in position the flattening progresses and the loop must be eliminated from the web.

[0047] FIGURE 2 depicts the cross section of an inventive bead by a plane

comprising its axis of symmetry. Again a metal sleeve 202 is carrying an abrasive layer 204 that consists of a metal matrix 206 wherein diamonds 208 are embedded. The inventive bead has been made by laser cladding which results in a rough outer surface 214 where some of the diamonds are protruding 208'.

[0048] The metal sleeve 202 has an axis of symmetry 212 and an outer diameter indicated with 'Dmin'. The abrasive layer 204 extends to a maximum diameter 'Dmax'. The working area A(D) is the area of the intersection of the abrasive layer 204 with an imaginary cylinder 'G' having a diameter 'D'. The average working length L(D) at diameter 'D' is equal to the ratio of the working area A(D) divided by the circumference of the cylinder 'G' i.e. L(D)=A(D)ATTD. The average working length at Dmin is equal to Lmax.

[0049] FIGURE 3 shows how the average working length L(D) relates to the

working area A(D).The figure represents the worn surface of a bead when its' diameter has been reduced to a diameter D. It is composed of several pictures that are stitched together. Protruding diamonds 308 are visible that are followed by their 'comet tails 318'. The 'comet tails' are formed in the metal matrix 306 as they are in the shadow of the protruding diamond 308: there the metal matrix material 306 is not abraded. 316 and 316' indicate the edges of metal sleeve 302. By digital image processing the edges of the worn surface 320 and 320' can be identified. The full circumference is determined by the reoccurrence of features when one full turn has been imaged. Again by digital processing the area A(D) can be obtained. Out of that L(D) can be obtained. This is for example done at four to ten instances in the usage of the bead.

[0050] Alternatively for each circumferential distance ΘΌ/2 one can identify a local axial length /(0). Then the working area is:

A(D) = 1(θ)Ωάθ/2 = πΌ ^— = πΌ ^■ L(D)

Jn 2π In practise it suffices to take a number of lengths (say 10) of 1(9) and average them to find the average working length. This is a good

alternative to the digital image processing method.

[0051 ] In FIGURES 4a, 4b and 5a and 5b the working of the invention is

explained on a bead with a Dmin of 5 mm, a Dmax of 7.6 mm and an

Lmax of 9 mm.

[0052] FIGURE 4a describes how the working length of a prior art bead changes during the use of the bead: as the diameter of the saw bead decreases the average working length L(D) (in mm) remains constant at 9 mm. The corresponding working area A(D) (in mm²) linearly diminishes from 215 mm² to 141 mm² that is a change of one third of the original working surface: see FIGURE 4b.

[0053] FIGURE 5a and 5b show three different cases for the inventive saw

beads:

- In the first case (depicted with a Andreas-cross and a dashed line) the average working length of the saw bead diminishes at a rate of one third of Lmax/Dmin i.e. 0.60 or ALJAD =0.60. This means that the average working length will increase by 60 μιτι for every 100 μιτι of diameter that is worn away. The working area still diminishes from 178 mm² to 141 mm² during the use of the saw bead but the decrease is only one fifth from the original working area. The volume of the abrasive layer is 91 % of that of the prior art bead; - In the second case (depicted with a triangle 'A' and a dash dot line) the average working length of the bead increases at a rate of

Lmax/Dmin i.e. 1 .80. Hence for every 100 μιτι of bead diameter that is abraded away the length increases with 180 μιτι. The surface area increases during use from 103 mm² to 141 mm² i.e. an increase of 37%. However the volume decreases to 72% of that of the prior art bead;

- In the third case (depicted with a star '>κ' and a full line) the average working length of the bead increases at a rate of 1 .18 that is equal to Lmax/Dmax. For every 100 μιτι in diameter that is abraded away the average length increases with 1 18 μιτι. The working area remains practically constant throughout the use of the bead. The volume is

82% of that of the prior at bead.

[0054] As clear from FIGURE 2 saw beads that are produced through laser

cladding show a rough surface that is beneficial for first use. The inventors made different versions of the saw beads with different levels of powder gas flow, different levels of powder speed with more or less overlap between nozzle feed and laser beam and with lower or higher

temperatures.

[0055] The resulting beads showed different shapes in terms of the rate of

increase of average working length versus diameter decrease. The Lmax was 8.1 mm and Dmin was 5 mm. By varying the above process parameters the overall shape could be modulated resulting in values of AL/AD of 0.96, 0.984, 1 .05, 1 .085, 1 .53, 1 .667, 1 .712, 1 .75, and 2.263. In the field the beads values of 2.263 were not workable as they did not contain enough abrasive material to fulfil lifetime expectations. The other beads performed well and did show less flattening behaviour than competing products based on prior art beads.

Claims

1 . A saw bead for use on a saw cord, said saw bead comprising

- a metal sleeve, said metal sleeve having an axis of symmetry with an outer sleeve diameter of Dmin;

- an abrasive layer outer circumferentially attached to said metal sleeve and radially extending to a maximum diameter Dmax;

said abrasive layer having a working area, said working area being equal to the area of the intersection of said abrasive layer with a cylinder concentric to said axis of symmetry, said cylinder having a diameter D decreasing from Dmax to Dmin, wherein the average working length is equal to said working area divided the circumference of said cylinder with said diameter D characterised in that said average working length increases monotonically with said decreasing diameter D.

2. The saw bead according to claim 1 wherein said average working length increases strictly monotonically with said decreasing diameter.

3. The saw bead according to any one of claims 1 to 2 wherein the average working length at Dmin is Lmax and wherein the rate of increase of said average working length over said diameter decrease is at least one third of Lmax Dmin and at most Lmax/Dmin.

4. The saw bead according to any one of claims 1 to 2 wherein the average working length at Dmin is Lmax and wherein the rate of increase of said average working length over said diameter decrease is about Lmax Dmax.

5. The saw bead according to any one of claims 1 to 4 wherein said average working length at Dmin is between 8 and 9 mm and wherein Dmin is between 4.5 and 5.5 mm and wherein said average working length increases with at least 50 micrometer per 100 micrometer of said decreasing diameter.

6. The saw bead according to claim 5 wherein said average working length increases not more than 180 micrometer per 100 micrometer of said decreasing diameter.

7. The saw bead according to any one of claims 5 to 6 wherein said average working length increases with at least 75 micrometer and not more than 120 micrometer per 100 micrometer of said decreasing diameter.

8. The saw bead according to claim 1 wherein said working area at any

working diameter remains smaller than the product of the circumference of the cylinder at that working diameter with the average working length at said outer sleeve diameter Dmin for any diameter larger than Dmin and smaller or equal to said maximum diameter Dmax.

9. The saw bead according to claim 8 wherein said working area increases or remains substantially constant with said decreasing diameter.

10. The saw bead according to any one of claims 1 to 9 in the unused state, wherein said abrasive layer comprises abrasive particles held in a metal matrix, said abrasive layer having an outer surface, said outer surface showing protruding abrasive particles held in said metal matrix material.

1 1 .The saw bead according to any one of claims 1 to 10 wherein said abrasive layer comprises abrasive particles held in a metal matrix, said metal matric material showing a dendritic metallographic structure.

12. The saw bead according to any one of claims 1 to 1 1 wherein said abrasive layer is deposited by means of a laser cladding technique.

13. A saw cord comprising a carrier cord and saw beads according to any one of the preceding claims, said saw beads being threaded on said carrier cord, said saw beads being separated from one another by a polymer sleeve

14. The saw cord according to claim 13 wherein said saw beads are firmly attached to said carrier cord by means of a polymer.