Shaped saw wire with controlled curvature at bends

Abstract

A saw wire to cut hard and brittle materials is disclosed that comprises a steel wire that is provided with bends with segments in between. The average degree of bending of the bends is between 0.5% and 5%. Such a saw wire has a higher breaking load compared to saw wires having a conventional, higher average degree of bending. A method to measure the curvature is described as well as a process to make the inventive saw wire. The invention is applicable to any shaped saw wire for example a single crimped saw wire, a saw wire with at least two crimps in different planes, a saw wire with crimps rotating in a plane.

Claims

1. A saw wire for cutting hard and brittle materials comprising a steel wire with a diameter d and a centreline, said saw wire having bends with segments in between, said centreline having a top curvature k.sub.i at each of said bends when measured with a load of about one newton on said saw wire, wherein the average of the products of said top curvatures with half said diameter, over a length of saw wire comprising at least N bends, with N being not less than 50, is between 0.5 and 5 percent or in formula: $0.005<\frac{\underset{i=1}{\overset{N}{.Math.}}{k}_{i}d/2}{N}<0.050$ wherein said segments have a radius of curvature that is larger than 100d, wherein the total length of said segments is higher than 33% of the total centre line length of said steel wire, wherein the total length of said segments is lower than 85% of the total centre line length of said steel wire, and wherein the number of bends is at least 10 over an axial length of 100 times the diameter d.

2. The saw wire according to claim 1 wherein for said steel wire with diameter between 200 m and 300 m said average is between 3 to 5%.

3. The saw wire according to claim 1 wherein the maximum value of said products k.sub.id/2 does not exceed 0.05.

4. The saw wire according to claim 1 wherein the standard deviation of said products k.sub.id/2, over a length of saw wire comprising at least 50 bends is lower than 0.005.

5. The saw wire according to claim 1 wherein said saw wire has a helicoidal shape around an axis and wherein said bends are oriented radially outward of said axis.

6. The saw wire according to claim 1 wherein said saw wire comprises crimps in the form of a wave in at least one plane comprising the axis of said saw wire.

7. The saw wire according to claim 6 wherein a first wave crimp is in a first plane, a second wave crimp is in a second plane, said first plane being different from said second plane, said first and second plane crossing one another along the axis of said saw wire.

8. The saw wire according to claim 6 wherein said crimps in the form of a wave in at least one plane rotate around said axis along the axial length of said saw wire.

9. The saw wire according to claim 1 further comprising an abrasive layer fixed on the surface of said steel wire.

10. The saw wire according to claim 7 wherein said first plane and said second plane rotates around said axis along the axial length of said saw wire.

11. The saw wire according to claim 1 wherein for said steel wire with diameter between 120 m and 200 m said average is between 0.5% to 3%.

12. The saw wire according to claim 1 wherein for said steel wire with diameter thinner or equal to 120 m said average is between 0.5% and 2%.

13. The saw wire according to claim 1 wherein an axial length L is the straight length between two fixation points of the saw wire when held under a load of one newton, and a curve length S is the length along the centreline of the wire over said axial length L and wherein the extra length in the saw wire is the difference between the curve length and the axial length SL, and wherein the extra length is larger than 0.06% of the axial length L and not larger than 0.6% of the axial length L.

Description

BRIEF DESCRIPTION OF FIGURES IN THE DRAWINGS

(1) FIGS. 1a and 1b, 2a and 2b, 3a and 3b show different clarifications on curvature.

(2) FIGS. 4a and 4b shows the centreline of the same piece of saw wire in the X-Z and Y-Z plane.

(3) FIG. 5a shows the curvature as a function of curve length of the same piece of saw wire as in FIGS. 4a and 4b.

(4) FIG. 5b is an enlargement of a section of FIG. 5a.

(5) FIG. 6 shows the relationship between relative breaking load of the wire and average degree of bending.

(6) FIG. 7 illustrates the relation between the teeth radius of and the tension on the average bending degree.

MODE(S) FOR CARRYING OUT THE INVENTION

(7) FIGS. 1, 2 and 3 show three plane wave forms in the Y-Z plane. They can be regarded as a unit cell representation of a crimp of a saw wire. By repeating the unit cell a representation of the centreline of a saw wire with one plane crimp is obtained. All the three representations 1a, 2a, and 3a have the same wavelength, 100 units, and amplitude namely 25 units. An isometric scaling of the coordinates is intended (but can, due to reproduction of the graph, have been altered). The curvature as calculated from the curves is represented in FIGS. 1b, 2b, and 3b. They have been calculated by the numerical procedures as described above.

(8) In FIG. 1a the crimp is in the form of two half-circles of radius 25 units that match at 50 units in Z direction. FIG. 1b shows the corresponding calculated curvature K (in inverse units). In abscissa the curve length s along the curve is used. Note that the s length is longer than the wavelength of 100 units, because the length of the centreline is longer than the axial length. As the crimp is composed of half-circles with a radius of 25 units, the curvature remains constant at a value of 1/25 or 0.04 inverse units.

(9) FIG. 2a represents a crimp in the form of a sinus. Again the wavelength is 100 units and the amplitude is 25 units, as in the case of FIG. 1a. Now the curvature K (in 1/units) shows a varying behaviour between 0 and 0.10 units.sup.1. At the points of inflection (at Z=0, 50 and 100 units) the curvature becomes zero as the second derivative y at those points becomes zero. Note that for a single wavelength, two peaks occur.

(10) FIG. 3a shows a saw tooth curve generated by summing a limited number of terms in the Fourier series of a saw tooth. The corresponding curvature plot is represented in FIG. 3b. Now the regions of high curvature are very much restricted to there where the tops and valleys of the curve occur (at Z=25 and 75 units). As the bends at the tops and valleys are shorter, the curvature K rises to about 0.32 units.sup.1 at those positions. The lobes that are present between the peaks are a consequence of the limited number of terms taken in the series. As the curvature is composed of second order derivatives of the space curve it is very sensitive to tiny variations in direction of the curve.

(11) In FIGS. 4a and 4b a saw wire having bends with segments in between has been analysed with the apparatus as described in WO 95/16816 according the procedure of the second aspect of the invention. The steel wire has a diameter d of 116 m. The wire was clamped between the chucks without any twisting of the wire and then slightly tensioned (1N). The scan length is 100 mm in this case. FIG. 4a shows a screenshot of a computer screen that shows the Z and X coordinates as read in from the measuring apparatus. Thereafter the chucks were turned 90 and a second trace was recorded and is represented in FIG. 4b: the Y-Z plane. With these two traces, the position of the centreline is completely recorded in 3D space at the discrete points: (x(z.sub.j), y(z.sub.j), z.sub.j).

(12) These discrete points can now be manipulated computationally. For example by mathematically rotating the wire around the Z-axis at an angle of 59 the centreline of the wire shows a single crimp in one plane with a wavelength of 3.62 mm and a peak-to-peak amplitude of 59 m. When virtually turning the wire further, a single second crimp occurs in a plane at an angle of 148 with a wavelength of 3.06 mm and an amplitude of 31 m. So the saw wire is of the type that comprises two different crimps in planes that are under an angle of 89 to one another and cross at the axis of the saw wire.

(13) In the software package LabVIEW (from National Instruments) the traces were numerically differentiated according the Savitsky-Golay procedure. This procedure is a readymade Virtual Instrument (*.vi) available in the software package (Savitzky-Golay Filter Coefficients.vi). In this procedure the results of course depend on the degree n of the polynomial used and the number of data points 2m+1 in each vector.

(14) After due experimentation the inventors found the settings n=5 and m=9 (i.e. there are 19 datapoints in the vector {13}) as most appropriate for the analysis of a saw wire. The length taken into account is then 1950 m or 0.95 mm which is about 8 diameters of the metal wire. Saw wires should be analysed over a length of between 4 to 10 times their diameter. Increasing the number of samples point in the analysis interval will average out all features of the space curve. Using less sample points increases the noise too much.

(15) The degree of the polynomial used should at least be 4. This is because a space curve in the tripod tangent, normal and binormal can be locally expressed in a third order polynomial in the curve length s. Higher order terms remain for absorbing the error. Using a polynomial degree that is higher than 5 is not useful as only the first three derivatives are used in curvature and torsion formulas. The higher order terms allow a better fit, but are of no use as only the lower order terms appear in the derivation.

(16) It is further noteworthy to mention that the curvature is completely independent of the orientation of the wire between the chucks: the clamping of the wire must not be exactly diametrical to one another in order to obtain reliable results. It is only when one deforms the wire by applying tension that the curvature results change due to the deformation of the wire.

(17) By the Savitsky-Golay procedure numerical estimates were obtained for the first and second derivatives in X and Y as per formula {14} and subsequently used in the expression for the curvature {8}. In this way for every data point (except the first 9 and 9 last points) a curvature k can be calculated. For each point also the curve length s can be calculated by using {15}. By now plotting the quantity kd/2 as a function of s the graph of FIG. 5a is obtained.

(18) In FIG. 5a, the curve shows a sequence of peaks of which the top value corresponds with the maximum curvature determined at the bends. These are the top curvatures k.sub.id/2 as in the language of the claims and are indicated by a small circle. The dashed line corresponds to a curvature of 0.5% which i.e. a radius of curvature of 100d. Hence, the points under the line belong to segments, while the points that are on or above the line belong to bends.

(19) FIG. 5b, is an enlargement of FIG. 5a of the range 30 to 60 mm. It shows the peaks more clearly and also the straight segments can be readily extracted from the graph.

(20) In a further module of LabVIEW, the top curvatures are detected and identified. Obviously only the peaks above the 0.5% threshold are identified. One can then easily extract the following statistics: 87 peaks are present in the range from 0 to 100 mm i.e. N=87 Hence the number of peaks per mm is 0.87 and the number of peaks per 100d is 10.092. The average of the 87 k.sub.id/2 top bending values is 0.95% and the standard deviation is 0.24% The maximum k.sub.id/2 value observed is 2.5% (at s equal to about 92 mm)

(21) In a series of experiments a steel wire of diameter 115 m with a tensile strength of 3650 N/mm.sup.2 was deformed between a pair of toothed wheels thus forming a single crimp wire. The following parameters were varied: The tension T on the wire during crimping; The teeth radius R.sub.t by using different toothed wheels with 0.3 (2.6d), 0.5 (4.35d), 1 (8.70d), 1.5 (13d) mm teeth radius. The wavelength of the crimp: 1.8, 2.8, 3.1 and 3.7 mm.
The samples obtained where analysed geometrically as described above, as well as their mechanical properties determined and in particular the tensile strength. The results are depicted in FIG. 6.

(22) In FIG. 6 the relative breaking load (in %, relative to the value of a straight, not crimped wire) as a function of the average measured degree of bending (in %) is depicted. The different symbols depict various combinations of the above parameters. It is clear that as the average bending degree goes over the 5% limit, a loss of more than 14% of tensile strength relative to the straight wire can be expected and this becomes too much for saw wire applications.

(23) For saw wires with an average bending degree of between 3 and 5% a tensile strength loss of between 10 and 14% can be expected. For thicker saw wires in the range of 200 m to 300 m this is still acceptable. This is indicated by the solid line bracket in FIG. 6.

(24) For wires with an average bending degree of between 1.5% and 3% a loss in tensile strength of between 5.5% and 10% is acceptable for wires of diameter 120 m to 200 m (the dashed bracket in FIG. 6).

(25) Finally for wires with an average bending degree of between 0.5 and 1.5% the smallest loss in tensile strength of between 1.5 and 5.5% is expected and therefore most appropriate for wires smaller or equal to 120 m. This is indicated by the dotted bracket in FIG. 6.

(26) In a further series of experiments, the influence of the processing conditions was investigated. A straight steel wire with diameter d of 120 m was led through a first pair of deformation wheels of which the teeth have radii of 12.5 times d and at different tension levels. The tension level is measured after passage through the bending apparatus. The indentation of the wheel was set to 2d. Thereafter the average degree of bending was determined on the wires. In a second series of tests the same straight wire was deformed through a pair of wheels with teeth radii of 8.3d, with the same different tension levels and the same degree of indentation.

(27) The results are depicted in FIG. 7. There the different tension levels T applied are expressed as fractions of the breaking load F.sub.m in abscissa: T/Fm (in %). In ordinate the average degree of bending (AVG kdi/2) is represented in percent in ordinate. When a higher tooth radius is used (12.5d), a larger tension must be applied to obtain the desired minimum degree of bending. However, a large tooth radius has the advantage that the wire is not easily deformed too much and that the standard deviation remains low (as indicated by the one standard deviation error bars).

(28) A tooth radius of 8.3d results in an average degree of bending within the preferred region of 0.50 to 1.50% for the smaller diameter of the steel wire. By preference the tension is held between 10 to 30% of the breaking load. However, the curvature shows a higher standard deviation.