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Interferometric inspection of small wire-drawing dies
Volume
1, number 5
OPTICS COMMUNICATIONS
INTERFEROMETRIC
INSPECTION
OF SMALL
November/December
WIRE-DRAWING
1969
DIES
S. J. BENNETT Metrology
Centre,
National Physical Received
Laboratory, 6 October
Teddington,
Middlesex,
UK
1969
The conical bores of small wire-drawing dies can be inspected by observing the fringe pattern produced by light reflected from the internal surface of the bore interfering with light which passes directly through the aperture. Information about cone angle, roundness and surface roughness can be obtained in this way.
method of inspection is necessary. Mould impressions of such small apertures would be difficult and rather tedious to make, while direct observation with a microscope is impossible. An interference technique has therefore been developed which makes use of the fact that the angle of the drawing cone is such that, when the die is illuminated in a direction parallel to its axis, light reflected from the conical surface is able to pass through the aperture. The reflected wave-front interferes with the direct wave-front in the region of the parallel bore (fig. 2), producing concentric circular interference fringes. If the cone angle is constant, these fringes will be equally spaced, but variations in the angle will result in unequal spacing of the fringes. Roughness and errors of circularity in the cone will produce irregularities in the fringes. This fringe pattern may be regarded as being holographic in nature as it is produced by inter-
The dies used for drawing fine wires are usually of diamond, and the bores may be as small as 30 Mm in diameter. The wire is drawn through a set of dies, each slightly smaller than the previous one, and it may be travelling at speeds up to 50 m/set at the final die. Fig. 1 illustrates the general features of the form of a die. The profile exhibits three distinct regions. These are the conical entrance, the parallel bore and the exit cone. The drawing pressure is greatest near the inner end of the entrance cone, close to the parallel section of the die profile (heavily shaded in fig. 1). It is in this region that wear is heaviest, so that some method of inspecting it is required. In order to permit observation of the development of wear in a die, as well as the inspection of new dies before they are used, a non-destruc-
I
I
Entrancecane
I
Parallel
bore
I
Exit cone
tive
I I _-_-_---
Fig. 1. Form
of die profile.
Fig. 2. Formation
-,_+_--
of interference
fringes.
231
Volume 1, number 5
November/December 1969
OPTICS COMMUNICATIONS
ference between a direct (reference) beam and a beam reflected from the surface under inspection (object beam). Although a magnified image, reconstructed from a hologram, might be easier to inspect than the original die, it is much quicker (and quite adequate in this case) to obtain information about the conical surface by direct observation of the (hologram) fringe pattern. The fringe pattern may be observed by projection with a lens of adequate numerical aperture. That is, if the half-angle of the entrance cone is 6, then the angle between incident and reflected wave-fronts will be 20, so that the numerical aperture of the projection lens must be at least sin 28. This corresponds to a numerical aperture of 0.34 for a cone half-angle of 10’. A heliumneon laser illuminates the aperture directly and a microscope objective lens is used to project the interference pattern. The projected image can be viewed with an eye-piece or a low-power microscope. Fig. 3 illustrates the pattern observed when a new die (bore diameter 58.9 pm) is inspected in this way. The diameter of the parallel bore is not directly measurable, since the phase change on reflection produces a dark fringe adjacent to the edge of the aperture. The spacing of the fringes, however, indicates the angle of the cone, which is clearly not constant in this case. An accurate assessment of the shape of the conical section of a die may be obtained in the following way. The phase retardation on reflection (a) must be known and is assumed constant
A
O/T--P”
B
Fig. 4. Interpretationof fringes.
over the range of angles of incidence involved. The angle $ between the reflected and direct rays at a point in the pattern can be determined from the fringe spacing at that point. Let P, lie on the nth bright fringe from the edge and on a diameter AB (fig. 4) and let #n be the interference angle at P, calculated from the fringe spacing. Then if the ray reflected at Qfl intersects a direct ray in the plane of observation at P, as shown, the path difference between these two rays is given by Z,(l - cos $,) = [n - (6/2r)]h where I, = Q,P,. (If 6 = 0 there will be a bright, zero-order, fringe at the edge of the pattern and n must be replaced by (n - 1) in the above expression.) From the above, In = [n - (6/2r)]/(l
- cos $$J
and the coordinates of the point Qn with respect to the centre of the pattern can be written (see fig. 4) Xn = Yn + I, sin Gn ,
2% = I, cos q& .
In this way a number of points on the surface can
Fig. 3. Interference pattern, new die. 232
Fig. 5. Shapeof entrance cone, from fig. 3.
Volume 1. number 5
OPTICSCOMMUNICATIONS
November/December 1969
(b)
(a) Fig. 6. Interference patterns, worn dies. be established, and fig. 5 shows part of a generator of the entrance cone of the die which produced the pattern of fig. 3. The points were obtained in the above manner from the positions of fringes in the pattern (assuming 6 = a). By constructing a number of such curves in this way it is clearly possible to obtain a fairly complete idea of the form and dimensions of the cone. Departures from circularity of the conical bore and irregularities due to wear are clearly visible in the fringe pattern. Fig. 6 shows the patterns from two worn dies. The die which produced the pattern of fig. 6a had been removed from service because of the formation of ‘flutes’ in the bearing area, and that which produced the pattern of fig. 6b because of roughness in the bearing area and serious departures from circularity. It can be seen that the interference
patterns appear to agree well with these descriptions of the wear conditions. The bore diameters of these two dies are 60.8 pm (fig. 6a) and 71.0 pm (fig. 6b). The method described may be used for routine inspection of the entrance cones of wire-drawing dies as well as for investigation of the factors affecting wear and the way in which wear develops in the bearing area. It is a method which would be applicable to other problems of surface inspection, particularly when the surface is not accessible to existing methods. The work described was carried out at the National Physical Laboratory. The dies used were supplied by the Concordia Electric Wire and Cable Company Ltd.
233
1, number 5
OPTICS COMMUNICATIONS
INTERFEROMETRIC
INSPECTION
OF SMALL
November/December
WIRE-DRAWING
1969
DIES
S. J. BENNETT Metrology
Centre,
National Physical Received
Laboratory, 6 October
Teddington,
Middlesex,
UK
1969
The conical bores of small wire-drawing dies can be inspected by observing the fringe pattern produced by light reflected from the internal surface of the bore interfering with light which passes directly through the aperture. Information about cone angle, roundness and surface roughness can be obtained in this way.
method of inspection is necessary. Mould impressions of such small apertures would be difficult and rather tedious to make, while direct observation with a microscope is impossible. An interference technique has therefore been developed which makes use of the fact that the angle of the drawing cone is such that, when the die is illuminated in a direction parallel to its axis, light reflected from the conical surface is able to pass through the aperture. The reflected wave-front interferes with the direct wave-front in the region of the parallel bore (fig. 2), producing concentric circular interference fringes. If the cone angle is constant, these fringes will be equally spaced, but variations in the angle will result in unequal spacing of the fringes. Roughness and errors of circularity in the cone will produce irregularities in the fringes. This fringe pattern may be regarded as being holographic in nature as it is produced by inter-
The dies used for drawing fine wires are usually of diamond, and the bores may be as small as 30 Mm in diameter. The wire is drawn through a set of dies, each slightly smaller than the previous one, and it may be travelling at speeds up to 50 m/set at the final die. Fig. 1 illustrates the general features of the form of a die. The profile exhibits three distinct regions. These are the conical entrance, the parallel bore and the exit cone. The drawing pressure is greatest near the inner end of the entrance cone, close to the parallel section of the die profile (heavily shaded in fig. 1). It is in this region that wear is heaviest, so that some method of inspecting it is required. In order to permit observation of the development of wear in a die, as well as the inspection of new dies before they are used, a non-destruc-
I
I
Entrancecane
I
Parallel
bore
I
Exit cone
tive
I I _-_-_---
Fig. 1. Form
of die profile.
Fig. 2. Formation
-,_+_--
of interference
fringes.
231
Volume 1, number 5
November/December 1969
OPTICS COMMUNICATIONS
ference between a direct (reference) beam and a beam reflected from the surface under inspection (object beam). Although a magnified image, reconstructed from a hologram, might be easier to inspect than the original die, it is much quicker (and quite adequate in this case) to obtain information about the conical surface by direct observation of the (hologram) fringe pattern. The fringe pattern may be observed by projection with a lens of adequate numerical aperture. That is, if the half-angle of the entrance cone is 6, then the angle between incident and reflected wave-fronts will be 20, so that the numerical aperture of the projection lens must be at least sin 28. This corresponds to a numerical aperture of 0.34 for a cone half-angle of 10’. A heliumneon laser illuminates the aperture directly and a microscope objective lens is used to project the interference pattern. The projected image can be viewed with an eye-piece or a low-power microscope. Fig. 3 illustrates the pattern observed when a new die (bore diameter 58.9 pm) is inspected in this way. The diameter of the parallel bore is not directly measurable, since the phase change on reflection produces a dark fringe adjacent to the edge of the aperture. The spacing of the fringes, however, indicates the angle of the cone, which is clearly not constant in this case. An accurate assessment of the shape of the conical section of a die may be obtained in the following way. The phase retardation on reflection (a) must be known and is assumed constant
A
O/T--P”
B
Fig. 4. Interpretationof fringes.
over the range of angles of incidence involved. The angle $ between the reflected and direct rays at a point in the pattern can be determined from the fringe spacing at that point. Let P, lie on the nth bright fringe from the edge and on a diameter AB (fig. 4) and let #n be the interference angle at P, calculated from the fringe spacing. Then if the ray reflected at Qfl intersects a direct ray in the plane of observation at P, as shown, the path difference between these two rays is given by Z,(l - cos $,) = [n - (6/2r)]h where I, = Q,P,. (If 6 = 0 there will be a bright, zero-order, fringe at the edge of the pattern and n must be replaced by (n - 1) in the above expression.) From the above, In = [n - (6/2r)]/(l
- cos $$J
and the coordinates of the point Qn with respect to the centre of the pattern can be written (see fig. 4) Xn = Yn + I, sin Gn ,
2% = I, cos q& .
In this way a number of points on the surface can
Fig. 3. Interference pattern, new die. 232
Fig. 5. Shapeof entrance cone, from fig. 3.
Volume 1. number 5
OPTICSCOMMUNICATIONS
November/December 1969
(b)
(a) Fig. 6. Interference patterns, worn dies. be established, and fig. 5 shows part of a generator of the entrance cone of the die which produced the pattern of fig. 3. The points were obtained in the above manner from the positions of fringes in the pattern (assuming 6 = a). By constructing a number of such curves in this way it is clearly possible to obtain a fairly complete idea of the form and dimensions of the cone. Departures from circularity of the conical bore and irregularities due to wear are clearly visible in the fringe pattern. Fig. 6 shows the patterns from two worn dies. The die which produced the pattern of fig. 6a had been removed from service because of the formation of ‘flutes’ in the bearing area, and that which produced the pattern of fig. 6b because of roughness in the bearing area and serious departures from circularity. It can be seen that the interference
patterns appear to agree well with these descriptions of the wear conditions. The bore diameters of these two dies are 60.8 pm (fig. 6a) and 71.0 pm (fig. 6b). The method described may be used for routine inspection of the entrance cones of wire-drawing dies as well as for investigation of the factors affecting wear and the way in which wear develops in the bearing area. It is a method which would be applicable to other problems of surface inspection, particularly when the surface is not accessible to existing methods. The work described was carried out at the National Physical Laboratory. The dies used were supplied by the Concordia Electric Wire and Cable Company Ltd.
233