An innovation process in the marking of lasts for the footwear industry

Abstract

This paper describes a basic innovation in the production of special supports, called lasts, which are used in assembling the components of leather shoes in the footwear production process. Innovation concerns the so-called marking phase, in which labels of various kinds are imprinted on the last. Instead of using ink stamps and performing manually the marking process, as in the current practice, we propose and test the use of laser marking in an automated, flexible work cell. Realization of a work cell and industrialization of the process are described and advantages of the proposed procedure are discussed.

Appendices

Appendix 1

In laser marking, impressions are obtained as the projection of planar images onto the surface of the last. Since the surface of the last is not flat, this produces blurring and deformation that degrade the quality of the image. In this Appendix, we will consider the situation in which the impression is obtained by projecting a planar image that lays on the tangent plane to the last in a point O from a point S (the beam source) that belongs to the normal to the surface in O. In practice, this condition is obtained by orienting the last with respect to the laser in such a way that its tangent plane in the center of a rectangle that contains the label is perpendicular to the default direction of the beam (see Fig. 5 and Appendix 2). Blurring and deformation are, in this way, reduced as much as possible in the neighborhood of O. Note that impression is obtained in hand printing by rotating the stamp around a contact point O, so that any point of its surface come into contact with the last. In this case, the result is influenced by the way in which the stamp is rotated (i.e., according to the choice of the axis of rotation and of the order of rotation) and by the pressure exerted. Since precise standardization of the manual procedure with respect to the above factors turns out to be practically impossible, the hand-printing process presents scarce repeatability and no objective, quantitative evaluation procedures have been developed, in the shoe industry, to assess its quality. The only quantitative indication commonly accepted establishes that errors (with respect to the CAD model) in positioning dots used as markers must be smaller than 1 mm in all directions. This state of things, actually, complies well with the requirements, in terms of manufacturing precision, of the shoe industry. Here, we will refer to quantitative criteria (see e.g. [3]) for evaluating quality of the laser-printed labels in comparison with that of hand-printed ones, but, for the reason illustrated above, the results we derive will be mainly qualitative.

In evaluating quality, we focus on image perception and interpretation by human operators. In general terms, perception refers to the possibility and easiness to single out a given image from the background by detecting edges. In the case of monochromatic images, as the one we consider, this feature depends on edge contrast or, more precisely, on acutance, that is on the derivative of brightness with respect to space. The higher is the acutance, the sharper results the image in human perception. Figure 7 reproduces a digital picture (×3 magnification) of two impressions obtained by hand-stamping (number “37” on the left) and by laser printing (number “37” on the right) on a flat HPDE surface. Acutance of impressions is deteriorated by the camera in the digital photo process (in Fig. 7, it is also deteriorated by the reproduction process), but this applies to both of them in the same average measure.

Fig. 7

Picture of two impressions obtained respectively by hand-stamping (number “37” on the left) and by laser printing (number “37” on the right) on a flat HPDE surface

By applying simple edge detection algorithms, we get the results illustrated in Fig. 8 (digital image has been processed by means of the GIMP 2.8 software). A large number of tests has shown that such results are quite representative of the general case. Visual qualitative analysis of the above pictures suffices to show that edge detection gives better results on laser printed images than those it gives on hand-printed ones. Edges are blurred when printing on a curved surface, but this phenomenon affects both laser printed images and hand-printed ones. Therefore, we can conclude that the analysis of images printed on a flat surface applies to general situations.

Fig. 8

Image filtered, respectively, by the Gradient, Prewitt, and Sobel edge detection algorithms

Perceived sharpness is also influenced by resolution that is the number of high-contrast, distinguishable line pairs per millimeter in the image. The human eye can arrive to perceive up to 10 high-contrast line pairs per millimeter, that is a resolution of 10 l(ine)p(air)/mm. Experimentally, resolution is evaluated by means of patterns consisting of dark lines against a light background. In the USAF 1951 target, which represent the most used standard, these patterns consist of three pairs of dark and clear lines in vertical and in horizontal orientation. Line patterns are called elements, and each element is identified by two parameters p and q, conventionally indicated as group number and element number, which express the resolution in lp/mm of the pattern: in element p/q there are ${2}^{p+\frac{q-1}{6}}$ pairs of dark and clear lines per millimeter. Patterns have been printed by means of the Technifor TF410 laser on a flat HPDE surface by choosing different nominal resolutions and the results have been qualitatively evaluated by asking operators to indicate the patterns in which lines are subjectively distinguishable with naked eye. We point out once more that the choice of this way to evaluate resolution is motivated by the fact that, in the subsequent production phases, operators will look at printed images with naked eye. Figure 9 reproduces one of the printed patterns: obviously, resolution in reproduction is much lower than in reality and Fig. 9 is provided only for sake of illustration. Lines result to be clearly distinguishable, in several tests, in element 0/13, which contains four line pairs for millimeter, with a thickness of the dark line of 0.125 mm. This qualitative result indicates a resolution greater than that currently achieved by hand stamping, considering that the minimum thickness of single lines on currently used stamps is about 0.5 mm.

Fig. 9

Printed patterns used in evaluating resolution

In conclusion, by qualitative evaluation of acutance and of resolution, we can say that, in the considered situation, perceived sharpness is greater in laser printed images than in hand-printed ones. In considering interpretation of images by human operators, we assume that correctness of interpretation is directly related to correspondence of the printed image with a given model and to precision in positioning the printed image on the last with respect to the CAD model. Actually, the laser printing process causes deformation, due to the fact that printed images are obtained as the projection onto a curved surface of planar images that lay on the tangent plane. From this point of view, quality depends on the difference between the actual printed image and its planar model. In order to simplify the analysis of deformation, let us consider first the simpler two-dimensional case described in Fig. 10.

Fig. 10

Deformation in the simple two-dimensional case

By projecting form S, the segment OC onto the circle of radius r with center in D, the resulting images is the arc OE and the difference in length between OE and OC can be used as a measure of deformation. More precisely, letting l and l ₁ denote respectively the length of the segment OC and that of the arc OE, we call, respectively, absolute deformation and relative deformation the quantities ∆_abs = l ₁ − l and ∆_rel = 100(l ₁ − l)/l. Clearly, ∆_rel depends on the distance p, the radius r, and also the length l of OC. Elementary geometric reasoning shows that ${l}_1=r\cdotp \gamma =r\cdotp \arcsin \left(\frac{p\left(l+r\right)-\sqrt{{\left(l+r\right)}^2-\left({l}^2+2 lr\right)\left({p}^2/{l}^2+1\right)}}{ lr\left({p}^2/{l}^2+1\right)}\right)$. Note that deformation does not affect the entire segment in homogeneous way, since the distance between two points on the segment OC and the length of the arc defined by their projections differ by a factor that depends also on the distance from O. This aspect can be practically handled, as long as p is small, by taking into account both absolute deformation and relative deformation in evaluating the quality of the impression. When projecting a label containing a planar image on the last, we can assume that r is maximum curvature of its surface in the neighborhood of the point O where the center of the printed label has to be located and 2l is the longest side of the smallest rectangle that contains the label (referring to Fig. 5, the point O coincides with the origin O _L of the {O _L , X ₃, Y ₃, Z ₃} coordinate system and the rectangle at issue is the one containing the label ABCD). This means that, considering all curves obtained by intersecting the surface with the planes that contains its normal vector at the point O and, for each curve, taking the osculating circle in O, r is the radius of the smallest of those circles. Then, the quantity ∆_abs and ∆_rel, being related to deformation along the direction of the maximum curvature, give a measure of the difference between the printed image and its planar model. Note that deformation arises also in the traditional hand-printing process, since, also in that case, images are transferred from the planar surfaced of the stamp to the curved surface of the last. In the hand-printing process, deformation is somehow controlled by limiting the dimension of the stamp with respect to the maximum curvature r. This can be done in a much more precise way in laser marking, if p is fixed, by limiting l. Table 2 shows values of ∆_abs and ∆_rel for p = 50 cm, l = length OC = 5 cm and different values of r.

Table 2 Values of ∆_abs and ∆_rel for p = 50 cm, l = length OC = 5 cm and different values of r

The requirement to keep the position error due to deformation smaller than 1 mm for every point of the printed image is satisfied, in this case, if r is greater than or equal to 7 cm (or the curvature is smaller than 0.143). Table 3 shows the minimum value of r that guarantees to respect that requirement for p = 50 cm and for different values of l = length OC.

Table 3 Minimum value of r that guarantees a position error smaller than 1 mm for p = 50 cm and for different values of l = length OC

By looking at similar tables, that can easily be obtained by the previous formulas, the operator can conveniently match the dimension of each label with the area where it has to be printed, so to keep deformation in terms of ∆_abs and ∆_rel within acceptable limits and, hence, to have a good qualitative correspondence of the printed image with its planar model. We can say, in such situation, that the condition of keeping the printing area almost perpendicular to the default direction of the laser beam is approximately achieved. Large images on high curvature areas can be obtained by subdividing them into several labels.

Good qualitative correspondence between printed images and their planar models makes symbolic meaning easily understandable. In addition, when images contain markers to be used in the subsequent production phases, ∆_abs bounds the error in placing the markers with respect to point O due to deformation in the printing process. In case great precision is required, labels that contain just one single point marker at the center can be used, so to have ∆_abs = 0 for any curvature. The position of printed markers, in that case, may differ from the position in the CAD model only because of errors in positioning and orienting the last with respect to the laser (namely, referring to Fig. 5, in bringing {O _L , X ₃, Y ₃, Z ₃} to coincide with {O ₁, X ₁, Y ₁, Z ₁}), because of errors in focusing and because of discrepancies between the last and its CAD model. The first two sources of errors can be dealt with by the laser control system and by the manipulator control system and their effects can safely be disregarded with respect to the required precision (±1 mm). The third source is not related with the marking process and, therefore, the simplest and less expensive way to deal with it is to consider its effect as a random disturbance. Experimental measurements have been performed in order to assess the error in positioning point markers with respect to the CAD model on sets of nominally equal lasts, so to take into account also possible differences in the coupling between last and handling support, evaluating both the position with respect to the {O ₂, X ₂, Y ₂, Z ₂} coordinate system of Fig. 5 and the relative distance between point markers. In practice, we have taken measurements of the distance between laser printed point markers and fixed reference points on the handling support. Figure 11 shows two laser printed point markers (magnified, in black) on the last and four reference points (magnified, in red) on the handling support, located at the vertices. Assuming a perfect correspondence between the handling support and its CAD model (actual differences of the order of 10⁻² mm are safely negligible) and knowing the coordinates of the vertices in the {O ₂, X ₂, Y ₂, Z ₂} system, experimental measurements can be used to evaluate errors in positioning the markers with respect to the CAD model. In all cases, errors have been shown to be well within the margin of acceptance for the final product, that is ±1 mm.

Fig. 11

Markers (black dots) on the last and reference points (indicated by arrows) on the handling support

For the above reason, we can conclude that the laser marking process performs better than the hand-printing process in producing images that are easily perceived and interpreted by human operator and that convey correct information.

Appendix 2

Position and orientation of the labels on the last are decided in a dedicated design phase of the last CAD process. After having defined the shape of the last in the CAD environment, the designer specifies a label L in graphic terms (e.g., the ABCD label represented at the bottom of Fig. 5) and he chooses its location on the last. This is represented by the position, on the surface of the last, of the center of the smallest rectangle that contains the label (e.g., the point O _L , that is the origin of the {O _L , X ₃, Y ₃, Z ₃} coordinate system, in Fig. 5). By looking at tables like Table 3, as already pointed out in Appendix 1, the dimension of each label can be conveniently matched with the area where it should be printed and, in case, modifications, by splitting a large label into a set of smaller ones, can be made. Then, the operator draws the label L on the tangent plane π to the last in O _L with the desired orientation in the CAD environment and he simulates the effect of laser printing by projecting the label onto the last from a suitable point on the normal to the surface in O _L . The process is repeated by modifying the label, its position, and orientation until the operator is qualitatively satisfied of the result. At that point, the right-handed Cartesian coordinate system {O _L , X ₃, Y ₃, Z ₃} is automatically constructed by letting Z ₃ coincide with the normal to π, oriented outward of the last, and letting X ₃ and Y ₃ be parallel to the sides of the rectangle that contains the lasts. The vector v of coordinates of O _L in the Cartesian coordinate system {O ₂, X ₂, Y ₂, Z ₂} attached to the manipulator wrist and the rotation matrix M _L from {O ₂, X ₂, Y ₂, Z ₂} to {O _L , X ₃, Y ₃, Z ₃} (see Fig. 5) are then associated to the label L in preparing the work order for the last at issue and the process is repeated for all the required labels.

In order to position and to orient the last for printing the label L, the control system computes the vector v′ = −M _L v and it finds the Euler angles φ, θ, ψ associated to the rotation M _L . Then, it commands the manipulator controller to move in such a way to bring the wrist coordinate system {O ₂, X ₂, Y ₂, Z ₂} to the target position and to assume the attitude that are respectively defined, in the coordinate system {O ₁, X ₁, Y ₁, Z ₁} of the work cell, by the vector of coordinates v′ and by φ, θ, ψ. As a result, {O _L , X ₃, Y ₃, Z ₃} is brought to coincide with {O ₁, X ₁, Y ₁, Z ₁} and the printing can be performed.