analysIs of errors of profIle transformatIon

A necessity to improve the quality of textile products and reduce production costs associated with losses of raw materials in the processing requires the development of automated quality inspection systems for all steps of textile production. Promising is the use of contactless methods of nondestructive testing based on the methods of vision. The object of research is a device to inspect the shape of textile packages by shadow projection method for monitoring in real time. A series of experiments and theoretical research are conducted aimed at the study of structural parameters of the device to inspect the shape of the packing by the shadow projection method, providing the required accuracy. On the basis of the mutual arrangement of the structural elements of the light source, camera shutter and inspected bobbin, the impact of each of them on the scale transformation error for inspection of the package shape of cross winding is defined. This result allows to select the mutual arrangement of design elements and to set their permissible variations of devices to inspect the package shape of cross winding by the shadow projection method. Inspection of package shape in the process of their developments will prevent the formation of defective packages. It will increase a percentage of defect packages and the loss of raw material in the textile industry, which ultimately will raise its efficiency.


ISSN 2226-3780
Threats. There are difficulties associated with the use of research results. This is due to the fact that the ap plication of the chosen calculation model of potential cor respondence it is necessary to determine the number of departures and the number of arrivals in the transport system points. An occurrence of such state of the system, in which it will require transport enterprises to provide more volume of transport services, is possible.

Conclusions
1. Passenger transport correspondence between cities with different number of inhabitants is experimentally defined. The quantitative indicators of passenger transport correspondence are obtained. It is established that intercity passenger transport correspondence can be predicted. It is proved that gravity modeling of passenger transport correspondence is suitable for this system.

Introduction
Textile industry effectiveness is closely connected with the provision of the required quality for all technological steps. One of the most important processes in the textile industry is the winding process, which resulted in for ming textile packages of various shapes. Defects of textile packages results in increased breakage in subsequent steps, where the package is processed. Defective packages must be rewinding, which is associated with additional labor costs and an increase in the number of irretrievable loss of raw materials. One of the most important indi cators of quality of textile packages is their deviation from a given shape. Development of inspection meth ods for packages in the production process is an urgent task. Features of ensuring the accuracy of the shape of packages by shadow projection method are considered in the article.

the object of research and its technological audit
The object of research is a device to inspect the shape of textile packages by shadow projection method for moni toring in real time.
Shadow projection method ( Fig. 1) is used to measure the roughness of the slightly reflective surface more than 40 microns [1]. Shutter (S) is mounted above the testing surface for measuring by this method. It intercepts part of the light beam which is directed to the test surface from the light source, the optical axis О 1 О 1 of which is inclined at an angle α to the normal of the test surface. The shutter shadow falls on the surface and reproduces its profile. The shape and size of the cross section are determined by a visible image in the shadow in observation device. Its optical axis О 2 О 2 is directed at an angle β to the normal of test surface. Unlike the methods using the surface scanning, shadow projection method doesn't require a long time to remove the primary image and allows monitoring in real time.
Wellfounded choice of design parameters, providing the desired inspection accuracy, is necessary for use of this method in practice.

the aim and objectives of research
The aim of research is to develop a technique of theo retical analysis of the scale errors of the textile package profile transformation and development of technique of wellfounded choice of design parameters of the device, allowing to minimize them.
To achieve this aim it is necessary: 1. Identify the basic parameters of the device used to generate primary data about the shape of packages that affect the inspection results.
2. Prove the divergence of design parameters, pro viding the required transformation accuracy.

research of existing solutions of the problem
Device in [2] is proposed to inspect the bobbin out ofroundness. This device projects its image on the screen at certain points of which photocells are installed. The signals from the photocells are processed on a computer. As follows from the description, inspection of geometric dimensions in this device is carried out only at certain points, thus, because the bobbin image projection on the screen is analyzed, then information on the bobbin shaded areas is lost.
Device for inspection of the size and shape of the bobbin is proposed in [3]. It is used for automatic wind ing machine during the yarn winding. It is provided with a control head, installed in front of the bobbin board or in the zone of bobbin movement to the storage bin. The control head is equipped with a light source and a dispersing lens guiding the light beam onto a bobbin. The reflected light beams are directed to the host system of mirrors, where the beams are directed onerow photocells.
The beams pass through the focusing lens and arrive at the photocell corresponding to the determined diameter of the wending bobbin. Pulses of photocells are sent to the control electronic unit. Signals from this unit are sent to the drive unit of the winding head correcting a bobbin board rotation rate. A disadvantage of the device is that only one of the ends of the bobbin is inspected, wherein the bobbin outofroundness and diameter deviation are determined. Thus, the device doesn't allow for an integrated inspection of geometrical parameters of the winding body.
Device to inspect the shape of the bobbin is shown in [4]. This device is used on the winder for winding inspection and correct formation of the end face of bobbin. It is provided with a photoelectric sensor, which receives light rays reflected from the defective area of the bob bin. Light rays at the end surface bobbin are directed from the light source and pass through a dispersing lens. Signals are sent from photocell to the electronic noise block of analyzing unit. The formed signal is applied to the amplifier and analogtodigital converter coupled to the normalizing unit and the memory unit.
Described device, as the previous one, allows to in spect only one of the ends of the package that does not give full information about its shape. Unlike the previous device designed to inspect the outof roundness of the end, this device allows to determine its outofstraightness.
Some of the best results can be obtained by scanning the test winding body with a laser beam, as is done in inspection device of the bobbin winding [5].
The device is designed for noncontact determina tion of the lifting angle of the winding. Also this device, based on angle measurements, may adjust it within a pre determined range, which allows winding the bobbin of a regular shape. The next step in the development of devices based on bobbin image scanning is the automatic inspection system of yarn packages [6,7], which records the presence of broken yarns, stains and dirt, as well as inspection of package shape. System operation is based on an optical distance measurement that is independent of the gloss degree of inspected packages. The laser beam is used as a light source. It scans the package end surface, generally in the direction of its radius. The resulting linear profiles ISSN 2226-3780 are transformed into rectangular image. Reflected light from the package falls on the detector that captures not the amount of reflected light, and the location of the light spot. Location of the light spot is a measure of height. Since the detector operates independently of the amount of reflected light, device is suitable for scanning of natural yarn packages, partially oriented yarns and yarns obtained by texturing with extension.
Further development of the abovedescribed system is a system [8], which allows to inspect: -geometric parameters (diameter and saddle shaping and swelling); -structural parameters (presence of the running end, roving winding, etc.); -such parameters as yarn intersection, the presence of broken filaments, loops and fluff. This system has a modular design and allows to de fine all characteristics or only some of them. Use of the laser technology makes available a fixation of very small defects of the bobbins, unseen by the human eye. The system is equipped with an automatic vehicle and robots, which provide bobbin reception, setting them in the in spection places and other activities related to the bobbin inspection. Throughout the inspection human hand doesn't touch the bobbin during the inspection. Time for bobbin inspection is ~9 seconds. The system monitors more than 400 bobbins per 1 hour. Systems that are based on the laser scanning of investigated area are quite complex and, consequently, costly, requiring specially trained personnel to operate them.
Similar results at a much lower cost can be achieved using the cameras and matrix photocells as receiver.
Device for quality inspection of the yarn bobbins of all sizes, colors and materials is shown in [9]. The principle of device operation is based on the image acquisition of the bobbins and their processing using the computer to determine the presence of defects.
Device comprises two racks on which the image sen sors are installed, for example, matrix camera. Sensors scan the upper and lower ends of the bobbin, and its side surface. For this, they are moved along the rack by electromechanical drive. Image input unit, improvement unit, filter, image binarization unit, output characteristics unit and evaluation unit are used for processing of each image. Each input image is converted into twocolor digital image. Specific image geometrical characteristics of each defect are detected in each image. These characteristics are compared to stored characteristics with predetermined values in the storage unit. This makes it possible to assess the existence of the defect or lack of it.
Inspected bobbins in the device [10] are moved through inspection camera equipped with devices for optical in spection of the bobbins. Test of every bobbin is carried out for their sorting. At the same time the full bobbins continue to move on the support conveyor to the place of removal. Defected bobbins are transferred to another conveyor, from which they are removed elsewhere.
The following research methods are used: analysis of measurement error and geometrical optics.

research results
Using the method of shadow cross section projection in order to calculate the height of the surface profile in the normal section, M scale of profile transformation is used. It is calculated for nominal values of the angles α, β and j. The angle deviation from the nominal values will cause the scale error of profile transformation and, there fore, the error of surface profile measurement. It is known that the transformation scale depends on the angles α, β and j. The angle j varies with angular displacement of the axis of the inspected bobbin around the Zaxis. Angles α and β are changed in the case of [11][12][13][14]: -linear displacement of the light source and the ca mera along the X and Zaxes while maintaining the substantive position of the point O; -bobbin displacement along the Xaxis and its rota tion around this axis; -angular displacement of the shutter and the bobbin axis. According to [10,11,15], the error of the measured profile height can be determined by the following formula: where Δα, Δβ and Δj -deviations of corresponding angles. Substituting h' from the previous in (1), after differen tiation we obtain: Let's analyze the individual components of the transfor mation scale error caused by linear and angular displace ments of the individual components of device to inspect the package shape. Because these components are independent variables, the error of the angle α can be determined by the formula [11]: where Δα 1 -deviation caused by a linear displacement of the light source position; Δα 2 -deviation caused by the bobbin displacement along the X-axis; Δα 3 -devia tion caused by shutter rotation around the axis that is parallel to the Xaxis; Δα 4 -deviation caused by shutter rotation around the axis that is parallel to the Yaxis. Let's estimate the value of the error Δα 1 caused by this displacement. The distance between points B and C is determined by the formula: Let's drop a perpendicular from point B on the line OC. It is obviously that the segment AB is inclined to OX axis at an angle α. The inclination angle of segment BC to OX axis is calculated as follows: Angle ВЕF = ψ and it is external to the triangle DEB, so it is equal to the sum of the angles BDE and DBE. Then the angle DBE = ψ -α. Therefore, from the triangle ABC: From the triangle OAB get: Substituting (4), (5) and (6) in (7) and accept that tg Δα 1 ≈ ≈ Δα 1 taking into account that angle Δα 1 is small, define: where Δx c and Δy c -deviations in the position of the camera, respectively, in the Xaxis and Yaxis; R c -the distance from the camera to the point O.
Influence of angular deviations of the bobbin on the conversion scale is estimated by the formula (2) taking into account (3). Let's estimate the impact of displacement of the bobbin axis on the transformation scale error (Fig. 3).
Analyzed device is designed to record the profile of textile packages, so the surface of A and B can be con sidered as flat only under the survey of the flat ends of the package. A and B surfaces are cylindrical or conical surfaces upon registration of side surface of the package profiles. Fig. 3 shows the bobbin with the center О 1 in the nominal position with the center О 2 , displaced by a certain amount x b [16][17][18][19][20]. Displacement of the bobbin axis by the x b leads to a change of angles α and β by the same value Δα 2 . Moreover, if the angle α increases, than the angle β decreases. Thus, the sum of the angles α + β remains unchanged. The value of angle errors caused by the bobbin displacement can be determined as shown in Fig. 3 according to the formula: where R b = О 2 О -bobbin radius The angular deviation of the shadow on the test surface is taken place at the angular displacement of the shut ter from the nominal position. In Fig. 4, a, the shutter is deviated from its nominal position by rotation by an angle ψ х relating to ξ x axis. As a result, the edge of the shutter will occupy the positions shown in Fig. 4, a by the points a and b. Accordingly, the edge of the shadow, which, in the case of parallel arrangement of the shutter relative to the planes A and B are the points М А and М В , will move to the point and М′ А and М ′ В . This will cause additional rotation of observed shadow by an angle Δα 3 . The length of the segment ab can be calculated using the formula: Schematic beam path to estimate the shadow rotation angle Δα is shown in Fig. 4 Let's consider the effect of shutter rotation by an angle ψ Z relative to ξ Z axis (Fig. 5, a). Edges of the shadow are displaced in the planes of the shutter and occupy positions designated by the points a and b. The length of the segment ab can be calculated according to the formula ab = Ltg ψ Z . Beam path scheme for deviation estimation of Δα 4 angle is shown in Fig. 5 Lenses, particularly with high magnification, distort the image in such a way that a straight line on the object is transformed into a line that is curved at the edges of the image [9]. Profile image is curved at the edges, and only in the central zone of the field of view is observed with no distortion. Fig. 6 shows the profile image in the object plane Р 1 -Р 1 of the camera lens without distor tion (1) and with distortion (2). The curved average line of the profile in the adopted system of coordinates can be approximated by a parabola of the form: where а -empirical coefficient. Lines of projections and depressions -parabolas of the form: Then, assuming that the coefficients а = а 1 = а 2 , the maximum absolute error in the height of the profile at the edge of the observed image will be: Let's experimentally define the value of the coefficient a. To do this, flat plate is mounted instead of the bobbin, and shadow image of the shutter edge is photographed on a flat surface. Such image is shown in Fig. 7.
If there is no lens distortion, the shadow edge should be a straight line. However, as shown in Fig. 7, it is not so. The image is distorted near the boundaries of the field of view.
To quantify the error, caused by this curvature, the shadow image is placed in the AutoCAD program window ISSN 2226-3780 in an enlarged view. After that, by means of this program the coordinates of a shadow boundary in steps of 1 cm are defined. These data are approximated by a parabola. As a result, for used lens, coefficient a = 3,28 ⋅ 10 -4 . fig. 7. Shadow image for projection of the shadow edge on the plane The error associated with the curvature of the image due to optical imperfections is a systematic error that can be eliminated by the introduction of correction for data processing. These corrections are calculated using the formula (15). The required amendments have been taken into account in the development of software complex.

sWot analysis of research results
Strengths. Inspection of shape deviation in real time enables timely excluded the effective packages from the process and thereby increases an efficiency of textile pro duction.
Weaknesses. Installation of inspection devices on win ding equipment requires additional costs.
Opportunities. Further studies should be able to de bug the equipment using the proposed quality inspection method for bobbins.
Threats. External factors that negatively affect the application of the proposed method are the presence of foreignmade analogues, which have a much higher cost.

Conclusions
1. It is found that the main parameters of the device used to generate primary data about the shape of packages that affect the inspection results are: -Angles determining the position of the light source and the camera relative to the normal to the package.
-Displacement of the light source and the camera in the tangential direction to the package.
2. Permissible variations of design parameters are proved on the basis of knowledge of the general expressions for the total measurement error of the package profile. These varia tions ensure the required transformation accuracy. Overall error can be set at the level of 5 %, as is customary for tech nical measurements. After that, on the basis of formula (2), taking into account the members of its expression, it can be distributed over the individual components on the basis of the requirements of equal accuracy.