The introduction and use of information technologies is an integral part of the successful functioning of modern production. The analysis of the production processes of individual enterprises made it possible to determine specific requirements for planning their production activities. In many cases, planning departments create their own intellectual and informational systems for comprehensive planning of the production process even when accepting a production order. We have proposed a series of mathematical models for describing the geometric parameters of the part, which have a significant impact on the indicators of the energy consumption of the production process and the costs of performing assembly operations. Mathematical models are obtained by implementing a non-linear regression algorithm of a general type. The adequacy of mathematical models was checked by the value of the coefficients of determination R2 for the proposed approximating functions and input sets of discrete data. band saw technologies, rolled section, mathematical modeling, information systems, welding The use of profile blanks for the manufacture of body and frame structures involves the analysis of several technical and economic indicators. Among the technical indicators, it is worth noting such as the cross-sectional area of the profile, and among the technical and economic ones, the indicator for accounting for the length of the weld seam. The first indicator has the significance of the choice of equipment to ensure the mechanical processing of the used profile, and, accordingly, the power consumed per unit of time. The second indicator indicates the actual costs of consumables and the time required to perform a welding operation by an employee of a particular qualification. These indicators have a direct impact on the employee's salary.
PLANNING OF MECHANICAL PROCESSING AND WELDING OPERATIONS operation
A lot of researchers have been studying how band saws perform when used for machining. They've
been focusing on a few key areas, including analyzing the temperature in the cutting zone [
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at different types of dynamic loads and how they affect the process [
When planning a welding operation, it's crucial to consider the cross-sectional area and perimeter of
the channel. These parameters are necessary for calculating welding modes and working time. The goal
is to ensure that the welded structure has the same strength as the original material. To achieve this, it's
important to analyze the softening heat-affected zone parameters in the welded joint. The geometric
parameters of this zone are determined by the cross-sectional area and perimeter of the rolling products
section [
In order to determine how long it will take to weld each piece, we must combine the main arc burning
time and auxiliary time. The main arcing time is proportional by the size of the weld's cross-section and
inversely proportional by the arc current. The auxiliary time considers the length of the weld and the
number of passes required, which are determined by the cross-section size. If the channel's
crosssectional area changes, the welding time will also change. It's important to note that the welding speed
is inversely affected by the cross-sectional area of the seam [
Welded joints of channels often use butt seams. This type of connection is practical, straightforward,
and cost-effective. Welding is typically done from both sides to ensure adequate depth of penetration.
However, creating a proper edge preparation can be challenging for butt joint profiles, as incomplete
penetration can occur at the entrance corners. For low-stress structures with shaped profiles,
overlapping strapped butt joints are preferred. It's important to note that welding the strapping causes a
significant stress concentration due to the sudden change in the joint's cross-section [
In certain situations, the structure can be put under too much stress due to the active loads, causing
the weld's tensile strength calculation to be exceeded. To address this task, welded beams are assembled
for stretched belts of structures to make assembly joints. An oblique butt joint is created during this
welding operation, which is just as strong as the main section of the beam. To ensure it's strong enough,
you can use information about the cross-sectional area of the channel in the oblique joint to select the
optimal angle of inclination [
The advancement of production processes through automation and the creation of automated
production preparation systems [
During the research, non-linear regression of the general type, with 3D modeling and discrete set analysis algorithms was used.
According to DSTU 3436-96 "Hot-rolled steel channels (Rolling products)" the channel's geometric profile is determined by its dimensional characteristics (Fig. 1, a) and mass-geometric indicators (Fig. 1, b).
embodiment 1 embodiment 2 а) b)
In this article, we consider two main parameters: b, which represents the width of the channel shelf, and h, which represents the height of the channel. When constructing frame structures and trusses, there are two options for cutting the channel profile. The first option involves cutting along the channel shelf, and the height of the channel remains unchanged. The second option involves cutting along the profile height, and the width of the shelf remains unchanged.
In both cases, depending on the size of the cutting angle (displacement of the cutting blade of the saw along one of the geometric parameters), we get the values of the areas and perimeters, which will not be proportional to the values of the areas and perimeters in the normal section according to the right triangle rule. The angle value affects the resulting area and perimeter measurements non-proportional. Therefore, it is advisable to perform a study of changes in areas and perimeters for both cases regarding the most frequently used channel numbers both in general mechanical engineering and in other branches of economic activity. 4.1. The research and analysis alterations in the cross-sectional area and perimeter while displacement along the channel shelf
When moving the saw along the shelf of channel number 5U, which is manufactured according to DSTU 3436-96 " Hot-rolled steel channels (Rolling products)" (Fig. 2)
the value of the cross-sectional area depending on the amount of displacement along the channel shelf can be described by the equation:
( ) = 1.559 ∙ 1.559 − 2.684 ∙ + 626.714 where - displacement, mm.
After estimating the values of the studied parameter according to the proposed dependence, a comparison of the areas of the sheared layer with the actual indicators was carried out (see Table 1).
For the same channel, the equation of describing the perimeter of a channel's cross-section varies based on the displacement along the shelf of the channel too:
( ) = 0.105 ∙ 1.608 − 0.201 ∙ + 149.708
After estimating the values of the studied parameter according to the proposed dependence, a comparison of the perimeters of the sheared layer with the actual indicators was carried out (Table 2). Other standard channel sizes were also studied: - Channel №6.5U A proposed function for approximating the cross-sectional area is presented:
The outcomes of measurements and computations have been condensed into a table 3.
The outcomes of measurements and computations have been condensed into a table 4. 928.426 0021
30
A proposed function for approximating the cross-sectional perimeter is presented: 30 35
40 1138.719 The outcomes of measurements and computations have been condensed into a table 6. cross-sectional area 0.996 - Channel №8U A proposed function for approximating the cross-sectional area is presented:
The outcomes of measurements and computations have been condensed into a table 5. 0.027 0.03 cross-sectional area 0.996
A proposed function for approximating the cross-sectional perimeter is presented:
The outcomes of measurements and computations have been condensed into a table 8.
Estimated, mm - Channel №10U A proposed function for approximating the cross-sectional area is presented:
( ) = 1.287 ∙ 1.597 − 2.63 ∙ + 1.11 ∙ 103
The outcomes of measurements and computations have been condensed into a table 7. ( ) = 0.19 ∙ 1.606 − 0.391 ∙ + 361.55
25 cross-sectional area 0.995 - Channel №12U A proposed function for approximating the cross-sectional area is presented:
( ) = 1.157 ∙ 1.616 − 2.457 ∙ + 1.347 ∙ 103
The outcomes of measurements and computations have been condensed into a table 9. A proposed function for approximating the cross-sectional perimeter is presented: 40
( ) = 0.161 ∙ 1.624 − 0.342 ∙ + 423.723
The outcomes of measurements and computations have been condensed into a table 10. when using mathematical dependence for: cross-section perimeter 0.995
( ) = 1.121 ∙ 1.62 − 2.549 ∙ + 1.587 ∙ 103
The outcomes of measurements and computations have been condensed into a table 11.
( ) = 0.149 ∙ 1.627 − 0.339 ∙ + 486.283
The outcomes of measurements and computations have been condensed into a table 12.
R2 - Channel №16U A proposed function for approximating the cross-sectional area is presented:
( ) = 1.085 ∙ 1.623 − 2.61 ∙ + 1.837 ∙ 103
The outcomes of measurements and computations have been condensed into a table 13. A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.138 ∙ 1.631 − 0.332 ∙ + 548.485
The outcomes of measurements and computations have been condensed into a table 14. Perimeter: Actual, mm Estimated, mm Relative error, % - Channel №18U A proposed function for approximating the cross-sectional area is presented:
( ) = 1.03 ∙ 1.631 − 2.614 ∙ + 2.099 ∙ 103 The outcomes of measurements and computations have been condensed into a table 15. A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.126 ∙ 1.638 − 0.32 ∙ + 611.045
The outcomes of measurements and computations have been condensed into a table 16. 4.2. The research and analysis alterations in the cross-sectional area and perimeter while displacement along the height of the channel
When shifting the saw along the wall (leg) of channel number 5U with height h, which is manufactured according to DSTU 3436-96 " Hot-rolled steel channels (Rolling products)" (Fig. 3) the value of the cross-sectional area depending on the amount of displacement along the channel shelf can be described by the equation:
( ) = 0.614 ∙ 1.604 − 1.314 ∙ + 626.844
After estimating the values of the studied parameter according to the proposed dependence, a comparison of the areas of the sheared layer with the actual indicators was carried out (see Table 17). A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.086 ∙ 1.618 − 0.186 ∙ + 208.941.
The outcomes of measurements and computations have been condensed into a table 18. 30 35 40 45 50 Estimated, mm
Relative error, %
Displacement, mm
Perimeter:
R2 - Channel №6.5U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.466 ∙ 1.613 − 1.148 ∙ + 763.042.
The outcomes of measurements and computations have been condensed into a table 19. A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.072 ∙ 1.623 − 0.178 ∙ + 254.352
The outcomes of measurements and computations have been condensed into a table 20.
R2 - Channel №8U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.37 ∙ 1.626 − 1.035 ∙ + 911.461
The outcomes of measurements and computations have been condensed into a table 21.
( ) = 0.059 ∙ 1.635 − 0.167 ∙ + 299.229 A proposed function for approximating the cross-sectional perimeter is presented: The outcomes of measurements and computations have been condensed into a table 22.
10
R2 - Channel №10U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.313 ∙ 1.627 − 1.016 ∙ + 1.111 ∙ 103
The outcomes of measurements and computations have been condensed into a table 23. A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.052 ∙ 1.635 − 0.17 ∙ + 361.657
The outcomes of measurements and computations have been condensed into a table 24.
R2 - Channel №12U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.293 ∙ 1.62 − 1.044 ∙ + 1.348 ∙ 103
The outcomes of measurements and computations have been condensed into a table 25. A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.048 ∙ 1.627 − 0.173 ∙ + 423.754
The outcomes of measurements and computations have been condensed into a table 26.
423.686 426.859 436.135 450.867 470.203 493.272 519.301 Estimated, mm 423.754 426.598 436.317 451.068 470.115 493.015 519.456 Relative error, % 0.016 0.061 0.042 0.044 0.019 0.052 0.03
The coefficients of determination R2 were calculated for the proposed approximating functions using a discrete set of input data: - Channel №14U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.158 ∙ 1.705 − 0.498 ∙ + 1.586 ∙ 103 The outcomes of measurements and computations have been condensed into a table 27.
A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.026 ∙ 1.712 − 0.081 ∙ + 486.174
The outcomes of measurements and computations have been condensed into a table 28.
The coefficients of determination R2 were calculated for the proposed approximating functions using a discrete set of input data: - Channel №16U A proposed function for approximating the cross-sectional area is presented:
( ) = 0.244 ∙ 1.624 − 1.043 ∙ + 1.837 ∙ 103
The outcomes of measurements and computations have been condensed into a table 29.
A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.04 ∙ 1.63 − 0.171 ∙ + 548.51
The outcomes of measurements and computations have been condensed into a table 30.
The coefficients of determination R2 were calculated for the proposed approximating functions using a discrete set of input data:
R2 - Channel №18U A proposed function for approximating the cross-sectional area is presented: ( ) = 0.231 ∙ 1.624 − 1.064 ∙ + 2.099 ∙ 103
The outcomes of measurements and computations have been condensed into a table 31.
Displacement, mm Cross-sectional area: Actual, mm2 A proposed function for approximating the cross-sectional perimeter is presented:
( ) = 0.037 ∙ 1.63 − 0.172 ∙ + 611.096
The outcomes of measurements and computations have been condensed into a table 32. 5. Conclusions
In the process of cutting a part of a complex geometric profile (channel) at different angles, it has been observed that the perimeter and cross-sectional area do not change proportionally to the angle of the cut. This applies to both angular cuts made along the height and width of the profile.
For each standard size of the channel, we defined mathematical construction that explains how the perimeter and cross-sectional area of the profile change based on the displacement of the metal-cutting tool relative to the base points in the normal section. Studies have shown that the best way to present these mathematical models is through a non-linear regression of the general type.
The accuracy of the mathematical models developed was confirmed by calculating the coefficient of determination R2. The values obtained ranged from 0.994 to 0.997, with only one case showing 0.979. These results indicate that the proposed mathematical models accurately depict the measurement results obtained from both mathematics analysis and 3D modeling.
The coefficients of determination R2 were calculated for the proposed approximating functions using a discrete set of input data: 6. References