Modelling of combined thermomechanical processing of stainless steel wire

    Mathematical Modeling, Vol. 8 (2024), Issue 1, pg(s) 10-13

    In this article, a number of theoretical studies have been conducted on a new combined process of multicycle thermomechanical processing, including wire drawing and subsequent cooling in liquid nitrogen. When analyzing the deformation, it was found that the presence of intermediate heating to ambient temperature allows calculating the force according to the Krasilshchikov formula and the wellknown nomogram of the tensile strength of AISI-316 steel at 20°C with minimal errors. The lack of heating leads to the fact that the second and third drawing cycles take place at partially negative temperatures in the workpiece section. This leads to an increase in the difference in the force values obtained by calculation and during modeling. To be able to use the Krasilshchikov formula and the nomogram of the tensile strength of AISI-316 steel at 20°C, it is necessary to adjust the resulting force values by increasing by about 30% for a diameter of 6 mm and 20% for a diameter of 9 mm in the absence of heating of the workpiece and by 35% for a diameter of 6 mm and 25% for a diameter of 9 mm in in case of preheating the workpiece.

  • Modeling of the structural evolution of carbon steel hypereutectoid structure subjected to reforging under pulsating contact stress loading

    Materials Science. Non-Equilibrium Phase Transformations., Vol. 9 (2023), Issue 1, pg(s) 3-6

    The paper presents the results of microstructural studies of 16MnCrS5 steel hypereutectoid structure subjected to reforging under pulsating contact stress loading. It is revealed that the local evolution of the structure in the focus of contact loading has signs of selfimprovement with the transformation of the isotropic morphology of the carbide phase into an anisotropic one with signs of textural riveting. Instead of the initial structure with a uniform carbide phase distribution, signs of textural anisotropy with reinforcement elements of the modified layer high-carbon hypereutectoid zone with carbide inclusions are formed.


    Schedule process modelling of a “wood processing SME” based on IEC/EN 62264 standard

    Mathematical Modeling, Vol. 6 (2022), Issue 4, pg(s) 127-130

    The purpose of the research is to present a solution to production planning optimization problems, in cases of short-term customer orders and variable production load. The main reasons for the emergence of the task are the introduction of SMEs to unregulated electricity market and the increasing price of electricity due to the imposition of additional components in the formation of the price.The lack of traditional market and the small number of regular customers of SMEs make it difficult to forecast electricity consumption, and therefor impractical to request electricity for long-term periods of time. A possible solution related to the implementation of operational management systems, which, through the introduction of standard models, will enable the implementation of optimization algorithms for production planning.


    Applicability of different modeling approaches to process quality management, according to the human-machine system

    Industry 4.0, Vol. 6 (2021), Issue 3, pg(s) 83-86

    Quality is a process of continuous improvement or improvement of the processes creating the product. Our ability to manage quality characteristics has a significant impact on the depth of our knowledge of the process used for the desired transformation. The application of knowledge in process management depends on the dominant factor for management: human or machine. Each requires an appropriate form of transfer of knowledge. Depending on the type of “human-machine system”, it is possible to use various mathematical and logical tools to formalize the information. This article attempts to classify the types of mathematical and logical tools applicable to process management, depending on the “human-machine system” use.

  • Computer modeling of influence of previous deformation degree and strain rate on carbonitrides precipitation kinetics in low-carbon micro-alloyed steel

    Materials Science. Non-Equilibrium Phase Transformations., Vol. 5 (2019), Issue 3, pg(s) 81-83

    Using computer modelling with originally developed semi empirical physical grounded models a study was carried out to investigate influence of previous hot deformation on carbonitrides formation from austenite in low-carbon micro-alloyed steel. Studied in the article is an influence of degree and rate of the deformation on processes of nucleation and growth of Nb and Ti carbonitride particles. The model helps to predict not only process of changing in number and average size of the particles but also to estimate their final size distribution. One of additional peculiarities of the developed model is its ability to predict composition of the cabinetries formed in certain conditions. The model takes into account process of recrystallization and returning, which affect carbonitrides precipitation and are influenced by it. Acceleration was shown of both nucleation and growth rates of the particles due to increasing of deformation degree and strain rate. Another result is that previous deformation significantly affects size distribution function of the particles precipitated with rather lesser effect on their average size. Kinetic curves and final size distribution plots are given.

  • Power systems emulator based on DCS

    Innovations, Vol. 7 (2019), Issue 2, pg(s) 77-79

    Research, optimization and practical implementation of optimization processes in power subsystems of power plants, heating plants and industrial plants present a relatively complex task that is nowadays unimaginable without powerful specialized tools of computer support. The paper presents a power systems emulator concept (a tool for the design and application processes involving power systems) that is based on decentralized control systems (DCS) standardly used today. Basic principles of modular design of the emulator along with an example of its implementation based on the Siemens SIMATIC-S7 DCS system are presented.

  • Applying queue theory at study of refusals of requests received in universal automotive service

    Mathematical Modeling, Vol. 2 (2018), Issue 4, pg(s) 143-146

    The refusal of requests received in a universal automotive service workshop in the city of Rousse was investigated. The present work analyses the average monthly requests from the workshop customers. The number of the actual repairs was also determined. The work in the service have been seen as a mass service system with a non-stationary mid-month incoming stream with queries. The basic values of the system parameters were calculated under non-stationary conditions and Mat Lab application was created. After the model has been validated, a service conversion option was proposed to reduce the refusals. The proposed approach can serve as a methodology for analysing and optimizing of the activity of other universal automotive service.



    Mathematical Modeling, Vol. 1 (2017), Issue 4, pg(s) 192-195

    3D printing also called Layer based technology, Freeform fabrication, Additive manufacturing or Rapid Prototyping technologies has undergone significant development over the last decades. The growth is related to the expansion of the range of materials used, application areas, and range of possible sizes from nanometer to tens of meters as well as increasing machine accessibility. There is a growing consensus that 3D printing technologies will be at the heart of the next major technological revolutions. At present there are some technological specifics and associated difficulties in 3D printing one of which is the accuracy of the manufactured product. Research in this area would allow modelling of 3D printing processes.

    The article describes the possible types and sources of inaccuracies in 3D printing processes. The various types of test pieces used in practice are examined to quantify the errors in shape and sizes after building. Test pieces with predefined discrete points and methodology are provided to calculate inaccuracies. The results are presented in the terminology of “linear” and “shear” deformations. This gives opportunity to determine the variations in the shape and dimensions of the parts built by 3D printing. On the basis of the discreet results obtained, the possibility of 3D printing process modelling is discussed and presented.



    Science. Business. Society., Vol. 2 (2017), Issue 1, pg(s) 7-9

    Modeling is one of the methods used to solve practical hydrogeological problems associated with movement and assessment of groundwater sources. It is has long been in place in hydrogeology with the first well-described modeling methods dating back to the beginning of the 20th century. Analog and digital techniques advancements in the late sixties made it possible to apply them more actively. Nowadays it is unthinkable to address such type of scientific problems without the use of contemporary software tools for geological and hydrogeological modeling. Coupled with modules used in GIS media such tools enable resolution of specific tasks aiming to describe underground filtration flow.

    Combing innovative technologies for a detailed three-dimensional reconstruction (approximation) of a geological medium with detailed calculation procedures for a mathematical description of groundwater flow in such medium enable solving a wide spectrum of hydrogeological tasks of great complexity.

    Numerous are the research institutes, universities and private organization worldwide that focus on developing contemporary software products for mathematic modeling. Specialized modules are designed to support hydrogeological surveys. The products developed operate on a very high level input data automation, graphic interface, visualization, etc. Some of the companies employ MODFLOW which is one of the most frequently used computer codes in groundwater flow modeling. It is module-type software based on the finite difference methods, and has been created by US Geological Survey McDonald and Harbaugh (USGS) [6], the output code being free software.

    The approach employed in the case presented involves calculations and 3D visualization by means of our own simplified software (VISMAT) developed on the grounds of modern software and hardware solutions in combination with numerical methods. Part of MODFLOW code is also used in VISMAT development.



    Science. Business. Society., Vol. 1 (2016), Issue 4, pg(s) 11-13

    Digital environment progress towards real and virtual realities mixing is reasonably producing new understandings for ICT progress expectations. In todays’ mobile web world, augmented realities are practically integrating ‘Internet of Things’ (IoT) mobile concept and 3D visualization technologies into a new evolving smart world. This changes our everyday life concepts, adding capabilities with innovative functionalities. However, it also is generating multiple challenges from cybersecurity perspective. This paper studies the problem for human-machine interaction, accentuating on the multifaceted understanding of possible threat sources and attack vectors in the new augmented reality research area. In this context, a system model with prognostic analysis is proposed. The necessity of obtained results validation is finally discussed.


    Mechanization in agriculture & Conserving of the resources, Vol. 61 (2015), Issue 7, pg(s) 23-25

    One of the most important characteristics of the high performance operation of a state-of-the-art sugar beet harvester is the provision of the conditions that make impossible the damaging of sugar beet roots immediately during their digging out of the ground as well as their loss in the form of broken off tails, which either remain in the ground or get left on the field surface. It is quite obvious that the highest probability of damaging sugar beet roots exists at the instant of their impact interaction with the digging tools, because then the bodies of the roots are tight in the ground. This is to the greatest extent applicable to vibrating digging tools, which can be found on the majority of up-to-date sugar beet harvesters manufactured worldwide, when they operate under the conditions of dryer and harder soil.

    Therefore, we have carried out theoretical research into the process of impact interaction between the body of a sugar beet root fixed tight in the ground and the vibrating digging tool, the results of which provide sufficient grounds for determining the optimal kinematic and design parameters of the vibrating digging tool stipulated by the requirement to eliminate the damage of roots during their digging out of the ground. At first, we developed an equivalent schematic model of the force interaction between a sugar beet root fixed tight in the ground, which was approximated by a regular cone, and two shares of the vibrating digging tool simultaneously oscillating in the vertical longitudinal plane at the preset amplitude and frequency and moving onward. Under these conditions, the body of the sugar beet root made contact at one point with only one share of the digging tool, i.e. they came in asymmetric contact and their impact interaction took place. We introduced the axes of a three-dimensional Cartesian coordinate system and found the analytical expressions for all forces applied to the sugar beet root at the specified point and also for the force of its bond with the soil. Also, we took into account that an impact momentum was applied at the point of contact at the moment of impact, its value was found analytically, and further we found its projections on the coordinate axes. Then we applied the theorem of variation of the momentum during impact and, following the substitution into it of all found values and transformations, we obtained a new system of equations that characterised the impact interaction process under consideration.
    The obtained system of equations was solved using Cramer’s rule on a PC with the software programme developed for this purpose. As a result, we found the digging share vibration frequency and soil running depth ranges, within which the requirement to eliminate the damage of tail parts of root bodies fixed rather tight in the ground was met. Applying the devised theory it becomes possible to determine the kinematic and design parameters of the vibrating digging tool that ensure observance of the requirement to eliminate the breakage of root bodies during their lifting from the ground, within a wide range of the soil’s mechanical and physical characteristics.