Digital process simulation twins using statistics and information technologies

. This article presents the prospects for the development of virtual mathematical modeling of technological processes of various technical levels to simplify the process of manufacturing functional parts in production areas. A calculation model was drawn up, on the basis of which the thermal task was set for calculation, a change in temperature over a certain period of time was demonstrated. A study was also carried out aimed at identifying energy losses in the technological process, the main technical parameters of which are also presented in the materials of this work. The presented data confirm the practical significance of this and are aimed at stabilization of both technical and technological processes. The study conducted in the article is provided with graphic materials when entering and outputting information, tables with results, as well as a detailed description of each stage of the study.


Introduction
Today, modeling is an integral part of the modern world, as it has an active influence on the labor intensity of technological processes and on the quality indicators of finished functional products.Traditional quality testing methods are quite resource-intensive and do not allow you to quickly solve technical problems due to the high labor intensity of these processes.
When analyzing the process modeling market, the following trend was revealed that simulation modeling systems account for more than 80% of the total number of software and are actively introduced into the production practice of companies for various purposes.Additive technologies for layer-by-layer manufacturing of products also willingly apply this method in their work [1].As practice shows, more than 60% of additive companies aimed at manufacturing functional parts necessarily carry out an imitation modeling process, since various composite powders and high-precision laser installations are used as raw materials, printing on which has a high monetary component, therefore, virtual experiments can reduce the amount of economic costs.
According to a report by Zion Market Research, the global simulation modeling market totaled $3.2 billion in 2018 and is expected to reach $29.1 billion by 2025, increasing each year at a rate of 37.3% [2].Thus, the development of the digital twin market will be mainly due to the growth of its use in the aerospace sector in the coming years.The use of information technology with digital twin technology provides numerous advantages, such as eliminating repetitive tasks, reducing costs, and much more.In addition, technological developments observed in various industries can create new opportunities for market growth.
That is why this study is aimed at demonstrating the simulation of the process of extrusion of polymer pellets in the process of 3D printing, which shows not only the main stages, but also the tools to be paid attention to.After all, an important aspect of any study is to improve the life cycle of products at each of the seven stages, however, mathematical modeling with a simulation of the technological process works out all stages from the beginning to disposal, showing how the product will behave in any period of time.

Materials and methods of research
To investigate the temperature distribution inside the print head, which is necessary for an efficient technological process of extruding polymer pellets, a thermal calculation task was set up using the QForm Cloud 10.2.4 software [3].At the first stage of finite element modeling, the workpiece parameters are set (Table 1): the original material and initial temperature (Figure 1).The heating system consists of three workpieces: a cylinder with radiator made of tempered steel, a spiral heating element made of stainless steel and a copper nozzle [4].The initial temperature for the melted material movement system is 22℃ and for the heater is 350℃.The next step in creating a thermal problem is to construct a finite element grid of tetrahedral elements.Tetrahedra approximate the geometry of the model [5] and are used to build a mathematical model of the original design.When you create a mesh for each part, you define parameters such as, sampling rate, smoothness, local thickening of the mesh, and so on.Accuracy of optimal mesh size for screw cylinder and nozzle is 0.04 mm, and for heating unit -0.1 mm [6].Curve deflection is 0.15 mm and grid thickening smoothness is 1 mm by default for all elements.As for local thickenings, they are assigned manually in the zones of greatest interaction with temperatures: the main holes are the zones of material flow and connecting holes for inclusion of other heating elements in the system [7].
After defining all the blank parameters, conditions for stopping the calculation and boundary conditions are assigned with the determination of the zone of influence [8]: the heat flow for the radiator and the heat flow for the heating element with variable on and off times.The heat transfer of the cylinder with a radiator is 162 W with on periods at 1 and 9 seconds and off periods at 3 and 12 seconds (Figure 2a).The heat flow to the volume of the heater is 15000 W/m^3 with the following intervals: 3-9 and 12-19 seconds (Figure 2b).For this study, the stop condition for calculation was set at 20 seconds with a step of 500 ms.The problem considered in the work has the following formulation "Unsteady heat conduction" (Figure 3): thermal loads [9] have been acting recently and there is an active redistribution of temperature fields in the system, indicating a transient process.

Results
Based on the data obtained in the course of the study, it can be confirmed that the mathematical modeling process using information technology [10][11] allows you to gradually determine not only the temperature distribution inside the heating system at any time, but also the material consumption and the coefficient of friction against the wall of the printhead, which significantly affects heat losses.This approach demonstrates a virtual simulation of the technical process [12] to achieve most positive effect during a physical experiment.
The demonstration of the construction of a virtual mathematical model [13] for solving a technical problem is based on the heating system of the printhead.The article shows which technical characteristics can be set, which are key, and how these parameters affect the final result [14].All data is accompanied not only schematically, but also by tables with derived mathematical values, and statistical data that are consumed in the system.
According to the results of the thermal calculation, the micro-screw printing head design has certain losses of thermal energy (Figure 4), which reduces its performance (Тable 2) [15]: the friction clutch transfers the torque from the stepper motor to the screw, during which the first losses associated with the misalignment of the shafts and compensation of the starting torque on the stepper motor appear, then the energy is divided into two streams responsible for material movement and melting.During the flow of melted material into the nozzle, 7% of energy is lost [16]: due to friction -it depends on the thickness of the plug, due to heat exchange -it is related to the inefficiency of the heating system.When changing the physical state of the material, more than half of the energy of this flow is lost [17]: losses during heating -10%, losses when reaching the specified temperature.To compensate for the heating losses, it was decided to use a tape for thermal insulation, which will allow reaching the required nozzle temperature of 350°C in less than 60 seconds.The software presented in the article is specialized for the design and optimization of technological and technical processes.It is based on a hybrid approach that combines the finite element method and the finite volume method, which provides a fast and accurate calculation.QForm is intended for both industrial enterprises and research centers.It has flexible tools [3] for managing calculation and programming its own scientific models.

Discussion
Based on the results of the study, the following conclusion can be drawn: mathematical modeling of the technological process will allow you to quickly calculate the required parameters, assign material to increase process efficiency, and also set tasks based on previous experimental templates without unnecessary time and money.The calculation results (Table 2) helped determine the percentage of heat losses (Figure 4), the compensation of which will increase the performance of the printhead.
Controlled deposition of material in a predetermined and accurate way opens up fundamentally new possibilities in production, ranging from inexpensive creation of personalized objects at home to very complex parts of jet engines operating in extreme conditions.
Predicting how the final product depends on operating parameters is a complex problem that includes unstable fluid flow, free boundary, heat transfer, and solidification.The main changes are to add the source to the nozzle modeling, implicit processing of diffusion terms in momentum and energy equation and addition of temperature-dependent and sheardependent viscosity.

Conclusion
In conclusion, I would like to add that today computer modeling has a high potential and is actively being introduced into production spheres for various purposes to improve the stability of the technological process and reduce the number of production defects in the manufacture of functional products.

Fig. 1 .
Fig. 1.Mathematical modeling of the thermal problem: a -cylinder with radiator; b -spiral heating element; c -nozzle

Table 1 .
The workpiece parameters for thermal calculation task