Casting molding numerical simulation method based on tin-based solder

Abstract

The invention discloses a numerical simulation method based on tin-based solder casting molding. Comprising the steps that 1, a mold and a casting body needed by tin-based solder alloy casting are obtained and simplified, and a casting model is obtained; 2, the casting model is imported into ProCAST software to check the assembly interaction condition of the casting model, and grid division is conducted on the casting model; 3, setting attribute parameters of the tin-based solder alloy and a casting mold material and boundary conditions required by casting simulation; and 4, setting calculation conditions according to the attribute parameters and the boundary conditions in the step 3, performing numerical simulation calculation on the tin-based solder alloy casting process according to the calculation conditions, and outputting a simulation result. Through a casting molding numerical simulation method, the influence rule of key thermodynamic parameters such as the casting temperature and the heat exchange coefficient on the shrinkage cavity defect of the casting is researched, physical experiments which are time-consuming and high in cost are abandoned, and accurate prediction and analysis of the casting process and the defect in a virtual environment are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material forming and numerical simulation, and more particularly to a numerical simulation method for casting forming of tin-based solder. BACKGROUND

[0002] Tin-silver-copper alloy (Sn0.3Ag0.7Cu) has been widely used in electronic assembly, instruments and meters, etc. due to its excellent welding performance and mechanical properties. However, in actual production, tin-silver-copper alloy often encounters some problems in the process of casting forming, such as shrinkage cavity defects. The formation of shrinkage cavity is mainly due to the uneven volume shrinkage of metal during cooling and solidification. When the metal liquid cools in the mold, its density changes, and if the cooling speed is uneven, the metal liquid in some parts cannot be supplemented in time, thereby forming shrinkage cavity. This defect not only affects the internal quality of the casting, but also reduces the mechanical properties and reliability of the casting.

[0003] Therefore, it is an urgent problem for those skilled in the art to design a numerical simulation method for casting forming of tin-based solder to improve the quality and production efficiency of the casting and reduce the production cost. SUMMARY

[0004] Therefore, the present application provides a numerical simulation method for casting forming of tin-based solder to study the influence of casting temperature, heat transfer coefficient and other factors on the shrinkage cavity of tin-based solder casting, and save a lot of manpower and resources.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme: a numerical simulation method for casting forming of tin-based solder, comprising:

[0006] Step 1: Obtain the mold and casting body required for casting of tin-based solder alloy, and simplify to obtain a casting model;

[0007] Step 2: Import the casting model into ProCAST software to check the assembly interaction of the casting model, and divide the grid of the casting model;

[0008] Step 3: After grid division, set the attribute parameters of tin-based solder alloy and casting mold material and the boundary conditions required for casting simulation;

[0009] Step 4: Set the calculation conditions according to the attribute parameters and boundary conditions in step 3, and perform numerical simulation calculation on the process of tin-based solder alloy casting according to the calculation conditions, and output the simulation results.

[0010] Preferably, the simplified process in step 1 comprises: simplifying the casting process basic scene into a casting mold and a cast body, setting the heat dissipation mode of the pipe part in the casting mold as heat insulation, setting the heat dissipation mode of the remaining part of the casting mold as water cooling, pouring the tin-based solder alloy from the casting pipe into the cast body and cooling under the action of water cooling to obtain an ingot.

[0011] Preferably, the casting model comprises a casting mold and a cast body, and the built casting mold is assembled and exported in IGS format.

[0012] Preferably, the assembly interaction of the casting model is checked, comprising: importing the exported IGS format file into ProCAST software, and checking the interaction of face connectivity, shear at body intersection and overlapping assembly between mixed bodies in the software.

[0013] Preferably, step 3 comprises: setting related casting parameters for the casting model, giving the casting pipe and the casting mold properties and setting the materials of the casting pipe and the casting mold, and the materials of the remaining part of the casting pipe and the casting mold are the same.

[0014] Preferably, the boundary conditions required for the casting simulation in step 3 comprise: adopting a steady-state calculation method, researching the shrinkage hole condition of the casting simulation, adopting normal environment casting, determining the gravity casting direction of the tin-based solder alloy, setting the interfacial heat transfer coefficient between the casting mold and the cast body, determining the heat exchange mode between the casting mold and the cast body, setting the casting pipe part as heat insulation, setting the other part of the casting mold as water cooling, and setting the casting filling time.

[0015] Preferably, the calculation conditions in step 4 comprise: setting the calculation speed of the casting model in the ProCAST software, and monitoring the calculation conditions, time, casting percentage and solidification percentage through the observation window.

[0016] Preferably, it further comprises outputting and analyzing the simulation results, opening the post-processing module of the ProCAST software, observing the casting process and the obtained data types, and judging the integrity of the simulation process according to the obtained results.

[0017] Through the above technical solution, compared with the traditional experimental trial and error casting method, the present application provides a tin-based solder casting forming numerical simulation method, which can reduce the generation of ingot shrinkage holes by changing the casting temperature and heat transfer coefficient in actual production, i.e. cooling rate. The finite element simulation method provides an intuitive and efficient method for the optimization and improvement process of tin-based alloy casting process. It can accurately predict the heat transfer, flow and solidification behavior in the casting process, help optimize the process parameters, avoid casting defects, significantly shorten the research and development cycle, reduce the production cost, and ultimately improve the product quality and batch stability of tin ingot. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the drawings and descriptions provided in this document without any creative work.

[0019] Figure 1 A flow chart of the method provided by the present invention;

[0020] Figure 2 A line graph showing the specific heat capacity of the SAC0307 alloy provided by the present invention;

[0021] Figure 3 A line graph showing the solid phase fraction of the SAC0307 alloy provided by the present invention;

[0022] Figure 4 A schematic diagram of the assembly of the casting mold provided by the present invention;

[0023] Figure 5 A schematic diagram of mesh division of the casting model provided by the present invention;

[0024] Figure 6 A diagram showing shrinkage of the casting model provided by the present invention at different casting temperatures;

[0025] Figure 7 A line graph of shrinkage rates at different casting temperatures provided by the present invention;

[0026] Figure 8 This is a diagram of shrinkage under different heat transfer coefficients provided by the present invention;

[0027] Figure 9 A line graph of shrinkage rate under different heat transfer coefficients provided by the present invention;

[0028] Figure 10 This is a diagram of the ingot shrinkage situation before and after the improvement of the casting process provided by the present invention. DETAILED DESCRIPTION

[0029] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0030] like Figure 1 As shown, the embodiment of the present invention discloses a numerical simulation method based on tin-based solder casting, comprising:

[0031] Step 1: Obtain the mold and the casting body required for casting of the tin-based solder alloy, and simplify to obtain a casting model;

[0032] Step 2: Import the casting model into ProCAST software to check the assembly interaction of the casting model, and perform mesh division on the casting model;

[0033] Step 3: After mesh division, set the attribute parameters of the tin-based solder alloy and the casting mold material, and the boundary conditions required for casting simulation;

[0034] Step 4: Set the calculation conditions according to the attribute parameters and boundary conditions in Step 3, and perform numerical simulation calculation on the process of casting of the tin-based solder alloy according to the set calculation conditions, and output the simulation results.

[0035] Specifically, the simplification process in Step 1 includes: simplifying the casting process basic scene into a casting mold and a casting body, setting the heat dissipation mode of the pipe part of the casting mold as adiabatic, setting the heat dissipation mode of the remaining part of the casting mold as water cooling, pouring the tin-based solder alloy from the casting pipe into the casting body and cooling under the action of water cooling, and obtaining an ingot.

[0036] In an embodiment of the present application, a material library of Sn0.3Ag0.7Cu is established. Since the ProCAST software lacks a ready-made tin alloy material database, the embodiment needs to independently construct a material parameter library of SAC0307 (Sn0.3Ag0.7Cu) alloy and import it into the ProCAST finite element simulation software. In the early stage of the research, qualitative simulation analysis of the casting process is mainly performed, and the establishment of the material database is mainly based on theoretical calculation and literature data, rather than measurement results. According to the physical requirements of the casting process simulation, the following thermodynamic parameters of the alloy need to be obtained: thermal conductivity, density, specific heat capacity, solid fraction, solidification latent heat, liquidus and solidus temperature, etc., as shown in Figures 2-3 , which shows part of the material attribute data obtained by theoretical calculation.

[0037] Specifically, the casting model includes a casting mold and a casting body, and the built casting mold is assembled and exported as an IGS format.

[0038] In an embodiment of the present application, a corresponding modeling software is used to construct a simplified casting process model according to the on-site production process technical scene or a similar process technical scene, and the process basic scene of casting is simplified into a casting pipe (see the curved part in Figure 4 ), a casting mold (see the horizontal outer ring part in Figure 4 ), and a casting body (see Figure 4The heat dissipation mode of the pouring pipe part is set to be adiabatic, and the heat dissipation mode of the other part of the mold is set to be water cooling. Meanwhile, the pouring process is simplified to pouring the molten liquid from the pipe into the casting body part, and the molten liquid is cooled under the condition of water cooling. The degree of simplification is determined according to the following principles: the simplified process is consistent with the actual situation, and is convenient for finite element simulation. Based on this, finite element simulation is carried out, and the model is constructed by the pouring mold and the casting body. The built mold is assembled and exported in IGS format.

[0039] Specifically, the assembly interaction of the pouring model is checked, including: importing the exported IGS format file into the ProCAST software, and checking the interaction of the face connectivity, the shear at the body intersection and the overlapping assembly between the mixed bodies in the software in sequence.

[0040] In a specific embodiment of the present application, the exported file is imported into the ProCAST finite element simulation software. And the operation is carried out in the "Mesh" module in the software, and the face connectivity problem, the shear problem at the body intersection and the overlapping assembly problem between the mixed bodies are checked in sequence. Avoid the problem that the simulation cannot be carried out normally due to the assembly problem. By clicking the corresponding option, it is automatically checked whether there is a problem. If there is a problem, an error will be reported after checking. After the error is reported, the corresponding "automatic correction", "intersection all" and "assembly all" are clicked. The problem can be solved.

[0041] Specifically, the step 3 includes: setting the related pouring parameters of the pouring model, giving the pouring pipe and the pouring mold properties and setting the materials of the pouring pipe and the pouring mold. The materials of the pouring pipe and the pouring mold are the same.

[0042] In a specific embodiment of the present application, as shown in Figure 5As shown, after the above assembly problem check, the corresponding model is meshed, and the surface mesh is divided first. When meshing, attention should be paid to meshing according to the specific needs of the model (the mesh size is set according to experience, but the key research area is divided more carefully, and the non-key or less affected area is divided more roughly. The accuracy of the mesh is mainly based on the size of the object to be studied. When the size of the object to be studied is large and the shape is simple, the accuracy can be appropriately reduced to complete the simulation more efficiently, but when the size is small and the shape is complex, the accuracy should be improved to make the simulation results more in line with the actual situation). For example, the triangular meshing form is used to divide the mold and the casting body in this embodiment. The mold is meshed with larger mesh, and the casting body to be observed is meshed more carefully to achieve better observation effect. After the surface mesh is meshed, the surface mesh is checked, and if there is a problem, it can be automatically corrected (the software has a "correction" program, which only needs to click the "correction" option. During the inspection process, the software will automatically mark the problematic mesh in red. When the "correction" option is clicked, the red mesh disappears and the mesh is not severely deformed, indicating that the correction is successful). Then click to automatically generate volume mesh, and check and automatically correct the volume mesh.

[0043] Specifically, the boundary conditions required for casting simulation in step 3 include: using a steady-state calculation method to study the shrinkage of the casting simulation, using normal environmental casting to determine the gravity casting direction of the tin-based solder alloy, setting the heat transfer coefficient between the casting mold and the casting body, determining the heat exchange mode between the mold and the casting body, setting the casting pipe part as heat insulation, setting the other parts of the casting mold as water-cooled heat dissipation, and setting the casting filling time.

[0044] In one embodiment of the present application, the model is set with the relevant casting parameters, the casting pipe and the mold are endowed with the attribute of "Mold", the material of the mold is set, for example, in this embodiment, it is set as "Low-Carbon AISI 1008", then the volume of the mold is set as 100%, the temperature of the casting pipe is set as 178℃, the temperature of the rest is set as 43℃, and finally the mold is set as a rigid body. The cast body is set as the type of casting material, for example, in this embodiment, the type of casting material is "Alloy". The material of the cast body is set, for example, in this embodiment, it is set as "Sn0.3Ag0.7Cu", then the volume is set as 0%, indicating that the cast body is cast from nothing to something, the temperature of the cast body is set as 330℃, and finally the cast body is set as a linear elastic body. In addition, because the casting temperature is an important factor affecting casting, different casting temperatures are set for research: 290℃, 310℃, 330℃, 350℃, 370℃, 390℃, to study the shrinkage under different casting temperatures (starting with a casting temperature of 330℃ and a heat transfer coefficient of 2000, the finite element simulation of the casting process is successfully realized, and then the effects of different casting temperatures and heat transfer coefficients on the formation of shrinkage are studied).

[0045] Further, the various boundary conditions of casting are set to ensure that the simulation can obtain the required data, specifically including:

[0046] (1) Set the calculation method of finite element simulation: (steady state, non-steady state, centrifugal, tumbling), this embodiment adopts the calculation method of steady state. Then select the type of simulation research data needed, such as the need to study the shrinkage in this embodiment; set the casting condition of the melt, such as the normal environment casting, i.e. air mixing casting method.

[0047] (2) Determine the direction of casting, since this embodiment is gravity casting, the direction of gravity is determined (this direction is selected based on the actual production of gravity casting, not based on the consideration of process superiority and inferiority).

[0048] (3) Set the interface heat transfer coefficient for each part with heat exchange (the initial heat transfer coefficient is set as 2000). Since the heat transfer coefficient is an important factor affecting casting, this embodiment also sets different interface heat transfer coefficients between the mold and the cast body, such as 900, 1000, 2000, 3000, 4000, 5000 (these are the built-in casting heat transfer coefficients in the software, which reflect the size of different cooling speeds in real situations. The larger the value, the greater the heat transfer coefficient).

[0049] (4) Set the heat exchange mode for different parts of the mold, the position of the casting port, and the filling time of the casting. In this embodiment, the heat exchange mode at the casting conduit is adiabatic, and the other parts of the mold are set to water cooling. At the same time, the filling time of the casting is set to 15s, and the mass flow rate is calculated according to the following formula provided by the software to be 2.1318kg / s:

[0050]

[0051] Mass: mass (kg); Volume: volume (m 3 ); Fill Limit (%): Filling percentage; Density: density (kg / m 3 ); FillTime: time to complete filling (s); Mass Flow Rate: mass flow rate (kg / s).

[0052] (5) Set the casting to cool to 206°C and stop the mold calculation. (That is, the final temperature of all parts of the casting reaches 206 degrees Celsius) Set the maximum number of calculation steps, which is 50,000 steps in this embodiment, and set the maximum filling percentage of the casting to 100%. (The design of the calculation steps is set according to the corresponding simulation situation. When the situation to be simulated is relatively simple or the size is small, a smaller number of calculation steps can be set. When the simulation situation is more complex or the size is large, a larger number of calculation steps can be set. Or if a larger number of calculation steps is set but the set temperature is reached, the software will automatically stop the calculation. The maximum filling amount is also set according to the actual situation. For example, the casting process in this embodiment is to fill the mold, that is, the maximum filling amount is 100%. The filling amount in some die casting situations may not be 100%)

[0053] Specifically, the calculation conditions in step 4 include: setting the calculation speed of the casting model in the ProCAST software, and observing the calculation situation, time, casting percentage, and solidification percentage.

[0054] In a specific embodiment of the present application, the metal melt is regarded as a Newtonian fluid with constant viscosity during the filling process (in the casting process, the solid metal is melted into liquid at high temperature and then cast, so in this embodiment, the tin alloy melt is regarded as a Newtonian fluid), and in this embodiment, a metal liquid filling model coupled with heat transfer is used, and the flow follows the laws of conservation of mass, momentum and energy; there is a large amount of heat transfer during the solidification and formation of the casting, which can be divided into heat conduction, heat convection and heat radiation according to the physical nature of the heat transfer. After the metal liquid filling is completed, the cooling process of the casting is mainly through the heat dissipation of the mold, so the heat transfer mode of this process is mainly heat conduction. For numerical simulation calculation of the solidification process of the casting, the basic law is Fourier's law, and the basic mathematical model is the heat conduction partial differential equation. These constitutive equations have been integrated into the ProCAST software. Only the calculation speed needs to be set, that is, the number of CPU cores allocated for calculation. During simulation, the monitoring system can be opened at the same time to observe the calculation situation, time, percentage of casting and percentage of solidification.

[0055] Specifically, the simulation results are output and the shrinkage situation is analyzed, the post-processing module of the ProCAST software is opened, the casting process and the obtained data types are observed, and the integrity of the simulation process is judged according to the obtained results.

[0056] In a specific embodiment of the present application, the post-processing module of the ProCAST finite element simulation software is opened, and whether the casting process and the required data types are complete is checked. And the integrity of the simulation process can be judged according to the obtained results. (At the end of the simulation, whether the highest temperature of all parts of the ingot reaches the set temperature, whether there is the research content required by oneself, whether there is a shrinkage situation option bar, whether the casting body filling situation at different time periods, temperature distribution situation, etc. can be observed) If the data types are incomplete, the simulation of the casting process needs to be performed again. Then the analysis processing interface of the post-processing plate is opened, the cooling and solidification conditions of the ingot are determined by selecting the whole process of the casting process, the temperature and solidification conditions of the ingot at different times during the casting process are analyzed, the temperature and solidification conditions of the casting body at the same time at different positions during the casting process are analyzed, and the shrinkage situation under the condition of complete cooling is determined. (There are analysis selection bars for different casting conditions such as temperature, solidification condition, i.e. solid phase rate in ProCAST. After selecting the features to be analyzed such as temperature, solid phase rate and shrinkage rate, the situation of the selected features at different step numbers can be determined by selecting or dragging the simulation step number, and the corresponding time of the selected step number can be observed in the display window) to select the appropriate casting process.

[0057] This example studies the influence of different casting processes on the formation of shrinkage. According to the actual production influencing factors, the influence of different casting temperatures and heat transfer coefficients on the formation of shrinkage is selected for study. The distribution of shrinkage and the probability of shrinkage occurrence are studied, and the shrinkage rate under different conditions is counted.

[0058] As shown in Figures 6-7 , (PCT in the figure refers to casting temperature, mainly observing whether the horizontal part of the casting body produces shrinkage. The gray part is the part without shrinkage, and the purple part in the figure is the part that may appear shrinkage. The color corresponds to the right scale, which is the probability of shrinkage occurrence). This example refers to Figure 6 a-f, which respectively study the shrinkage under the conditions of casting temperature of 290°C, 310°C, 330°C, 350°C, 370°C, and 390°C. Combined with Figure 7 , it can be found that the casting temperature has an effect on the shrinkage. When the casting temperature is 350°C, the shrinkage rate of the ingot is the lowest.

[0059] As shown in Figures 8-9 , (HCT in Figure 8 refers to the interfacial heat transfer coefficient. Similarly, the horizontal part of the casting body is mainly observed, and whether the horizontal part produces shrinkage is mainly observed. The gray part is the part without shrinkage, and the purple part in the figure is the part that will appear shrinkage. The color corresponds to the right scale, which is the probability of shrinkage occurrence). At the same time, refer to Figure 8 a-f heat transfer coefficients, which are 900, 1000, 2000, 3000, 4000, and 5000, respectively. Combined with Figure 9 , it can be found that the heat transfer coefficient is an important factor affecting the formation of shrinkage, and when the heat transfer coefficient is 5000, the shrinkage of the ingot is significantly improved, and the shrinkage rate is the lowest. The simulation results are used as theoretical support, and the obtained conclusions are applied to actual production.

[0060] This example finds that the heat transfer coefficient is a key factor affecting the formation of internal shrinkage in the ingot. The heat transfer coefficient is comprehensively regulated by multiple process parameters, including cooling method, casting process parameters, mold temperature difference, and cooling medium temperature. Combined with actual production experience and numerical simulation results, this study proposes and verifies the strategy of improving the overall heat transfer coefficient during casting by increasing the cooling water flow rate. Figure 10 The influence of this improvement measure on the shrinkage of the ingot is clearly shown: Figure 10 (a) is the ingot before the cooling water flow rate is optimized, and there are significant macroscopic shrinkage defects in the central region; in contrast, Figure 10 (b) directly shows that after increasing the cooling water flow rate, the shrinkage phenomenon in the ingot has been significantly improved. This result powerfully proves that by regulating the cooling water flow rate to improve the heat transfer efficiency, the formation of ingot shrinkage can be effectively inhibited.

[0061] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0062] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A numerical simulation method for casting molding of a tin-based solder, characterized by, The method comprises the following steps: Step 1: Obtain the mold and the casting body required for casting the tin-based solder alloy, and simplify to obtain a casting model; Step 2: Import the casting model into ProCAST software to check the assembly interaction of the casting model, and divide the grid of the casting model; Step 3: After the grid division, set the attribute parameters of the tin-based solder alloy and the casting mold material, and the boundary conditions required for the casting simulation; Step 4: Set the calculation conditions according to the attribute parameters and the boundary conditions in step 3, and perform numerical simulation calculation on the casting process of the tin-based solder alloy according to the calculation conditions, and output the simulation results.

2. The numerical simulation method for casting and molding of tin-based solder according to claim 1, wherein The simplification process in step 1 comprises: simplifying the casting process basic scene into a casting mold and a casting body, setting the heat dissipation mode of the pipe part of the casting mold as heat insulation, setting the heat dissipation mode of the remaining part of the casting mold as water cooling, pouring the tin-based solder alloy from the casting pipe into the casting body and cooling under the action of water cooling, and obtaining an ingot.

3. The numerical simulation method for casting of tin-based solder according to claim 1, wherein The casting model comprises a casting mold and a casting body, and the built casting mold is assembled and exported in IGS format.

4. The numerical simulation method for casting of tin-based solder according to claim 3, wherein Checking the assembly interaction of the casting model comprises: importing the exported IGS format file into ProCAST software, and checking the interaction of face connectivity, body intersection cutting and overlapping assembly between mixed bodies in the software.

5. The numerical simulation method for casting of tin-based solder according to claim 1, wherein Step 3 comprises: setting related casting parameters for the casting model, giving the casting pipe and the casting mold attributes and setting the materials of the casting pipe and the casting mold, and the materials of the remaining part of the casting pipe and the casting mold are the same.

6. The numerical simulation method for casting of tin-based solder according to claim 1, wherein The boundary conditions required for the casting simulation in step 3 comprise: adopting a steady-state calculation method to study the shrinkage cavity of the casting simulation, adopting normal environment casting to determine the gravity casting direction of the tin-based solder alloy, setting the interface heat transfer coefficient between the casting mold and the casting body, determining the heat exchange mode between the casting mold and the casting body, setting the casting pipe part as heat insulation, setting the other part of the casting mold as water cooling heat dissipation, and setting the casting filling time.

7. The numerical simulation method for casting of tin-based solder according to claim 1, wherein The calculation conditions in step 4 comprise: setting the calculation speed of the casting model in ProCAST software, monitoring the calculation conditions, time, casting percentage and solidification percentage through the observation window.

8. The numerical simulation method for casting of tin-based solder according to claim 1, wherein It also comprises outputting and analyzing the simulation results, opening the post-processing module of ProCAST software, observing the casting process and the obtained data types, and judging the integrity of the simulation process according to the obtained results.

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