Three-roller planetary rotary rolling online process simulation and structure property prediction method

Abstract

The invention provides a three-roller planetary rotary rolling online process simulation and structure property prediction method, which comprises the following steps of: processing simulation data of finite element simulation software, and fitting to obtain data such as a temperature field, a stress field and an equivalent plastic strain field corresponding to a copper pipe blank under different heat exchange coefficients; converting the simulated discrete data into a continuous mathematical equation; then determining an actual heat exchange coefficient according to process parameters of a three-roller planetary rolling mill collected in real time in a production field, and then calculating data such as a temperature field, a stress field and an equivalent plastic strain field corresponding to the actual copper pipe blank by utilizing a linear interpolation method according to the actual heat exchange coefficient; finally, a calculation result is displayed in the form of numerical cloud strips and animations, online rapid calculation of the copper pipe three-roller planetary rotary rolling process state is achieved, and a necessary theory and model foundation is laid for three-roller planetary rotary rolling intelligent manufacturing.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of copper tube online process simulation and microstructure performance prediction calculation method, in particular to a three-roller planetary rotary rolling online process simulation and microstructure performance prediction method. BACKGROUND

[0002] The copper tube cast blank horizontally casted may have defects such as composition segregation, shrinkage, porosity and the like, and the mechanical properties are poor. The three-roller planetary rotary rolling is the core link designed to eliminate these defects and improve the material performance. In the three-roller planetary rotary rolling process, the copper tube blank is subjected to a multi-directional plastic deformation process of significant radial compression, circumferential extension and axial extension under the alternating contact and compression of three equally spaced planetary rollers. With the rotation and revolution of the rollers, the metal is periodically loaded and unloaded under the action of continuous alternating contact stress and friction, forming a spiral metal flow trajectory, and strong strain accumulation and recrystallization occur in the material. The copper tube blank enters four stages in turn, i.e. the reducing section, the concentrated deformation section, the finishing section and the rounding section.

[0003] Due to the complexity of the process and the lack of direct observation means to observe the deformation of the tube blank inside the rolling mill, the real state of the copper tube rotary rolling cannot be known, which leads to unstable quality of the copper tube blank after three-roller planetary rotary rolling, and further affects the quality of the finished copper tube.

[0004] Finite element simulation is a powerful analysis tool for studying rolling mechanical behavior and process parameters. However, since the analysis results are based on preset fixed parameters, the calculation results are obtained by offline calculation, and the calculation speed is slow, which cannot be real-time simulated with the dynamic changes of the actual running status of the rolling mill, resulting in that the online guidance and optimization value of the production process is limited.

[0005] At present, there is no method that can realize online rapid calculation of three-roller planetary rotary rolling process, so it is necessary to develop a method that can real-time calculate the rolling process of the copper tube blank according to the real-time process parameter changes in the production site, so as to adjust the rolling mill parameters to optimize the quality of the copper tube, and lay a foundation for intelligent manufacturing of copper tube three-roller rotary rolling. SUMMARY

[0006] The purpose of the present application is to obtain the microstructure performance of the copper tube blank corresponding to the temperature field, stress field, equivalent plastic strain field and the like of the copper tube inside the rolling mill in real time according to the real-time process parameter changes in the production site by the three-roller planetary rotary rolling online process simulation and microstructure performance prediction method based on interpolation method.

[0007] To achieve the above purpose, the present application provides a three-roller planetary rotary rolling online process simulation and microstructure performance prediction method, and the steps are as follows:

[0008] Step one: fitting simulation data to obtain copper tube blank state equation changing with time;

[0009] Step two: according to the actual rolling mill control parameters; calculate the actual comprehensive heat transfer coefficient;

[0010] Step three: according to the actual comprehensive heat transfer coefficient, interpolation is carried out on the copper tube blank state equation under different heat transfer coefficients to obtain the copper tube blank state corresponding to the actual rolling mill control parameters;

[0011] Step four: interpolation is carried out on the copper tube blank state at the corresponding position at the previous time and the newly calculated copper tube blank state at a certain time interval to simulate the change of the copper tube blank when the rolling mill control parameters change in the actual process;

[0012] Step five: through the above simulation, the state of the copper tube blank in continuous processing can be obtained. In order to make the display more intuitive, the results can be visualized in the form of finite element numerical cloud bar.

[0013] The fitting in step one is to fit the simulation data of copper tube blank under various field variables corresponding to various heat transfer coefficients and obtain the corresponding equation by polynomial fitting method. The image of the equation is shown in Figure 1 .

[0014] The actual comprehensive heat transfer coefficient calculation in step two involves the following specific calculation steps:

[0015] I. Water property calculation

[0016] The physical properties of water, including viscosity and thermal conductivity, change with temperature, and the accurate property values at any given water temperature need to be calculated by interpolation method through known discrete data points.

[0017] First, locate the interval: according to the input Cooling water temperature Find its temperature interval in the temperature reference point. For example: = 35℃, located in the [20, 40] interval. Then linear calculation: use the straight line equation to calculate the viscosity value at this temperature, known points: (20, 1.00), (40, 0.65), the viscosity at 35℃,

[0018] μ = 1.00 + (35-20) / (40-20) × (0.65-1.00)= 1.00 + 0.75 × (-0.35) =0.7375 .

[0019] In the formula, is the dynamic viscosity of water ), k is the thermal conductivity, which is obtained by interpolation in the same way.

[0020] II. Calculate the actual roll speed

[0021]

[0022] where is the roll speed (rpm), is the spindle motor speed (rpm), is the ratio of spindle speed to roll speed

[0023] III. Convert the pressure unit

[0024]

[0025] where is the cooling water pressure (Bar), P is the water pressure (Pa unit)

[0026] IV. Calculate the actual jet speed

[0027] where v is the actual jet speed of cooling water (m / s), is the nozzle efficiency coefficient, is the water density (kg / m³). Based on Bernoulli equation, considering the system loss coefficient 0.42 and nozzle efficiency .

[0028] V. Calculate the effective wetted area

[0029]

[0030] where is the effective wetted area (m²), is the wetted area ratio, is the roll diameter (m), is the contact characteristic length (m) ; considering the actual wetted ratio, not the entire roll surface is involved in heat exchange;

[0031] VI. Calculate the single-hole flow rate

[0032]

[0033] where is the single-hole flow rate (m³ / s), d is the jet diameter (m). The mass flow rate of cooling water per unit area, reflecting the cooling intensity.

[0034] VII. Calculate the flow density

[0035]

[0036] where is the flow density;

[0037] Eight, calculate the Reynolds number

[0038]

[0039] wherein is the Reynolds number, which characterizes the flow state (laminar / turbulent) and affects the heat transfer intensity;

[0040] Nine, calculate the Prandtl number

[0041]

[0042] wherein is the Prandtl number, is the specific heat capacity of water at constant pressure;

[0043] Ten, calculate the Nusselt number

[0044]

[0045] wherein is the Nusselt number, the calculation formula is an empirical correlation, which reflects the strength of convective heat transfer;

[0046] Eleven, calculate the basic heat transfer coefficient

[0047]

[0048] wherein is the basic heat transfer coefficient, which is obtained according to the Fourier heat conduction law, and defines the basic heat transfer capacity;

[0049] Twelve, calculate the rotation enhancement factor

[0050]

[0051] wherein is the rotation enhancement factor, which is enhanced due to the centrifugal force and disturbance caused by the rotation of the roller;

[0052] Thirteen, calculate the flow correction factor

[0053]

[0054] wherein is the flow correction factor, because the increase in flow rate improves the heat transfer efficiency, but there is a saturation effect;

[0055] Fourteen, calculate the high-temperature boiling correction factor

[0056]

[0057] wherein is the high temperature boiling correction factor, wherein The high temperature difference can cause nucleate boiling, which significantly enhances heat transfer.

[0058] Fifteen, calculate the overall heat transfer coefficient

[0059]

[0060] In the formula is the overall heat transfer coefficient .

[0061] In the third step, based on the two parts of data, the following interpolation method is used to obtain the change data of the copper pipe blank field variables in the rolling process corresponding to the actual heat transfer coefficient: first, sort the heat transfer coefficient of the simulation data, then read the current actual heat transfer coefficient, determine its position in the sequence of simulation heat transfer coefficient according to the size of the actual heat transfer coefficient, and finally complete the interpolation calculation according to the established calculation formula and process. The specific formula is as follows:

[0062]

[0063] In the formula: is the value of different heat transfer coefficients obtained from simulation. is the number of heat transfer coefficients, is the heat transfer coefficient calculated in actual processing. is the heat transfer coefficient calculation range to be interpolated.

[0064]

[0065] In the formula is the heat transfer coefficient corresponding to the copper pipe blank simulation equation, is the simulation equation after interpolation.

[0066] In the fourth step, the copper pipe blank state newly calculated at intervals is interpolated with the copper pipe blank state at the corresponding position at the previous time.

[0067] One, because the simulation data of the copper pipe represents the change of the state of different points on the copper pipe at the same time in the horizontal direction, and the change of the state of the same point on the copper pipe at different times in the vertical direction. And the speed of the copper pipe in the simulation is basically stable, so the appropriate simulation time interval can be calculated by the distance between the nodes of the copper pipe. The simulation matrix calculated in this way can have the following effects: the state of the next node of a node and the state at the next time are basically the same.

[0068] Two, for this matrix, as Figure 2Operation: that is, the data read at i+1 time, need to be interpolated with the data at i time which has not reached steady state, then put the new value calculated at i+1 time on the left of the interpolated data as the point to be shown later. After that, fill 0 under the interpolated data, that is, complete the update of the copper pipe state under the new heat transfer coefficient.

[0069] Said step five, for more intuitive representation of the copper pipe blank online organization performance, by making the calculated simulation data into the form of numerical cloud bar, more clearly observe the change of copper pipe blank in the processing process, such as Figure 3 The main processing flow is to take out a row of data from the calculated results according to time interval, then sort the array, and then correspond it to different colors. Finally, the corresponding color of the data is displayed in the rolling mill working diagram, such as Figure 4 And Figure 5 .

[0070] Advantages of the present application:

[0071] The three-roll planetary rolling online process simulation and organization performance prediction method provided by the present application can obtain the corresponding copper pipe blank organization performance of the temperature field, stress field, equivalent plastic strain field and other field variables of the copper pipe in the rolling mill in real time according to the real-time process parameter changes in the production site. The method can effectively solve the defect that the copper pipe deformation in the rolling mill cannot be directly observed in the production site, can help to adjust the rolling mill parameters on site, optimize the copper pipe production quality, and lay a foundation for intelligent manufacturing of copper pipe three-roll planetary rolling. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 is a part of temperature simulation data fitting result diagram of three-roll planetary rolling process;

[0073] Figure 2 is a data update principle diagram;

[0074] Figure 3 is a numerical cloud diagram fitted according to the simulation results;

[0075] Figure 4 is a copper pipe blank rolling state diagram according to the obtained data;

[0076] Figure 5 is a display diagram of the final results of software calculation. DETAILED DESCRIPTION

[0077] The present application will be further explained in connection with specific embodiments, but not limited to the present application, the structure, proportion, size, etc. shown in the drawings of the specification are only used to cooperate with the content disclosed in the specification, for those skilled in the art to understand and read, and are not used to limit the limiting conditions that the present application can be implemented, so they do not have technical significance, any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effect and purpose that the present application can produce, should still fall within the scope of the technical content disclosed by the present application.

[0078] The present embodiment provides a three-roll planetary roll online process simulation and microstructure performance prediction method, the steps are as follows:

[0079] Step one: fitting the simulation data to obtain the copper pipe blank state equation changing with time;

[0080] Step two: according to the actual rolling mill control parameters; calculate the actual comprehensive heat transfer coefficient;

[0081] Step three: according to the actual comprehensive heat transfer coefficient, the copper pipe blank state equation under different heat transfer coefficients is interpolated to obtain the copper pipe blank state corresponding to the actual rolling mill control parameters;

[0082] Step four: the copper pipe blank state newly calculated at intervals of a certain time is interpolated with the copper pipe blank state at the corresponding position at the previous time to simulate the change of the copper pipe blank when the rolling mill control parameters change in actual production;

[0083] Step five: through the above simulation, the state of the copper pipe blank in continuous processing can be obtained, in order to make the display more intuitive, the results can be visualized in the way of finite element numerical cloud bar;

[0084] The fitting in step one is to fit the simulation data of the copper pipe blank under various field variables corresponding to various heat transfer coefficients and obtain the corresponding equation by polynomial fitting method; the image of the equation is as shown in Figure 1 .

[0085] The actual comprehensive heat transfer coefficient calculation in step two is as follows:

[0086] I. Calculation of water properties

[0087] The physical properties of water, including viscosity and thermal conductivity, change with temperature, and the accurate property values at any given water temperature need to be calculated by interpolation method through known discrete data points.

[0088] Table 1. Water property value reference table

[0089]

[0090] First, locate the range: based on the input. Cooling water temperature Find the temperature range within the temperature reference point. For example: = 35℃, located in the interval [20, 40]. Then linear calculation: use the linear equation to calculate the viscosity values ​​at the known points: (20, 1.00), (40, 0.65), the viscosity at 35℃.

[0091] μ = 1.00 + (35-20) / (40-20) × (0.65-1.00)= 1.00 + 0.75 × (-0.35) =0.7375 .

[0092] In the formula: The dynamic viscosity of water ( ), where k is the thermal conductivity, which is obtained by interpolation using the same method.

[0093] II. Calculation of actual roll speed

[0094]

[0095] In the formula The speed of the rolling mill (rpm). The spindle motor speed (rpm) The ratio of spindle speed to roll speed

[0096] III. Perform pressure unit conversion

[0097]

[0098] In the formula P represents the cooling water pressure (Bar), where P is the water pressure (Pa).

[0099] IV. Calculating the actual jet speed

[0100]

[0101] In the formula, v is the actual jet velocity of the cooling water (m / s). This is the nozzle efficiency coefficient. Let be the density of water (kg / m³). Based on Bernoulli's equation, considering a system loss coefficient of 0.42 and nozzle efficiency... .

[0102] V. Calculate the effective wetting area

[0103]

[0104] In the formula Effective wetted area (m²) Wetted area ratio Roll diameter (m) Contact characteristic length (m), considering actual wetted ratio, not the whole roll surface is involved in heat transfer

[0105] Six, Calculate single-hole flow rate

[0106]

[0107] Where Single-hole flow rate (m³ / s), d is the nozzle diameter (m). The mass flow rate of cooling water per unit area reflects the cooling intensity.

[0108] Seven, Calculate flow density

[0109]

[0110] Where Flow density

[0111] Eight, Calculate Reynolds number

[0112]

[0113] Where Reynolds number, representing the flow state (laminar / turbulent) and affecting the heat transfer intensity.

[0114] Nine, Calculate Prandtl number

[0115]

[0116] Where Prandtl number Specific heat capacity of water at constant pressure.

[0117] Ten, Calculate Nusselt number

[0118]

[0119] Where Nusselt number, the calculation formula is an empirical correlation, reflecting the strength of convective heat transfer.

[0120] Eleven, Calculate the basic heat transfer coefficient

[0121]

[0122] Where Basic heat transfer coefficient, obtained according to Fourier's law of heat conduction, defines the basic heat transfer capacity.

[0123] Twelve, Calculate the rotation enhancement factor

[0124]

[0125] wherein is a rotation enhancement factor, which enhances heat transfer due to centrifugal force and disturbance caused by roll rotation.

[0126] Thirteen, calculating flow correction factor

[0127]

[0128] wherein is a flow correction factor, which enhances heat transfer efficiency because of increased flow, but has saturation effect.

[0129] Fourteen, calculating high temperature boiling correction factor

[0130]

[0131] wherein is a high temperature boiling correction factor, wherein high temperature difference can cause nucleate boiling, which significantly enhances heat transfer.

[0132] Fifteen, calculating comprehensive heat transfer coefficient

[0133]

[0134] wherein is a comprehensive heat transfer coefficient .

[0135] In the third step, based on the aforementioned two parts of data, the following interpolation method is used to obtain the change data of each field variable of the copper tube blank in the rolling process corresponding to the actual heat transfer coefficient: first, sort the heat transfer coefficient of the simulation data, then read the current actual heat transfer coefficient, determine its position in the sequence of the simulation heat transfer coefficient according to the size of the actual heat transfer coefficient, and finally complete the interpolation calculation according to the established calculation formula and process. The specific formula is as follows:

[0136]

[0137] wherein: is the value of different heat transfer coefficients obtained from simulation. is the number of heat transfer coefficients, is the heat transfer coefficient calculated in actual processing. is the calculation range of the heat transfer coefficient to be interpolated.

[0138]

[0139] wherein is the heat transfer coefficient corresponding to the copper tube blank simulation equation, The interpolation is performed on the simulation equation after interpolation.

[0140] In step four, the newly calculated copper tube blank state is interpolated with the copper tube blank state at the corresponding position at the previous time interval.

[0141] I. Since the simulation data of the copper tube represents the state change of different points on the copper tube at the same time in the horizontal direction and the state change of the same point on the copper tube at different times in the vertical direction, and the speed of the copper tube in the simulation is basically stable, the appropriate simulation time interval can be calculated by the distance between the nodes of the copper tube, so that the simulation matrix calculated in this way can have the following effect: the state of the next node of a node is basically consistent with the state at the next time.

[0142] II. The matrix is interpolated as follows Figure 2 Operation: the data read at time i+1 needs to be interpolated with the data at time i that has not reached a steady state, and then the new value calculated at time i+1 is placed on the left of the interpolated data as the point to be displayed later. Then fill 0 under the interpolated data, which can complete the update of the copper tube state under the new heat transfer coefficient.

[0143] The fifth step is to make the calculated simulation data into the form of a numerical cloud bar to more clearly observe the changes of the copper tube blank in the processing process Figure 3 . The main processing flow is to take out a row of data from the calculated results according to the time interval, then sort the array, and then correspond it to different colors. Finally, the corresponding color of the data is displayed in the rolling mill working diagram Figure 4 and Figure 5 .

[0144] The remaining matters of the present application are known technologies.

[0145] Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for online process simulation and microstructure / property prediction of three-roll planetary spinning, characterized in that: The method for online process simulation and microstructure and property prediction of three-roll planetary spinning includes the following steps: Step 1: Fit the simulation data to obtain the state equation of the copper tube blank as it changes over time; Step 2: Based on the actual rolling mill control parameters on site; Calculate the actual overall heat transfer coefficient; Step 3: Based on the actual comprehensive heat transfer coefficient, interpolate the state equation of the copper tube billet under different heat transfer coefficients to obtain the state of the copper tube billet that corresponds to the actual rolling mill control parameters. Step 4: Interpolate the newly calculated state of the copper billet at a certain time interval with the state of the copper billet at the corresponding position at the previous moment to simulate the changes in the copper billet when the mill control parameters change in actual operation. Step 5: The previous simulation can be used to obtain the state of the copper tube blank during continuous processing. To make the display more intuitive, the results can be visualized by imitating the finite element numerical cloud bar method.

2. The method for online process simulation and microstructure and property prediction of three-roll planetary spinning according to claim 1, characterized in that: The fitting in step one involves using a polynomial fitting method to fit the simulation data of the copper tube blank under various heat transfer coefficients and obtain their corresponding equations.

3. The method for online process simulation and microstructure and property prediction of three-roll planetary spinning according to claim 1, characterized in that: The calculation of the actual comprehensive heat transfer coefficient involved in step two is as follows: I. Calculation of Water Properties The physical properties of water, including viscosity and thermal conductivity, vary with temperature. It is necessary to calculate the accurate physical property values ​​at any given water temperature using known discrete data points and interpolation methods. First, locate the range: based on the input. Cooling water temperature Find the temperature range in which it is located at the temperature reference point; = 35℃, within the interval [20, 40]; then linear calculation: use the linear equation to calculate the viscosity values ​​at known points: (20, 1.00), (40, 0.65), the viscosity at 35℃. μ = 1.00 + (35-20) / (40-20) × (0.65-1.00)= 1.00 + 0.75 × (-0.35) =0.7375 ; In the formula: The dynamic viscosity of water ( k is the thermal conductivity, which is obtained by interpolation using the same method; II. Calculation of actual roll speed ； In the formula The speed of the rolling mill (rpm). The spindle motor speed (rpm) The ratio of the spindle speed to the roll speed; III. Perform pressure unit conversion ； In the formula P represents the cooling water pressure (Bar), where P is the water pressure (Pa). IV. Calculating the actual jet speed ； In the formula, v is the actual jet velocity of the cooling water (m / s). This is the nozzle efficiency coefficient. The density of water is (kg / m³); based on Bernoulli's equation, considering the system loss coefficient of 0.42 and nozzle efficiency... ; V. Calculate the effective wetting area ； In the formula For the effective wetting area (m²), This represents the proportion of the wetted area. The diameter of the roll (m) The contact characteristic length (m) is taken into account; considering the actual wetting ratio, not the entire roll surface participates in heat exchange. VI. Calculate the flow rate of a single orifice ； In the formula d is the flow rate per single nozzle (m³ / s), and d is the nozzle diameter (m); the mass flow rate of cooling water per unit area reflects the cooling intensity. VII. Calculate the flow density ； In the formula For flow density 8. Calculate the Reynolds number ； In the formula The Reynolds number represents the flow state (laminar / turbulent) and affects the heat transfer intensity.

9. Calculate Prandtl numbers ； In the formula For Prandtl numbers, The specific heat capacity of water at constant pressure; 10. Calculate the Nusselt number ； In the formula The Nusselt number is calculated using an empirical correlation formula, reflecting the strength of convective heat transfer. XI. Calculate the basic heat transfer coefficient ； In the formula The basic heat transfer coefficient is obtained according to Fourier's law of thermal conductivity, and the basic heat transfer capacity is defined.

12. Calculate the rotational strengthening factor ； In the formula As a rotational strengthening factor, the centrifugal force and disturbance generated by the rotation of the rolls will enhance heat transfer; 13. Calculate the flow correction factor ； In the formula This is a flow rate correction factor, because increasing the flow rate improves heat exchange efficiency, but there is a saturation effect; XIV. Calculate the high-temperature boiling correction factor ； In the formula This is a high-temperature boiling correction factor, in which The high temperature difference may induce nucleate boiling, significantly enhancing heat transfer; 15. Calculate the overall heat transfer coefficient ； In the formula For the comprehensive heat transfer coefficient .

4. The method for online process simulation and microstructure and property prediction of three-roll planetary spinning according to claim 1, characterized in that: In step three, based on the aforementioned two sets of data, the following interpolation method is used to obtain the change data of each field variable of the copper tube billet corresponding to the actual heat transfer coefficient during the rolling process: First, the heat transfer coefficients of the simulation data are sorted, then the current actual heat transfer coefficient is read, and its position in the simulation heat transfer coefficient sequence is determined according to the magnitude of the actual heat transfer coefficient. Finally, the interpolation calculation is completed according to the established calculation formula and process. The specific formula is as follows: ； In the formula: These are the values ​​of different heat transfer coefficients obtained from simulations; The number of heat transfer coefficients. The heat transfer coefficient is calculated during actual processing; The calculation range for the heat transfer coefficient to be interpolated; ； In the formula heat transfer coefficient The corresponding simulation equation for copper tube blank, The simulation equations are after interpolation.

5. The method for online process simulation and microstructure and property prediction of three-roll planetary spinning according to claim 1, characterized in that: In step four, the newly calculated state of the copper tube blank at a certain interval is interpolated with the state of the copper tube blank at the corresponding position in the previous moment.

1. Since the simulation data of the copper pipe represents the change of state of different points on the copper pipe at the same time in the horizontal direction, and the change of state of the same point on the copper pipe at different times in the vertical direction; and the speed of the copper pipe is basically stable in the simulation, the appropriate simulation time interval can be calculated by the distance between the nodes of the copper pipe. The simulation matrix calculated in this way can have the following effect: the state of the next node of a certain node is basically the same as the state at the next time. Second, perform the following operations on this matrix: The data read at time i+1 needs to be interpolated with the data at time i that has not reached a steady state. Then, the new value calculated at time i+1 is placed to the left of the interpolated data as the point to be displayed later. After that, zeros are added to the interpolated data to complete the update of the copper tube state under the new heat transfer coefficient.

6. The method for online process simulation and microstructure and property prediction of three-roll planetary spinning according to claim 1, characterized in that: Step five, to more intuitively illustrate the online microstructure and properties of the copper tube billet, involves creating numerical cloud bars from the calculated simulation data. The process is as follows: data is extracted from the calculated results at time intervals, the array is sorted, and then each row is assigned a different color. Finally, the colors corresponding to the data are displayed in the rolling mill operation diagram.

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