A method and system for heating a billet for interval rolling

Abstract

The present application relates to the field of billet heating, and relates to a kind of billet heating method and system of interval rolling, the method includes: the remaining heating time of current billet to the outlet of current furnace section is calculated, and the remaining heating time of current billet to the outlet of each downstream furnace section is calculated, to obtain the remaining heating time of current billet in current furnace section and the remaining heating time of current billet in each downstream furnace section;According to the remaining heating time of current billet in current furnace section and the target outlet temperature of current furnace section, the required hearth temperature of current furnace section is calculated;According to the remaining heating time of billet in each downstream furnace section and the target outlet temperature of corresponding furnace section, the required hearth temperature of corresponding furnace section when current billet reaches each downstream furnace section is calculated;According to the required hearth temperature of each furnace section calculated, the preset target temperature rising curve is combined to heat billet.The method of the present application can effectively improve the heating effect of billet.

Description

Technical Field

[0001] This invention relates to the field of billet heating. More specifically, this invention relates to a method and system for heating billets in intermittent rolling. Background Technology

[0002] In the steel production process, heating furnaces are used to heat steel billets to the target temperature suitable for rolling. For continuous rolling production lines, the billet exiting the furnace is relatively uniform and can be easily matched with the rolling mill rhythm. However, in intermittent rolling production lines, due to the pauses between different batches of the rolling mill, the time intervals between the exits of each billet in the heating furnace are inconsistent, resulting in a non-uniform exit rhythm.

[0003] Existing intermittent billet heating methods mostly rely on fixed heating curves or empirical formulas for furnace temperature control, considering only the target tapping temperature and neglecting the dynamic positions of different billets within the furnace, remaining residence time, and variations in tapping rhythm. When using this method, the significant differences in residence time among billets can easily lead to underheating or overheating of individual billets. Furthermore, the inability to accurately predict the remaining heating time of billets in each furnace section results in large deviations in furnace temperature settings. When the rolling rhythm is adjusted, existing methods struggle to promptly correct the heating strategy, leading to deterioration in rolling quality and reduced production efficiency.

[0004] In summary, existing intermittent rolling billet heating methods suffer from technical problems such as uneven heating, insufficient control precision, and deterioration in rolling quality and reduced production efficiency when the rolling rhythm changes. Summary of the Invention

[0005] To address the technical problems of uneven heating, insufficient control precision, and deterioration in rolling quality and reduced production efficiency when the rolling rhythm changes in existing intermittent rolling billet heating methods, this invention provides solutions in the following aspects.

[0006] In a first aspect, the present invention provides a method for heating intermittently rolled steel billets, comprising:

[0007] Calculate the remaining heating time from the current billet to the outlet of the current furnace section, and the remaining heating time from the current billet to the outlet of each downstream furnace section, and then obtain the remaining heating time of the current billet in the current furnace section and the remaining heating time of the current billet in each downstream furnace section.

[0008] Calculate the required furnace temperature for the current furnace section based on the remaining heating time of the billet in the current furnace section and the target outlet temperature of the current furnace section; calculate the required furnace temperature for the corresponding furnace section when the billet reaches each downstream furnace section based on the remaining heating time of the billet in each downstream furnace section and the target outlet temperature of the corresponding furnace section.

[0009] The steel billet is heated based on the calculated furnace temperature required for each furnace section and a preset target heating curve; the calculation of the remaining heating time from the current steel billet to the outlet of a certain furnace section includes:

[0010] Obtain the distance L from the current billet to the furnace section outlet, and obtain the number N of billets within the range where the distance from the outlet is less than or equal to L; calculate the remaining heating time from the current billet to the furnace section outlet based on the number N and the furnace exit rhythm. The calculation expression is:

[0011] ;

[0012] In the formula, This indicates the remaining time before the steel billet is removed from the furnace. This indicates the tapping rhythm of the k-th billet, where k represents the billet number. The billet about to be tapped is numbered 1. Starting from the billet about to be tapped, the billet number increases by 1 in increments towards the direction away from the furnace outlet.

[0013] Preferably, the expression for calculating the remaining time before the billet is removed from the furnace is:

[0014] ;

[0015] In the formula, This indicates the scheduled time for the steel billet to be removed from the furnace. Indicates the current moment.

[0016] Preferably, obtaining the remaining heating time of the current billet in the kth downstream furnace section includes: subtracting the remaining heating time of the current billet from the exit of the kth downstream furnace section to the exit of the (k-1)th downstream furnace section, thereby obtaining the remaining heating time of the current billet in the kth downstream furnace section.

[0017] Preferably, the calculation of the required furnace temperature for the current furnace section includes:

[0018] Based on the specific heat capacity of the steel billet Given the mass m, calculate the heat Q1 that the billet needs to absorb in this section. The calculation expression is as follows:

[0019] ;

[0020] Calculate the heat transferred to the steel billet in the current furnace section. The calculation expression is:

[0021] ;

[0022] make This allows us to obtain the required furnace temperature for that section. ;

[0023] Of the above formulas, This indicates the target outlet temperature of the current furnace section. This indicates the current temperature of the steel billet. The average temperature of the steel billet in the current furnace section is K, where K is the heat transfer coefficient. This represents the remaining heating time of the current steel billet in the current furnace section.

[0024] Preferably, calculating the required furnace temperature for a downstream section when the current steel billet reaches that section includes:

[0025] Based on the specific heat capacity of the steel billet Given the mass m, calculate the heat Q3 that the billet needs to absorb in this downstream furnace section. The calculation expression is as follows:

[0026] ;

[0027] Calculate the heat transferred to the billet in the downstream furnace section. The calculation expression is:

[0028] ;

[0029] make This allows us to obtain the required furnace temperature for that section. ;

[0030] Of the above formulas, This indicates the target outlet temperature of the downstream furnace section. This indicates the target outlet temperature of the upstream furnace section for the downstream furnace section. This indicates the average temperature of the billet in the downstream furnace section. This represents the remaining heating time for the current steel billet in this downstream furnace section.

[0031] Preferably, it also includes real-time feedback adjustment, including: real-time monitoring of the billet temperature through a furnace temperature detection device, adjusting the furnace temperature according to the target temperature of each section, increasing the furnace temperature of that section when the billet temperature is lower than the target temperature, and decreasing the furnace temperature of that section when the billet temperature is higher than the target temperature.

[0032] Preferably, the method for generating the target heating curve includes:

[0033] The heat flux density from furnace gas to the surface of steel billet in the heating section is calculated based on the temperature rise coefficient of the heating section, and the heat flux density from furnace gas to the surface of steel billet in the preheating section is calculated based on the temperature rise coefficient of the preheating section.

[0034] A heat transfer equation is established, with the initial conditions set as follows: the surface temperature of the billet at the time of exiting the furnace is equal to the target temperature at the time of exiting the furnace, and the center temperature of the billet at the time of exiting the furnace is equal to the difference between the target temperature at the time of exiting the furnace and the target homogenization temperature; the termination condition is set as follows: the temperature difference between the center temperature of the billet and the surface temperature of the billet is greater than a preset temperature difference threshold; the heat transfer equation is solved in reverse using the finite difference method, thereby obtaining the surface temperature and center temperature of the billet at each discrete time point corresponding to the homogenization section, as well as the surface temperature that the billet needs to reach when entering the homogenization section;

[0035] Based on the heat flux density from the furnace gas to the surface of the billet in the heating section, the reverse recursive formula for the surface temperature of the billet in the heating section is obtained. Combined with the surface temperature that the billet needs to reach when entering the soaking section, the surface temperature of the billet at each discrete time point in the heating section, as well as the surface temperature that the billet needs to reach when entering the heating section, are calculated iteratively.

[0036] Based on the heat flux density from furnace gas to the billet surface in the preheating section, a reverse recursive formula for the billet surface temperature in the preheating section is obtained. Combined with the surface temperature that the billet needs to reach when entering the heating section, the billet surface temperature at each discrete time point in the preheating section is iteratively calculated.

[0037] The target temperature rise curve of the billet is generated based on the surface temperature of the billet at each discrete time point corresponding to the preheating section, heating section, and soaking section; the calculation expression of the reverse recursive formula for the surface temperature of the billet in the i-th heating section is:

[0038] ;

[0039] In the formula, This represents the temperature of the M-th spatial node corresponding to the k-th discrete time point. and Let M and M-1 represent the temperatures of the M-th spatial node corresponding to the (k+1)-th discrete time point, respectively. This represents the heat flux density from the furnace gas to the surface of the steel billet within the i-th segment of the heating furnace.

[0040] Preferably, the reverse solution of the heat transfer equation using the finite difference method includes:

[0041] The steel billet is divided into M+1 equidistant spatial nodes from the center to the surface, with the node numbers increasing sequentially from the center to the surface. The node at the center is numbered 0, and the nodes on the surface are numbered M. The time step between adjacent discrete time points is set to... The spacing between spatial nodes is ;

[0042] Based on the heat transfer equation, the reverse recursive formulas for the center temperature of the billet and the reverse recursive formulas for the surface temperature of the billet in the soaking zone are obtained.

[0043] Based on the billet surface temperature at the time of exiting the furnace and the reverse recursive formula for the billet surface temperature in the soaking zone, the billet surface temperature at each discrete time point before the exiting time is calculated iteratively starting from the exiting time. Based on the billet center temperature at the time of exiting the furnace and the reverse recursive formula for the billet center temperature, the billet center temperature at each discrete time point before the exiting time is calculated iteratively starting from the exiting time. The termination condition of the iteration is: the temperature difference between the billet center temperature and the billet surface temperature is greater than the preset temperature difference threshold.

[0044] The reverse recursive formula for the center temperature of the steel billet is:

[0045] ;

[0046] The reverse recursive formula for the surface temperature of the billet in the soaking zone is:

[0047] ;

[0048] In the above two formulas, , Let these represent the temperatures of the 0th and Mth spatial nodes corresponding to the kth discrete time point, respectively. , , as well as Let represent the temperatures of the 0th, 1st, Mth, and (M-1th)th spatial nodes corresponding to the (k+1)th discrete time point, respectively; and let c represent the temperature value. The specific heat capacity of the steel billet at that time. The temperature value is indicated. and The average value is the thermal conductivity of the steel billet.

[0049] Preferably, calculating the surface temperature of the steel billet at each discrete time point corresponding to the i-th segment of the heating furnace includes:

[0050] Based on the surface temperature that the billet needs to reach when entering the downstream section of the i-th heating furnace, and combined with the reverse recursive formula for the surface temperature of the billet in the i-th heating furnace, the surface temperature of the billet at each discrete time point within a first preset time period before entering the downstream section of the i-th heating furnace is iteratively calculated, starting from the moment of entering the downstream section of the i-th heating furnace; the first preset time period is equal to the total residence time of the billet in the i-th heating furnace.

[0051] In a second aspect, the present invention provides a billet heating system for intermittent rolling, the billet heating system comprising a processor and a memory, the memory storing computer program instructions that, when executed by the processor, implement the billet heating method of the present invention for intermittent rolling.

[0052] The beneficial effects of this invention are as follows: The billet heating method for intermittent rolling in this embodiment calculates the distance between the billet and the exit of each furnace section, and combines this distance with the number of billets within that range and the furnace exit rhythm to calculate the remaining heating time of the billet to the furnace section exit. This allows for a more accurate prediction of the remaining heating time of the billet to the furnace section exit, resulting in more accurate predictions of the remaining heating time of the billet in each furnace section, which helps improve the accuracy of furnace temperature setting. Furthermore, by dynamically correcting the heating process, underheating or overheating of the billet caused by intermittent rolling is avoided, improving the temperature uniformity of the billet cross-section and longitudinal direction. Moreover, the method in this embodiment can adjust the heating scheme in real time according to the actual furnace exit rhythm, adapting the heating process to the rhythm changes of intermittent rolling, ensuring the continuity and stability of the rolling process, and thus ensuring high rolling quality and production efficiency for the billet. Attached Figure Description

[0053] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, and like or corresponding reference numerals denote like or corresponding parts, wherein:

[0054] Figure 1 This is a schematic flowchart illustrating a method for heating a steel billet in intermittent rolling according to an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram illustrating the positions of various steel billets inside a heating furnace according to an embodiment of the present invention;

[0056] Figure 3 This is a schematic diagram illustrating the structure of a billet heating system for intermittent rolling according to an embodiment of the present invention. Detailed Implementation

[0057] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0058] Example of a heating method for intermittently rolled steel billets:

[0059] like Figure 1 As shown, the intermittently rolled steel billet heating method of the present invention includes:

[0060] S101. Obtain the remaining heating time of the current billet in the current furnace section and each downstream furnace section. Specifically, calculate the remaining heating time of the current billet from the outlet of the current furnace section to the outlet of each downstream furnace section, and then obtain the remaining heating time of the current billet in the current furnace section and the remaining heating time of the current billet in each downstream furnace section.

[0061] S102. Calculate the required furnace temperature for the current furnace section and each downstream furnace section. Specifically, calculate the required furnace temperature for the current furnace section based on the remaining heating time of the current billet in the current furnace section and the target outlet temperature of the current furnace section; calculate the required furnace temperature for the corresponding furnace section when the current billet reaches each downstream furnace section based on the remaining heating time of the billet in each downstream furnace section and the target outlet temperature of the corresponding furnace section.

[0062] S103. Heat the steel billet according to the calculated furnace temperature required for each furnace section and the preset target heating curve.

[0063] In this embodiment, calculating the remaining heating time from the current billet to the outlet of a certain furnace section includes:

[0064] Obtain the distance L from the current billet to the furnace section outlet, and obtain the number N of billets within the range where the distance from the outlet is less than or equal to L; calculate the remaining heating time from the current billet to the furnace section outlet based on the number N and the furnace exit rhythm. The calculation expression is:

[0065] (1)

[0066] In the formula, This indicates the remaining time before the steel billet is removed from the furnace. This indicates the tapping rhythm of the k-th billet, where k represents the billet number. The billet about to be tapped is numbered 1. Starting from the billet about to be tapped, the billet number increases by 1 in increments towards the direction away from the furnace outlet.

[0067] like Figure 2 As shown, assuming the remaining time for the billet to be unloaded is 3 seconds, and all billets are unloaded at the same pace of 5 seconds, the current billet is M3 in the preheating section. The distance from this billet to the preheating section outlet is L2. As shown in the diagram, there are 4 billets within a distance of L2 or less from the outlet. Therefore, the remaining heating time for this billet to reach the outlet of this section is 23 seconds. The distance from this billet to the heating section outlet is L2+L3. As shown in the diagram, there are 11 billets within a distance of L2+L3 or less from the outlet. Therefore, the remaining heating time for this billet to reach the outlet of the heating section is 3 + 11 × 5 = 58 seconds. The distance between the steel billet and the furnace outlet is L2+L3+L4. As shown in the figure, there are 17 steel billets whose distance from the furnace outlet is less than or equal to L2+L3+L4. Therefore, the remaining heating time for the steel billet to reach the furnace outlet is 3+5×17=88 seconds.

[0068] In this embodiment, the furnace exit rhythm refers to the time interval between two adjacent steel billets being pushed out of the heating furnace outlet.

[0069] The billet heating method for intermittent rolling in this embodiment calculates the distance between the billet and the exit of each furnace section, and combines this distance with the number of billets within that range and the furnace exit rhythm to calculate the remaining heating time of the billet to the furnace section exit. This allows for a more accurate prediction of the remaining heating time of the billet to the furnace section exit, resulting in more accurate predictions of the remaining heating time of the billet in each furnace section and improving the precision of furnace temperature setting. Furthermore, by dynamically correcting the heating process, underheating or overheating of the billet caused by intermittent rolling is avoided, improving the temperature uniformity of the billet cross-section and longitudinal direction. Moreover, the method in this embodiment can adjust the heating scheme in real time according to the actual furnace exit rhythm, adapting the heating process to the rhythm changes of intermittent rolling, ensuring the continuity and stability of the rolling process, and thus guaranteeing high rolling quality and production efficiency for the billet.

[0070] In one embodiment, the expression for calculating the remaining time for the billet to be tapped from the furnace is:

[0071] ;

[0072] In the formula, This indicates the scheduled time for the steel billet to be removed from the furnace. Indicates the current moment.

[0073] In one embodiment, obtaining the remaining heating time of the current billet in the kth downstream furnace section includes: subtracting the remaining heating time of the current billet from the exit of the kth downstream furnace section to the exit of the (k-1)th downstream furnace section, thereby obtaining the remaining heating time of the current billet in the kth downstream furnace section.

[0074] In one embodiment, calculating the required furnace temperature for the current furnace section includes:

[0075] Based on the specific heat capacity of the steel billet Given the mass m, calculate the heat Q1 that the billet needs to absorb in this section. The calculation expression is as follows:

[0076] (2)

[0077] Calculate the heat transferred to the steel billet in the current furnace section. The calculation expression is:

[0078] (3)

[0079] make This allows us to obtain the required furnace temperature for that section. ;

[0080] Of the above formulas, This indicates the target outlet temperature of the current furnace section. This indicates the current temperature of the steel billet. The average temperature of the steel billet in the current furnace section is K, where K is the heat transfer coefficient. This represents the remaining heating time of the current steel billet in the current furnace section.

[0081] In one embodiment, calculating the required furnace temperature for a downstream section when the current steel billet reaches that section includes:

[0082] Based on the specific heat capacity of the steel billet Given the mass m, calculate the heat Q3 that the billet needs to absorb in this downstream furnace section. The calculation expression is as follows:

[0083] (4)

[0084] Calculate the heat transferred to the billet in the downstream furnace section. The calculation expression is:

[0085] (5)

[0086] make This allows us to obtain the required furnace temperature for that section. ;

[0087] Of the above formulas, This indicates the target outlet temperature of the downstream furnace section. This indicates the target outlet temperature of the upstream furnace section for the downstream furnace section. This indicates the average temperature of the billet in the downstream furnace section. This represents the remaining heating time for the current steel billet in this downstream furnace section.

[0088] In one embodiment, the method further includes real-time feedback adjustment, which includes: monitoring the billet temperature in real time through a furnace temperature detection device, adjusting the furnace temperature according to the target temperature of each section, increasing the furnace temperature of that section when the billet temperature is lower than the target temperature, and decreasing the furnace temperature of that section when the billet temperature is higher than the target temperature.

[0089] By adjusting the furnace temperature in real time, the temperature of the steel billet inside the heating furnace can be kept as close as possible to the target temperature of the corresponding furnace section, thereby further ensuring the quality of the steel billet rolling.

[0090] In one embodiment, the method for generating the target heating curve includes:

[0091] S201. Calculate the heat flux density from furnace gas to the surface of steel billet in the heating section based on the heating section temperature rise coefficient, and calculate the heat flux density from furnace gas to the surface of steel billet in the preheating section based on the preheating section temperature rise coefficient.

[0092] S202. Establish the heat transfer equation and set the initial conditions as follows: the surface temperature of the billet at the time of exiting the furnace is equal to the target temperature at the time of exiting the furnace, and the center temperature of the billet at the time of exiting the furnace is equal to the difference between the target temperature at the time of exiting the furnace and the target homogenization temperature; set the termination condition as follows: the temperature difference between the center temperature of the billet and the surface temperature of the billet is greater than the preset temperature difference threshold; use the finite difference method to solve the heat transfer equation in reverse, thereby obtaining the surface temperature and center temperature of the billet at each discrete time point corresponding to the homogenization section, as well as the surface temperature that the billet needs to reach when entering the homogenization section;

[0093] S203. Based on the heat flux density from the furnace gas to the surface of the billet in the heating section, obtain the reverse recursive formula for the surface temperature of the billet in the heating section. Combined with the surface temperature that the billet needs to reach when entering the soaking section, iteratively calculate the surface temperature of the billet at each discrete time point corresponding to the heating section, as well as the surface temperature that the billet needs to reach when entering the heating section.

[0094] S204. Based on the heat flux density from the furnace gas to the surface of the billet in the preheating section, obtain the reverse recursive formula for the surface temperature of the billet in the preheating section. Combined with the surface temperature that the billet needs to reach when entering the heating section, iteratively calculate the surface temperature of the billet at each discrete time point corresponding to the preheating section.

[0095] S205. Generate the target heating curve of the billet based on the surface temperature of the billet at each discrete time point corresponding to the preheating section, heating section, and soaking section; the calculation expression of the reverse recursive formula for the surface temperature of the billet in the i-th heating section is:

[0096] (6)

[0097] In the formula, This represents the temperature of the M-th spatial node corresponding to the k-th discrete time point. and Let M and M-1 represent the temperatures of the M-th spatial node corresponding to the (k+1)-th discrete time point, respectively. This represents the heat flux density from the furnace gas to the surface of the steel billet within the i-th segment of the heating furnace.

[0098] The target heating curve generation method in this embodiment uses the final product quality indicators "average heat" and "target furnace exit temperature" as the initial inputs of the algorithm. Through reverse deduction, it ensures that the generated heating curve will theoretically meet the most critical metallurgical process requirements, fundamentally solving the problem of the disconnect between the target and the result in traditional methods.

[0099] Secondly, this method can generate a unique optimal heating curve in real time for steel billets of different sizes, steel grades, and initial temperatures, achieving refined heating with a "one billet, one strategy" approach, significantly improving process flexibility and adaptability to changing operating conditions. By introducing a "heating rate coefficient for each furnace section," this method can accurately utilize the heating characteristics of different furnace sections and rationally allocate the heating tasks for each section. For example, rapid heating can be achieved in the high-efficiency heating section, while focusing on temperature homogenization in the soaking section, thereby optimizing heating time and energy consumption while ensuring quality.

[0100] Furthermore, this invention provides a clear and automatically executable algorithm process that transforms the complex heating process into a solvable mathematical model, freeing it from reliance on human experience and providing core technical support for the unmanned and intelligent operation of heating furnaces.

[0101] In one embodiment, it also includes:

[0102] S901. Compare the billet surface temperature at the earliest discrete time point of the preheating section with the actual billet temperature entering the furnace. If the deviation between the two is greater than the preset deviation threshold, adjust the furnace gas temperature of the preheating section and the heating section, and re-obtain the reverse recursive formula for the billet surface temperature of the heating section and the reverse recursive formula for the billet surface temperature of the preheating section, and then regenerate the target heating curve of the billet.

[0103] S902. Iteratively regenerate the target heating curve of the billet until the deviation between the billet surface temperature at the earliest discrete time point of the preheating section and the actual furnace temperature of the billet is less than the preset deviation threshold.

[0104] In this embodiment, the deviation threshold can be set to 0.5 degrees Celsius.

[0105] The method in this embodiment compares the billet surface temperature at the earliest discrete time point of the preheating section with the actual billet temperature when it enters the furnace, and adjusts the furnace gas temperature of the preheating and heating sections to iteratively regenerate the target heating curve, thereby minimizing the occurrence of cold charging and hot charging of the billet when it enters the furnace.

[0106] In one embodiment, solving the heat transfer equation in reverse using the finite difference method includes:

[0107] S301. Divide the steel billet into M+1 equidistant spatial nodes from the center to the surface. The node numbers increase sequentially from the center to the surface, with the node number at the center being 0 and the node number at the surface being M. Set the time step between adjacent discrete time points to be... The spacing between spatial nodes is ;

[0108] S302. Obtain the reverse recursive formula for the center temperature of the billet and the reverse recursive formula for the surface temperature of the billet in the soaking zone based on the heat transfer equation.

[0109] S303. Based on the billet surface temperature at the time of exiting the furnace and the reverse recursive formula for the billet surface temperature in the soaking zone, the billet surface temperature at each discrete time point before the exiting time is calculated iteratively from the exiting time. Based on the billet center temperature at the time of exiting the furnace and the reverse recursive formula for the billet center temperature, the billet center temperature at each discrete time point before the exiting time is calculated iteratively from the exiting time. The termination condition of the iteration is: the temperature difference between the billet center temperature and the billet surface temperature is greater than the preset temperature difference threshold.

[0110] The reverse recursive formula for the center temperature of the steel billet is:

[0111] (7)

[0112] The reverse recursive formula for the surface temperature of the billet in the soaking zone is:

[0113] (8)

[0114] Because the temperature distribution along the thickness direction approximates a parabola in steady state or near-steady state, the temperature at the intermediate node when exiting the furnace can be obtained using quadratic function interpolation. The intermediate node refers to the spatial node between the 0th and Mth spatial nodes.

[0115] The derivation process of the reverse recursive formulas for the billet center temperature and the billet surface temperature in the soaking zone is as follows:

[0116] A. The above heat transfer equation can be simplified as follows:

[0117] (9)

[0118] B. Write it in explicit difference form:

[0119] (10)

[0120] C. After simplification, the temperature recursive formula for forward solution is obtained:

[0121] (11)

[0122] D. Rearrange equation (11) by transposing terms:

[0123] (12)

[0124] E. Due to the time step between adjacent discrete time points Small enough that the right side of equation (12) can be reduced to use Approximate substitution use Approximate substitution use By approximating and substituting, we obtain the core recursive formula for the reverse solution:

[0125] (13)

[0126] F. Reverse recursive formula for obtaining the billet center temperature based on the center boundary conditions: Due to symmetry, no heat flow passes through the billet center (j=0). In the difference scheme, a virtual node is set... To achieve this, we substitute it into the core recursive formula to obtain the reverse recursive formula for the billet center temperature:

[0127] (14)

[0128] G. Obtaining the reverse recursive formula for the billet surface temperature in the soaking zone based on surface boundary conditions: In the soaking zone, the furnace gas temperature is very close to the billet surface temperature, and the main phenomenon is internal heat equilibrium. Therefore, it can be approximated that the heat exchange between the surface and the outside is very weak, that is, the surface is approximately adiabatic. The inverse solution formula can be obtained as follows:

[0129] (15)

[0130] In equations (7) to (15), , Let these represent the temperatures of the 0th and Mth spatial nodes corresponding to the kth discrete time point, respectively. , , as well as Let represent the temperatures of the 0th, 1st, Mth, and (M-1th)th spatial nodes corresponding to the (k+1)th discrete time point, respectively; and let c represent the temperature value. The specific heat capacity of the steel billet at that time. The temperature value is indicated. and The average value of is the thermal conductivity of the steel billet; T represents the temperature of the steel billet, and x represents the distance from the center of the steel billet. , , Let represent the temperatures of the (j-1)th, jth, and (j+1)th spatial nodes corresponding to the kth discrete time point, respectively. This represents the temperature of the j-th spatial node corresponding to the (k+1)-th discrete time point.

[0131] In one embodiment, calculating the surface temperature of the billet at each discrete time point corresponding to the i-th heating furnace includes: based on the surface temperature that the billet needs to reach when entering the downstream furnace section of the i-th heating furnace, combined with the reverse recursive formula for the surface temperature of the billet in the i-th heating furnace, iteratively calculating the surface temperature of the billet at each discrete time point within a first preset time period before entering the downstream furnace section of the i-th heating furnace; the first preset time period is equal to the total residence time of the billet in the i-th heating furnace.

[0132] After obtaining the surface temperature that the billet needs to reach when entering the heating section, the surface temperature that the billet needs to reach when entering the heating section can be used as the initial condition. The surface temperature of the billet at discrete time points within a second preset time period before entering the heating section can be iteratively calculated using the reverse recursive formula of the billet surface temperature in the preheating section. The second preset time period is equal to the total residence time of the billet in the preheating section.

[0133] In one embodiment, the heat flux density from furnace gas to the billet surface within the i-th segment of the heating furnace is... The calculation expression is:

[0134] (16)

[0135] In the formula, This represents the temperature rise coefficient of the i-th segment of the heating furnace. Let represent the fourth power of the furnace gas temperature of the i-th segment of the heating furnace. This represents the temperature of the Mth spatial node corresponding to the (k+1)th discrete time point.

[0136] The derivation process of the reverse recursive formula for the surface temperature of the steel billet in the i-th segment of the heating furnace is as follows:

[0137] I. Establishing Control Volume

[0138] For an internal node j, its control volume is centered at node j, and its thickness is... A thin sheet, the area of ​​which is a unit area. For the central node, its control volume is from the centerline to x= At this location, the thickness is A thin sheet; for surface node M, its control volume is from to the surface The thickness is also A thin sheet. This surface controls volume on two sides: an inner side and an outer side.

[0139] The inner side is located At this location, it is adjacent to the control volume of the internal subsurface node M-1. The outer surface is the physical surface of the steel billet, located at... It comes into direct contact with the furnace gas environment.

[0140] II. Applying the law of conservation of energy.

[0141] In a tiny time interval Δt, the energy change follows this rule: the increase in internal energy of the control volume = heat entering the control volume - heat leaving the control volume.

[0142] 2.1 Calculate the increase in internal energy:

[0143] The change in the internal energy of a volume is manifested as a change in its temperature.

[0144] The volume of the controlled volume is: (17)

[0145] Control the mass of the container to (18)

[0146] During the time interval Δt, the temperature of the control volume changes from... Become The increase in internal energy is:

[0147] (19)

[0148] 2.2 Calculate the difference between the heat entering the control volume and the heat leaving the control volume.

[0149] Calculate the heat entering through the outer surface (physical surface): this heat comes from the radiation of the furnace gas. The heat flux density passing through a unit area per unit time is equal to the heat flux density from the furnace gas to the surface of the steel billet. The amount of heat entering through the outer surface during the time interval Δt is: (20)

[0150] Calculate the heat entering through the inner surface:

[0151] This heat originates from heat conduction within the subsurface layer inside the steel billet (the region where node M-1 is located). According to Fourier's law, the heat flux density conducted through the inner surface is... (twenty one)

[0152] Using the difference approximation of this derivative, at the inner surface x=(M-1 / 2)Δx, at the (k+1)th discrete time point, the temperature gradient can be approximated as:

[0153] (twenty two)

[0154] Therefore, the expression for the heat flux density conducted through the inner surface can be transformed into:

[0155] (twenty three)

[0156] During the time interval Δt, the amount of heat transferred in through the inner surface is:

[0157] (twenty four)

[0158] The total net inflow rate P is:

[0159] (25)

[0160] 2.3 Setting the rate of change of internal energy equal to the rate of net heat inflow, we get:

[0161] (26)

[0162] Equation (26) is an implicit equation for forward solution. To obtain an explicit inverse solution formula, we perform transformation and approximation. We move all terms at time k to the left and all terms at time k+1 to the right, and use the temperature at time k+1 to approximate the heat flux term:

[0163] (27)

[0164] After simplification, we can obtain the reverse recursive formula for the surface temperature of the steel billet in the heating section, as shown in equation (6).

[0165] In equations (17) to (27), A numerical value representing the thickness of a thin sheet. Let be the density of the steel billet, and c represent the temperature at which the value is... The specific heat capacity of the steel billet at that time. The temperature value is indicated. and The average value of the thermal conductivity of the steel billet is . , , Let represent the temperature of the Mth spatial node corresponding to the (k+1)th discrete time point, the temperature of the Mth spatial node corresponding to the kth discrete time point, and the temperature of the (m-1)th spatial node corresponding to the (k+1)th discrete time point, respectively.

[0166] The reverse recursive formula for the surface temperature of the billet in the preheating section is constructed in the same way as the reverse recursive formula for the surface temperature of the billet in the heating section, and will not be repeated here.

[0167] Example of a billet heating system for intermittent rolling:

[0168] The present invention also provides a heating system for intermittently rolled steel billets. For example... Figure 3 As shown, the intermittently rolled billet heating system includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement an intermittently rolled billet heating method according to the present invention.

[0169] The intermittently rolled billet heating system also includes other components well known to those skilled in the art, such as communication buses and communication interfaces. Their setup and functions are known in the art and will not be described in detail here.

[0170] While this specification has shown and described numerous embodiments of the invention, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of this invention.

Claims

1. A method for heating a billet for interval rolling, characterized by, The method comprises the following steps: calculating the remaining heating time of the current billet to the outlet of the current furnace section, and the remaining heating time of the current billet to the outlet of each downstream furnace section, thereby obtaining the remaining heating time of the current billet in the current furnace section and the remaining heating time of the current billet in each downstream furnace section; calculating the required furnace temperature of the current furnace section according to the remaining heating time of the current billet in the current furnace section and the target outlet temperature of the current furnace section, and calculating the required furnace temperature of each downstream furnace section when the current billet reaches the corresponding furnace section according to the remaining heating time of the billet in each downstream furnace section and the target outlet temperature of the corresponding furnace section; heating the billet according to the required furnace temperature of each furnace section calculated in combination with the preset target temperature rising curve; wherein the calculation of the remaining heating time of the current billet to the outlet of a certain furnace section comprises the following steps: acquire the distance L of the current billet to the outlet of the furnace section, acquire the number N of billets in the range whose distance to the outlet is less than or equal to L; calculate the remaining heating time of the current billet to the outlet of the furnace section according to the number N of billets in combination with the tapping rhythm The calculation expression is: ； In the formula, represents the remaining time to the delivery of the steel billet, represents the delivery rhythm of the kth steel billet, k represents the serial number of the steel billet, the serial number of the steel billet to be delivered is 1, and the serial number of the steel billet increases by 1 in the direction away from the outlet of the heating furnace starting from the steel billet to be delivered; and the method for generating the target temperature rising curve comprises: calculating the heat flux density from the furnace gas to the surface of the billet in the heating section according to the temperature rising amount coefficient of the heating section, and calculating the heat flux density from the furnace gas to the surface of the billet in the preheating section according to the temperature rising amount coefficient of the preheating section; establishing a heat transfer equation, setting the initial condition as the surface temperature of the billet at the outlet being equal to the target temperature at the outlet, and the center temperature of the billet at the outlet being equal to the difference between the target temperature at the outlet and the target soaking degree, and setting the termination condition as the temperature difference between the center temperature of the billet and the surface temperature of the billet being greater than a preset temperature difference threshold; and inversely solving the heat transfer equation by using the finite difference method, thereby obtaining the surface temperature and the center temperature of the billet at each discrete time point corresponding to the soaking section, and the surface temperature that the billet needs to reach when entering the soaking section; obtaining the surface temperature inverse recursion formula of the billet in the heating section according to the heat flux density from the furnace gas to the surface of the billet, and iteratively calculating the surface temperature of the billet at each discrete time point corresponding to the heating section in combination with the surface temperature that the billet needs to reach when entering the heating section; obtaining the surface temperature inverse recursion formula of the billet in the preheating section according to the heat flux density from the furnace gas to the surface of the billet, and iteratively calculating the surface temperature of the billet at each discrete time point corresponding to the preheating section in combination with the surface temperature that the billet needs to reach when entering the heating section; generating the target temperature rising curve of the billet according to the surface temperature of the billet at each discrete time point corresponding to the preheating section, the heating section and the soaking section; the calculation expression of the surface temperature inverse recursion formula of the billet in the i-th heating furnace is: ； In the formula, This represents the temperature of the M-th spatial node corresponding to the k-th discrete time point. and Let M and M-1 represent the temperatures of the M-th spatial node corresponding to the (k+1)-th discrete time point, respectively. This represents the heat flux density from the furnace gas to the surface of the steel billet within the i-th segment of the heating furnace. A numerical value representing the thickness of a thin sheet. Let be the density of the steel billet, and c represent the temperature at which the value is... The specific heat capacity of the steel billet at that time. The temperature value is indicated. and The average value of the thermal conductivity of the steel billet is . This indicates a preset time period.

2. The method of heating a billet for interval rolling according to claim 1, characterized by, the calculation expression of the remaining time of the billet at the outlet is: ； In the formula, represents the scheduled time of the steel billet to be discharged, represents the current time.

3. The method of the patent claim 1, characterized in that, obtaining the remaining heating time of the current billet in the k-th downstream furnace section comprises: subtracting the remaining heating time of the current billet to the outlet of the k-1-th downstream furnace section from the remaining heating time of the current billet to the outlet of the k-th downstream furnace section, thereby obtaining the remaining heating time of the current billet in the k-th downstream furnace section.

4. The method of the patent claim 1, characterized in that, The calculation of the required furnace temperature of the current furnace section comprises: According to the specific heat capacity of the billet and the mass m, the heat Q1 to be absorbed by the billet in the section is calculated, the calculation expression being as follows: ； calculating the heat transferred by the current furnace zone hearth to the billet the calculation expression is ； Let , so that the required furnace temperature for the segment is obtained ; in the above formulae, represents the target outlet temperature of the current furnace section, represents the current temperature of the billet, is the average temperature of the current billet in the current furnace section, K is the heat transfer coefficient, is the remaining heating time of the current billet in the current furnace section.

5. The method of the patent claim 1, characterized in that, The calculation of the required furnace temperature of each downstream furnace section when the current billet reaches the corresponding furnace section comprises: According to the specific heat capacity of the billet and the mass m, the heat Q3 to be absorbed by the billet in the downstream furnace section is calculated, the calculation expression being as follows: ； calculating the heat transferred by the downstream furnace section to the billet the calculation expression is: ； Let , so that the required furnace temperature for the segment is obtained ; in the above equations, represents the outlet target temperature of the downstream furnace section, represents the upstream furnace section outlet target temperature of the downstream furnace section, represents the average temperature of the billets in the downstream furnace section, is the remaining heating time of the current billet in the downstream furnace section.

6. The method of the patent claim 1, characterized in that, It also includes real-time feedback adjustment, which comprises: monitoring the temperature of the billet in real time through the in-furnace temperature detection device, adjusting the furnace temperature according to the target temperature of each section, increasing the furnace temperature of the section when the temperature of the billet is lower than the target temperature, and vice versa.

7. The method of the patent claim 1, characterized in that, Solving the heat transfer equation in reverse direction by finite difference method comprises: The steel billet is divided into M+1 equidistant space nodes from the center to the surface, and the serial numbers of the space nodes increase sequentially from the center to the surface, wherein the serial number of the space node located at the center is 0, and the serial number of the space node located at the surface is M, the time step between adjacent discrete time points is set as ; and the spacing between the space nodes is ; Obtaining a reverse recursion formula of the billet center temperature and a reverse recursion formula of the billet surface temperature in the soaking section according to the heat transfer equation; According to the billet surface temperature at the time of tapping and the reverse recursion formula of the billet surface temperature in the soaking section, the billet surface temperatures at each discrete time point before the time of tapping are iteratively calculated from the time of tapping, and according to the billet center temperature at the time of tapping and the reverse recursion formula of the billet center temperature, the billet center temperatures at each discrete time point before the time of tapping are iteratively calculated from the time of tapping; the termination condition of iteration is that the temperature difference between the billet center temperature and the billet surface temperature is greater than a preset temperature difference threshold; The reverse recursion formula of the billet center temperature is: ； The reverse recursion formula of the billet surface temperature in the soaking section is: ； In the above two formulas, , respectively represent the temperature of the 0th spatial node and the temperature of the Mth spatial node corresponding to the kth discrete time point, , , and respectively represent the temperature of the 0th spatial node, the temperature of the 1st spatial node, the temperature of the Mth spatial node and the temperature of the M-1th spatial node corresponding to the k+1th discrete time point; c represents the specific heat capacity of the billet when the temperature value is , represents the thermal conductivity of the billet when the temperature value is and .

8. The method of the patent claim 7, characterized in that, The billet surface temperatures at each discrete time point corresponding to the i-th heating furnace are calculated by: According to the billet surface temperature to be reached when entering the downstream furnace section of the i-th heating furnace and the reverse recursion formula of the billet surface temperature in the i-th heating furnace, the billet surface temperatures at each discrete time point within a first preset time length before the time of entering the downstream furnace section of the i-th heating furnace are iteratively calculated from the time of entering the downstream furnace section of the i-th heating furnace; the first preset time length is equal to the total residence time of the billet in the i-th heating furnace.

9. An intermediate rolled billet heating system comprising a processor and a memory, the memory storing computer program instructions, wherein, When the computer program instructions are executed by the processor, the method for heating the billet in the interval rolling is realized. The computer program product comprises a computer readable storage medium storing computer program instructions, and the computer program instructions are executed by the processor to realize the method for heating the billet in the interval rolling.

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