Prediction method and assessment method

Abstract

The purpose of the present disclosure is to provide a method for predicting changes over time in the surface pressure of a wound coil, taking into account the progression of transformation. A prediction method according to one embodiment of the present disclosure is a method for predicting changes in the surface pressure of a coil formed by winding a hot-rolled sheet that has been hot-rolled, wherein the prediction method includes: a first calculation step in which the initial stress state of the coil immediately after winding is calculated using the shape of the hot-rolled sheet and operating conditions that include cooling conditions and winding conditions; a second calculation step in which changes in the stress state within the coil based on volume changes in the coil are calculated using a temperature distribution and a transformation ratio of the coil over time after winding; and a step in which changes over time in the surface pressure of the coil are predicted using the initial stress state calculated in the first calculation step and the changes in the stress state within the coil calculated in the second calculation step.

Description

Prediction and Judgment Methods

[0001] The present disclosure relates to prediction and determination methods.

[0002] The hot-rolled sheet is cooled in a cooling zone such as a hot run table and wound into a coil. The wound coil may be deformed during storage, cooling, etc., in a storage location such as a coil yard. If the amount of deformation of the coil is large, there is a high risk of an increase in surface defects in the next process. Furthermore, if the amount of deformation of the coil is large, it may be necessary to discard the coil.

[0003] Japanese Patent Application Publication No. 6-277753

[0004] Development of a simulator for predicting the shape of a single ring after hot rolling, Nippon Steel Technical Report, No. 379 (2003), pp. 43-48

[0005] The present inventors have found that if it is possible to predict the change in contact pressure over time for a coil after winding, taking into account the progression of transformation, it is possible to predict whether or not the coil will deform during slow cooling, etc.

[0006] Patent Document 1 also describes that in order to suppress deformation of the coils when stacked in multiple layers, the coil winding tension is determined based on the thickness and width of the strip and the outer diameter of the coil after winding.

[0007] However, the method described in Patent Document 1 makes it impossible to predict the change over time in the contact pressure of the coil around which the hot-rolled strip is wound.

[0008] Furthermore, Non-Patent Document 1 describes that the flatness of the plate after cooling the coil is determined by analyzing heat transfer, the progress of transformation, and the stress distribution within the plate through cooling on the hot run table and the subsequent cooling of the coil.

[0009] The technique described in Non-Patent Document 1 determines the flatness of a plate by calculating the stress in the longitudinal direction of the plate. However, this technique does not allow for direct calculation of the surface pressure of the coil, making it difficult to determine the deformation of the coil.

[0010] The present disclosure has been made in light of the above circumstances, and aims to provide a method for predicting changes in contact pressure over time for a coil after winding, taking into account the progression of transformation.

[0011] A prediction method according to one aspect of the present disclosure is a method for predicting changes in surface pressure of a coil around which a hot-rolled hot-rolled sheet has been wound, and includes: a first calculation step of calculating an initial stress state immediately after winding the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and winding conditions; a second calculation step of calculating a change in the stress state within the coil based on a volume change of the coil using the temperature distribution and transformation rate of the coil over time after winding; and a step of predicting changes in surface pressure of the coil over time using the initial stress state calculated in the first calculation step and the change in the stress state within the coil calculated in the second calculation step.

[0012] A prediction method according to one aspect of the present disclosure can predict the change in contact pressure over time for a wound coil, taking into account the progression of transformation.

[0013] FIG. 1 is a flow diagram showing a prediction method according to an embodiment of the present disclosure. FIG. 2 is a graph showing an example of the relationship between the heat pattern of a hot-rolled sheet and the transformation rate in a first calculation step of the prediction method of FIG. 1 . FIG. 3 is a graph showing an example of an initial stress state in the first calculation step of the prediction method of FIG. 1 . FIG. 4 is a graph showing an example of the relationship between the temperature distribution of a coil over time and the transformation rate in a second calculation step of the prediction method of FIG. 1 . FIG. 5 is a graph showing an example of a stress distribution within a coil in the second calculation step of the prediction method of FIG. 1 . FIG. 6 is a flow diagram showing a determination method according to an embodiment of the present disclosure. FIG. 7 is a graph showing an example of a stress distribution within a coil in the second calculation step of Example 1. FIG. 8 is a graph showing an example of a stress distribution within a coil in the second calculation step of Example 1. FIG. 9 is a graph showing an example of a change over time in a value obtained by integrating the surface pressure of a coil in the radial direction in Example 2. FIG. 10 is a graph showing an example of a change over time in a value obtained by integrating the surface pressure of a coil in the radial direction in Example 2.

[0014] [Description of Embodiments of the Present Disclosure] First, embodiments of the present disclosure will be listed and described.

[0015] (1) A prediction method according to one aspect of the present disclosure is a method for predicting a change in surface pressure of a coil around which a hot-rolled hot-rolled sheet has been wound, and includes: a first calculation step of calculating an initial stress state immediately after winding the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and winding conditions; a second calculation step of calculating a change in the stress state within the coil based on a volume change of the coil using the temperature distribution and transformation rate of the coil over time after winding; and a step of predicting a change in surface pressure of the coil over time using the initial stress state calculated in the first calculation step and the change in the stress state within the coil calculated in the second calculation step.

[0016] This prediction method predicts the change in surface pressure of a coil over time using the initial stress state calculated in the first calculation step and the change in the stress state within the coil calculated in the second calculation step, and therefore can appropriately predict the change in surface pressure over time for a coil made by winding a hot-rolled sheet, taking into account the progression of transformation.

[0017] (2) In the above (1), the shape of the hot-rolled sheet may include the thickness and width of the hot-rolled sheet, the cooling conditions may include a heat pattern in a cooling zone before coiling the hot-rolled sheet, and the coiling conditions may include the temperature and coiling tension of the coil during coiling. According to this aspect, it is possible to easily and reliably predict changes in the surface pressure of the coil over time.

[0018] (3) In the above (1) or (2), the temperature distribution over time of the coil after winding may be calculated using a two-dimensional axisymmetric heat conduction equation in which a radiation boundary condition is used as a boundary condition and different emissivities are assigned to the outer periphery, the inner periphery, and the region between the outer periphery and the inner periphery of the coil. According to this aspect, it is possible to more appropriately predict changes in the stress state in the coil based on changes in the volume of the coil after winding.

[0019] (4) In any of the above (1) to (3), the change in the stress state in the coil may be obtained by repeatedly calculating the stress distribution in the coil after a short time has elapsed. According to this aspect, it is possible to more appropriately predict the change in the surface pressure of the coil over time.

[0020] (5) A determination method according to another aspect of the present disclosure is a method for determining deformation of a coil formed by winding a hot-rolled hot-rolled sheet, and includes: a first calculation step of calculating an initial stress state immediately after winding the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and winding conditions; a second calculation step of calculating a change in the stress state within the coil based on a volume change of the coil using the temperature distribution and transformation rate of the coil over time after winding; and a step of determining whether or not the coil is deformed using the initial stress state calculated in the first calculation step and the change in the stress state within the coil calculated in the second calculation step.

[0021] This determination method determines whether or not the coil is deformed using the initial stress state calculated in the first calculation process and the change in the stress state within the coil calculated in the second calculation process, and therefore can appropriately determine whether or not the coil is deformed.

[0022] (6) In the above (5), it is preferable to determine that the coil is deformed when the surface pressure of the coil over time becomes equal to or less than a predetermined value in the determining step. According to this aspect, it is possible to more easily determine the deformation of the coil.

[0023] (7) In the above (5), the determining step may include calculating a value obtained by integrating the surface pressure of the coil in the radial direction over time based on the surface pressure of the coil over time, and determining that the coil is deformed when this value is equal to or less than a predetermined value. According to this aspect, deformation of the coil can be more easily determined.

[0024] In the present disclosure, the term "short time" does not refer to a specific time, but may be, for example, a significant time during which a change in surface pressure occurs in the coil. For example, the short time may be 10 seconds or less, may be in the range of 0.1 seconds to 10 seconds, may be in the range of 0.1 seconds to 1 second, or may be in the range of 0.1 seconds to 0.6 seconds.

[0025] [Details of Embodiments of the Present Disclosure] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings as appropriate.

[0026] [Prediction Method] A prediction method according to one embodiment of the present disclosure is a method for predicting a change in contact pressure of a coil obtained by coiling a hot-rolled sheet. As shown in Fig. 1 , the prediction method includes a first calculation step S1 of calculating an initial stress state immediately after coiling the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and coiling conditions, a second calculation step S2 of calculating a change in the stress state in the coil based on a volume change of the coil using a time-dependent temperature distribution and transformation rate of the coil after coiling, and a step (prediction step S3) of predicting a change in the contact pressure of the coil over time using the initial stress state calculated in the first calculation step S1 and the change in the stress state in the coil calculated in the second calculation step S2.

[0027] This prediction method predicts the change in surface pressure of a coil over time using the initial stress state calculated in the first calculation step S1 and the change in the stress state within the coil calculated in the second calculation step S2, so it can appropriately predict the change in surface pressure over time for a coil made by winding a hot-rolled sheet, taking into account the progress of transformation.

[0028] The prediction method may be performed for each type of hot-rolled sheet, including, for example, each steel grade. By performing the prediction method for each type of hot-rolled sheet, it is possible to predict in advance the change in contact pressure over time of a coil wound with various types of hot-rolled sheet. As a result, it is possible to determine in advance how to handle the coil for each type of hot-rolled sheet.

[0029] (First Calculation Step) The first calculation step S1 includes, for example, a step of acquiring the operating conditions (first step), a step of calculating the progression of transformation of the hot-rolled sheet in a cooling zone such as a hot run table through which the hot-rolled sheet passes after finish rolling (second step), a step of determining the transformation rate immediately after completion of cooling in the cooling zone and the coil temperature at the time of coiling as initial values ​​of the transformation rate and the coil temperature, respectively (third step), and a step of calculating the initial stress state immediately after coiling of the coil from the coiling conditions of the coil and the physical properties of the steel type at the temperature at the time of coiling (fourth step). Note that the first to fourth steps do not necessarily have to be performed in this order. For example, it is also possible to perform part of the first step after the second step.

[0030] In the first step, the operating conditions are acquired. The shape of the hot-rolled sheet acquired in the first step includes, for example, the thickness and width of the hot-rolled sheet. The cooling conditions acquired in the first step include, for example, the heat pattern in the cooling zone before coiling the hot-rolled sheet. The coiling conditions acquired in the first step include, for example, the temperature and coiling tension of the coil during coiling. The various operating conditions may be actual measured values, standard values ​​defined based on the steel type, etc., or values ​​calculated by calculation. By including the above information as the operating conditions, the prediction method can easily and reliably predict changes in the contact pressure of the coil over time.

[0031] In the second step, the progress of the transformation of the hot-rolled sheet in the cooling zone is calculated using, for example, a TTT curve (isothermal transformation curve) and a CCT curve (continuous cooling transformation curve). In the second step, for example, the shape of the TTT curve is assumed, and a CCT curve is calculated by the summation rule, and the progress of the transformation is calculated using the equation for diffusion during isothermal transformation expressed by the following equation 1.

[0032] In the above formula 1, t ｉ : time, Δt:t ｉ＋１ -t ｉ , T ｉ :Temperature, T ｉ＋１ : Temperature when moved by Δt from time ti, X ｉ :Temperature T ｉ and the transformation rate at time ti, ΔX: temperature T ｉ＋１ At time t ＊ where n is the number of data points (number of divisions), and k is a function that depends only on the transformation temperature.

[0033] In the third step, the transformation rate immediately after the completion of cooling in the cooling zone is determined based on the transformation rate calculated in the second step using the above formula 1. Figure 2 shows an example of the relationship between the heat pattern of a hot-rolled sheet and the transformation rate. In Figure 2, cooling in the cooling zone is completed 20 seconds after the start of cooling. In the third step, the transformation rate at 20 seconds in Figure 2 is determined as the transformation rate immediately after the completion of cooling in the cooling zone.

[0034] In the third step, the coil temperature during winding is determined as the initial value of the coil temperature.

[0035] In the fourth step, an initial stress state immediately after winding of the coil is calculated. In the fourth step, the surface pressure at a plurality of positions in the radial direction of the coil may be calculated as the initial stress state. Figure 3 shows an example of the relationship between the radial position and the surface pressure immediately after winding of the coil. As shown in Figure 3, immediately after winding, the surface pressure is greater than 0 at all positions in the radial direction.

[0036] In the fourth step, the initial stress state immediately after winding the coil is calculated using, for example, the following equation 2.

[0037] In the above formula 2, p represents the surface pressure at the radial position r, a represents the equivalent inner radius of the coil, and b represents the outer diameter of the coil. σ represents the winding tension, which is calculated as σ = T (total tension) / (thickness t of the hot-rolled sheet × width B of the hot-rolled sheet). The coil length L, outer diameter b of the coil, and number of turns n of the coil required for calculating the surface pressure can be determined as follows: L = coil weight W / density of the hot-rolled sheet ρ × thickness t of the hot-rolled sheet × width B of the hot-rolled sheet, b = ((L × t) / π) + a ２ ) ０．５ , n=(ba) / t

[0038] (Second calculation step) The second calculation step S2 includes, for example, a step of calculating the temperature distribution inside the coil from after winding until the end of slow cooling (fifth step), a step of calculating the transformation rate of each part inside the coil after a small amount of time has elapsed (sixth step), a step of calculating the stress distribution inside the coil after a small amount of time has elapsed from the temperature distribution calculated in the fifth step and the change in the transformation rate calculated in the sixth step (seventh step), and a step of repeating the fifth to seventh steps until the coil is cooled to the target temperature (eighth step).

[0039] In the fifth step, it is preferable to calculate the temperature distribution over time of the coil after winding using a two-dimensional, axisymmetric heat conduction equation in which a radiation boundary condition is used as the boundary condition and different emissivities are assigned to the outer periphery, inner periphery, and the region between the outer periphery and inner periphery (also referred to as the "center of winding thickness") of the coil. In the coil, the outer periphery is most easily cooled, and the inner periphery is less easily cooled than the outer periphery but more easily cooled than the center of winding thickness. Therefore, by calculating the temperature distribution over time of the coil after winding using the heat conduction equation, it is possible to more appropriately predict changes in the stress state within the coil based on changes in the volume of the coil after winding.

[0040] The fifth to seventh steps can be performed by calculating the following equations 3 and 4, taking into consideration the calculation result of the above equation 1. In the fifth to seventh steps, it is preferable to perform calculations for a plurality of radial positions r of the coil.

[0041] In the above formulas 3 and 4, p is the surface pressure, Δp is the change in surface pressure after winding, a is the equivalent inner radius of the coil, b is the outer diameter of the coil, T(r) is the temperature at the radial position r, β(T) is the coefficient of linear expansion at the temperature T, E is Young's modulus, and ν is Poisson's ratio.

[0042] As shown in the above formula 4, in the fifth to seventh steps, the stress distribution in the coil is calculated using the linear expansion coefficient as the volume change of the coil, and thus the prediction method can appropriately predict the change in the surface pressure of the coil over time.

[0043] In the sixth step, it is preferable to determine the progression of the transformation by calculating the latency of the transformation from the temperature distribution (heat pattern) over time of the coil and the transformation curves (the above-mentioned TTT curve and CCT curve) obtained in the fifth step. According to this aspect, the transformation rate of each part in the coil after a short time has elapsed can be more appropriately determined.

[0044] In the eighth step, as described above, the fifth to seventh steps are repeated until the coil is cooled to the target temperature. That is, in the second calculation step S2, it is preferable to obtain the change in the stress state in the coil by repeatedly calculating the stress distribution in the coil after a short time has elapsed. According to this aspect, it is possible to more appropriately predict the change in the surface pressure of the coil over time.

[0045] Figure 4 shows an example of the calculation results for the temperature and transformation progress at various parts of the coil during slow cooling. Note that the transformation rate at time 0 in Figure 4 is the transformation rate immediately after the end of cooling in the cooling zone determined in the third step. As shown in Figure 4, the cooling rate decreases in the order of the outer periphery of the coil, the inner periphery of the coil, and the center of the winding thickness. Also, as shown in Figure 4, transformation completes earliest at the outer periphery of the coil, followed by the inner periphery and the center of the winding thickness.

[0046] Figure 5 shows an example of the stress distribution inside the coil calculated in the seventh step. Figure 5 shows the surface pressure inside the coil calculated using volume changes due to heat and transformation. As shown in Figure 5, the surface pressure inside the coil is smaller at the inner and outer peripheries of the coil.

[0047] (Prediction step) In the prediction step S3, a change in the surface pressure of the coil over time is predicted based on the calculation results in the first calculation step S1 and the second calculation step S2. In the prediction step S3, a change in the surface pressure over time for a coil of the same type as the coil actually calculated may be predicted based on the calculation results in the first calculation step S1 and the second calculation step S2.

[0048] [Determination Method] Next, a method for determining deformation of a coil obtained by winding a hot-rolled sheet will be described with reference to Fig. 6. The determination method includes a first calculation step S1 for calculating an initial stress state immediately after coiling the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and coiling conditions; a second calculation step S2 for calculating a change in the stress state in the coil based on a volume change of the coil using the temperature distribution and transformation rate of the coil over time after coiling; and a step (determination step S4) for determining whether or not the coil is deformed using the initial stress state calculated in the first calculation step S1 and the change in the stress state in the coil calculated in the second calculation step S2. The first calculation step S1 and the second calculation step S2 are similar to the first calculation step S1 and the second calculation step S2 in the prediction method of Fig. 1, and therefore description thereof will be omitted.

[0049] This determination method determines whether or not the coil is deformed using the initial stress state calculated in the first calculation step S1 and the change in the stress state within the coil calculated in the second calculation step S2, so that it can appropriately determine whether or not the coil is deformed.

[0050] (Determination Step) In the determination step S4, it may be determined that the coil is deformed if the surface pressure of the coil over time becomes equal to or less than a predetermined value. The predetermined value may be, for example, a value based on the stress distribution in the coil immediately after winding, or may be 0. For example, in the determination step S4, it may be determined that the coil is deformed if there is a portion where the surface pressure is 0 in the stress distribution in the coil after winding calculated in the second calculation step S2 (see FIG. 5). According to this aspect, it is possible to more easily determine the deformation of the coil.

[0051] Furthermore, in the determination step S4, a value W obtained by integrating the surface pressure of the coil in the radial direction over time based on the surface pressure of the coil over time may be determined, and it may be determined that the coil is deformed when this value W is equal to or less than a predetermined value. The value W obtained by integrating the surface pressure in the radial direction can be calculated, for example, using the following equation 5 from the surface pressure p obtained by the above equation 4.

[0052]

[0053] The predetermined value may be a value W obtained by integrating the surface pressure in the radial direction immediately after winding. In the determination step S4, it may be determined that the coil is deformed, for example, if the value W obtained by integrating the surface pressure in the radial direction becomes smaller over time than it was immediately after winding. According to this aspect, it is possible to more easily determine the deformation of the coil.

[0054] [Other Embodiments] The above-described embodiments do not limit the configuration of the present invention. Therefore, the above-described embodiments may include omissions, substitutions, or additions of components based on the description in this specification and common general technical knowledge, and all of these should be construed as falling within the scope of the present invention.

[0055] For example, in this determination method, it is also possible to perform the determination step S4 after performing the prediction step S3 in the prediction method. This aspect also makes it possible to appropriately determine whether or not the coil is deformed.

[0056] The present disclosure will be described in detail below based on examples, but the present disclosure should not be construed as being limited based on the description of these examples.

[0057] Example 1 The following procedure was used to predict the change in contact pressure of a coil formed by winding a hot-rolled sheet, and to determine whether or not the coil was deformed.

[0058] (First calculation step) The operating conditions, including the shape of the hot-rolled sheet, the cooling conditions, and the coiling conditions, were obtained, the shape of the TTT curve was assumed, the CCT curve was calculated by the summation rule, and the progress of transformation was determined by the diffusion equation for isothermal transformation expressed by the above-mentioned Equation 1. Next, the transformation rate immediately after completion of cooling calculated by the above-mentioned Equation 1 and the temperature of the coil during coiling were determined as initial values. Furthermore, the initial stress state of the coil immediately after coiling was calculated by the above-mentioned Equation 2.

[0059] (Second Calculation Step) Taking into consideration the calculation result of the above-mentioned formula 1, the changes in the stress state in the coil after winding were calculated for a plurality of radial positions r of the coil using the above-mentioned formulas 3 and 4.

[0060] (Prediction Step) From the calculation results in the first calculation step and the second calculation step, the change in surface pressure over time for a coil of the same type as the coil actually calculated was predicted.

[0061] (Determination step) The presence or absence of deformation of the coil was determined based on the change in the surface pressure of the coil over time. Figures 7 and 8 show an example of the stress distribution in the coil used in the determination step. In Figure 7, the surface pressure is maintained above 0 from the inner periphery to the outer periphery of the coil, and it can be determined that the coil is not deformed. On the other hand, in Figure 8, there is a portion where the surface pressure is 0, and it can be determined that the coil is deformed in this portion.

[0062] Example 2 After the first calculation step and the second calculation step in Example 1, a determination step was performed in the following manner.

[0063] (Determination Step) Using the surface pressure obtained by the above-mentioned Equation 4, the value W obtained by integrating the surface pressure of the coil in the radial direction was calculated using the above-mentioned Equation 5. Figures 9 and 10 show an example of the change over time in the value W obtained by integrating the surface pressure of the coil in the radial direction, calculated by the above-mentioned Equation 5. In Figure 9, the value W obtained by integrating the surface pressure in the radial direction does not become smaller over time than it was immediately after winding, so it can be determined that the coil is not deformed. On the other hand, in Figure 10, there is a time period in which the value W obtained by integrating the surface pressure in the radial direction is smaller than it was immediately after winding, so it can be determined that the coil is deformed.

Claims

1. A method for predicting changes in surface pressure of a coil formed by winding a hot-rolled sheet, comprising: a first calculation step of calculating an initial stress state immediately after winding the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and winding conditions; a second calculation step of calculating changes in the stress state within the coil based on volume changes of the coil using the temperature distribution and transformation rate of the coil over time after winding; and a step of predicting changes in surface pressure of the coil over time using the initial stress state calculated in the first calculation step and the changes in the stress state within the coil calculated in the second calculation step.

2. The prediction method according to claim 1, wherein the shape of the hot-rolled sheet includes the thickness and width of the hot-rolled sheet, the cooling conditions include a heat pattern in a cooling zone before coiling the hot-rolled sheet, and the coiling conditions include the temperature and coiling tension of the coil during coiling.

3. A prediction method according to claim 1, in which the temperature distribution over time of the coil after winding is calculated using a two-dimensional axisymmetric heat conduction equation, in which a radiation boundary condition is used as the boundary condition and different emissivities are given to the outer periphery, inner periphery, and region between the outer periphery and inner periphery of the coil.

4. A prediction method according to claim 1, wherein the change in the stress state within the coil is determined by repeatedly calculating the stress distribution within the coil after a short time has elapsed.

5. A method for determining deformation of a coil formed by winding a hot-rolled sheet, comprising: a first calculation step of calculating an initial stress state immediately after winding the coil using operating conditions including the shape of the hot-rolled sheet, cooling conditions, and winding conditions; a second calculation step of calculating a change in the stress state within the coil based on a volume change of the coil using the temperature distribution and transformation rate of the coil over time after winding; and a step of determining whether or not the coil is deformed using the initial stress state calculated in the first calculation step and the change in the stress state within the coil calculated in the second calculation step.

6. The method according to claim 5, wherein in the step of determining, it is determined that the coil is deformed if the surface pressure of the coil over time becomes equal to or less than a predetermined value.

7. A method for determining the presence or absence of deformation of the coil as described in claim 5, wherein the determining step involves determining a value obtained by integrating the surface pressure of the coil in the radial direction over time based on the surface pressure of the coil over time, and determining that the coil is deformed if this value is equal to or less than a predetermined value.

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