The present invention relates to an internal oxide layer thickness estimation device, an internal oxide layer thickness estimation method, and a program. This application claims priority based on Japanese Patent Application No. 2020-185639 filed on Nov. 6, 2020, the content of which is incorporated herein by reference.
In many cases, hot-rolled steel sheets manufactured by hot rolling cast pieces are coiled and then cooled. In this cooling step, an internal oxide layer is formed in a base metal portion immediately below a scale layer. The internal oxide layer is a layer in which metal oxides are dispersed at grain boundaries and in crystal grains. The metal oxide is mainly composed of an oxide of an element (for example, Si, Mn, Al, Cr, or the like) that is less noble than iron. The scale layer is relatively easily removed by a pickling step after the cooling process. However, it is difficult to remove the internal oxide layer in the pickling step. Therefore, there is a problem that the excessive formation of the internal oxide layer significantly reduces the speed of the pickling step. In a steel material, such as high tensile strength steel (high-tensile steel), containing a large number of elements that are less noble than iron, the internal oxide layer is likely to be formed. Therefore, this problem is particularly remarkable. Therefore, a method for controlling an appropriate thickness of the internal oxide layer is required.
It is widely accepted that the thickness of the scale layer follows a so-called parabolic law. This is based on the assumption that the thickness of the scale layer is proportional to the square root of time. Meanwhile, findings for the thickness of the internal oxide layer have been described in Non-Patent Document 1 and Patent Document 1. However, it was not possible to accurately estimate the thickness of the internal oxide layer on the basis of these findings.
Specifically, Non-Patent Document 1 discloses that there is a temperature (internal oxidation starting temperature Tcr) at which the generation of an internal oxide layer substantially starts, and that the internal oxide layer is not formed in a temperature range equal to or lower than the internal oxidation starting temperature. In addition, the thickness of the internal oxide layer is treated as being proportional to time. However, the thickness of the internal oxide layer is not simply proportional to time, which will be described in detail below.
Patent Document 1 discloses Expression A in which the thickness of the internal oxide layer is proportional to the square root of a value obtained by integrating an Arrhenius growth rate over time. However, the presence of the internal oxidation starting temperature is not reflected in Expression A, and the integration is performed until the temperature falls below the internal oxidation starting temperature to reach room temperature. Therefore, there is also a problem in the accuracy of estimation.
The invention has been made in view of the above problems, and an object of the invention is to provide an internal oxide layer thickness estimation device, an internal oxide layer thickness estimation method, and a program that can estimate a thickness of an internal oxide layer in a hot-rolled steel sheet with higher accuracy.
In order to solve the above-described problems, according to an aspect of the invention, there is provided an internal oxide layer thickness estimation device that estimates a thickness of an internal oxide layer formed in a hot-rolled steel sheet. The internal oxide layer thickness estimation device includes: a first temperature definition unit that defines a temperature of a portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet; a second temperature definition unit that defines an internal oxidation starting temperature at which internal oxidation of the hot-rolled steel sheet starts; a cumulative temperature calculation unit that calculates a cumulative temperature on the basis of the temperatures defined by the first temperature definition unit and the second temperature definition unit and a predetermined period of time from an estimation start time at which estimation of the thickness of the internal oxide layer is started to an estimation evaluation time; a first correlation expression derivation unit that derives a first correlation expression indicating a correlation between the cumulative temperature calculated by the cumulative temperature calculation unit and an estimated value of the thickness of the internal oxide layer; and an internal oxide layer thickness estimation unit that estimates the thickness of the internal oxide layer on the basis of the first correlation expression.
Here, the internal oxide layer may be formed when the hot-rolled steel sheet is cooled in a coiled state.
In addition, the cumulative temperature calculation unit may calculate the cumulative temperature on the basis of the following Expression (1).
S
T=∫t0t1(T−Tcr)dt (1)
In Expression (1), ST is the cumulative temperature, T is the temperature of the portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet, Tcr is the internal oxidation starting temperature at which the internal oxidation of the hot-rolled steel sheet starts, t0 is the estimation start time when the estimation of the thickness of the internal oxide layer is started, t1 is the estimation evaluation time, and T−Tcr is 0 in an integration interval where T−Tcr is equal to or less than 0.
In addition, the first correlation expression may be represented by any one or a combination of two or more of the following Expressions (2) to (4).
H=αS
T
+H
0 (2)
H=βS
T
1/2
+H
0 (3)
H=γS
T
+δS
T
2
+H
0 (0≤ST≤−γ/(2δ): a local maximum value of the thickness of the internal oxide layer at this time is Hm)
H=φ{S
T+γ/(2δ)}+Hm(ST>−γ/(2δ)) (4)
In Expressions (2) to (4), H is the estimated value of the thickness of the internal oxide layer, α, β, γ, φ, and δ are constants, H0 is an initial value of the thickness of the internal oxide layer, and ST is the cumulative temperature and has a value of ST≥0. In a case in which the first correlation expression is configured by Expression (4), in a range of the cumulative temperature after the local maximum value of the thickness of the internal oxide layer, the first correlation expression is set such that at least the estimated value of the thickness of the internal oxide layer is not decreased.
Further, in the case in which the first correlation expression is configured by Expression (4), the first correlation expression derivation unit may make the estimated value of the thickness of the internal oxide layer constant at the local maximum value in the range of the cumulative temperature after the local maximum value of the thickness of the internal oxide layer.
Furthermore, the second temperature definition unit may define the internal oxidation starting temperature on the basis of a correlation between the cumulative temperature and a measured value of the thickness of the internal oxide layer when the internal oxidation starting temperature is changed.
Moreover, the second temperature definition unit may change the internal oxidation starting temperature to derive a temperature-determining correlation expression indicating a correlation between the cumulative temperature and the estimated value of the thickness of the internal oxide layer and may define the internal oxidation starting temperature on the basis of a degree-of-freedom determination coefficient R2 of the temperature-determining correlation expression.
In addition, the hot-rolled steel sheet may be coiled, and the estimation start time may be a coiling completion time at which the coiling of the hot-rolled steel sheet is completed.
Further, the internal oxide layer thickness estimation device may further include a second correlation expression derivation unit that derives a second correlation expression indicating a correlation between the cumulative temperature and a coiling completion temperature of the hot-rolled steel sheet.
According to another aspect of the invention, there is provided an internal oxide layer thickness estimation method that estimates a thickness of an internal oxide layer formed in a hot-rolled steel sheet. The internal oxide layer thickness estimation method includes: a first temperature definition step of defining a temperature of a portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet; a second temperature definition step of defining an internal oxidation starting temperature at which internal oxidation of the hot-rolled steel sheet starts; a cumulative temperature calculation step of calculating a cumulative temperature on the basis of the temperatures defined by the first temperature definition step and the second temperature definition step and a predetermined period of time from an estimation start time at which estimation of the thickness of the internal oxide layer is started to an estimation evaluation time; a first correlation expression derivation step of deriving a first correlation expression indicating a correlation between the cumulative temperature calculated by the cumulative temperature calculation step and an estimated value of the thickness of the internal oxide layer; and an internal oxide layer thickness estimation step of estimating the thickness of the internal oxide layer on the basis of the first correlation expression.
According to still another aspect of the invention, there is provided a program that causes a computer to estimate a thickness of an internal oxide layer formed in a hot-rolled steel sheet. The program causes the computer to function as: a first temperature definition unit that defines a temperature of a portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet; a second temperature definition unit that defines an internal oxidation starting temperature at which internal oxidation of the hot-rolled steel sheet starts; a cumulative temperature calculation unit that calculates a cumulative temperature on the basis of the temperatures defined by the first temperature definition unit and the second temperature definition unit and a predetermined period of time from an estimation start time at which estimation of the thickness of the internal oxide layer is started to an estimation evaluation time; a first correlation expression derivation unit that derives a first correlation expression indicating a correlation between the cumulative temperature calculated by the cumulative temperature calculation unit and an estimated value of the thickness of the internal oxide layer; and an internal oxide layer thickness estimation unit that estimates the thickness of the internal oxide layer on the basis of the first correlation expression.
According to the above-described aspects of the invention, the thickness of the internal oxide layer is estimated on the basis of the cumulative temperature having a very high correlation with the thickness of the internal oxide layer. Therefore, it is possible to estimate the thickness of the internal oxide layer with higher accuracy.
Hereinafter, preferred embodiments of the invention will be described in detail with reference to the accompanying drawings. The inventors thoroughly studied parameters having a high correlation with a thickness of an internal oxide layer in order to estimate the thickness of the internal oxide layer. As a result, the inventors found that a cumulative temperature described below had a very high correlation with the thickness of the internal oxide layer. An internal oxide layer thickness estimation device, an internal oxide layer thickness estimation method, and a program according to this embodiment are achieved on the basis of these findings.
<1. Type of Hot-Rolled Steel Sheet>
A hot-rolled steel sheet (in which the thickness of an internal oxide layer is estimated by this estimation method) to be subjected to the internal oxide layer thickness estimation method according to this embodiment is not particularly limited. Any hot-rolled steel sheet may be used as long as an internal oxide layer can be formed therein. The hot-rolled steel sheet may be, for example, alloy steel including metal that is less noble than iron (for example, Si, Mn, Al, or Cr or any combination thereof). The hot-rolled steel sheet may be, specifically, high tensile strength steel (high-tensile steel) or the like. In particular, the high-tensile steel is a preferable example of the object to which this embodiment is applied because the internal oxide layer is easily formed.
A thermal history of the hot-rolled steel sheet when the thickness of the internal oxide layer is estimated is not particularly limited. For example, the hot-rolled steel sheet is coiled and then cooled by any cooling method such as air cooling or water cooling (cooling step). In this cooling step, the internal oxide layer is formed immediately below a scale layer. In this case, the thermal history of the hot-rolled steel sheet follows a relatively simple cooling process. Of course, the thermal history of the hot-rolled steel sheet is not limited to this example. For example, the hot-rolled steel sheet may be cooled to a certain temperature in the cooling step after being coiled and then may be soaked or reheated for the purpose of annealing or the like. Further, the above-described cooling, annealing, and the like may be performed on the hot-rolled steel sheet in an uncoiled state in which the hot-rolled steel sheet is stretched into a flat sheet shape. Furthermore, the hot-rolled steel sheet may be cooled to a temperature that is equal to or lower than an internal oxidation starting temperature Tcr which will be described below and then may be reheated to a temperature that is equal to or higher than the internal oxidation starting temperature Tcr. That is, in the calculation of the cumulative temperature which will be described below, there may be an integration interval in which the temperature T of a portion to be estimated is equal to or lower than Tcr. In this integration interval, T−Tcr may be set to 0, which will be described below.
<2. Overall Configuration of Internal Oxide Layer Thickness Estimation Device>
<3. Cumulative Temperature>
In summary, the internal oxide layer thickness estimation method according to this embodiment estimates the thickness of the internal oxide layer formed in the hot-rolled steel sheet on the basis of the cumulative temperature represented by the following Expression (1). The cumulative temperature represented by Expression (1) has a very high correlation with the thickness of the internal oxide layer, which will be described in detail below. Since the internal oxide layer thickness estimation device 10 according to this embodiment estimates the thickness of the internal oxide layer on the basis of the cumulative temperature, it is possible to estimate the thickness of the internal oxide layer with high accuracy.
S
T=∫t0t1(T−Tcr)dt (1)
Therefore, the cumulative temperature is a very important parameter in this embodiment. Each parameter constituting the cumulative temperature will be described in detail.
T is the temperature of the portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet. The first temperature definition unit 11 defines the temperature of the portion to be estimated. Here, the scale layer is formed in the hot-rolled steel sheet. Therefore, here, it is assumed that the “temperature of the portion to be estimated” means the temperature of a base metal (base steel sheet) portion immediately below the scale layer. When the hot-rolled steel sheet is thin (for example, about 2 to 5 mm) and the temperature of the portion to be estimated is considered to be uniform in the sheet thickness direction, the temperature of the portion to be estimated may be the temperature of any portion in the sheet thickness direction or may be the temperature of the surface portion of the base metal. In a case in which the temperature fluctuates in the sheet thickness direction, it is preferable that the temperature of the portion to be estimated is the temperature of the surface of the base metal. The temperature of the portion to be estimated may be actually measured using a thermocouple or the like (in this case, the operator may input an output value of the thermocouple to the internal oxide layer thickness estimation device 10. The first temperature definition unit 11 recognizes the input temperature as the temperature of the portion to be estimated). For example, the temperature may be derived by a simulation (heat conduction calculation) typified by Non-Patent Document 1 (in this case, the first temperature definition unit 11 may perform the simulation). In this simulation, the thermal history of the hot-rolled steel sheet described above is taken into consideration.
Tcr is the internal oxidation starting temperature at which the internal oxidation of the hot-rolled steel sheet starts. Therefore, Expression (1) is a value obtained by integrating the difference between the temperature T of the portion to be estimated and the internal oxidation starting temperature Tcr over time. In this embodiment, it is considered that the internal oxide layer is formed (or grows) in a case in which the temperature of the portion to be estimated exceeds the internal oxidation starting temperature Tcr. Conversely, in a case in which the temperature of the portion to be estimated is equal to or lower than the internal oxidation starting temperature Tcr, the internal oxide layer is not formed (in a case in which the internal oxide layer has already been formed, the growth thereof stops). The internal oxidation starting temperature Tcr is a constant unique to the kind of steel. Therefore, an appropriate internal oxidation starting temperature Tcr is given to the steel material to which the invention is applied. The internal oxidation starting temperature Tcr may be set in a range of, for example, 200 to 1000° C. An appropriate value of Tcr may be set with reference to documents and the like. In addition, the value may be calculated independently by the following method. The second temperature definition unit 12 defines the internal oxidation starting temperature Tcr.
t0 is the estimation start time when the estimation of the thickness of the internal oxide layer is started. Here, the estimation start time may be determined by an external input, or a preset time may be set as the estimation start time. The estimation start time is set to any time in the process in which the internal oxide layer is assumed to be formed. Here, it is generally said that the internal oxide layer is formed in a state in which the scale layer is formed and the internal oxide layer is isolated from the outside air (atmosphere including oxygen). For example, when the coiled hot-rolled steel sheet (hereinafter, the hot-rolled steel sheet in this state is also simply referred to as a “coil”) is cooled, the scale layer is formed on each portion to be measured in the hot-rolled steel sheet, and the portion to be measured is isolated from the outside air. Therefore, it is considered that the internal oxide layer is formed in a coil cooling step. Then, the coil cooling step is started from the coiling completion time of the hot-rolled steel sheet. Therefore, the estimation start time t0 may be regarded as the coiling completion time of the hot-rolled steel sheet. Of course, the estimation start time t0 may be set to any time during the cooling step. In a case in which annealing or the like is performed during the cooling step, the estimation start time t0 may be set to a time period for which the annealing or the like is performed. For example, an annealing start time (the time when the portion to be estimated in the hot-rolled steel sheet reaches an inlet of an annealing furnace) may be set as the estimation start time t0, or a time in the middle of annealing may be set as the estimation start time to. In addition, as described above, in the cooling step, there may be an integration interval in which the temperature T of the portion to be estimated is lower than the internal oxidation starting temperature Tcr. In this case, for example, the portion to be estimated is cooled to the internal oxidation starting temperature Tcr or lower during the cooling step, and the portion to be estimated is reheated to the internal oxidation starting temperature Tcr or higher by the annealing.
t1 is the estimation evaluation time. Here, the estimation evaluation time may be determined by an external input, or a preset time may be set as the estimation evaluation time. Therefore, in this embodiment, it can be said that the thickness of the internal oxide layer at the estimation evaluation time t1 is estimated. The estimation evaluation time t1 is set to a time after the estimation start time t0. For example, any time during the coil cooling step may be set as the estimation evaluation time t1. Specifically, in a case in which annealing or the like is performed during the coil cooling step, the time when the annealing ends (the time when the portion to be estimated in the hot-rolled steel sheet reaches an outlet of the annealing furnace) may be set as the estimation evaluation time t1, or a time during the annealing may be set as the estimation evaluation time t1. Furthermore, any time during the cooling step after the annealing ends may be set as the estimation evaluation time t1. In this case, the time when the temperature T of the portion to be estimated finally reaches the internal oxidation starting temperature Tcr (after all of the above-described annealing and the like are performed) in the coil cooling step may be set as the estimation evaluation time t1. A time thereafter (that is, the time when the temperature T of the portion to be estimated is further cooled) may be set as the estimation evaluation time t1. As described above, in an integration interval after the temperature T of the portion to be estimated reaches the internal oxidation starting temperature Tcr, T−Tcr is equal to or less than 0. However, since T−Tcr is 0 in this integration interval, there is no effect on the accuracy of estimation.
In the calculation of the cumulative temperature, the temperature T of the portion to be measured may be actually measured or may be calculated by a simulation considering the thermal history of the hot-rolled steel sheet. In the former case, the operator may input the measured value to the internal oxide layer thickness estimation device 1. In the latter case, the first temperature definition unit 12 or a simulation unit (not shown) may simulate (estimate) the temperature T of the portion to be measured. In a case in which T−Tcr is equal to or less than 0 in any of the integration intervals, T−Tcr is set to 0 in the integration interval. In addition, in the integration operation, the integration interval (t0 to t1) may be divided into minute intervals Δt, and the discrete values of the cumulative temperatures in each interval Δt may be summed to calculate the cumulative temperature. The cumulative temperature calculation unit 13 calculates the cumulative temperature on the basis of the temperature defined by the first temperature definition unit 11 and the second temperature definition unit 12 and the above-described Expression (1). The operator may input t0 and t1 to the internal oxide layer thickness estimation device 1. The cumulative temperature calculation unit 13 recognizes the input values as t0 and t1 in Expression (1). Alternatively, t0 and t1 may be preset as specified values.
<4. Method for Determining Tcr>
The second temperature definition unit 12 may determine (define) the internal oxidation starting temperature Tcr using the following method. That is, the internal oxidation starting temperature Tcr may be determined, for example, on the basis of the correlation between the cumulative temperature and the measured value of the thickness of the internal oxide layer when the internal oxidation starting temperature Tcr is changed. For example, the internal oxidation starting temperature Tcr may be determined such that the correlation between the cumulative temperature and the measured value of the thickness of the internal oxide layer is the highest.
In a case in which the internal oxidation starting temperature Tcr is calculated, the second temperature definition unit 12 and the cumulative temperature calculation unit 13 perform, for example, the following process. First, the cumulative temperature calculation unit 13 sets the internal oxidation starting temperature Tcr to any value (for example, any value in a range of 200° C. to 1000° C.). Then, the portions to be measured are set at a plurality of positions on the surface of the hot-rolled steel sheet, and the cumulative temperatures of these portions to be measured are calculated on the basis of the above-described Expression (1). A specific calculation method is as described above. The portion to be measured may be set by the cumulative temperature calculation unit 13 or by the operator. In the former case, the internal oxide layer thickness estimation device 1 may display the portion to be measured on a display or the like. In the latter case, the operator may input the portion to be measured to the internal oxide layer thickness estimation device 1. The setting of the portion to be measured may be performed for the total length of the hot-rolled steel sheet in a rolling direction and the total width of the hot-rolled steel sheet in the sheet width direction or may be performed for a part of the total length and the total width. In an example described below, the portion to be measured is set for the total length and the total width. In addition, it is preferable that the portion to be measured is set in a sheet width center quarter portion. The reason is that the cumulative temperature in the sheet width center quarter portion has a high correlation with the measured value of the thickness of the internal oxide layer, which will be described below. Here, the sheet width center quarter portion means a region in a range from the center (center portion) of the hot-rolled steel sheet in the sheet width direction to portions (quarter portions) which are ¼ of the sheet width away from the center toward both ends in the sheet width direction (that is, a region interposed between a quarter portion close to one end portion in the width direction and a quarter portion close to the other end portion).
On the other hand, the operator actually measures the thickness of the internal oxide layer in the portion to be measured at the estimation evaluation time t1 and inputs the thickness to the internal oxide layer thickness estimation device 1. The thickness of the internal oxide layer is measured, for example, by cutting the hot-rolled steel sheet in parallel in the thickness direction, performing nital etching on a cut surface, and then observing the cut surface with a scanning electron microscope (SEM) or the like. In a region in which the internal oxide layer is formed, a metal oxide (grain boundary oxide) that is present at a grain boundary and a metal oxide (intragranular oxide) that is present within a crystal grain are observed. A region in which these oxides are observed may be determined to be the internal oxide layer. In addition, the thickness of the internal oxide layer may be measured at several points in the portion to be measured, and an average value thereof may be used as the thickness of the internal oxide layer in the portion to be measured. In this way, the cumulative temperature and the measured value of the thickness of the internal oxide layer are obtained for the plurality of portions to be measured. In addition, this test may be performed as an offline test.
Then, the cumulative temperature calculation unit 13 plots the obtained cumulative temperature and the obtained measured value of the thickness of the internal oxide layer as measurement points on the xy plane having the cumulative temperature and the thickness of the internal oxide layer as the x-axis and the y-axis. An example is shown in
Then, the cumulative temperature calculation unit 13 performs regression analysis on a plurality of measurement points to calculate an approximate expression (temperature-determining correlation expression) of these measurement points. The regression analysis may be, for example, simple regression analysis using a least-square method or may be multiple regression analysis. Here, it is preferable that the portion to be measured is set in the sheet width center quarter portion. This is because the cumulative temperature and the measured value of the thickness of the internal oxide layer in the sheet width center quarter portion have a high correlation. Furthermore, the internal oxide layer is likely to be formed particularly thickly in the sheet width center quarter portion, particularly, in the center portion. In this respect, it is preferable that the portion to be measured is set in the sheet width center quarter portion. In the example shown in
Then, the second temperature definition unit 12 determines the internal oxidation starting temperature Tcr on the basis of the correlation between the cumulative temperature and the measured value of the thickness of the internal oxide layer when the internal oxidation starting temperature Tcr is changed. For example, the cumulative temperature calculation unit 13 derives the above-described temperature-determining correlation expression, using various different values of the internal oxidation starting temperature Tcr, and calculates each degree-of-freedom determination coefficient R2. Then, the second temperature definition unit 12 selects the internal oxidation starting temperature Tcr when the degree-of-freedom determination coefficient R2 of the temperature-determining correlation expression has the largest value (that is, the correlation between the cumulative temperature and the measured value of the thickness of the internal oxide layer is the highest).
Both the graphs L2 and L3 have a peak. The graph L2 has a peak at an internal oxidation starting temperature Tcr of 500° C., and the graph L3 has a peak at an internal oxidation starting temperature Tcr of 450° C. The temperature of the edge portion is lower than the temperature of the sheet width center quarter portion, and unevenness is also large. Therefore, it is considered that this tendency appears. In any case, the peak of the graph L3 is lower than the peak of the graph L2. Therefore, as can be seen from the example shown in
<5. Derivation of First Correlation Expression>
Then, the first correlation expression derivation unit 14 derives the first correlation expression which will be described below. The gist of an internal oxide layer thickness estimation step according to this embodiment is that the thickness of the internal oxide layer formed in the hot-rolled steel sheet is estimated on the basis of the cumulative temperature represented by the above-described Expression (1). As a specific estimation method, an estimation method using the first correlation expression (model formula) indicating the correlation between the estimated value of the thickness of the internal oxide layer and the cumulative temperature is given. Therefore, the first correlation expression is an important expression for estimating the thickness of the internal oxide layer.
The first correlation expression derivation unit 14 derives the first correlation expression indicating the correlation between the cumulative temperature calculated by the cumulative temperature calculation unit 13 and the estimated value of the thickness of the internal oxide layer. The first correlation expression may be, for example, any one or a combination of two or more of Expressions (2) to (4) having the following format.
H=αS
T
+H
0 (2)
H=βS
T
1/2
+H
0 (3)
H=γS
T
+δS
T
2
+H
0 (0≤ST≤−γ/(2δ): a local maximum value of the thickness of the internal oxide layer at this time is Hm)
H=φ{S
T+γ/(2δ)}+Hm (ST>−γ/(2δ)) (4)
In Expressions (2) to (4), H is the estimated value of the thickness of the internal oxide layer at the estimation evaluation time, and ST is the cumulative temperature and has a value of ST≥0. α, β, γ, φ, and δ are constants, and H0 is an initial value of the thickness of the internal oxide layer.
Here, the initial value H0 of the thickness of the internal oxide layer means the thickness of the internal oxide layer at the estimation start time t0. The initial value H0 of the thickness of the internal oxide layer can be measured by rapidly cooling the hot-rolled steel sheet to the internal oxidation starting temperature Tcr or lower at the estimation start time t0 and then observing the cross section. This process may be performed by the operator. When it is clear that the internal oxide layer is not formed at the estimation start time to, this measurement may not be performed, and the initial value H0 may be set to 0.
The parameters α, β, γ, and δ in the correlation expression are regression constants. The first correlation expression derivation unit 14 may determine the parameters using regression analysis on the basis of a plurality of sets of measured data of ST and H (ST is calculated by the cumulative temperature calculation unit 13 and H is actually measured by the operator).
In the example shown in
In addition, since 6 in Expression (4) has a negative value, Expression (4) has a local maximum value (Hm) with respect to the estimated value of the thickness of the internal oxide layer. In a case in which the thickness of the internal oxide layer is defined by H=γST+δST2+H0 in the entire range of the cumulative temperature in Expression (4), the estimated value of the thickness of the internal oxide layer starts to decrease in the range of the cumulative temperature after the local maximum value. This does not fit the reality. Therefore, as shown in Expression (4), in the range of the cumulative temperature after the local maximum value (ST>−γ/(2δ)), the estimated value of the thickness of the internal oxide layer may be constant at the local maximum value (in this case, φ=0 at H=φ{ST+γ/(2δ)}+Hm).
An example is shown in
<6. Internal Oxide Layer Thickness Estimation Step>
After the first correlation expression is derived from the above-described step, the internal oxide layer thickness estimation unit 15 can estimate the thickness of the internal oxide layer on the basis of the first correlation expression. For example, first, the cumulative temperature calculation unit 13 measures the cumulative temperature of a portion, in which the thickness of the internal oxide layer is to be known, using the above-described method. Then, the internal oxide layer thickness estimation unit 15 can apply this cumulative temperature to the first correlation expression to estimate the thickness of the internal oxide layer in the portion. As shown in
In addition, the parameters fluctuate depending on the type (for example, chemical composition) and thermal history of the hot-rolled steel sheet. Therefore, it is preferable to derive the first correlation expression according to the type (for example, chemical composition) and thermal history of the hot-rolled steel sheet.
<7. Method for Determining Coiling Completion Temperature of Hot-Rolled Steel Sheet>
It is possible to determine the coiling completion temperature of the hot-rolled steel sheet using the above-described internal oxide layer thickness estimation method. Hereinafter, a method for determining the coiling completion temperature of the hot-rolled steel sheet using the internal oxide layer thickness estimation method will be described. In addition, in the determination method, it is premised that the hot-rolled steel sheet is coiled.
First, (1) the first correlation expression derivation unit 14 derives the first correlation expression on the basis of the thermal history after the coiling is completed. Here, the estimation start time t0 may be a coiling completion time. A specific derivation method is as described above. (2) Meanwhile, the second correlation expression derivation unit 16 derives the second correlation expression indicating the correlation between the coiling completion temperature and the cumulative temperature. The second correlation expression is an expression indicating the correlation between the cumulative temperature calculated by the cumulative temperature calculation unit 13 and the coiling completion temperature. Here, a portion in which the cumulative temperature is calculated is not particularly limited. The cumulative temperature may be calculated in a center portion in which the internal oxide layer is likely to be formed particularly thickly. That is, the cumulative temperature may be calculated at any one point of the center portion, or the cumulative temperature may be measured at a plurality of points of the center portion and an average value of the measured values may be used. Specifically, the second correlation expression derivation unit 16 changes the coiling completion temperature to several conditions (five conditions in a right figure of
The second correlation expression derivation unit 16 may display the derived first and second correlation expressions in comparison with each other. An example thereof is shown in
In the right figure, the horizontal axis indicates the coiling completion temperature (° C.), and the vertical axis indicates the cumulative temperature (° C.·min). A point P7 indicates the coiling completion temperature and the cumulative temperature, and a graph L13 indicates a connection of the points P7, that is, the second correlation expression. The cumulative temperature at the point P7 is the cumulative temperature of the center portion. It is assumed that the coiling completion temperature is the temperature of the hot-rolled steel sheet at the time when the coiling of the hot-rolled steel sheet is completed and is uniform on the entire surface of the hot-rolled steel sheet.
Then, the operator determines the coiling completion temperature on the basis of the cumulative temperature corresponding to the thickness of the internal oxide layer, which is equal to or less than a predetermined value, and the second correlation expression such that the thickness of the internal oxide layer estimated by the first correlation expression is equal to or less than the predetermined value.
Specifically, (3) the operator determines the predetermined value of the thickness of the internal oxide layer. In the example shown in
<7. Internal Oxide Layer Thickness Estimation Method>
Next, the internal oxide layer thickness estimation method according to this embodiment will be described with reference to a flowchart shown in
In Step S10, the first temperature definition unit 11 defines the temperature T of the portion to be estimated, in which the thickness of the internal oxide layer is to be estimated, in the hot-rolled steel sheet. The first temperature definition unit 11 derives the temperature T of the portion to be estimated using, for example, the simulation (heat conduction calculation) typified by Non-Patent Document 1.
In Step S20, the second temperature definition unit 12 defines the internal oxidation starting temperature Tcr at which the internal oxidation of the hot-rolled steel sheet is started. The details of the definition are as described in <4. Method for Determining Tcr>. In general, the second temperature definition unit 12 determines (defines) the internal oxidation starting temperature Tcr such that the correlation between the measured value of the thickness of the internal oxide layer and the cumulative temperature is the highest.
In Step S30, the cumulative temperature calculation unit 13 calculates the cumulative temperature of a desired portion to be estimated. The cumulative temperature is defined in Expression (1).
In Step S40, the first correlation expression derivation unit 15 derives the first correlation expression indicating the correlation between the cumulative temperature calculated by the cumulative temperature calculation unit 13 and the estimated value of the thickness of the internal oxide layer. Examples of the first correlation expression include the above-described Expressions (2) to (4).
In Step S50, the internal oxide layer thickness estimation unit 15 estimates the thickness of the internal oxide layer on the basis of the first correlation expression. For example, the internal oxide layer thickness estimation unit 15 applies the cumulative temperature calculated in Step S30 to the first correlation expression to estimate the thickness of the internal oxide layer in the portion. For example, an estimation result may be displayed on the display.
In Step S60, the second correlation expression derivation unit 16 derives the second correlation expression indicating the correlation between the coiling completion temperature of the hot-rolled steel sheet and the cumulative temperature. Then, the second correlation expression derivation unit 16 displays the first correlation expression and the second correlation expression in comparison with each other, for example, as shown in
As described above, according to the internal oxide layer thickness estimation method of this embodiment, the thickness of the internal oxide layer is estimated using the cumulative temperature having a high correlation with the thickness of the internal oxide layer. Therefore, it is possible to estimate the thickness of the internal oxide layer with high accuracy. Furthermore, according to the method for determining the coiling completion temperature of this embodiment, the coiling completion temperature is determined using the internal oxide layer thickness estimation method. Specifically, the coiling completion temperature is determined such that the thickness of the internal oxide layer estimated by the internal oxide layer thickness estimation method is equal to or less than a predetermined value. Therefore, it is possible to determine the coiling completion temperature corresponding to the desired thickness of the internal oxide layer with high accuracy.
Next, an example of this embodiment will be described. In this example, the following experiments were performed in order to check the effect of this embodiment. Of course, the invention is not limited to the example described below. It is obvious that those skilled in the art to which the invention belongs can conceive of various changes or modification examples within the scope of the technical idea described in the claims. Of course, it is understood that these also fall within the technical scope of the invention.
First, as a test piece of the hot-rolled steel sheet, a steel material containing C: 0.1875%, Si: 0.58%, Mn: 3.25% (the unit of each element is mass % with respect to the total mass (excluding the scale layer) of the test piece of the hot-rolled steel sheet), and a remainder of iron and impurities was prepared. Here, the impurities are components that are mixed due to raw materials, such as ores and scraps, and various factors of a manufacturing step when steel is manufactured industrially and are permissible as long as they do not adversely affect the invention.
Then, the test piece was coiled at a coiling completion temperature of 600° C. and then air-cooled to room temperature. Meanwhile, a plurality of portions on the surface of the test piece were set as the portions to be measured, and the cumulative temperatures of these portions to be measured were derived by the simulation described in Non-Patent Document 1. The internal oxidation starting temperature Tcr was 500° C., the estimation start time t0 was the coiling completion time, and the estimation evaluation time t1 was the time when the temperature T reached the internal oxidation starting temperature Tcr. In addition, in the test piece after cooling, the thickness of the internal oxide layer in the portion to be measured was measured by the above-described method (a cross section was observed after nital etching). As a result, the results shown in
The preferred embodiment of the invention has been described in detail above. However, the invention is not limited to the embodiment. It is obvious that those skilled in the art to which the invention belongs can conceive of various changes or modification examples within the scope of the technical idea described in the claims. Of course, it is understood that these also fall within the technical scope of the invention.
Number | Date | Country | Kind |
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2020-185639 | Nov 2020 | JP | national |
Filing Document | Filing Date | Country | Kind |
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PCT/JP2021/040402 | 11/2/2021 | WO |