JP3182269B2 - Roll roll profile learning calculation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of calculating the distribution of the change in the radius of a roll estimated by using a roll thermal expansion calculation model and a roll wear model in hot rolling at any time during the rolling operation. The method of learning calculation.

[0002]

2. Description of the Related Art In hot rolling, it is important to accurately estimate a work roll profile during a rolling operation in order to improve the accuracy of sheet thickness and sheet crown / shape. Using the roll thermal expansion calculation model, or the roll thermal expansion model and the roll wear amount calculation model as the above work roll profile estimation method, the work roll profile at any time during the rolling operation is estimated from the rolling operation conditions. There is a prior art to do.

[0003] With regard to the above-mentioned thermal expansion calculation model, as a conventional technique for calculating the temperature distribution inside a work roll accurately during rolling in hot rolling and estimating the thermal expansion, for example, the plastic working spring in 1983 Lecture meeting, p301
The temperature distribution in the radial direction of the roll is polynomial-approximated, the temperature inside the roll is calculated by the axially symmetric finite element method in which only the axial direction is divided, and the average temperature in the radial direction of the roll is used. A method calculated by equation (1) is known as a generalized plane distortion problem.

U = (θ _m −θ ₀ ) · β · R (1) where u: thermal expansion amount per roll radius, θ _m : average temperature in the roll radial direction, θ ₀ : roll initial temperature , Β: coefficient of thermal expansion, R: roll radius.

On the other hand, with respect to the roll wear amount calculation model, a method of estimating roll wear from a rolling distance and a load per unit plate width is generally known. This calculation model, after sufficiently cooling the roll after the end of rolling, measure the roll profile in the absence of roll thermal expansion, compare with the initial roll profile, and analyze based on the rolling operation conditions Can be modeled. In addition, it is known that this conventional technique can provide industrially sufficient accuracy by performing analysis and modeling based on the type of roll used for hot rolling, the type of rolled steel, and the like.

[0006]

According to the above-mentioned conventional thermal expansion calculation model, the temperature distribution in the radial direction of the roll is as follows.
It is represented by one approximate polynomial. However, most of the work rolls currently used for hot rolling are composed of a core material and an outer layer material as shown in FIG. 8, and have different roll physical property values. In such a case, as shown in FIG. 11, at the boundary between the core material and the outer layer material, there is a discontinuous roll radial temperature gradient necessarily resulting from the continuity of the heat flux due to the difference in the thermal conductivity between the two. Will do. For this reason, it is difficult to express the temperature distribution in the roll radial direction by one approximate polynomial as in the related art. In other words, the conventional method of calculating the temperature distribution in a roll cannot accurately represent the temperature distribution in the roll radial direction, and causes an industrially significant error in calculating the thermal expansion amount of the work roll. was there. Also, in consideration of the influence of the roll physical property values, even if the temperature distribution in the roll can be accurately expressed from the rolling operation conditions, errors relating to heat input / extraction to the work roll, for example, a roll surface error. Due to the estimation error of the heat transfer coefficient, etc., there is some error between the estimated value by the roll thermal expansion calculation model and the actual thermal expansion of the work roll,
There has been a problem that the number of rolls increases as the number of rolls increases.

The present invention solves the problem of modeling the physical properties of the roll in the thermal expansion calculation model, and provides means for calculating the thermal expansion of the work roll in a practical time during the rolling operation. It is an object of the present invention to provide a method for correcting the estimation error of the thermal expansion calculation relating to the heat input and heat removal at any time during the rolling operation by using inexpensive means.

[0008]

SUMMARY OF THE INVENTION In order to achieve the above object, the gist of the present invention is to provide, in hot rolling, a work roll comprising a core material having different physical properties and an outer layer material. The temperature distribution is expressed as a mathematical expression of the temperature distribution in the radial direction of the roll. Using a polynomial that can represent continuity, during the rolling operation, the thermal expansion distribution u _t (z) in the roll axis direction of the work roll, z is the roll axis direction coordinate,
The work roll profile is estimated from the model for calculating the roll wear amount u _w (z) in the roll axis direction, and further, during the suspension of the rolling operation, the lowering device is operated to contact the upper and lower work rolls. Then, by comparing and analyzing the relationship between the reduction set value obtained by tightening and the reaction force measured by the rolling reaction force measuring device with the same relationship immediately after the work roll change, the roll from the initial work roll profile is obtained. after calculating the roll axis direction average value [Delta] R _m of the radius of the change in the roll direction average value u _tm and roll wear amount of the roll thermal expansion amount calculated thermal expansion amount of the roll axis direction can be calculated from the model distribution u _t (z) seeking the roll axis direction average value u _wm of the roll shaft direction abrasion weight distribution u _w (z) can be calculated from the total model, the thermal expansion satisfying the relation _{ΔR m = a · u tm +} u wm Learning coefficient of the computational model A
Is calculated, and the roll axis direction distribution ΔR (z) of the change amount of the work roll radius thereafter is calculated from the roll thermal expansion amount calculation model by the estimated value u _{t of} the roll axis direction thermal expansion amount distribution. a (z) is multiplied by the learning coefficient a, a ΔR (z) = a · u t (z) + u w roll profile learning calculation process of rolling roll, characterized in that modifying as (z).

[0009]

The present inventors have found that most of the work rolls currently used in hot rolling are composed of two regions having different physical property values in the radial direction, that is, a core material and an outer layer material as shown in FIG. We paid attention to that. As described above, the inventors have found that due to the difference in the physical properties of the two rolls, especially the thermal conductivity, the continuity of the heat flux at the boundary between the core material and the outer layer material necessarily results from the continuity of the heat flux as shown in FIG. As a mathematical expression expressing a continuous roll radial temperature gradient, as shown in FIG. 5 and equation (2), in two regions of a core material and an outer layer material,
In order to approximate the radial temperature distribution with different polynomials, a roll thermal expansion calculation model described below was proposed in the earlier application.

Θ = θ ₁ (r) core material region, θ = θ ₂ (r) outer layer material region (2) where, θ: temperature distribution in the roll radial direction, r: radial coordinate, lower suffix 1 , 2: a core material and an outer layer material, respectively; Equation (3) shows an axisymmetric heat conduction equation taking physical properties into consideration in the roll radial direction.

[0011]

(Equation 3)

Here, ρ: density, c: specific heat, λ: thermal conductivity, z: coordinates in the roll axis direction. Here, as shown in FIG. 5, since the temperature distribution in the roll radial direction is approximated to two regions in the roll radial direction by different polynomials for the core material and the outer layer material, the equation (3) is calculated by the above equation (2). ) Can be divided by the application range of the polynomial and expressed by equation (4).

[0013]

(Equation 4)

Here, α is a heat transfer coefficient; then, for example, by solving equation (4) under the boundary conditions of equation (5), the temperature distribution in the roll can be obtained.

The boundary condition of the roll surface expressed by the equation (5) -3 is disclosed in, for example, “Materials and Processes” published by the Iron and Steel Institute of Japan, Vol. 5 (1992) -592. 3 shows an example of boundary condition modeling in which boundary conditions that change in the roll circumferential direction are made uniform by integral averaging.

Next, the inventors compared a high-precision solution based on the axially symmetric finite element method in which elements were also divided in the radial direction and a calculation result based on the above-described roll thermal expansion calculation model. As a result, in the above-described roll thermal expansion calculation model, the radial temperature distribution of the core material and the outer layer material is polynomial approximated using the radial coordinates with the roll center as the origin as shown in FIG. 6 and equation (6), for example. In this case, if the polynomial expressing the temperature distribution in the core material in the radial direction is approximated by a quadratic equation and the polynomial expressing the temperature distribution in the outer layer in the radial direction is approximated by a 20th-order equation or more, the error from the above-described high-precision solution will Found that there is little.

[0017] _{θ = θ 1 (r c)} (0 ≦ r c <r 1), θ = θ 2 (r c) (r 1 ≦ r c ≦ R) ··· (6) where, r _c: Radial coordinates with the roll center as the origin r ₁ : roll core radius R: roll radius

Regarding the calculation of the amount of thermal expansion, first, equation (6)
The average temperature θ _m1 and θ _m2 of the core material and the outer layer material are obtained as shown by the equation (7) using the temperature distribution in the roll radial direction in the above.

[0019]

(Equation 7)

[0020] Then, the integrated average over the roll cross section of the strain thermal expansion multiplied by the radius R, expressed as the thermal expansion amount u _t per roll radius as shown in equation (8); u _t = [(theta _{m1 ^{-θ 0) β 1 r 1 2}} + (θ m2 -θ 0) β 2 (R 2 -r 1 2) ] / R ··· (8) where, β _1, β ₂ is the roll core, respectively, and The coefficient of linear expansion of the outer layer material.

Further, the present inventors also use a radial coordinate having an origin at a radial position other than the roll center as a polynomial to express the radial temperature distribution of the outer layer material as shown in Expression (9). in the radial direction temperature distribution of the outer layer material was found to be able to _{express; θ = θ 2 (r s} ) (r s1 ≦ r s ≦ R s) ··· (9) where, r _s: radius of the non-roll center radial coordinates with the origin of the direction position, r _s1, R _s: a boundary position and roll radial position of the core material and the outer layer material in r _s coordinates, respectively. At this time, the average temperature of the outer layer material is obtained by equation (10) using the equation (9) calculated by the roll thermal expansion calculation model, and then the thermal expansion amount of the outer layer material is obtained by equation (8). Will be.

[0022]

(Equation 10)

Further, the inventors have found that the polynomial using the radial coordinates having the origin at the radial position other than the roll center is the order of the polynomial as the origin of the radial coordinates is closer to the core material radial position. I found that it could be reduced. For example, as shown in FIG. 7, in the case of using the radial coordinates with the core material radial position as the origin as in Expression (11), the polynomial expressing the radial temperature distribution of the outer layer material is a sixth-order equation or more. It has been found that there is almost no error from the above-mentioned high-precision solution if approximated.

Θ = θ ₂ (r _s ) (0 ≦ r _s ≦ R _s = R−r ₁ ) (11) At this time, r _s1 in the equation (9) is based on the core material radial position as the origin. It becomes zero because it is.

The parameters of the approximate polynomial expressed by the equation (2) include, for example, the average temperature of the core material and the outer layer material,
Temperature variables within the roll, such as roll temperature, temperature gradient, etc., can also be employed. According to this, since the average temperature of the core material and the outer layer material can be directly calculated, the calculation process of the average temperature of the core material and the outer layer material in Expressions (7) and (10) is not required.

Next, in order to verify the accuracy of the roll thermal expansion calculation method, a calculation result by the roll thermal expansion calculation model and a high-precision solution by an axially symmetric finite element method in which elements are also divided in the radial direction are obtained. Was compared. The roll thermal expansion calculation model was calculated using, for example, an approximate polynomial shown in Expression (12) as an approximate polynomial in radial coordinates with the origin at the roll center as shown in Expression (6).

[0027] _{θ 1 (r c) = a} 1 · r c 4 + Φ 1 (r c) (0 ≦ r c <r 1), θ 2 (r c) = a 2 · r c 20 + Φ 2 (r c ) (r in _{1 ≦ r c ≦ R) ···} (12) where, a: coefficient, Φ ₁ (r _c): a function of third order or less of r _c coordinates containing the coefficients, Φ ₂ (r _c): Is a function of the r _c coordinate of 19 or less, including the coefficients.

Table 1 shows the rolling conditions used in the comparative calculation, and Table 2 shows the physical properties of the rolls.

[0029]

[Table 1]

[0030]

[Table 2]

Also, the calculation was performed under the same conditions as those of the above-described roll thermal expansion calculation model, and the boundary conditions of the high-precision solution by the axially symmetric finite element method in which elements were also divided in the radial direction. FIG. 9 shows the temperature distribution in the radial direction at the center of the roll at the end of the twentieth rolling, and FIG. 10 shows the change in the amount of thermal expansion at the center of the roll. From this result, the error of the high-precision solution and the present invention is almost non-existent when viewed as the temperature distribution in the roll radial direction, and at most 1.5 μm per roll radius when viewed as the amount of thermal expansion.
It was about. Further, the above-described roll thermal expansion calculation model was able to process the calculation in a practical time during the rolling operation.

However, even if the roll thermal expansion calculation model according to the present invention, which can accurately represent the temperature distribution in the roll from the rolling operation conditions, is used in consideration of the influence of the physical properties of the roll, even if the roll thermal expansion calculation model according to the present invention is used. Due to errors related to heat input and heat removal, such as errors in estimating the heat transfer coefficient on the roll surface, the estimated value of the thermal expansion by the roll thermal expansion calculation model and the actual thermal expansion of the work roll There is still a problem that there is some error between them, and the error increases as the number of rolls increases.

We analyze this problem by:
At any time during the rolling operation, the roll profile was actually measured, and the amount of change in the roll radius from the initial work roll profile, that is, the amount of thermal expansion and wear in the roll axis direction was observed in detail. Regarding the actual measurement of the roll profile, the work roll was taken out of the rolling mill during the rolling operation, and was immediately measured using a roll profile measuring device.

FIG. 4 shows a comparison between the change amount of the roll radius of the work roll based on the actual measurement results and the estimated value calculated using the roll thermal expansion calculation model according to the present invention and the conventional wear amount calculation model. As a result, as shown in FIG. 4, it was found that the actual measurement result and the calculation model were almost similar between the roll body lengths. At this time, regarding the roll wear, after sufficiently cooling the work roll, the roll wear was actually measured in the absence of thermal expansion, and the result was compared with an estimated value by a roll wear amount calculation model. It was confirmed that there was almost no difference between the two.

From the above, the inventors have found that the roll profile estimation error during the rolling operation is mostly due to the roll thermal expansion calculation model, and as shown in FIG. It has also been found that the measured value of the thermal expansion amount excluding the roll wear and the thermal expansion amount estimated using the roll thermal expansion calculation model according to the present invention are substantially similar. That is, this means that the thermal expansion amount estimated and calculated using the roll thermal expansion amount calculation model according to the present invention is simply multiplied by a certain learning coefficient, and as shown in FIG. It has been found that it can be corrected to the amount of thermal expansion.

In order to find a learning coefficient by which the estimated value of the thermal expansion calculation model is multiplied, the work roll is taken out of the rolling mill during the rolling operation, the roll profile is measured, and the rolling operation is performed using the work roll. It is practically impossible to continue because of problems such as productivity and workability.
Accordingly, the inventors have disclosed in Japanese Patent Application Laid-Open
Using the methods disclosed -295009 discloses, i.e. using a method for detecting an average amount of change [Delta] R _m in the rolling operation for the roll barrel length of the roll radius from the initial work roll profile, to seek the learning coefficient I learned. Here, the outline of the roll profile detection method disclosed in the above-mentioned JP-A-63-29509 will be described.

In this method, as shown in FIG. 2, during the interruption period of the rolling operation, the lowering device is operated to bring the upper and lower work rolls into contact with each other, and the rolling installation value g obtained by further tightening and the rolling reaction force measuring device In this method, the average change amount ΔR _m of the roll radius from the initial roll profile is detected by comparing and analyzing the relationship between the measured reaction force P and the relationship immediately after the work roll change. At this time, Δg
Is the difference between the pressure set value for the same rolling reaction force P ₁ in a state where the data obtained is almost parallel to the interruption period of the data and the rolling operation immediately after roll changing set as shown in FIG. That is, this Δg reflects the change ΔR in the average radius of the work roll, since it is considered that the contact load between the rolls is the same and the average deformation is the same if the rolling reaction force P ₁ is the same. Will be. Further, assuming that the upper and lower work roll profile changes are the same, the change amount ΔR of the average radius of the work roll can be obtained from Expression ₍₁₃₎ .

ΔR _m = (1/4) · Δg (13) If this detection method is used, the kiss roll is tightened using the interruption period of the rolling operation, and the change amount ΔR _m of the average radius of the work roll. , The reduction in production is not a substantial problem.

Hereinafter, a method of calculating the learning coefficient of the work roll profile according to the present invention will be described in detail.

Assuming that the distribution in the roll axis direction of the change amount of the work roll radius at the end of a certain number of rolls is ΔR (z),
Relationship between the average radius variation [Delta] R _m of the work rolls obtained above rolling discontinuance period can be expressed by the following equation.

[0041]

[Equation 14]

Here, z: coordinates in the roll axis direction with the origin at the center of the roll body length, and 1 (lowercase letter L): length of the roll body length. Furthermore, the distribution of the roll radius in the roll axis direction is represented by ΔR (z), and the change in the roll radius obtained by substituting the rolling operation conditions into the thermal expansion calculation model according to the present invention and the conventional roll wear calculation model. The relationship of the amount distribution can be expressed by the following equation when viewed as an average change amount of the roll radius.

[0043]

(Equation 15)

[0044] Here, A: learning coefficient to be calculated above, u _t (z): estimated value of the thermal expansion amount distribution of the roll axis direction calculated from a roll of thermal expansion computation model according to the present invention, u _w (z): This is an estimated value of the roll wear distribution in the roll axis direction calculated from the conventional roll wear calculation model. At this time, since the roll wear amount calculation model has sufficient estimation accuracy as described above, the learning coefficient A may be multiplied by the estimated thermal expansion amount of the roll thermal expansion amount calculation model. I understand. That is, equation (1)
From 4) and (15), the learning coefficient A can be obtained as in the following equation.

[0045]

(Equation 16)

Next, by multiplying the learning coefficient A obtained by the equation (16) with the estimated value of the thermal expansion of the roll thermal expansion calculation model, the roll profile at the time of tightening the kiss roll is detected as shown in the equation (17). can be; ΔR (z) = a · u t (z) + u w way (z) ··· (17), for example, in the short term use of high-speed steel rolls, etc., a roll such as roll wear can be largely ignored When used, the learning coefficient A may be determined with u _w (z) in equation (17) set to zero.

Next, the inventors carried out the kiss roll tightening at the end of the 20th rolling and the 100th rolling, for example, after the work roll change, and calculated the learning coefficient A. As a result, the number of rolls 20, 40, 60, 8
The learning coefficients at the end of the 0th and 100th courses are A ₂₀ ,
Assuming that A ₄₀ , A ₆₀ , A ₈₀ and A ₁₀₀ , the respective learning coefficients are A ₂₀ = 0.976 A ₄₀ = 0.970 A ₆₀ = 0.965 A ₈₀ = 0.961 A ₁₀₀ = 0.955 Met.

From the above, it can be seen that the learning coefficient used for correcting the estimated value of the thermal expansion calculation model hardly changes even if the number of rolls increases. From this, the inventors, as described above, the learning coefficient calculated by performing the kiss roll tightening during the suspension of the rolling operation at any time,
In estimating the amount of thermal expansion in subsequent rolling operations,
It has been found that it can be used continuously as a learning coefficient for multiplying the roll thermal expansion calculation model of the present invention.

A specific example of the roll profile learning calculation method of the present invention will be described below. FIG. 3 shows an example of a flow for explaining a specific example of the present invention. In the present invention, first, the kiss roll is tightened immediately after the roll change, and the kiss roll shown in FIG.
Collect data. Simultaneously with the start of the rolling operation, the roll axis distribution ΔR (z) of the change amount of the work roll radius is calculated from the roll thermal expansion calculation model according to the present invention and a known roll wear model based on the rolling operation conditions. Next, during the suspension of the rolling operation, the kiss rolls were tightened, the two data in FIG. 2 were collected, and compared and analyzed with the one data in FIG.
From 3), the average change amount ΔRm of the roll radius from the initial roll profile is determined. This is compared with ΔR (z) calculated from each of the above calculation models at the same time as the kiss roll tightening, and a learning coefficient A for multiplying the roll thermal expansion calculation model by equation (16) is obtained. Subsequently, the distribution of the change amount of the work roll radius in the roll axis direction ΔR (z) thereafter is expressed by the following equation (1).
7).

If the roll profile learning method using a kiss roll according to the present invention is divided at least twice between immediately after the work roll change shown in FIG. 3 and the next roll change, the roll thermal expansion calculation model can be further improved. It goes without saying that the accuracy of estimating the amount of thermal expansion can be improved.

In the case of the present invention, by using a highly accurate roll thermal expansion calculation model as described above and combining the above-described roll thermal expansion calculation model learning method and a conventional roll wear calculation model, The roll profile can be estimated with high accuracy from immediately after the work roll change to the next roll change.

[0052]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention was applied to a continuous rolling mill of continuous hot rolling. For the roll thermal expansion calculation model, the roll thermal expansion calculation model proposed by the inventors was used, and the upper and lower work rolls were brought into contact with each other by operating the pressing device during the suspension of the rolling operation after the end of the 20th rolling. Then, a learning coefficient A for multiplying the roll thermal expansion calculation model was calculated. Then, the learning coefficient A was continuously used as a learning coefficient for multiplying the estimated value of the amount of thermal expansion by the subsequent roll thermal expansion calculation model, and the roll profile was estimated in combination with the roll wear calculation model.

Then, after the 100th rolling, the profile of the work roll was immediately measured, and the measured value was compared with the estimated value of the roll profile using the learning coefficient A. As a result, the error between the measured value and the estimated value at the center position of the work roll in the roll body length direction was 10.5 μm. Also, when viewed in the entire roll body length direction, the maximum error was 13 μm.

[0054]

According to the present invention, the amount of thermal expansion of a work roll can be calculated with high accuracy in a practical time during a rolling operation, and the rolling operation can be interrupted by using existing equipment. Since the learning calculation of the work roll profile can be performed using the period, a great effect can be obtained in improving the accuracy of the thickness and crown / shape of the rolled sheet.

[Brief description of the drawings]

FIG. 1 is a graph showing measured and calculated values of the amount of thermal expansion of a roll that led to finding a roll profile learning calculation method in the present invention.

FIG. 2 is a graph showing a relationship between a rolling reaction force due to tightening of a work roll (kiss roll) and a set rolling value (roll gap).

FIG. 3 is a flowchart showing a process of one embodiment of a roll profile learning calculation according to the present invention.

FIG. 4 is a graph showing actual measured values and estimated calculated values of a roll profile.

FIG. 5 is a graph showing a temperature distribution in a roll radial direction in a work roll, where (a) shows a temperature distribution from the center of the roll to the surface of the outer layer material, and (b) shows a center of the roll. And (c) shows the temperature distribution from the boundary to the surface of the outer layer material.

FIG. 6 is a graph showing the division of the temperature distribution in the roll radial direction in the work roll in the roll thermal expansion calculation model of the present invention.

FIG. 7 is a graph showing only an outer layer material region shown in FIG. 6;

FIG. 8 is a cross-sectional view showing the distribution of the core material and the outer layer material in half of the cross section of the work roll.

FIG. 9 is a graph showing a temperature distribution calculated according to the present invention and a temperature distribution obtained by a high-precision solution.

FIG. 10 is a graph showing a relationship between the number of rolled coils and a calculated value of a thermal expansion amount of a work roll.

FIG. 11 is a graph showing a roll temperature distribution calculated by a conventional roll thermal expansion calculation model.

12A and 12B show boundary conditions of a roll thermal expansion calculation model used in the present invention, wherein FIG.
(B) is a sectional view taken along line BB of (a).

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G01N 25/16 B21B 28/00

Claims (1)

(57) [Claims] In hot rolling, a temperature distribution in a roll of a work roll composed of a core material having different physical property values and an outer layer material is expressed as a mathematical expression of a temperature distribution in a roll radial direction. At the boundary of the work roll, during the rolling operation, using a polynomial that can express the discontinuity of the roll radial temperature gradient resulting from the continuity of the heat flux due to the difference between the two thermal conductivities, the thermal expansion amount distribution u _t (z), z estimates the work roll profile from the model to calculate the model, and the roll axial direction of the roll wear amount u _w a (z) for computing the roll axial direction coordinates, further, During the interruption period of the rolling operation, the relationship between the set value obtained by bringing the upper and lower work rolls into contact with each other by operating the rolling device and further tightening and the reaction force measured by the rolling reaction force measuring device is shown by the work load. After calculating the roll axis direction average value [Delta] R _m of the roll radius changes from the initial work roll profile by comparing and analyzing the same relationship after Le reclassification, the roll axis direction can be calculated from the roll of thermal expansion quantity calculation model seeking the roll axis direction average value u _wm of thermal expansion distribution u _t roll direction average value u _tm and the roll axis wear amount can be calculated from the roll wear amount calculation model distribution u _w of (z) (z), ΔR m = A · u _tm + u _wm The learning coefficient A of the above thermal expansion calculation model that satisfies the relationship
Then, the roll axis direction distribution ΔR (z) of the change amount of the work roll radius is calculated from the roll thermal expansion amount calculation model by the estimated value u of the roll axis direction thermal expansion amount distribution.
is multiplied by the learning coefficient A in _{t (z), ΔR (z} ) = A · u t (z) + u w (z) modified profile learning calculation process of rolling rolls which is characterized in that a.