Method for calculating rolling load distribution, method for calculating rolling load, method for calculating contact arc length, and rolling method.

Abstract

This rolling load distribution calculation method for a rolling mill 10 includes: a step in which the contact arc length of at least an elastic restoration region or an elastic reduction region is calculated on the basis of Hooke's law with a material to be rolled 1 in a state of plane strain, the balance of forces within a roll bite of the rolling mill 10, and the distribution of rolling direction stress approximated by a function dependent on positional coordinates in a rolling direction of the rolling mill 10; and a step in which the rolling load distribution for at least the elastic restoration region or the elastic reduction region is calculated on the basis of the contact arc length.

Description

Technical Field

[0001] The present disclosure relates to a method for calculating a rolling load distribution, a method for calculating a rolling load, a method for calculating a contact arc length, and a rolling method.

Background Art

[0002] The rolling load in a rolling mill determines the plate thickness and shape on the exit side of the rolling stand. Therefore, accurately predicting the rolling load is important from the viewpoints of stable operation and quality assurance.

[0003] Conventionally, various methods for accurately predicting and calculating the rolling load have been proposed (for example, Patent Document 1 and Non-Patent Document 1).

[0004] For example, the method shown in Non-Patent Document 1 is generally used in the prediction calculation of the rolling load in the elastic region. Here, the term "elastic region" is used as a general term for both the elastic recovery region and the elastic reduction region.

[0005] FIG. 4 shows a schematic diagram of the elastic recovery region and the elastic reduction region. The elastic recovery region is the elastic region on the exit side of the rolling mill. The elastic reduction region is the elastic region on the entrance side of the rolling mill. The elastic region is a region where the material to be rolled contacts the rolling roll but undergoes elastic deformation without plastic deformation.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Non-Patent Documents

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] The method disclosed in Non-Patent Document 1 calculates the load distribution in the elastic region and the contribution of the elastic region to the rolling load by neglecting frictional stress in the elastic region and approximating that the stress in the rolling direction is constant in the elastic region. Here, the contribution of the elastic region to the rolling load corresponds to the integral of the load distribution in the elastic region.

[0009] Non-patent document 1 discloses a method for calculating the rolling load distribution in the elastic recovery region using the following formula.

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[0010] Furthermore, Non-Patent Document 1 discloses a method for calculating the rolling load distribution in the elastic reduction region using the following formula.

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[0011] Furthermore, Non-Patent Document 1 discloses a method for calculating the contribution of the elastic recovery region to the rolling load by integrating the rolling load distribution in the elastic recovery region. Furthermore, Non-Patent Document 1 discloses a method for calculating the contribution of the elastic reduction region to the rolling load by integrating the rolling load distribution in the elastic reduction region.

[0012] Furthermore, Non-Patent Document 1 discloses a method for calculating the contact arc length in the elastic recovery region using the following formula.

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[0013] Furthermore, Non-Patent Document 1 discloses a method for calculating the contact arc length in the plastic region using the following formula.

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[0014] Non-Patent Document 1 also discloses a method for calculating the contact arc length in the elastic compression region by the following formula.

Equation

[0015] Non-Patent Document 1 obtains the load distribution and contact arc length in the elastic region by these calculations. Therefore, for the plastic region, for example, by using a model such as Bland & Ford, Non-Patent Document 1 can obtain the load distribution of the entire contact region.

[0016] However, the method disclosed in Non-Patent Document 1 ignores the influence of the frictional stress in the elastic region as described above, so there is a problem that the approximation error becomes large under rolling conditions where the frictional stress increases. Examples of rolling conditions where the frictional stress increases include rolling with a dull roll having a large roll roughness, rolling of high-strength high-tensile steel, etc.

[0017] To address such problems, Non-Patent Document 1 discloses a method using an exact theoretical formula based on Airy's stress function. However, this method has a problem that it is not suitable for online calculation on a process computer because it is necessary to calculate the numerical solution of a differential equation to obtain the load distribution in the elastic region.

[0018] Also, Patent Document 1 discloses a method of introducing a correction parameter to the theoretical formula for obtaining the roll flat radius and improving the prediction accuracy of the rolling load in rolling with a dull roll. However, this method has a problem that it is necessary to obtain the correction parameter in advance for various rolling conditions, and furthermore, the physical meaning of this correction parameter is unclear.

[0019] An object of the present disclosure is to calculate the rolling load distribution in the elastic region or the contribution of the elastic region to the rolling load at high speed and with high accuracy even under rolling conditions where the frictional stress increases.

Means for Solving the Problem

[0020] [1] A method for calculating the rolling load distribution of a rolling mill, A step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill; A step of calculating the rolling load distribution of at least one of the elastic recovery region and the elastic reduction region based on the contact arc length, A method for calculating rolling load distribution, including the method described above.

[0021] [2] The rolling load distribution calculation method according to [1] above, wherein in the step of calculating the rolling load distribution, the rolling load distribution in the elastic recovery region is calculated based on the following formula (1), and the rolling load distribution in the elastic reduction region is calculated based on the following formula (2).

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[0022] [3] The rolling load distribution calculation method according to [1] or [2] above, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (8), and the contact arc length in the elastic reduction region is calculated based on the following formula (9).

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[0023] [4] A method for calculating the rolling load of a rolling mill, A step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill; A step of calculating the contribution to the rolling load by at least one of the elastic recovery region and the elastic reduction region based on the contact arc length, A method for calculating rolling load, including the method described above.

[0024] [5] The rolling load calculation method according to [4] above, wherein in the step of calculating the contribution to the rolling load, the contribution to the rolling load due to the elastic recovery region is calculated based on the following formula (1), and the contribution to the rolling load due to the elastic reduction region is calculated based on the following formula (2).

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[0025] [6] The rolling load calculation method according to [4] or [5] above, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (8), and the contact arc length in the elastic reduction region is calculated based on the following formula (9).

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[0026] [7] A method for calculating the contact arc length of a rolling mill, A method for calculating contact arc length, comprising the step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and a rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill.

[0027] [8] The method for calculating the contact arc length according to [7] above, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (1), and the contact arc length in the elastic reduction region is calculated based on the following formula (2).

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[0028] [9] A rolling method that changes the roll gap based on the rolling load distribution calculated using the rolling load distribution calculation method described in any one of the above items [1] to [3], reflecting the current lubrication conditions.

[0029]

[10] A rolling method that changes the roll gap based on the rolling load calculated using the rolling load calculation method described in any one of the above items [4] to [6], taking into account the current lubrication conditions. [Effects of the Invention]

[0030] According to the method disclosed herein, even under rolling conditions where frictional stress is high, the rolling load distribution in the elastic region or the contribution of the elastic region to the rolling load can be calculated quickly and accurately. [Brief explanation of the drawing]

[0031] [Figure 1] This figure shows an example of a rolling mill equipment to which a rolling load distribution calculation method, a rolling load calculation method, and a contact arc length calculation method according to one embodiment of this disclosure are applied. [Figure 2] This figure shows the results of calculating the rolling load distribution using the method disclosed herein and the results of calculating the rolling load distribution using a conventional method. [Figure 3] This table compares the results obtained using the method disclosed herein with those obtained using conventional methods. [Figure 4] This is a schematic diagram of the elastic recovery region and the elastic reduction region. [Modes for carrying out the invention]

[0032] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings.

[0033] Figure 1 shows an example of a rolling mill equipment to which the rolling load distribution calculation method, rolling load calculation method, and contact arc length calculation method according to one embodiment of the present disclosure are applied.

[0034] The rolling mill equipment comprises rolling mills 10-1 to 10-5, a control device 20, a process computer 30, and an online computer 40.

[0035] When there is no need to distinguish between rolling mills 10-1 to 10-5, they may simply be referred to as "rolling mill 10" in the description. Figure 1 shows five rolling mills 10, labeled 10-1 to 10-5, but this is just one example. There may be one or more rolling mills 10.

[0036] The rolling mill 10 is equipped with rolling rolls. The rolling mill 10 rolls the material to be rolled 1 using the rolling rolls. The material to be rolled 1 is, for example, a steel plate. The material to be rolled 1 may also be a non-ferrous metal such as aluminum or titanium.

[0037] The control device 20 is a device that controls the rolling mill 10. The control device 20 controls the roll gap of the rolling rolls of the rolling mill 10. The control device 20 also controls the roll speed of the rolling rolls of the rolling mill 10.

[0038] The process computer 30 is a general-purpose computer such as a workstation or personal computer. Alternatively, the process computer 30 may be a dedicated computer configured to function as the process computer 30 for the rolling mill equipment shown in Figure 1.

[0039] The process computer 30 executes the rolling load distribution calculation method, rolling load calculation method, and contact arc length calculation method according to this disclosure. This allows the process computer 30 to calculate the rolling load distribution in at least one of the elastic recovery region and the elastic reduction region. Furthermore, the process computer 30 can calculate the contribution of at least one of the elastic recovery region and the elastic reduction region to the rolling load. Additionally, the process computer 30 can calculate the contact arc length in at least one of the elastic recovery region and the elastic reduction region.

[0040] Here, the elastic recovery region is the elastic region on the exit side of the rolling mill 10. The elastic reduction region is the elastic region on the inlet side of the rolling mill 10. In this embodiment, the term "elastic region" is used as a general term for both the elastic recovery region and the elastic reduction region.

[0041] Details of the calculation of the rolling load distribution, the contribution to the rolling load, and the contact arc length using the process computer 30 will be described later.

[0042] The process computer 30 controls the control device 20 based on the calculated rolling load distribution, contribution to the rolling load, and contact arc length, and controls the roll gap of the rolling rolls of the rolling mill 10 and the roll speed of the rolling rolls of the rolling mill 10.

[0043] The online computer 40 is a general-purpose computer such as a workstation or personal computer. Alternatively, the online computer 40 may be a dedicated computer configured to function as the online computer 40 for the rolling mill equipment shown in Figure 1.

[0044] The online computer 40 calculates the coefficient of friction and other factors in reverse from rolling performance data such as the rolling load of the rolling mill 10, the plate thickness of the rolled material 1, and the tension of the rolled material 1, as well as preset data such as the roll diameter of the rolling rolls of the rolling mill 10.

[0045] The online computer 40 can calculate the coefficient of friction stably and quickly by using preset data such as the roll diameter of the rolling rolls of the rolling mill 10, which are set according to the calculation results of the process computer 30.

[0046] Furthermore, the online computer 40 can feed back the calculation results, such as the coefficient of friction, to the process computer 30. The process computer 30 can use the calculation results, such as the coefficient of friction, fed back from the online computer 40 for calculations such as the rolling load distribution.

[0047] (Calculation of contact arc length) The process by which the process computer 30 calculates the contact arc length of the rolling mill 10 will be described.

[0048] The process computer 30 calculates the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material 1, the equilibrium of forces within the roll bite of the rolling mill 10, and the rolling direction stress distribution approximated by a function that depends on the position coordinates in the rolling direction of the rolling mill 10.

[0049] The process computer 30 calculates the contact arc length in the elastic recovery region based on equation (1) below, and the contact arc length in the elastic reduction region based on equation (2) below.

[0050]

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[0051] <Approximation using a linear polynomial> Next, we will explain the process by which the process computer 30 approximates the stress in the rolling direction in the elastic recovery region with a linear polynomial relating to the position coordinates in the rolling direction and calculates the contact arc length in the elastic recovery region. Note that the position coordinates in the rolling direction are set to 0 at the roll bite exit.

[0052] The process computer 30 approximates the stress q in the rolling direction with a linear polynomial relating to the position coordinates in the rolling direction, according to equation (14) below.

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[0053] From the balance of forces within the roll bite of the rolling mill 10, the following equation (15) holds true.

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[0054] In equation (15) above, we assume that the plate thickness is minimized at the exit yield point, as shown in equation (16) below.

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[0055] Furthermore, in equation (15) above, we approximate it as shown in equation (17) below.

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[0056] Substituting the assumptions in equation (16) and the approximation in equation (17) into equation (15), we obtain equation (18) below.

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[0057] Therefore, at the exit yield point, the following equation (19) holds.

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[0058] On the other hand, the yield condition at the exit yield point can be expressed as shown in equation (20) below.

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[0059] Furthermore, the plate thickness h(x) is expressed as shown in equation (21) below.

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[0060] In that case, equations (22) and (23) below approximately hold at the exit yield point.

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[0061] Solving equation (23) above for x0 yields equation (24) below.

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[0062] The process computer 30 can calculate the contact arc length in the elastic recovery region using the above equation (24).

[0063] Furthermore, if the coefficient of friction μ is set to 0 in equation (24) above, the result is consistent with the conventional result that ignores friction.

[0064] Next, we will explain the process by which the process computer 30 approximates the stress in the rolling direction in the elastically reduced region with a linear polynomial relating to the position coordinates in the rolling direction and calculates the contact arc length in the elastically reduced region.

[0065] The process computer 30 approximates the stress q in the rolling direction with a linear polynomial relating to the position coordinates in the rolling direction, according to equation (25) below.

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[0066] From the balance of forces within the roll bite of the rolling mill 10, the approximate equation (26) below can be obtained.

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[0067] On the other hand, when x is approximately equal to l, equations (27) and (28) below hold.

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[0068] Then, we obtain equation (29) below.

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[0069] Similar to the case of the elastic recovery region, the following equation (30) can be obtained from the relationship at the boundary between the elastic and plastic regions.

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[0070] From equation (30) above, the contact arc length in the elastic reduction region can be obtained as shown in equation (31) below.

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[0071] The process computer 30 can calculate the contact arc length in the elastic reduction region using the above equation (31).

[0072] <Approximation using a cubic polynomial> Next, we will explain the process by which the process computer 30 approximates the stress in the rolling direction in the elastic recovery region with a cubic polynomial relating to the position coordinates in the rolling direction to calculate the contact arc length in the elastic recovery region.

[0073] The process computer 30 approximates the stress q in the rolling direction in the elastic recovery region using the following equation (32).

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[0074] Here, the rolling load distribution p in the elastic recovery region is approximated by the quadratic polynomial in equation (33) below.

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[0075] In equation (33) above, a quadratic function was chosen, but this is just one example; other functions may also be used. For example, a linear function or an elliptic function could be used for approximation. Regardless of which function is chosen, the subsequent discussion will proceed in much the same manner.

[0076] At this time, the expression of the stress q in the rolling direction as a cubic polynomial can be obtained by the following equation (34).

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[0077] Furthermore, the value at the exit yield point can be obtained by the following equation (35).

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[0078] On the other hand, since p(x0) = q(x0) + k0, substituting this into the right-hand side of equation (35) above and solving for q(x0), we obtain a rational function representation of the variable x0 as shown in equation (36) below.

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[0079] Therefore, equations (37) to (39) below are obtained.

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[0080] Here, β0 and η are defined as shown in equations (40) and (41) below.

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Mathematics

[0081] Then, the cubic equation of the above formula (39) is expressed as the following formula (42) as a cubic equation with respect to the variable β0.

Mathematics

[0082] When the above formula (42) has three real solutions, p and q are defined as in the following formulas (43) and (44).

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[0083] Then, the solution to be obtained for the above formula (42) is expressed as in the following formula (45).

Mathematics

[0084] Therefore, the process computer 30 can calculate the contact arc length in the elastic recovery region by the following formula (46).

Mathematics

[0085] Subsequently, the process of calculating the contact arc length when the process computer 30 approximates the stress in the rolling direction in the elastic rolling region by a cubic polynomial with respect to the position coordinates in the rolling direction will be described.

[0086] The process computer 30 performs calculations similar to those in the elastic recovery region even in the elastic rolling region, and obtains the value at the entrance yield point as in the following formula (47).

Mathematics

[0087] On the other hand, since the rolling load distribution p(x1) is also q(x1) + k1, substituting this into the above equation (47) and solving for p(x1) gives the following equation (48).

Mathematics

[0088] Also, the rolling load distribution p(x1) is also expressed as in the following equation (49).

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[0089] Therefore, the following equation (50) is obtained.

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[0090] Here, β1, d, c, and b are defined as in the following equations (51) to (54).

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[0091] Also, p and q are expressed as in the following equations (55) and (56).

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[0092] Therefore, β1 can be expressed as shown in equation (57) below.

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[0093] Therefore, from the definition of β1, the process computer 30 can calculate the contact arc length in the elastic reduction region using the following equation (58).

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[0094] (Calculation of rolling load distribution) The process by which the process computer 30 calculates the rolling load distribution of the rolling mill 10 will be described.

[0095] The process computer 30 calculates the rolling load distribution of at least one of the elastic recovery region and the elastic reduction region based on the calculated contact arc length.

[0096] The process computer 30 calculates the rolling load distribution in the elastic recovery region based on the following equation (59), and calculates the rolling load distribution in the elastic reduction region based on the following equation (60).

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[0097] <Explanation of rolling load distribution using differential equations> Next, we will explain the calculation of the rolling load distribution using differential equations. First, we will explain the calculation of the rolling load distribution in the elastic recovery region.

[0098] In the elastic recovery region, the following relationship holds as a differential equation relating to the rolling load: Equation (66).

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[0099] Here, E0 and a0 are defined as shown in equations (67) and (68) below.

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[0100] Then, equation (66) above can be expressed as equation (69) below.

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[0101] The initial value problem (p(0)=0) for equation (69) above can be solved analytically, and its solution is expressed as shown in equation (70) below.

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[0102] Next, we will explain how to calculate the rolling load distribution in the elastic reduction region.

[0103] In the elastic reduction region, the following relationship (71) holds as a differential equation relating to the rolling load.

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[0104] Here, E1, a1, and z are defined as shown in equations (72) to (74) below.

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[0105] Then, equation (71) above can be expressed as equation (75) below.

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[0106] The initial value problem (p(0)=0) related to equation (75) above can be solved analytically, and its solution is expressed as shown in equation (76) below.

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[0107] Furthermore, based on the approximate solution p0(x) for the rolling load distribution in the elastic recovery region described above, q(x) in the elastic recovery region can be approximated as shown in equation (77) below.

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[0108] Furthermore, noting that p0(x0) = q0(x0) + k0 at the exit yield point, the transcendental equation (78) below holds.

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[0109]

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[0111] The contact arc length in the elastic recovery region can also be obtained by truncating equation (79) above at an appropriate order and solving for x0. For example, if truncated to the first-order term, the following equation (80) is obtained.

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[0112] Similar calculations can be performed for the elastic reduction region as well.

[0113] (Calculation of contribution to rolling load) The process by which the process computer 30 calculates the rolling load of the rolling mill 10 will be described.

[0114] The process computer 30 calculates the contribution to the rolling load by at least one of the elastic recovery region and the elastic reduction region, based on the calculated contact arc length.

[0115] The process computer 30 calculates the contribution to the rolling load due to the elastic recovery region based on equation (81) below, and calculates the contribution to the rolling load due to the elastic reduction region based on equation (82) below.

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[0116] <Explanation of the contribution to rolling load using definite integrals> The contribution of the elastic recovery region to the rolling load can be expressed as an elementary function by the definite integral of the above p0(x) with the elastic recovery region as the integration interval, as shown in equation (88) below.

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[0117] Furthermore, the contribution of the elastic reduction region to the rolling load can be expressed as an elementary function by the definite integral of p1(x) over the elastic reduction region, as shown in equation (89) below.

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[0118] As described above, the rolling load distribution calculation method, rolling load calculation method, and contact arc length calculation method according to this embodiment calculate the contact arc length of at least one of the elastic recovery region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material 1, the equilibrium of forces within the roll bite of the rolling mill 10, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill 10. Then, based on the calculated contact arc length, the rolling load distribution of at least one of the elastic recovery region and the elastic reduction region is calculated. Furthermore, based on the calculated contact arc length, the contribution of at least one of the elastic recovery region and the elastic reduction region to the rolling load is calculated. In this way, in order to consider the effect of frictional stress in the elastic region, the rolling direction stress distribution is approximated by a function dependent on the position coordinates in the rolling direction, so that calculation errors in rolling conditions where frictional stress is large can be reduced. Rolling conditions where frictional stress is large include, for example, rolling with dull rolls with large roll roughness and rolling of high-strength high-tensile steel.

[0119] Furthermore, the method according to this embodiment provides an analytical approximation, similar to the method in Non-Patent Document 1 that ignores the influence of frictional stress in the elastic region. Therefore, the method according to this embodiment can calculate the rolling load distribution and the contribution of the elastic region to the rolling load without going through a calculation process to obtain numerical solutions to equations, as in the method based on Airy's stress function shown in Non-Patent Document 1. Therefore, the method according to this embodiment is suitable for online calculations on the process computer 30. In addition, the method according to this embodiment can be calculated using a known theoretical formula for determining the roll flattening radius without introducing the correction parameters shown in Patent Document 1. Therefore, the method according to this embodiment has the effect of not requiring the calculation of correction parameters in advance.

[0120] Furthermore, according to the method of this embodiment, in order to consider the effect of frictional stress in the elastic region, the stress distribution in the rolling direction is approximated by a function that depends on the position coordinates in the rolling direction, so that the effect of frictional stress in the elastic region can be considered in the calculation of the rolling load distribution.

[0121] Furthermore, the method according to this embodiment provides an analytical approximation of the rolling load distribution in the elastic region, as well as analytical approximations of the contact arc length in both the elastic and plastic regions. Therefore, by combining the method according to this embodiment with a model that provides an analytical approximation in the plastic region (such as the Bland & Ford model), the rolling load distribution can be calculated at high speed. Consequently, it can be used, for example, to visualize the rolling state by inversely calculating the friction coefficient and deformation resistance based on the rolling load and advance rate in real time, using actual rolling data.

[0122] Furthermore, the method according to this embodiment can be combined with a model that provides a numerical solution rather than an analytical solution in the plastic region (such as a numerical solution to Karman's differential equation). In this case, instead of calculating the contact arc length in the elastic region using the Newton-Raphson method or the like, the contact arc length in the elastic region calculated by the method according to this embodiment can be used to speed up load calculations.

[0123] Thus, the method according to this embodiment can calculate the rolling load distribution in the elastic region or the contribution of the elastic region to the rolling load at high speed and with high accuracy, even under rolling conditions where frictional stress is large.

[0124] Furthermore, when calculating the rolling load distribution using the rolling load distribution calculation method according to this embodiment, the rolling load distribution may be calculated while reflecting the current lubrication conditions. In this case, the actual load may be obtained, and the friction coefficient may be changed using the rolling load distribution calculation method according to this embodiment to estimate a friction coefficient that matches the estimated load and the actual load. The estimated friction coefficient may then be used as the friction coefficient that reflects the current lubrication conditions, etc., and applied when estimating the rolling load thereafter. In this case, the friction coefficient may be set based on a table and model equation based on the operating factors. Furthermore, the roll gap may be changed based on the rolling load distribution calculated in this manner. Similarly, when calculating the rolling load using the rolling load calculation method according to this embodiment, the calculation may reflect the current lubrication conditions, and the roll gap may be changed based on the calculation results.

[0125] (Examples) Figure 2 shows the results of calculating the rolling load distribution using the method of this disclosure and the results of calculating the rolling load distribution using a conventional method. In Figure 2, the friction coefficient and deformation resistance models are fixed. Figure 2 also shows the results of applying the method according to this embodiment to the calculation of the rolling load distribution assuming rolling with a dull roll.

[0126] In Figure 2, "BlandAndFord" shows the result of calculating the rolling load distribution using a conventional method. "BlandAndFord" calculates the rolling load distribution in the elastic region using a known method, and the rolling load distribution in the plastic region using the known Bland&Ford method.

[0127] Furthermore, in Figure 2, "BlandAndFord1" is the result of calculating the contact arc length in the elastic region by approximating the stress q in the rolling direction with a linear polynomial using the method of this embodiment, and then calculating the rolling load distribution in the elastic region based on the calculated contact arc length. Note that "BlandAndFord1" uses the well-known Bland&Ford method to calculate the rolling load distribution in the plastic region.

[0128] Furthermore, in Figure 2, "BlandAndFord3" shows the result of calculating the contact arc length in the elastic region by approximating the stress q in the rolling direction with a cubic polynomial using the method of this embodiment, and then calculating the rolling load distribution in the elastic region based on the calculated contact arc length. Note that "BlandAndFord3" uses the well-known Bland&Ford method to calculate the rolling load distribution in the plastic region.

[0129] Furthermore, in Figure 2, "Karman" represents the result of calculating the rolling load distribution as an exact numerical solution using Karman's equation.

[0130] Referring to Figure 2, it was confirmed that the calculation results of the rolling load distribution using "BlandAndFord1" and "BlandAndFord3" to which the method of this embodiment was applied are almost equivalent to the results of "Karman," which calculated an exact numerical solution.

[0131] Figure 3 shows a table comparing the results obtained using the method of this embodiment with those obtained using the conventional method.

[0132] In Figure 3, "Bland & Ford" and "Bland & Sims" represent the results obtained using the conventional method.

[0133] Furthermore, in Figure 3, "Bland&Ford1" and "Bland&Sims1" are the results calculated by approximating the stress q in the rolling direction with a linear polynomial in the method of this embodiment. Also, in Figure 3, "Bland&Ford3" and "Bland&Sims3" are the results calculated by approximating the stress q in the rolling direction with a cubic polynomial in the method of this embodiment.

[0134] Furthermore, in Figure 3, "Karman" represents the result of calculating an exact numerical solution. Also in Figure 3, "Karman3" represents the result of approximating the stress q in the rolling direction in the elastic region with a cubic polynomial.

[0135] Referring to Figure 3, the calculation time for calculating the rolling load using the method of this embodiment is less than 1 / 100th of the time required by "Karman," which calculates an exact numerical solution. Furthermore, the results obtained by calculating the rolling load using the method of this embodiment are almost equivalent to the results obtained by calculating the rolling load using "Karman," which calculates an exact numerical solution.

[0136] This disclosure is not limited to the embodiments described above. For example, multiple blocks described in the block diagram may be combined, or a single block may be divided. Instead of executing multiple steps described in the flowchart in chronological order as described, they may be executed in parallel or in a different order, depending on the processing capacity of the device performing each step, or as necessary. Other modifications are possible without departing from the spirit of this disclosure.

[0137] For example, Figure 1 shows a configuration in which the process computer 30 and the online computer 40 are separate devices, but these devices may be composed of a single device. In this case, the process computer 30 may have the functions of the online computer 40.

[0138] For example, the method relating to this disclosure can also be applied when using Orowan's theory, which takes into account the effect of shear stress in the calculation of the plastic region. [Explanation of Symbols]

[0139] 1 Rolled material 10 Rolling mill 20 Control device 30 Process Computers 40 Online Calculators

Claims

1. A method for calculating the rolling load distribution of a rolling mill, A step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill; A step of calculating the rolling load distribution of at least one of the elastic recovery region and the elastic reduction region based on the contact arc length, Includes, A method for calculating rolling load distribution, wherein in the step of calculating the rolling load distribution, the rolling load distribution in the elastic recovery region is calculated based on the following formula (1), and the rolling load distribution in the elastic reduction region is calculated based on the following formula (2). [Math 1] [Math 2] However, in equation (1), the following relationships exist between equations (3) and (4): [Math 3] [Math 4] However, in equation (2), the following relationships exist: [Math 5] [Math 6] [Number 7] However, in equations (1) to (7), p ０ (x) is the rolling load distribution in the elastic recovery region, p １ (x) is the rolling load distribution in the elastic reduction region, x is the position coordinate in the rolling direction, [Number 8] [Number 9] [Number 10]

2. The rolling load distribution calculation method according to claim 1, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (8), and the contact arc length in the elastic reduction region is calculated based on the following formula (9). [Math 11] [Math 12] However, in equation (8), the following relationships exist: [Number 13] [Number 14] [Number 15] [Number 16] However, in equation (9), the following relationships exist between equations (14) and (20): [Number 17] [Number 18] [Number 19] [Number 20] [Math 21] [Number 22] [Number 23] However, in equations (8) to (20), [Number 24] [Number 25] [Number 26] [Number 27] [Number 28] [Number 29]

3. A method for calculating the rolling load of a rolling mill, A step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill; A step of calculating the contribution to the rolling load by at least one of the elastic recovery region and the elastic reduction region based on the contact arc length, A method for calculating rolling load, including the method described above.

4. The rolling load calculation method according to claim 3, wherein in the step of calculating the contribution to the rolling load, the contribution to the rolling load due to the elastic recovery region is calculated based on the following formula (1), and the contribution to the rolling load due to the elastic reduction region is calculated based on the following formula (2). [Number 30] [Number 31] However, in equation (1), the following relationships exist between equations (3) and (4): [Number 32] [Number 33] However, in equation (2), the following relationships exist: [Number 34] [Number 35] [Number 36] However, in equations (1) to (7), [Number 37] [Number 38] [Number 39] [Number 40] [Number 41] [Number 42]

5. The rolling load calculation method according to claim 3 or 4, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (8), and the contact arc length in the elastic reduction region is calculated based on the following formula (9). [Number 43] [Number 44] However, in equation (8), the following relationships exist: [Number 45] [Number 46] [Number 47] [Number 48] However, in equation (9), the following relationships exist between equations (14) and (20): [Number 49] [Number 50] [Number 51] [Number 52] [Number 53] [Number 54] [Number 55] However, in equations (8) to (20), [Number 56] [Number 57] [Number 58] [Number 59] [Number 60] [Number 61]

6. A method for calculating the contact arc length of a rolling mill, The process includes the step of calculating the contact arc length of at least one of the elastic restoration region and the elastic reduction region based on Hooke's law in the plane strain state of the rolled material, the equilibrium of forces within the roll bite of the rolling mill, and the rolling direction stress distribution approximated by a function dependent on the position coordinates in the rolling direction of the rolling mill, A method for calculating the contact arc length, wherein in the step of calculating the contact arc length, the contact arc length in the elastic recovery region is calculated based on the following formula (1), and the contact arc length in the elastic reduction region is calculated based on the following formula (2). [Number 62] [Number 63] However, in equation (1), the following relationships exist: [Number 64] [Number 65] [Number 66] [Number 67] However, in equation (2), the following relationships exist between equations (7) and (13): [Number 68] [Number 69] [Number 70] [Number 71] [Number 72] [Number 73] [Number 74] However, in equations (1) to (13), [Number 75] [Number 76] [Number 77] [Number 78] [Number 79] [Number 80]

7. A rolling method comprising changing the roll gap based on the rolling load distribution calculated using the rolling load distribution calculation method described in claim 1, reflecting the current lubrication conditions.

8. A rolling method comprising changing the roll gap based on the rolling load distribution calculated using the rolling load distribution calculation method described in claim 2, reflecting the current lubrication conditions.

9. A rolling method comprising changing the roll gap based on the rolling load calculated using the rolling load calculation method described in claim 3 or 4, reflecting the current lubrication conditions.

10. A rolling method comprising changing the roll gap based on the rolling load calculated using the rolling load calculation method described in claim 5, taking into account the current lubrication conditions.

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