Rolling load and forward slip calculation device and method

Abstract

To provide a rolling load and forward slip calculation device and method, capable of calculating rolling load and forward slip regardless of whether they are positive or negative.SOLUTION: A rolling load and forward slip calculation device 1000 alternately executes rolling load calculation processing of obtaining first to third rolling loads by first to third rolling load models on the basis of the first to third radii of a work roll, and radius calculation processing of obtaining the first to third radii by calculation of roll flat deformation on the basis of the first to third rolling loads with an initial value as the radius of the work roll until the first to third rolling loads and the first to third radii converge. The device also obtains the first to third forward slips by first to third forward slip models on the basis of the obtained first to third radii, and determines the final rolling load and forward slip from the obtained first to third rolling loads and first to third forward slips.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a rolling load and forward slip ratio calculation device and a rolling load and forward slip ratio calculation method for determining the rolling load and forward slip ratio in a rolling mill that rolls a material to be rolled with a pair of work rolls. [Background technology]

[0002] In general, rolling theory is used to analyze the rolling process when a material is rolled with a pair of work rolls. This rolling theory started with Karman's theory, and through the research of various approximate analysis methods, it has developed into, for example, Nadai's solution and Bland & Ford's cold rolling theory. These are generally called classical rolling theories, and in contrast, with the development of computers, the analysis of the rolling process by numerical analysis using the finite element method has also been researched and developed.

[0003] In this classical rolling theory, the speed of the rolled material at the exit v and the surface speed of the work roll (roll peripheral speed) v R The leading edge f S (=(vv R ) / v R ) is a positive value, and the surface speed of the work roll v is greater than the exit speed v of the rolled material. R However, in actual rolling, the forward slip ratio f S It is known that the forward slip ratio can become negative. When controlling a rolling mill, the negative forward slip that actually occurs must be taken into consideration, and this is proposed, for example, in Patent Document 1.

[0004] The method of setting a rolling schedule for cold rolling disclosed in Patent Document 1 involves determining the forward slip ratio from the roll speed of each stand and the sheet speed at the exit of each stand during rolling of a strip in a cold tandem mill, creating friction coefficient prediction equations from the obtained forward slip ratios for regions where the forward slip ratio is positive and regions where it is negative, and correcting the reduction distribution, tension, and rolling speed of each stand from these friction coefficient prediction equations so as to achieve a target forward slip ratio, thereby setting a rolling schedule. More specifically, R The actual measurement of the forward advance rate f s is required, and the forward advance rate f S If is negative, then |f s As |f S The forward slip ratio f is calculated using the friction coefficient prediction formula used when S The friction coefficient μ when is negative is sought. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 03-151107 Summary of the Invention [Problem to be solved by the invention]

[0006] In recent years, the demand for high tensile steel sheets (high tensile strength steel sheets) has been growing. In the production of high tensile steel sheets, a negative forward slip often occurs, and therefore there is a demand for the calculation of the forward slip and the rolling load not only in the positive forward slip region but also in the negative forward slip region. In the above-mentioned Patent Document 1, the forward slip f S is measured and not calculated.

[0007] The present invention has been made in consideration of the above-mentioned circumstances, and an object of the present invention is to provide a rolling load and forward slip ratio calculation device and a rolling load and forward slip ratio calculation method that can calculate the rolling load and forward slip ratio regardless of whether they are positive or negative. [Means for solving the problem]

[0008] As a result of various investigations, the inventors of the present invention have found that the above object can be achieved by the present invention described below. That is, a rolling load and forward slip calculation device according to one aspect of the present invention is a device for calculating a rolling load and forward slip in a rolling mill which rolls a material to be rolled with a pair of work rolls, and includes a first calculation processing unit which alternately executes a rolling load calculation process for calculating first to third rolling loads by first to third rolling load models based on first to third radii of the work rolls and a radius calculation process for calculating the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll as an initial value, until the first to third rolling loads and the first to third radii converge, a second calculation processing unit which calculates the first to third forward slips by first to third forward slip models based on the first to third radii calculated by the first calculation processing unit, and a determination processing unit which determines a final rolling load and forward slip from the first to third rolling loads calculated by the first calculation processing unit and the first to third forward slips calculated by the second calculation processing unit. A rolling load and forward slip calculation method according to another aspect of the present invention is a method executed by a computer for determining a rolling load and forward slip in a rolling mill which rolls a material to be rolled with a pair of work rolls, and includes a first calculation processing step in which a rolling load calculation process for determining first to third rolling loads using first to third rolling load models based on first to third radii of the work roll and a radius calculation process for determining the first to third radii by calculating roll flattening deformation based on the first to third rolling loads are alternately performed with an initial value being the radius of the work roll until the first to third rolling loads and the first to third radii converge; a second calculation processing step for determining first to third forward slips using first to third forward slip models based on the first to third radii determined in the first calculation processing step; and a determination processing step for determining a final rolling load and forward slip from the first to third rolling loads determined in the first calculation processing step and the first to third forward slips determined in the second calculation processing step.Here, in the above-mentioned rolling load and forward forward ratio calculation device and method, the first to third rolling load models are model formulas for calculating the rolling load, which are obtained based on a differential equation obtained from the balance of forces acting on a minute area of ​​the rolled material in the roll bite, the first to third forward forward ratio models are model formulas for calculating the forward forward ratio, which are obtained based on the differential equation, the first rolling load, the first forward forward ratio and the first radius are the rolling load and forward forward ratio when the neutral point is on the outside of the entry side of the roll bite, the second rolling load, the second forward forward ratio and the second radius are the rolling load and forward forward ratio when the neutral point is inside the roll bite, and the third rolling load, the third forward forward ratio and the third radius are the rolling load and forward forward ratio when the neutral point is on the exit side of the roll bite.

[0009] Such a rolling load and forward slip ratio calculation device and rolling load and forward slip ratio calculation method can calculate the rolling load and forward slip ratio based on the first to third rolling load model equations and the first to third forward slip ratio model equations of the analytical solution which are approximately obtained based on the differential equation only by dividing the cases into three. Therefore, the rolling load and forward slip ratio can be calculated regardless of whether they are positive or negative.

[0010] In another aspect, in the above-mentioned rolling load and forward advance ratio calculation device and method, the determination processing unit and the determination processing step, respectively, determine the third rolling load and the third forward advance ratio as the final rolling load and forward advance ratio when the third forward advance ratio is negative, determine the first rolling load and the first forward advance ratio as the final rolling load and forward advance ratio when the first forward advance ratio is greater than the second forward advance ratio, and determine the second rolling load and the second forward advance ratio as the final rolling load and forward advance ratio except when the third forward advance ratio is negative and when the first forward advance ratio is greater than the second forward advance ratio.

[0011] Such a rolling load and forward slip ratio calculation device and rolling load and forward slip ratio calculation method determine the final rolling load and forward slip ratio for each case, and what actually exists as an actual phenomenon is a forward slip ratio calculated so as not to contradict the above case classification, and only in this case can the rolling load and forward slip ratio be calculated appropriately.

[0012] In another aspect, in the above-mentioned rolling load and forward forward ratio calculation device and method, the first to third rolling load models and the first to third forward forward ratio models are set to a friction coefficient of μ, a shear stress coefficient due to the relative speed between the work roll surface and the rolled material is set to α, the speed of the rolled material during rolling is set to v, and the surface speed of the work roll during rolling is set to v R The friction law is expressed as follows: τ={μ+α·(vv R )}·s, which is the model equation obtained by solving the differential equation.

[0013] According to this, the friction law is τ={μ+α·(vv R It is possible to provide a rolling load and forward ratio calculation device and a rolling load and forward ratio calculation method using the rolling load and forward ratio calculation device and method.

[0014] In another embodiment, in the above-mentioned rolling load and forward forward ratio calculation device and method, the thickness of the rolled material on the delivery side is h2, the rolling reduction is Δh, the radius of the work roll after flattening deformation is R, the friction coefficient is μ, the shear stress coefficient due to the relative speed between the work roll surface and the rolled material is α, and the surface speed of the work roll is v R The rolling tension on the delivery side is σ out The deformation resistance on the delivery side of the rolled material is σ out,y The rolling tension on the entry side is σ in The deformation resistance on the entry side of the rolled material is σ in,yIn this case, the first forward slip model equation is Equation 1 described later, the first rolling load model equation is Equation 2 described later, the second forward slip model equation is Equation 3 described later, the second rolling load model equation is Equation 4 described later, the third forward slip model equation is Equation 5 described later, and the third rolling load model equation is Equation 6 described later.

[0015] According to this, a rolling load and forward ratio calculation device and a rolling load and forward ratio calculation method can be provided that use the first forward ratio model formula, the first rolling load model formula, the second forward ratio model formula, the second rolling load model formula, the third forward ratio model formula and the third rolling load model formula with Equations 1 to 6 described below. Effect of the Invention

[0016] The rolling load and forward slip ratio calculation device and the rolling load and forward slip ratio calculation method according to the present invention can calculate the rolling load and forward slip ratio regardless of whether they are positive or negative. [Brief description of the drawings]

[0017] [Figure 1] FIG. 2 is a block diagram showing a configuration of a rolling load and forward thrust ratio calculation device in the embodiment. [Diagram 2] FIG. 1 is a diagram for explaining the balance of forces acting on a minute area of ​​a material being rolled by a roll bite. [Diagram 3] 4 is a flowchart showing the operation of the rolling load and forward ratio calculation device. [Figure 4] FIG. 11 is a diagram for explaining the calculation results of an embodiment and a comparative example, as an example. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In addition, configurations with the same reference numerals in each drawing indicate that they are the same configurations, and their description will be omitted as appropriate. In this specification, when referring to a general term, a reference numeral without a subscript is used, and when referring to an individual configuration, a reference numeral with a subscript is used.

[0019] The rolling load and forward slip calculation device in the embodiment is a device for calculating a rolling load and forward slip in a rolling mill which rolls a material to be rolled with a pair of work rolls. The rolling load and forward slip calculation device includes a first calculation processing unit which alternately executes a rolling load calculation process for calculating first to third rolling loads by first to third rolling load models based on first to third radii of the work roll and a radius calculation process for calculating the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll as an initial value, until the first to third rolling loads and the first to third radii converge, a second calculation processing unit which calculates the first to third forward slips by first to third forward slip models based on the first to third radii calculated by the first calculation processing unit, and a determination processing unit which determines a final rolling load and forward slip from the first to third rolling loads calculated by the first calculation processing unit and the first to third forward slips calculated by the second calculation processing unit. Hereinafter, such a rolling load and forward thrust calculation device and the rolling load and forward thrust calculation method implemented therein will be described in more detail.

[0020] FIG. 1 is a block diagram showing the configuration of a rolling load and forward thrust calculation device according to an embodiment.

[0021] The rolling load and forward slip ratio calculation device 1000 in the embodiment is a device that calculates the rolling load and forward slip ratio in a rolling device that rolls a rolled material with a pair of work rolls, and for example, as shown in FIG. 1, is equipped with a control processing unit 1, an input unit 2, an output unit 3, an interface unit (IF unit) 4, and a memory unit 5.

[0022] The rolling mill may be of any type (kind) of equipment, such as a tandem rolling mill in which multiple rolling stands are arranged in series, or a reverse rolling mill in which one rolling mill moves back and forth. Among these, the rolling mill may be a double roll mill having only a pair of work rolls, a quadruple roll mill further including a pair of backup rolls, or a cluster mill having multiple backup rolls.

[0023] The input unit 2 is connected to the control processing unit 1 and is a device for inputting various commands such as a command to start calculation, and various data required for operating the rolling load and forward advance calculation device 1000, such as the subject of calculation and various parameters required for the calculation described below, to the rolling load and forward advance calculation device 1000, and is, for example, a keyboard, a mouse, and a plurality of input switches to which predetermined functions are assigned. The output unit 3 is connected to the control processing unit 1 and is a device for outputting commands, data, calculation results, etc. input from the input unit 2 under the control of the control processing unit 1, and is, for example, a display device such as a CRT display, an LCD (liquid crystal display device), an organic EL display, or a printing device such as a printer.

[0024] The input unit 2 and the output unit 3 may be configured with a touch panel. In the case of configuring this touch panel, the input unit 2 is a position input device that detects and inputs an operation position, for example, a resistive film type or a capacitive type, and the output unit 3 is a display device. In this touch panel, a position input device is provided on the display surface of the display device, and one or more input contents that can be input to the display device are displayed. When a user touches a display position that displays the input content that the user wants to input, the position is detected by the position input device, and the display content displayed at the detected position is input to the rolling load and forward advance calculation device 1000 as the user's operation input content. In such a touch panel, the user can easily intuitively understand the input operation, so that a rolling load and forward advance calculation device 1000 that is easy for the user to handle is provided.

[0025] The IF unit 4 is connected to the control processing unit 1 and is a circuit that inputs and outputs data to and from, for example, an external device under the control of the control processing unit 1, and is, for example, an interface circuit of RS-232C, which is a serial communication method, an interface circuit using the Bluetooth (registered trademark) standard, an interface circuit using the USB standard, etc. The IF unit 4 may also be, for example, a communication interface circuit that transmits and receives communication signals to and from an external device, such as a data communication card or a communication interface circuit conforming to the IEEE802.11 standard, etc.

[0026] The storage unit 5 is a circuit connected to the control processing unit 1 and stores various predetermined programs and various predetermined data according to the control of the control processing unit 1. The various predetermined programs include, for example, a control processing program, and the control processing program includes, for example, a control program, a first calculation processing program, a second calculation processing program, and a determination processing program. The control program is a program that controls each of the units 2 to 5 of the rolling load and forward slip calculation device 1000 according to the function of each unit. The first calculation processing program is a program that alternately executes a rolling load calculation process that obtains the first to third rolling loads by a first to third rolling load model based on the first to third radii of the work roll, and a radius calculation process that obtains the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll as an initial value, until the first to third rolling loads and the first to third radii converge. The second calculation program is a program for calculating the first to third forward slips by first to third forward slip models based on the first to third radii calculated by the first calculation processing program. The determination processing program is a program for determining a final rolling load and forward slip from the first to third rolling loads calculated by the first calculation processing program and the first to third forward slips calculated by the second calculation processing program. The various predetermined data include data required for executing each of these programs, such as the subject of the calculation, various parameters required for the calculation, and calculation results.

[0027] Such a storage unit 5 includes, for example, a ROM (Read Only Memory) which is a nonvolatile storage element, an EEPROM (Electrically Erasable Programmable Read Only Memory) which is a rewritable nonvolatile storage element, etc. The storage unit 5 also includes a RAM (Random Access Memory) which serves as a so-called working memory of the control processing unit 1 for storing data generated during execution of the predetermined program, etc. The storage unit 5 may also be configured to include a hard disk device with a relatively large storage capacity.

[0028] The control processing unit 1 is a circuit for controlling each of the units 2 to 5 of the rolling load and forward slip ratio calculation device 1000 in accordance with the function of each unit, and for determining the rolling load and forward slip ratio in the rolling device. The control processing unit 1 is configured, for example, with a CPU (Central Processing Unit) and its peripheral circuits. In the control processing unit 1, a control unit 11, a first calculation processing unit 12, a second calculation processing unit 13, and a decision processing unit 14 are functionally configured by executing the control processing program.

[0029] The control unit 11 controls each of the units 2 to 5 of the rolling load and forward slip ratio calculation device 1000 in accordance with the function of each unit, and is responsible for the overall control of the rolling load and forward slip ratio calculation device 1000.

[0030] The first calculation processing unit 12 alternately executes a rolling load calculation process for determining first to third rolling loads using first to third rolling load models based on the first to third radii of the work roll, and a radius calculation process for determining the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll being set as an initial value, until the first to third rolling loads and the first to third radii converge.

[0031] The second calculation processing unit 13 calculates the first to third forward advance rates by first to third forward advance rate models based on the first to third radii calculated by the first calculation processing unit 12.

[0032] The determination processing unit 14 determines a final rolling load and forward forward ratio from among the first to third rolling loads calculated by the first calculation processing unit 12 and the first to third forward forward ratios calculated by the second calculation processing unit 13. More specifically, when the third forward forward ratio is negative, the determination processing unit 14 determines the third rolling load and the third forward forward ratio as the final rolling load and forward forward ratio, when the first forward forward ratio is greater than the second forward forward ratio, the determination processing unit 14 determines the first rolling load and the first forward forward ratio as the final rolling load and forward forward ratio, and when the third forward forward ratio is negative or the first forward forward ratio is greater than the second forward forward ratio, the determination processing unit 14 determines the second rolling load and the second forward forward ratio as the final rolling load and forward forward ratio.

[0033] The control unit 11 outputs the final rolling load and forward slip ratio calculated by the determination processing unit 14 to the output unit 3 as the calculation results.

[0034] The first to third rolling load models are model formulas for calculating a rolling load, which are obtained based on a differential equation obtained from the balance of forces acting on a minute area of ​​the rolled material in the roll bite. The first to third forward slip models are model formulas for calculating a forward slip, which are obtained based on the differential equation. The first rolling load P + , the first forward rate f S+ and the first radius R' + is the rolling load P and forward force f when the neutral point is on the outside of the entry side of the roll bite. S The second rolling load P0 and the second forward slip f S0 and the second radius R'0 is the rolling load P and forward rate f when the neutral point is in the roll bite. S0 The third rolling load P - , the third forward rate f S- and the third radius R' -is the rolling load P and forward force f when the neutral point is on the exit side of the roll bite. S It is.

[0035] The first to third rolling load models and the first to third forward slip models will now be described in more detail.

[0036] These first to third rolling load models and first to third forward slip models are obtained based on differential equations obtained from the balance of forces acting on a minute area of ​​the roll bite in the rolled material.

[0037] Fig. 2 is a diagram for explaining the balance of forces acting on a minute region of the rolled material in the roll bite. In Fig. 2, the minute region MR of the rolled material is illustrated, and the pair of work rolls is omitted. When Fig. 2 is viewed from the front, the right side of the paper is the entrance side of the rolling mill, and the left side of the paper is the exit side of the rolling mill.

[0038] The minute region MR in the rolled material in the roll bite is subjected to, for example, surface pressure s at the contact surface CF between the work roll and the rolled material during rolling, and shear stress τ at the contact surface CF between the work roll and the rolled material during rolling, as shown in Fig. 2. If the angle formed by the line segment connecting the center point (rotation axis) CP1 of the work roll and the center point CP2 of the contact surface CF is taken as θ with respect to the vertical direction, and the width of the minute region MR is taken as dx, then the length of the contact surface CF (contact arc length) is dx / cosθ, and therefore the vertical balance of the forces acting on the minute region MR is expressed by the following equation W1, and the horizontal balance of the forces acting on the minute region MR is expressed by the following equation W2.

[0039]

number

[0040]

number

[0041] Here, h is the plate thickness at the exit side in the infinitesimal region MR, h+dh is the plate thickness at the entry side in the infinitesimal region MR, q is the stress in the longitudinal direction of rolling in the infinitesimal region MR, and q+dq is the stress in the longitudinal direction at a position at a minute distance away in the infinitesimal region MR. P is the rolling load per unit width.

[0042] If we ignore dhdq in equation W2 as it is sufficiently small compared to the other terms and eliminate the surface pressure s from equation W2 using equation W1, we obtain the differential equation expressed by the following equation W3.

[0043]

number

[0044] Furthermore, by using the Bland & Ford approximation formula; d(hk) / dx=0, equation W3 becomes the following equation W4. This equation W4 is the differential equation to be solved analytically. The friction law used to solve this differential equation W4 is the well-known τ={μ+α·(vv R )}·s is used. In the Bland & Ford approximation, k is the deformation resistance of the material at the position in the rolling direction.

[0045]

number

[0046] In order to solve the differential equation W4, it is necessary to determine an integral constant so as to satisfy the boundary conditions. Therefore, in this embodiment, the differential equation W4 is solved in three separate cases.

[0047] In the first case, the neutral point is outside the roll bite at the entry side of the roll bite (i.e., the first forward rate f S+ is the second leading rate f S0 In this case, the rolling load (first rolling load) P + is expressed by the following equation 1, and the forward rate (first forward rate) f S+ is expressed by the following equation 2.

[0048]

number

[0049]

number

[0050] In the second case, the neutral point is in the roll bite (i.e., the third forward rate f S- When is negative and the first leading rate f S+ is the second leading rate f S0 In this case, the rolling load (second rolling load) P0 is expressed by the following formula 3, and the forward ratio (second forward ratio) f S0 is expressed by the following equation 4.

[0051]

number

[0052]

number

[0053] In the third case, the neutral point is outside the roll bite at the exit side of the roll bite (i.e., the third forward rate f S- is negative), in this case, the rolling load (third rolling load) P - is expressed by the following equation 5, and the forward advance rate (third forward advance rate) f S- is expressed by the following equation 6.

[0054]

number

[0055]

number

[0056] Here, A1, B1, C1, D1, DD, E + , E - ,F,t n and t L is expressed by the following Equations 7-1 to 7-10.

[0057]

number

[0058] Furthermore, R is the radius of the work roll after flattening (roll radius). h1 is the plate thickness at the entry side of the rolling mill (the entry side thickness of the material being rolled), and h2 is the plate thickness at the exit side of the rolling mill (the exit side thickness of the material being rolled). △h is the reduction amount of the rolling mill. μ is the friction coefficient between the work roll and the material being rolled. σ in is the rolling tension at the entry side of the rolling mill, and σ out is the rolling tension at the exit side of the rolling mill. σ in,y is the deformation resistance of the rolled material at the entry side of the rolling mill, and σ out,y is the deformation resistance of the rolled material at the exit of the rolling mill. v is the plate speed (speed of the rolled material) during rolling. v R is the surface speed of the work roll during rolling. α is the shear stress coefficient due to the relative speed between the work roll surface and the rolled material.

[0059] In this way, the model equations of the first to third rolling load models and the first to third forward slip models are obtained. More specifically, the first calculation processing unit 12 first calculates the first to third radii R of the work rolls using the radius R0 of the work roll as an initial value. + , R0, R - (Here, R + =R0=R - =R0) according to Equation 1, Equation 3 and Equation 5, the first to third rolling loads P + , P0, P - Next, the first calculation processing unit 12 executes a rolling load calculation process (initial (first) rolling load calculation process) to obtain the first to third rolling loads P +, P0, P - Based on the calculation of roll flattening deformation, the first to third radii R' + , R'0, R' - The first calculation processing unit 12 executes a radius calculation process (initial (first) radius calculation process) to calculate the roll flattening deformation. The following formula 8, which is the Hitchcock flattening deformation formula, is used to calculate the roll flattening deformation. Next, the first calculation processing unit 12 calculates the first to third rolling loads P + , P0, P - and the first to third radii R' + , R'0, R' - If the result of this determination is that the radius R′ has not converged, the first calculation processing unit 12 calculates the radius R′ obtained by the first radius calculation process. + , R'0, R' - The first to third radii R used in the second rolling load calculation process + , R0, R - Then, using the result, a second radius calculation process is performed and a convergence determination is performed. On the other hand, if the radius result shows convergence, the first calculation processing unit 12 ends the process and notifies the second calculation processing unit 13 of the end of the process.

[0060]

number

[0061] Here, R is the radius of the work roll before the roll flattening calculation, R' is the radius of the work roll after the roll flattening calculation, ε is the Young's modulus of the work roll, η is the Poisson's ratio of the work roll, and π is the constant of the circumference of the circle.

[0062] The convergence judgment is performed, for example, by determining whether the first to third radii R + , R0, R - and the first to third rolling loads P + , P0, P - Each of the first to third radii R + , R0, R -and the first to third rolling loads P + , P0, P - (The first to third radii R used in this calculation + , R0, R - and the first to third rolling loads P + , P0, P - ) Absolute value of the difference between |△R + |, |△R0|, |△R - |, |△P + |, |△P0|, |△P - | and calculate the absolute value of their difference |△R + |, |△R0|, |△R - |, |△P + |, |△P0|, |△P - |Each has a predetermined threshold (convergence judgment threshold) thR + , thR0, thR - , thP + , thP0, thP - Determine whether or not the absolute value of the difference |△R + |, |△R0|, |△R - |, |△P + |, |△P0|, |△P - |Each is the convergence threshold thR + , thR0, thR - , thP + , thP0, thP - If it is equal to or less than the threshold value, it is determined that the convergence has occurred, and if not, it is determined that the convergence has not occurred. + , thR0, thR - , thP + , thP0, thP - is appropriately set in advance, and the convergence judgment threshold thR + , thR0, thR - may be the same or different, and the convergence determination threshold thP + , thP0, thP - The values ​​of and may be equal to each other or may be different.

[0063] Here, from Equation 3 and Equation 7-8, the second rolling load P0 in the rolling load calculation process is calculated using the second forward ratio f S0For this reason, the first calculation processing unit 12 calculates the second forward ratio f based on the second radius R when calculating the second rolling load P0 in the rolling load calculation process. S0 It can also be seen that the second rolling load P0 is determined by calculating

[0064] When the first calculation processing unit 12 notifies the second calculation processing unit 13 of the end of the processing, the second calculation processing unit 13 calculates the first to third radii R + , R0, R - Based on the above, the first to third advance rates f S+ , f S0 , f S- Request.

[0065] Then, the determination processing unit 14 determines the third leading rate f S- If is negative, the third rolling load P - and the third leading rate f S- The final rolling load P and forward advance rate f S The first advanced rate f S+ is the second leading rate f S0 If it is larger, the first rolling load P + and the first leading rate f + The final rolling load P and forward forward rate f S The third advanced rate f S- When is negative and the first leading rate f S+ is the second leading rate f S0 Except when the second rolling load P0 and the second forward ratio f S0 The final rolling load P and forward forward rate f S is decided.

[0066] The work roll radius R0, inlet plate thickness h1, outlet plate thickness h2, rolling reduction △h, friction coefficient μ, inlet rolling tension σ required for the calculation of formulas 1 to 8 are in , exit side rolling tension σ out , σ in,y is the deformation resistance of the rolled material at the entry side of the rolling mill σ in,y , deformation resistance of the rolled material at the exit σ out,y, plate speed v, work roll surface speed v R The shear stress coefficient α due to the relative speed between the work roll surface and the rolled material, Young's modulus ε of the work roll, and Poisson's ratio η of the work roll are inputted as the various parameters, for example, from the input unit 2 or the IF unit 4, before the above calculation, and are stored in the memory unit 5.

[0067] The control processing unit 1, the input unit 2, the output unit 3, the IF unit 4 and the storage unit 5 can be configured by, for example, a desktop or notebook computer.

[0068] Next, the operation of this embodiment will be described with reference to a flowchart shown in FIG.

[0069] When the power supply is turned on, the rolling load and forward advance calculation device 1000 having such a configuration initializes each required part and starts its operation. In the control processing unit 1, a control unit 11, a first calculation processing unit 12, a second calculation processing unit 13 and a decision processing unit 14 are functionally configured by executing the control processing program.

[0070] In FIG. 3, for example, when an instruction to start calculation is input from the input unit 2, the rolling load and forward thrust calculation device 1000 performs the rolling load calculation process and the radius calculation process by the first calculation processing unit 12 of the control processing unit 1, with the radius R0 of the work roll as the initial value, and calculates the first to third rolling loads P + , P0, P - and the first to third radii R + , R0, R - are alternately performed until convergence, which results in the first, second and third radii R + , R0, R - and the first to third rolling loads P + , P0, P - is calculated and stored in the storage unit 5 (S1, first calculation processing step).

[0071] Next, the rolling load and forward thrust calculation device 1000 calculates the first to third radii R + , R0, R - Based on the first to third forward rate models, the first to third forward rates f S+ , f S0 , f S- is calculated and stored in the storage unit 5 (S2, second calculation processing step).

[0072] Next, the rolling load and forward thrust calculation device 1000 determines the first to third rolling loads P + , P0, P - and the first to third forward rates f S+ , f S0 , f S- Among them, the final rolling load P and forward thrust f S is determined (selected) and stored in the storage unit 5 (S3, determination processing step).

[0073] Then, the rolling load and forward slip ratio calculation device 1000 calculates the final rolling load P and forward slip ratio f determined by the determination processing unit 14 in the process S3 by the control unit 11 of the control processing unit 1. S The control unit 11 outputs the final rolling load P and forward slip ratio f to an external device via the IF unit 4 as necessary (S4), and the process ends. S may be output.

[0074] Next, examples and comparative examples will be described.

[0075] Fig. 4 is a diagram for explaining the calculation results of an embodiment and a comparative example as an example. Fig. 4A shows the calculation results of the embodiment, and Fig. 4B shows the calculation results of the comparative example. The horizontal axis of each of Fig. 4A and Fig. 4B is the actual value of the forward ratio, and each of these vertical axes is the calculated value (predicted value) of the forward ratio.

[0076] The calculation results of the embodiment are the calculated values ​​of the forward ratio calculated by the rolling load and forward ratio calculation device 1000 described above. In contrast, the calculation results of the comparative example are calculated values ​​calculated by the forward ratio formula in the cold rolling theory of Bland & Ford. As can be seen by comparing FIG. 4A and FIG. 4B, in the comparative example, even if the forward ratio is negative in the actual value, the calculated value is positive, and the calculation is not performed properly. In contrast, in the embodiment, when the forward ratio is negative in the actual value, the calculated value is also negative, and the calculation is performed more appropriately. Of course, the forward ratio can also be calculated properly in the positive forward ratio region.

[0077] Therefore, by using the rolling load and forward slip ratio calculation device 1000 in the embodiment, the rolling load and forward slip ratio calculation can be predicted and simulated without actually performing rolling.

[0078] As described above, the rolling load and forward ratio calculation device 1000 in the embodiment and the rolling load and forward ratio calculation method implemented therein can calculate the rolling load P and the forward ratio f based on the first to third rolling load model equations (Equation 1, Equation 3, Equation 5) and the first to third forward ratio model equations (Equation 2, Equation 4, Equation 6) of the analytical solutions approximately obtained based on differential equations by dividing the cases into three. S Therefore, regardless of whether it is positive or negative, the rolling load P and forward ratio f S can be calculated.

[0079] The above rolling load and forward slip ratio calculation device 1000 and the rolling load and forward slip ratio calculation method determine the final rolling load and forward slip ratio for each case, and what can actually exist as an actual phenomenon is a forward slip ratio calculated so as not to contradict the above case classification, and only in this case can the rolling load and forward slip ratio be appropriately determined.

[0080] In order to express the present invention, the present invention has been described adequately and sufficiently through the embodiments with reference to the drawings in the above description, but it should be recognized that those skilled in the art can easily change and / or improve the above-mentioned embodiments. Therefore, unless the changes or improvements made by those skilled in the art are at a level that departs from the scope of the claims described in the claims, the changes or improvements are interpreted as being included in the scope of the claims. [Explanation of symbols]

[0081] 1 Control processing section 2 Input section 3. Output section 4. Interface section (IF section) 5 Storage section 11 Control section 12 First arithmetic processing unit 13 Second arithmetic processing unit 14 Decision Processing Unit

Claims

1. A rolling load and forward slip ratio calculation device for calculating a rolling load and forward slip ratio in a rolling mill that rolls a material to be rolled with a pair of work rolls, comprising: a first calculation processing unit which alternately executes a rolling load calculation process for determining first to third rolling loads by first to third rolling load models based on the first to third radii of the work roll, and a radius calculation process for determining the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll as an initial value, until the first to third rolling loads and the first to third radii converge; a second processor for calculating first through third forward advances by first through third forward advance models based on the first through third radii calculated by the first processor; a determination processing unit that determines a final rolling load and forward slip from the first to third rolling loads calculated by the first calculation processing unit and the first to third forward slips calculated by the second calculation processing unit, the first to third rolling load models are model formulas for calculating a rolling load, which are obtained based on a differential equation obtained from a balance of forces acting on a minute area of ​​a rolled material in a roll bite, the first to third forward advance models are model equations for calculating forward advances calculated based on the differential equation, the first rolling load, the first forward slip rate, and the first radius are rolling load and forward slip rate when a neutral point is on an outer side of an entry side of the roll bite, the second rolling force, the second forward slip, and the second radius are rolling force and forward slip when the neutral point is within the roll bite; the third rolling load, the third forward slip rate, and the third radius are rolling load and forward slip rate when the neutral point is on the delivery side of the roll bite, Rolling load and advance rate calculator.

2. The determination processing unit: If the third forward slip is negative, the third rolling load and the third forward slip are determined to be the final rolling load and forward slip; If the first forward slip is greater than the second forward slip, the first rolling load and the first forward slip are determined as the final rolling load and forward slip; determining the second rolling load and the second forward slip ratio as the final rolling load and the final forward slip ratio, except when the third forward slip ratio is negative and when the first forward slip ratio is greater than the second forward slip ratio; The rolling load and forward ratio calculation device according to claim 1.

3. In the first to third rolling load models and the first to third forward slip models, a friction coefficient is μ, a shear stress coefficient due to the relative speed between the work roll surface and the rolled material is α, a speed of the rolled material during rolling is v, and a surface speed of the work roll during rolling is v Ｒ The friction law is expressed as follows: τ = {μ + α · (v - v Ｒ )}·s is a model equation obtained by solving the differential equation, The rolling load and forward ratio calculation device according to claim 1.

4. The thickness of the rolled material on the delivery side is h ２ The rolling reduction is Δh, the radius of the work roll after flattening deformation is R, the friction coefficient is μ, the shear stress coefficient due to the relative speed between the work roll surface and the rolled material is α, and the surface speed of the work roll is v Ｒ The rolling tension on the delivery side is σ ｏｕｔ The deformation resistance on the delivery side of the rolled material is σ ｏｕｔ，ｙ The rolling tension on the entry side is σ ｉｎ The deformation resistance on the entry side of the rolled material is σ ｉｎ，ｙ In this case, the first forward slip model formula is the following formula 1, the first rolling load model formula is the following formula 2, the second forward slip model formula is the following formula 3, the second rolling load model formula is the following formula 4, the third forward slip model formula is the following formula 5, and the third rolling load model formula is the following formula 6. The rolling load and forward ratio calculation device according to claim 1. [0010] [0025] [0030] [0045] [0050] [006] However, A １ , B １ , C １ , D １ , D.D., E. ＋ , E － , F,t ｎ and t Ｌ is defined by the following Equations 7-1 to 7-10. [0070]

5. A method for calculating a rolling load and a forward slip ratio in a rolling mill that rolls a material to be rolled with a pair of work rolls, the method being executed by a computer, comprising: a first calculation processing step for alternately executing a rolling load calculation process for determining first to third rolling loads by first to third rolling load models based on the first to third radii of the work roll and a radius calculation process for determining the first to third radii by calculating roll flattening deformation based on the first to third rolling loads, with the radius of the work roll as an initial value, until the first to third rolling loads and the first to third radii converge; a second calculation process for calculating first to third forward advances by first to third forward advance models based on the first to third radii calculated in the first calculation process; a determination process step of determining a final rolling load and forward slip ratio from the first to third rolling loads obtained in the first calculation process step and the first to third forward slip ratios obtained in the second calculation process step, the first to third rolling load models are model formulas for calculating a rolling load, which are obtained based on a differential equation obtained from a balance of forces acting on a minute area of ​​a rolled material in a roll bite, the first to third forward advance models are model equations for calculating forward advances calculated based on the differential equation, the first rolling load, the first forward slip rate, and the first radius are rolling load and forward slip rate when a neutral point is on an outer side of an entry side of the roll bite, the second rolling force, the second forward slip, and the second radius are rolling force and forward slip when the neutral point is within the roll bite; the third rolling load, the third forward slip rate, and the third radius are rolling load and forward slip rate when the neutral point is on the delivery side of the roll bite, Rolling load and advance ratio calculation method.

6. The decision process includes: If the third forward slip is negative, the third rolling load and the third forward slip are determined to be the final rolling load and forward slip; If the first forward slip is greater than the second forward slip, the first rolling load and the first forward slip are determined as the final rolling load and forward slip; determining the second rolling load and the second forward slip ratio as the final rolling load and the final forward slip ratio, except when the third forward slip ratio is negative and when the first forward slip ratio is greater than the second forward slip ratio; The rolling load and forward ratio calculation method according to claim 5.

7. In the first to third rolling load models and the first to third forward slip models, a friction coefficient is μ, a shear stress coefficient due to the relative speed between the work roll surface and the rolled material is α, a speed of the rolled material during rolling is v, and a surface speed of the work roll during rolling is v Ｒ The friction law is expressed as follows: τ = {μ + α · (v - v Ｒ )}·s is a model equation obtained by solving the differential equation, The rolling load and forward ratio calculation method according to claim 5.

8. The thickness of the rolled material on the delivery side is h ２ The rolling reduction is Δh, the radius of the work roll after flattening deformation is R, the friction coefficient is μ, the shear stress coefficient due to the relative speed between the work roll surface and the rolled material is α, and the surface speed of the work roll is v Ｒ The rolling tension on the delivery side is σ ｏｕｔ The deformation resistance on the delivery side of the rolled material is σ ｏｕｔ，ｙ The rolling tension on the entry side is σ ｉｎ The deformation resistance on the entry side of the rolled material is σ ｉｎ，ｙ In this case, the first forward slip model formula is the following formula 1, the first rolling load model formula is the following formula 2, the second forward slip model formula is the following formula 3, the second rolling load model formula is the following formula 4, the third forward slip model formula is the following formula 5, and the third rolling load model formula is the following formula 6. The rolling load and forward ratio calculation method according to claim 5. [0080] [0090] [0089] ##EQU00011## ##EQU00012## ##EQU00013## However, A １ , B １ , C １ , D １ , D.D., E. ＋ , E － , F,t ｎ and t Ｌ is defined by the following Equations 7-1 to 7-10. ##EQU14##

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