JPH0372364B2 - - Google Patents

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a symmetrical component of the thickness distribution in the width direction in plate rolling, that is, a plate crown, and a method of controlling the plate shape that is closely related to this. It is.

[Conventional technology]

Conventional sheet crown/shape control methods model the relationship between the sheet crown or sheet shape obtained as a result of rolling and rolling conditions through statistical processing of actual rolling data or numerical analysis results, and then calculate rolling as a relatively simple formula. This is used for control.

However, the plate crown and plate shape that are actually obtained are greatly influenced by the widthwise load distribution between the work roll and the material, and furthermore, this widthwise load distribution is greatly influenced by the deformation characteristics of the rolled material.
When applying conventional control methods to the rolling of materials with different deformation characteristics, it is necessary to either create a new model equation for the material or review each coefficient of the model equation.

One way to deal with such problems is to introduce a learning function based on actual rolling data.

[Problem to be solved by the invention]

However, in the conventional model equation, the deformation characteristics of the rolling mill and the deformation characteristics of the rolled material are not sufficiently separated, making it extremely difficult to create an effective learning logic. In addition, numerical analysis results are often used to create model formulas, but when such analysis methods are evaluated accurately, the current deformation analysis is difficult because all deformation on the rolling mill side is an elastic deformation analysis. Although it is thought that sufficient accuracy can be expected with analytical theory, there are many aspects of the deformation characteristics of materials that are still unclear, such as the widening characteristics of materials, and it is thought that sufficient accuracy cannot be expected.

Therefore, when creating model formulas for the plate crown and plate shape that are calculated as a result of simultaneously solving the deformation characteristics of the rolling mill and the deformation characteristics of the material, it is possible to calculate the error related to the deformation characteristics of the material from the beginning. This results in a model with reduced accuracy.

The present invention aims to solve the problems of the conventional method as described above.

[Technical fields for solving problems]

A first aspect of the present invention is realized in a rolling control method for a rolling mill having a device capable of controlling the thickness distribution in the width direction of a rolled plate, when the load distribution in the width direction between the rolled plate and the work roll is uniform. A model formula showing the relationship between the widthwise plate thickness distribution and rolling conditions, and the widthwise plate thickness distribution and the widthwise plate thickness of the rolled plate on the entry side of the rolling machine, which are calculated by substituting the rolling conditions into the model formula. The operation amount of the width direction thickness distribution control device is determined using the calculation formula for the width direction thickness distribution of the rolled plate on the exit side of the rolling mill, which is configured as a linear combination of distributions, and the width To control the directional plate thickness distribution control device.

The second gist is that in a rolling control method for a rolling mill that has a device that can control the widthwise thickness distribution of a rolled plate, the rolling load during rolling is detected and the widthwise load distribution between the rolled plate and the work rolls is controlled. The width direction plate thickness distribution, which is calculated by substituting the actual measured value of the rolling load described above into the model formula showing the relationship between the width direction plate thickness distribution and rolling conditions that would be realized when the width direction plate thickness distribution is uniform, is the target determined at the time of setting calculation. The operation amount of the widthwise plate thickness distribution control device is determined so as to be closest to the target value corrected by feedback control.

The third gist is that in a method for controlling a rolling mill that includes a device that can control the thickness distribution in the width direction of a rolled plate and a shape detection device for the rolled plate, the difference between the actual plate shape measured by the plate shape detection device and the target plate shape is determined. The difference is converted into a difference in plate thickness distribution, and the widthwise plate thickness distribution achieved when the widthwise plate thickness distribution between the rolled plate and the work roll is uniform and the widthwise plate of the rolled plate on the entrance side of the rolling machine. Using the calculation formula for the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill, which is configured as a linear combination of thickness distributions, the converted value of the difference in thickness distribution is calculated as the thickness in the width direction between the rolled plate and the work roll. This is converted into the difference in the thickness distribution in the width direction that is realized when the distribution is uniform, and is also calculated as the difference in the thickness distribution in the width direction that is realized when the load distribution in the width direction between the rolled plate and the work roll is uniform. Using a model equation showing the relationship between rolling conditions, the operation amount of the widthwise plate thickness distribution control device is determined to eliminate the difference in plate thickness distribution.

The fourth gist is a rolling control method for a continuous rolling mill having a device capable of controlling the thickness distribution in the width direction of a rolled plate and a device capable of measuring the thickness distribution in the width direction of the finished product. In order to eliminate the difference between the plate thickness distribution actually measured by the distribution measuring device and the target plate thickness distribution in the last stage rolling mill, and to avoid disturbing the product shape, the rolling mill immediately before the last stage rolling machine Determine the amount of correction for the similar width direction thickness distribution with respect to the difference in thickness distribution and the exit side sheet thickness, and if the disturbance in the sheet shape between rolling mills due to this amount of correction exceeds the allowable range for rolling operations, make this correction. After further distributing the amount to the rolling mill in the previous stage, the thickness distribution in the width direction achieved when the thickness distribution in the width direction between the rolled plate and the work roll is uniform and the width of the rolled plate at the entrance side of the rolling mill. Using the calculation formula for the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill, which is configured as a linear combination of the thickness distribution in the direction, the amount of modification of the thickness distribution in the width direction on the exit side of each rolling machine is calculated as follows: This is converted into the amount of modification of the thickness distribution in the width direction that is realized when the thickness distribution in the width direction between the work rolls is uniform, and furthermore, when the load distribution in the width direction between the rolled plate and the work rolls is uniform. The operation amount of the width direction plate thickness distribution control device corresponding to the amount of correction of the plate thickness distribution is determined using a model formula showing the relationship between the width direction plate thickness distribution and rolling conditions realized in the method.

The present invention will be explained in detail below.

It is well known that even in the four-high rolling mill, which is the most widely used plate rolling mill at present, if the rolling load changes, the plate thickness distribution in the width direction also changes. A plate thickness distribution control device is a device that can control the thickness distribution in the width direction even under the condition that the rolling load is constant, and includes roll bending devices, variable crown rolls, work roll shifts, roll crosses, and 6-high rolling mills. The so-called crown shift function, such as the intermediate roll shift of the
It means the shape control end.

The plate thickness distribution achieved when the load distribution in the width direction between the rolled plate and the work rolls is uniform is determined by the rolling mill's dimension, the setting conditions of the crown shape control end, the rolling load, and the rolling conditions of the rolled material. If given, it depends solely on the deformation characteristics of the rolling mill, independently of the deformation characteristics of the other rolled materials. The plate crown determined from such a plate thickness distribution will be referred to as a mechanical plate crown below. As mentioned above, the mechanical plate crown is a basic amount that is determined only by the deformation characteristics of the rolling mill, but in actual rolling, the load distribution in the width direction changes variously depending on the entrance side plate crown and the deformation characteristics of the rolled material. Therefore, the exit side plate crown does not necessarily match the mechanical plate crown. Therefore, the relationship between the exit side plate crown and the mechanical plate crown that occurs during actual rolling will be explained below.

It is thought that the entry side sheet crown has a fairly large influence on the exit side sheet crown obtained in actual rolling, but in order to quantitatively express such an influence, we have used Koe Nakajima et al. In "Research on Control Methods (5th Report)" (30th Plastic Working Union Lecture No. 102-1979-), the concept of crown genetic coefficient was introduced.

The crown genetic coefficient η is defined as the influence coefficient on the exit side plate crown Ch when only the entry side plate crown C _H changes by ΔC _H while all other rolling conditions remain the same. That is, when the amount of change in the exit side plate crown that occurs at this time is ΔCh, there is a relationship as follows: ΔCh=η·ΔC _H (1).

The reason why the exit side plate crown is influenced by the entry side plate crown is that the change in the entrance side plate crown causes a slight difference in the elongation rate distribution in the width direction, and as a result, the tension in the roll bite in the width direction This can be explained by the mechanism that a large difference occurs in the distribution, the rolling load distribution in the width direction changes, and the roll deformation changes. Considering this, the elongation distribution in the width direction is determined by the difference between the entrance side plate crown ratio and the exit side plate crown ratio, so the influence of the entrance side plate crown is more than ΔCh/ It can be seen that it is more appropriate to express it in the form h=η〓・ΔC _H /H, that is, ΔCh=η〓・(1−r)・ΔC _H (2). Here, h is the exit side plate thickness, H is the entrance side plate thickness, r is the rolling reduction ratio, and η〓 is called the modified crown genetic coefficient.

From formula (2), the entrance plate crown C ⁰ _H which is a certain standard
When it is known that the exit plate crown at the time is C ⁰ h, the exit plate crown Ch corresponding to the input plate crown ΔC _H can be obtained by the following formula.

Ch＝C ⁰ h＋η〓・(1−r)・(C _H −C ⁰ _H ) (3) We will consider the plate crown model equation starting from equation (3), but C ⁰ _H , C ⁰ It is most reasonable to select h when the elongation distribution in the width direction is uniform (when the material temperature is uniform in the width direction, the rolling load distribution in the width direction is also uniform). At this time, the entry side plate crown ratio and the exit side plate crown ratio are equal, so the following relationship is established: C ⁰ _H = C ⁰ h・H/h=C ⁰ h・1/(1−r)…(4) By substituting into equation (3), the following equation is obtained.

Ch=(1-η〓)C ⁰ h+η〓(1-r)C _H ...(5) By the way, Ch in equation (5) is the exit crown when the elongation rate distribution in the width direction is uniform. If the distribution of deformation resistance in the width direction is uniform, then the rolling load distribution in the width direction will also be uniform, and C ⁰ h will match the mechanical plate crown η〓. Therefore, the following equation is obtained as the basic equation of the plate crown model.

Ch=(1−η〓)・〓+η〓(1−r)・C _H (6) If the widthwise conversion resistance distribution of the rolled material cannot be ignored, its influence term can be added to 〓.

Next, we will change our perspective and consider the exit side plate crown with the entrance side plate crown as a reference. When the temperature distribution in the width direction is uniform, the exit side plate crown C _H has the same crown ratio as the entrance side plate crown.
Considering the definition of 〓, it is clear that rolling with an equal crown ratio is actually achieved only when h/H is equal to h/H. Then, when there is a difference between _〓 and C _H・h/H+ζ(〓−C _H・h/H) That is, it is given by Ch=ζ〓+(1−ζ)(1−r)C _H …(7). Here, ζ represents the influence coefficient that changes in the mechanical plate crown due to changes in the roll curve, roll bending force, etc. have on the exit side plate crown, and will be referred to as the plate crown correction coefficient.

ζ and η〓 are completely different concepts from their definitions, but when comparing equations (6) and (7), the following relationship must hold: ζ=1−η〓 (8). In other words, equations (6) and (7) originally express the same content in different expressions, and their ultimate meaning is
This means equation (8).

Incidentally, the relational expression (6) or (7) can also be determined using a concept similar to that of the mill stiffness curve and plasticity modulus curve when determining the thickness of a rolled plate. As shown in Figure 1, if we take the plate crown C on the horizontal axis and the difference ΔP between the loads between the plate ends and the plate center on the vertical axis, then the deformation on the rolling mill side is ΔP = 0.
When C=〓, and for C<〓, the load at the edge of the plate must be greater than the load at the center of the plate. Therefore, if the relationship between C and ΔP is approximated by a straight line, and the absolute value of the gradient is k, then the deformation on the rolling mill side is expressed by the following equation.

ΔP=-k(C-〓)...(9) On the other hand, if we assume that the deformation resistance distribution in the width direction is uniform when C=(1-r)C _H for the deformation on the material side,
ΔP=0, and for C>(1-r)C _H , ΔP
>0. Therefore, if the relationship between C and ΔP is approximated by a straight line, and its slope is defined as m, the deformation on the material side is expressed by the following equation.

ΔP=m [C-(1-r)C _H ] (10) The plate crown Ch produced by rolling is determined at the intersection of the straight lines expressed by equations (9) and (10), and Ch=〓k/(m+k )+C _H (1-r)m/(m
+k) is obtained. If we set m/(m+k)=η〓, equation (11) matches equation (6).

It is academically very important that formula (8) holds true, and the present inventors have confirmed this through experiments. Ch is expressed as a linear combination of 〓 and C _H as in Ch=ζ・〓+η〓(1−r)C _H …(12), and η〓 and ζ are quantities that depend on the deformation characteristics of the rolled material. It is important that , 〓 are quantities determined by the deformation characteristics of the rolling mill.

Although η〓 and ζ can be determined from numerical analysis results as described above, it is ultimately preferable to confirm them through rolling experiments and learn from actual machine operation data. At the moment,
Regarding hot strip rolling, the above-mentioned literature by Nakajima et al. reports the results of determining the value of the crown heritability coefficient η through experiments and theory, and this is defined as 〓=η/(1−r) …(13) The plate crown correction coefficient ζ is also determined by converting it into a modified crown hereditary coefficient using the formula and further applying formula (8).

Therefore, the following explanation will be given assuming that the values of ζ and η〓 in equation (12) are known.

Now that we have clarified the relationship between the plate crown and the mechanical plate crown using equation (12), we will next explain the model equation for determining the value of the mechanical plate crown.

Here, the model formula means a relatively simple formula that can be incorporated into a process computer and does not require repeated calculations.

Mechanical plate crown is an amount essentially determined by the crown of the work roll, deflection, and flattening deformation due to contact with the rolled material.

It is known that roll crowns gradually change due to wear and thermal expansion as rolling operations continue, but these are considered to be known through estimation using mathematical models or direct measurements. .

Strictly speaking, numerical calculations must be used to determine roll flattening deformation due to contact with the rolled material, but as will be explained later, the inventors used the definition of a mechanical plate crown, that is, that the load distribution in the width direction is uniform. We developed a simple approximation formula using this fact. However, the influence of roll flattening on the thickness distribution in the width direction is often concentrated at the edge of the plate, so if the plate crown definition point is set slightly inside the edge of the plate, the effect of flattening of the work roll can be reduced. There is no need to consider it.

In the case of a two-high rolling mill, the deflection of the work roll can be easily determined by material mechanics, since the roll can be regarded as a beam with both ends variable, but in a multi-high rolling mill with reinforcing rolls, the deflection of the work roll is Since the linear load distribution acting between the reinforcing rolls depends on the deflection of the work roll, it becomes an indeterminate problem.The work roll deflection is calculated by first assuming the line load distribution, and then the work roll Either use an iterative method of calculating the line load distribution using the deflections and recalculate until it substantially matches the line load distribution used when calculating the work roll deflections last time, or discretize the roll deflections. We will have no choice but to rely on full-scale numerical calculations.

Since these methods cannot provide a model equation for a process computer that requires an instantaneous answer, the inventors solved this problem as follows.

One of the factors that has a large effect on the deflection of work rolls is the roll crown.

Figures 2a and 2b show the principle diagram when the work roll 3 has a concave curve, but when a roll curve is provided, the cast between the unloaded work roll and the reinforcing roll is shown in Figure 2a. As shown in , there is a widthwise distribution that follows the roll curve. Even if rolling is carried out in this state, in most cases the work roll and reinforcing roll will come into complete contact as shown in FIG. 2b. Therefore, the widthwise distribution of the roll gap that exists when there is no load affects the deflection of the work roll through the widthwise distribution of the load acting on the contact surface between the work roll and the reinforcing roll.

Therefore, if a work roll is given a crown that is C _R in terms of the plate crown definition point (the radius is positive on the convex crown side), the effect this has on the mechanical plate crown is the roll gap under no load. In addition to the contribution of -2C _R , the increment of work roll deflection due to C _R -2αC _R is added, and -2C R is added.
(1+α) _CR becomes.

As shown in Figures 3a and 3b, the value of α is α=0 when the bending rigidity of the work roll is infinite, and α=1 when the bending rigidity is 0. 0< depending on the bending rigidity of the roll
Takes the value α<1.

As can be seen from the above considerations, the parameter α can be used to calculate the influence of the width direction load distribution between the work roll and the reinforcing roll on the work roll deflection, which exists when there is no load, that is, when there is no width direction load distribution. This is a parameter that can be determined from the widthwise distribution of the gap between reinforcing rolls, and is an important concept that can solve the difficulties in calculating the work roll deflection mentioned above all at once, as described below.

When determining the deflection of the work roll, the load distribution acting between the work roll and the reinforcing roll is required, and this is first calculated assuming that it is uniform in the width direction. If such an assumption is made, the deflection of the work roll can be easily calculated using material mechanics. On the other hand, the deflection of the reinforcing roll can also be calculated based on the same assumption, but as shown in FIG. 4, these deflection curves generally do not match, resulting in a gap in the width direction.

This situation is the same as in FIG. 2a, and the deflection that occurs in the work roll due to this widthwise gap distribution can be determined by α.

In other words, if the difference between the mill center and the plate crown definition point of the work roll deflection and reinforcing roll deflection calculated based on the above assumptions (the positive sign indicates the direction of the medium convex plate crown) is C _BW and C _BB , respectively. The effect these have on the mechanical plate crown can be expressed as 2 [C _BW −α (C _BW − C _BB )].

As can be seen from Figure 4, the sign in front of α is negative when C _BW −C _BB > 0.
This is because the effect of α acts in the direction of bending C _BW back.

By introducing the parameter α as described above, it was possible to create a simplified model for calculating work roll deflection, which conventionally could only be done through repeated calculations.

In other words, the effect of the work roll flattening deformation due to contact with the rolled material on the mechanical plate crown is
If Cf is assumed, then the mechanical plate crown can be calculated using the following formula, taking into account the reinforcing roll's crown C _RB (radius converted to plate crown definition point).

〓=2[C _BW −α(C _BW −C _BB )] −2(1+α)C _R −2αC _RB +2Cf …(14) Note that each term in equation (14) is doubled by the upper and lower This is because the roll portion is taken into account and is based on the precondition of vertical symmetry.

In the case of vertical asymmetry, the upper and lower rolls can be calculated and added together.

Since the mechanical plate crown is determined only by the geometrical initial conditions of the rolling mill and elastic deformation, (14)
The effects of each factor can be superimposed as shown in the equation.

Note that, as described above, depending on how the plate crown defining points are taken, it is possible to omit the term Cf in equation (14).

Furthermore, in a normal steel plate rolling mill, the diameter of the reinforcing roll is much larger than the diameter of the work roll, so the influence of C _BB is small, and it can often be omitted.

α in equation (14) is a very important concept, and will be referred to as a nonlinear load distribution correction coefficient below.

Next, a method for specifically determining the nonlinear load distribution correction coefficient α will be explained.

During rolling, the upper and lower work rolls do not come into contact at the body except in special cases, so the upper and lower roll systems can be considered separately. As shown in Fig. 2a, the roll axial distribution of the gap existing between the reinforcing roll and the work roll in the initial state is calculated as follows:
Approximate with the following formula.

υ＝fg・x ² (15-1) However, x is WS with the mill center as the origin
This is the coordinate in the roll axis direction with (work side) taken in the positive direction.

Since the present inventors are concerned only with the ratio of change in roll deflection relative to the initial roll gap when transitioning from the initial state shown in Figure 2a to the actual rolling state shown in Figure 2b, these widthwise distributions are idealized to some extent. You can think of it in terms of what you did. Therefore, it is assumed that not only the inter-roll gap distribution but also the distribution of roll deflection changes due to this gap distribution is a quadratic curve distribution. In other words, when the reinforcement roll deflection and work roll deflection due to υ are respectively y _B and y _W , y _B = f _B・x ² …(15-2) y _B = f _W・x ² …(15-3) Assume that However, y _B and y _W are positive in the direction away from the rolled material.

From equations (15-2) to (15-3), the linear load distribution P _BW generated by υ is determined by the inter-roll spring model (Shohet, KN & Townsend, NA: J.Iron
and Steel Inst., 206-11 (1968), 1088), it can be calculated as follows.

P _BW = K _BW (fg+f _B −f _W ) (l _BW ² /12−xx ² )
...(15-4) However, l _BW is the length of the contact area between the reinforcing roll and the work roll, and is usually equal to the roll body length. Equation (15-4) extracts the nonlinear component of the load distribution, so it alone satisfies the force equilibrium condition. Further, K _BW is a spring constant per unit body length of the contact flatness between the reinforcing roll and the work roll, and is obtained as the reciprocal of the equation regarding the amount of approach between the axes of the two cylinders, differentiated with respect to the line load. For example, Nakajima et al.
25}, the axial center approach amount δ _I is δ _I =C・P _BW [ln{2(D _B +D _W ) /(C・P _BW )}−1] …(15-5) C=2 (1−ν ² )/(π·E) (15-6) Therefore, the spring constant K _BW is given by the following formula.

1/K _BW = C [ln{2(D _B +D _W )/(C・P _BW )}-2]
(15-7) However, D is the roll diameter, E is the Young's modulus, ν is the Boatsson's ratio, and the subscripts B and W mean the reinforcing roll and the work roll, respectively.In this specification, in order to simplify the notation, the rolling mill The elastic constant of all rolls is the same, and the amount of axial center approach, that is, the amount of roll flattening, is calculated using equations (15-5) and (15-6).Rolling using a combination of rolls with significantly different elastic constants When analyzing the machine, use equation (15−
5) Instead of Loo's formula {Loo, TT: J.of
Applied Mechanics, 25-1 (1958), 122} may be used.

Equation (15-7) shows that K _BW is strictly a function of P _BW , but since the change in K _BW due to P _BW is generally very small, here we use the average value of P _BW in the trunk length direction. We will calculate K _BW and treat it as a constant in equation (15-4).

When the roll deflection caused by the load distribution in equation (15-4) is calculated using the beam theory in materials mechanics under the boundary conditions of x=0, y=0, and dy/dx=0, the following equation is obtained. obtain.

y _B = K _BW /12(fg+f _B −f _W ) [−1/EI _B {x ⁶ /30−(lB
W/2) ² x ⁴ /6+(l _BW /2) ⁴ x ^2/2 }+4/3GSB{x ⁴
−2(l _BW /2) ² x ² }]
…(15-8) y _W = K _BW /12(fg+f _B −f _W ) [1/E _IW {x ⁶ /30−(l _BW
/2) ² x ⁴ /6+(l _BW /2) ⁴ x ² /2}-4/3GSW{x ⁴
−2(l _BW /2) ² x ² )]...(15-9) Where, I is the second moment of area of the roll, and S
is the cross-sectional area of the roll, and G is the transverse elastic modulus of the mail.

On the right side of equations (15-8) and (15-9), there are 4th and 6th order terms of x, while equations (15-2) and (15
-3), y _B and y _W were approximated by quadratic equations.
Therefore, strictly speaking, f _B and f _W must be functions of the plate width, but here, in the sense that the average deflections are the same, equations (15-2), (15-3) and ( A method was adopted in which the right-hand side of 15-9) was integrated over the entire contact area between the rolls, and the results were equated to determine f _B and f _W . As a result, the nonlinear load distribution correction coefficient α _B for the gap between the reinforcement roll and the work roll of the reinforcement roll is given by the following equation.

α _B = f _B / fg = A _BW / (1 + A _BW + A _WB )
...(15-10) In addition, the nonlinear load distribution correction coefficient α regarding the gap between the work roll reinforcement roll and the work roll, which is necessary to find the work roll deflection, is given by the following equation.

α=f _W /fg=A _WB /(1+A _BW +A _WB ) (15) Here, A _BW and A _WB are given by the following equations.

A _BW = K _BW / π (l _BW / D _B ) ² {29/2101/E (l _BW / D _B )
+7/451/G} …(16) A _WB =K _BW /π(l _BW /D _W ) ² {29/2101/E(l _BW /D _W )
² +7/451/G} …(17) Finally, the effect of flattening of the work roll due to contact with the rolled material on the mechanical plate crown.
We will explain how to obtain Cf.

When a concentrated load P acts on the surface of a semi-infinite body, the displacement at a point separated by a distance r from the point of application of the load is given by the following equation (for example, Timoshenko, SP
& Goodier, J.N.: Theory of Elasticity,
(1970), 402, see Mc Graw-Hill).

w=P(1−ν ² )/(πEr) …(18) Therefore, the displacement at point (x, y) due to any distributed load q(ξ, η) is given by the following equation based on the principle of superposition. .

Now, when y is the rolling direction and x is the roll axis direction, the distribution of q(x, y) in the x-axis direction is uniform due to the definition of mechanical plate crown, but the y-axis direction generally has a friction hill. Although the shape is close to a rectangular distribution, here, for simplicity, we assume a rectangular distribution and perform the integration of equation (19). As a result, the work roll flattening amount Wc at the center of the plate at the exit of the roll bite and the work roll flattening amount Wβ at a position β from the plate end at the exit of the roll bite are respectively given by the following equations.

Wc=1−υ ² /πEp/b{b/Lln√b ² +
4L ² +2L/b+2ln√b ² +4L ² +b/2L}…(19-1) Wβ=1−υ ² /πEp/b [{β/Lln√β ² +L ² +L
/β+ln√β ² +L ² +β/L}+{b−β/L ln√(b−β) ² L ² +L/b−β+ln√(b−
β) ² +L ² +b-β/L}]...(19-2) The influence Cf of the flattening of the work roll on the mechanical plate crown can be calculated by Cf=Wc-Wβ, so it is given by the following equation.

Cf=1−ν ² /πEP/b [{b/Lln√b ² +4L ² +2L
/b+2ln√b ² +4L ² +b/2L}-{β/Lln√β ² +L ²
+L/β +ln√β ² +L ² +β/L}-{b-β/Lln√(b
−β) ² +L ² +L/b−β+ln√(b−β) ² +L ² +b−
β/L}]...(20) where P: rolling load b: plate width L: projected contact arc length β: distance from the plate edge to the plate crown definition point ν: Poisson's ratio.

Equation (20) is essentially the same as the equation derived by Fujisawa et al. (Fujisawa, Komatsu: Plasticity and Processing, Vol. 4, No. 27 (1963) p. 195), and Tozawa et al. (Tozawa, Ueda: It can be said that this model is a simplified version of the numerical analysis conducted in Plasticity and Processing, Vol. 11, No. 108 (1970) p. 29). However, this calculation method, which uses equation (18) as the starting point, has the following problem: (19)
It has the property that the displacement determined by the formula becomes infinite, and it contains an obvious contradiction with the two-dimensional solution of the contact problem of an infinitely long cylinder.

In order to eliminate this contradiction, Nakajima et al. (Nakajima, Matsumoto:
The 24th Plasticity Series (1973) p.29 corrects the formula so that it approaches a two-dimensional solution as the plate width approaches infinity.

In Nakajima et al.'s method, equation (19) is corrected as shown below and the solution is obtained by performing numerical integration.

However, d=D _W /e (e=2.718282...) Here, a model formula for Cf was derived based on formula (21). Using the same assumptions used to obtain equation (20) from equation (19), perform the integration of equation (21) to calculate Wc and Wβ, and use Cf=Wc−W〓, Cf is given by the following equation. It will be done.

(22) is somewhat complicated, but in general L/d≪
It is possible to further simplify by utilizing the fact that 1,L/(b-β)≪.

As described above, the values of α and Cf, which were academically unresolved in equation (14), can be determined, and the mechanical plate crown model equation for the 4Hi mill has been obtained. Basically, four-high rolling mills, such as rolling mills with a double chock type roll bending device, rolling mills with a variable crown roll type, and furthermore, rolling mills with a roll cross type, are based on the above-mentioned concept. Equation (14) can be easily extended and applied. Equation (14) can also be applied to rolling _mills using work roll shift, reinforcing roll shift, or sleeve shift methods because they are basically four-high rolling mills. The load distribution between the rolls in the body length direction is generally a linear load distribution with a slope as shown in FIG. 5, which makes calculations somewhat complicated. However, in the scope of materials mechanics, C _BW
can be calculated in advance, so this calculation is omitted here.

Next, a mechanical plate crown model formula obtained as a result of expanding the above calculation method will be shown for the case of a six-high rolling mill having a function of shifting the rolls in the axial direction.

First, regarding the nonlinear load distribution correction coefficient, 4
The following results can be obtained by extending the calculations made for two rolls for a high-pressure rolling mill to include three rolls.

Nonlinear load distribution correction coefficient α _BI for the gap between the reinforcement roll and the intermediate roll

Claims (1)

[Claims] 1. A rolling control method for a rolling mill having a device capable of controlling the widthwise thickness distribution of a rolled plate, which is realized when the widthwise load distribution between the rolled plate and the work rolls is uniform. A model formula showing the relationship between the widthwise thickness distribution and rolling conditions, the widthwise thickness distribution calculated by substituting the rolling conditions into the model formula, and the widthwise thickness distribution of the rolled plate on the entry side of the rolling machine. The operation amount of the width direction plate thickness distribution control device is determined using the calculation formula for the width direction plate thickness distribution of the rolled plate on the exit side of the rolling mill, which is configured as a linear combination, and the operation amount of the width direction plate thickness distribution control device is determined based on this. A rolling control method characterized by controlling a thickness distribution control device. 2 In a rolling control method for a rolling mill that has a device that can control the thickness distribution of the rolled plate in the width direction, the rolling load during rolling is detected and the load distribution in the width direction of the rolled plate and work roll is uniform. The thickness distribution in the width direction, which is calculated by substituting the actual measured value of the rolling load described above into the model formula showing the relationship between the thickness distribution in the width direction and the rolling conditions, is determined by the target value determined at the time of setting calculation or by feedback control. A rolling control method characterized by determining the operation amount of the widthwise plate thickness distribution control device so as to be closest to the corrected target value. 3. In a method of controlling a rolling mill that includes a device capable of controlling the thickness distribution in the width direction of a rolled plate and a shape detection device of the rolled plate, the difference between the plate shape actually measured by the plate shape detection device and the target plate shape is determined as the thickness distribution. This is a linear combination of the thickness distribution in the width direction and the thickness distribution in the width direction of the rolled plate at the entrance of the rolling mill, which is realized when the thickness distribution in the width direction between the rolled plate and the work roll is uniform. Using the calculation formula for the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill, which is configured as Converting to the difference in thickness distribution in the width direction realized in a certain case,
Furthermore, using a model formula that shows the relationship between the widthwise thickness distribution and rolling conditions that would be realized when the widthwise load distribution between the rolled plate and the work rolls is uniform, the above-mentioned difference in plate thickness distribution is eliminated. A rolling control method, comprising: determining the amount of operation of the widthwise plate thickness distribution control device. 4. In a rolling control method for a continuous rolling mill that has a device that can control the thickness distribution in the width direction of a rolled plate and a device that can measure the thickness distribution in the width direction of the finished product, actual measurement using the thickness distribution measuring device in the width direction is performed. In order to eliminate the difference between the calculated plate thickness distribution and the target plate thickness distribution in the last stage rolling mill, and not to disturb the product shape, the difference in plate thickness distribution is Determine the amount of modification of the similar thickness distribution in the width direction with respect to the exit side sheet thickness, and if the disturbance of the sheet shape between rolling mills due to this amount of correction exceeds the tolerance range for rolling operations, this amount of correction is further applied to the previous stage. After distribution to the rolling mill, the widthwise thickness distribution achieved when the widthwise load distribution between the rolled plate and the work rolls is uniform, and the first-order widthwise thickness distribution of the rolled plate on the entrance side of the rolling mill. Using the calculation formula for the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill, which is configured as a joint, the amount of correction of the thickness distribution in the width direction on the exit side of each rolling mill is calculated in the width direction between the rolled plate and the work roll. This is converted into the amount of modification of the thickness distribution in the width direction that is realized when the thickness distribution is uniform, and the amount of correction in the width direction that is realized when the load distribution in the width direction between the rolled plate and the work roll is uniform. A rolling control method, characterized in that a model equation showing a relationship between a plate thickness distribution and rolling conditions is used to determine an operation amount of the widthwise plate thickness distribution control device corresponding to an amount of correction of the plate thickness distribution.