JPH0510165B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention rolls the left-right symmetrical component of the thickness distribution in the width direction of a rolled plate, that is, the plate crown, and the plate shape that is closely related to this to a predetermined target value. This paper relates to a method for setting a widthwise plate thickness distribution control device among rolling mill setting calculations for the purpose of this invention.

"Multiple rolling" literally means that the rolled material is rolled multiple times, and when rolling is performed multiple times with a reverse type rolling mill, or when rolling is performed continuously with multiple rolling mills. , and a combination thereof.

The width direction plate thickness distribution control device referred to in the present invention is a device that can control the width direction plate thickness distribution even under the condition that the rolling load is constant, and includes a roll bending device, a variable crown roll, a work roll shift, a roll cross , intermediate roll shift of 6-high rolling mill,
It refers to the so-called crown shape control end, such as the sleeve shift function of a rolling mill that has a sleeve on the reinforcing roll.

Roll bending equipment has been in practical use for a relatively long time as a width direction plate thickness distribution control device, but until now it has been mainly used as a control end for automatic shape control during rolling, and when setting it up, it is initially In most cases, a fixed value determined by a standard was used, and then corrections were made based on the results of automatic control. There also seem to have been attempts to determine the set value of the roll bending force using mathematical models, but these mathematical models do not seem to calculate the relationship between the plate crown or plate shape obtained as a result of rolling and the rolling conditions. , is a model created by statistical processing of actual rolling data or numerical analysis results, and the deformation characteristics of the rolling mill and the deformation characteristics of the rolled material are not sufficiently separated, making it difficult to expand the range of applicable steel types and making it less effective. There were problems in that learning was difficult and the accuracy was not at a satisfactory level.

The present invention has been made with the aim of solving the problems of the conventional method as described above, and the gist thereof is to produce a rolled original plate using a rolling mill equipped with a device that can control the thickness distribution of the rolled plate in the width direction. In the rolling process in which a rolled plate with a predetermined thickness is obtained by rolling multiple times from A model formula showing the relationship between the width direction plate thickness distribution and rolling conditions that would be realized in the case of uniformity, and the width direction plate thickness distribution calculated by substituting the rolling conditions into the model formula and the relationship between the width direction plate thickness distribution and the rolling machine entry side. The plate shape is estimated from the calculation formula for the widthwise thickness distribution of the rolled plate on the exit side of the rolling mill, which is configured as a linear combination of the widthwise thickness distribution of the rolled plate, and the difference between the inlet side thickness distribution and the outlet side thickness distribution. Using the calculation formula,
Each rolling pass exit side that can achieve the target width direction thickness distribution and sheet shape of the finished product from the width direction thickness distribution of the rolled original sheet without the sheet shape at the exit side of each rolling pass exceeding the sheet passing limit shape. of the widthwise plate thickness distribution is within the capability of the widthwise plate thickness distribution control device, and in the latter half of the pass, the end elongation control ability side of the control device is maximized within a predetermined limit. The end elongation limit schedule for the end of the second half pass is determined, and the end elongation limit schedule is determined to be within the capability of the above-mentioned width direction plate thickness distribution control device, and as the second half pass progresses, the mid-elongation control capability of the device is maximized within a predetermined limit. The utilized maximum elongation schedule during the second half pass is determined, and the set target value of the thickness distribution in the width direction at the exit side of each rolling pass is determined as the internal division point between the maximum elongation schedule at the end of the second half pass and the maximum elongation schedule during the second half pass, and the set target value is determined. From the values, it is constructed as a linear combination of the thickness distribution in the width direction and the thickness distribution in the width direction of the rolled plate on the entrance side of the rolling mill, which would be realized when the widthwise load distribution between the rolled plate and the work rolls is uniform. Using the above formula for calculating the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill,
The target value of the thickness distribution in the width direction that would be achieved when the load distribution in the width direction between the rolled plate and the work rolls is uniform is calculated backwards, and the load distribution in the width direction between the rolled plate and the work rolls is uniform. The purpose is to back-calculate and determine the set value of the width direction plate thickness distribution control device using the above model formula that indicates the relationship between the width direction plate thickness distribution and the rolling conditions realized in the case where .

The present invention will be explained in detail below. First, a prediction formula for plate crown, which is the most distinctive feature of the present invention, will be explained.

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 dimension, the setting conditions of the crown shape control end, the rolling load, the plate width of the rolled material, etc. Given the rolling conditions, it is determined only by the deformation characteristics of the rolling mill, regardless of the deformation characteristics of 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 〓 is defined as the influence coefficient on the exit side plate crown Ch when only the entry side plate crown C _H changes by 〓C _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 〓Ch, the following relationship exists: 〓Ch=〓・_〓CH ... (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 can be expressed as 〓Ch /h=〓～・〓C _H /H In other words, it can be seen that it is more appropriate to express it in the form: 〓Ch=〓～・(1−r)・〓C _H ……(2). Here, h is the exit side plate thickness, H is the entrance side plate thickness, r is the rolling reduction ratio, and 〓~ will be called the modified crown hereditary coefficient.

From equation (2), we can see that the entrance plate crown C゜_H is a certain standard.
When it is known that the exit plate crown is C゜h, the exit plate crown Ch corresponding to the entry plate crown C _H can be calculated using the following formula.

Ch＝C゜h＋＋〓〜・(1−r)・(C _H −C゜_H )……(3
) Now we will consider the plate crown model equation starting from equation (3), but C゜_H and C゜h are calculated when the elongation distribution in the width direction is uniform (the material temperature is uniform in the width direction). In some cases, it is most rational to select a method in which the rolling load distribution in the width direction is also uniform. At this time, the entrance side plate crown ratio and the exit side plate crown ratio are equal, so C゜_H 〕C゜h・H/h=C゜h・1/(1−r)
...(4) The following relationship is established, and by substituting this into equation (3), the following equation is obtained.

Ch=(1-〓～)C゜h+〓～(1-r)C _H ...(5) By the way, C゜h in equation (5) is the exit crown when the elongation distribution in the width direction is uniform. However, 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゜h will match the mechanical plate crown. Therefore, the following equation is obtained as the basic equation of the plate crown model.

Ch＝(1−〓〜)・〓+〓〜・(1−r)・C _H ……(6
) If the width direction deformation 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, it is assumed that the exit side plate crown changes in proportion to the difference, and if the proportionality constant is 〓, then the exit side plate crown is Ch = C _H・h/H+〓(〓−C _H・h/H) That is, Ch=〓〓〓+(1−〓)(1−r)C _H ……(7). Here, 〓 indicates 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.

〓 and 〓~ are completely different concepts from their definitions, but when comparing equations (6) and (7), the following relationship must hold: 〓=1−〓~... (8). In other words, equations (6) and (7) originally express the same content in different expressions, and their ultimate meaning is
This becomes 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 the horizontal axis is the plate crown C and the vertical axis is the difference in load between the edge of the plate and the center of the plate, P, then the deformation on the rolling mill side is P=
When C=〓, and C<〓, the load at the edge of the plate must be larger than that at the center of the plate. Therefore, if the relationship between C and 〓P 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.

〓P=-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 , then 〓P= 0, and in order for C>(1-r)C _H to be 〓
P>0 must be satisfied. So C and 〓P
If the relationship 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.

〓P=m[C-(1-r)C _H ]...(10) The plate crown Ch produced by rolling is found 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) ...(11) is obtained. If we set m/(m+k)=〓~, 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 like Ch=〓・〓+〓~(1-r)C _H ...(12), and 〓~
It is important that and 〓 are quantities that depend on the deformation properties of the rolled material, and 〓 is a quantity that depends on the deformation properties of the rolling mill.

There is a method of determining 〓～,〓 from the numerical analysis results as described above, but ultimately it is preferable to confirm it 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 〓 by experiment and theory, and this is calculated as 〓〜＝〓/(1−r)...(13) The plate crown correction coefficient 〓 can also be determined by converting it into a modified crown hereditary coefficient using the definition formula, and further applying formula (8).

Therefore, the following explanation will be given assuming that the values of 〓 and 〓~ 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 a quantity determined basically 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 by 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 using material mechanics by considering the roll as a support beam at both ends, but in the case of 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. First, the line load distribution is determined, the work roll deflection is calculated, and then the work roll calculated just now is calculated. You can use an iterative method of calculating the line load distribution using the roll deflections and recalculating it until it substantially matches the line load distribution used when calculating the work roll deflections last time, or you can calculate the roll deflections discretely. We will have no choice but to rely on advanced 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.

Fig. 2a and Fig. 2b show the principle diagram when the work roll 3 has a concave curve, but when a roll curve is provided, the gap between the work roll and the reinforcing roll at no load is As shown in the figure, 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 −2〓C _R is added, and −2C R is added.
2(1+〓)C _R.

Here, the value of 〓 is 〓 = 0 when the bending rigidity of the work roll is infinite, as shown in Figures 3a and 3b, and 〓 = 1 when the bending rigidity is 0. It takes a value of 0<〓<1 depending on the bending rigidity of the roll.

As can be seen from the above considerations, the parameter 〓 is used to evaluate the influence of the width direction load distribution between the work roll and the reinforcing roll on the work roll deflection. 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 that shown in FIG. 2a, and the deflection caused in the work roll due to this widthwise gap distribution can be determined by ≦.

In other words, 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 direction of the medium convex plate crown is taken as a positive sign) is C _B w, C _BB , respectively. Then, the effect these have on the mechanical plate crown can be expressed as 2 [C _B w - (C _B w - C _BB )].

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

By introducing the parameter 〓 as described above, it was possible to create a simple model for calculating work roll deflection, which conventionally could only be done by repetitive calculation.

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 _B w−〓(C _B w−C _BB )〕 −2(1+〓)C _R −2〓C _RB +2Cf ……(14) In addition, each term in equation (14) is doubled. This is because the upper and lower rolls are taken into consideration, and is based on the precondition that the upper and lower sides are symmetrical.

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 elastic deformation of the rolling mill, the effects of each factor can be superimposed as shown in equation (14).

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 _CBB is small, and it can often be omitted.

〓 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 obtaining the nonlinear load distribution correction coefficient 〓 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.

= fg・x ² ... (15-1) However, x is the coordinate in the roll axis direction with the mill center as the origin and WS (work side) 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 -3). However, y _B and y _W are positive in the direction away from the rolled material.

From equations (15-1) to (15-3), the linear load distribution P _B w generated by ≦ is expressed as the following equation.

P _B w=K _B w (fg+f _B −fw) (l _B w ² /12−x ² )
(15-4) However, l _B w 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 _B w is a spring constant per unit body length of the contact flatness between the reinforcing roll and the work roll, and is determined 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, according to the solution of Nakajima et al. {Koei Nakajima, Hiromi Matsumoto: 1973 Spring Lectures on Molding, (1973), 25}, the amount of axial center approach = BW I
is 〓BW I=C・P _B w[ln{2(D _B +Dw)/(C・P _B
w)}-1] ... (15-5) C=2(1-〓 ² )/(〓・E) ... (15-6) Therefore, the spring constant K _B w is given by the following formula .

1/K _B w=C[ln{2(D _B +Dw)/(C・P _B
w)}-2] ... (15-7) where D is the roll diameter, E is Young's modulus, 〓 is Boatzson'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 elastic constants of all the rolls of the rolling mill are common, and the amount of axial center approach, that is, the amount of roll flattening, is calculated using equations (15-5) and (15-6). do. When analyzing a rolling mill that combines rolls with significantly different elastic constants, the formula (15−
5) Instead of Loo's formula {Loo, T, T.: J.of
Applied Mechanics, 25-1 (1958), 122} may be used.

From Equation (15-7), it can be seen that K _B w is strictly a function of P _B w, but since the change in K _B w due to P _B w is generally very small, here, P _B w is expressed in the torso length direction. Calculate K _B w using the average value and use formula (15-4)
We will treat it as a constant in .

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

y _B = K _B w/12 (fg+f _B −fw) [−1/EI _B {x ⁶ /30−
(l _B w/2) ² x ⁴ /6+(l _B w/2) ⁴ x ² /2}+4/3G
S _B {x ⁴ −2(l _B w/2) ² x ² }]
... (15‐8) yw＝K _B w/12(fg＋f _B −fw) [1/EIw{x ⁶ /30−(l
_B w/2) ² x ⁴ /6+(l _B w/2) ⁴ x ² /2}-4/3GS _w
{x ⁴ −2(l _B w/2) ² x ² }]
... (15-9) where I is the second moment of area of the roll, 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 ( 15-8) and (15-9) are integrated over the entire contact area between the rolls and equated to give f _B ,
We adopted the method of finding f _W. As a result, the nonlinear load distribution correction coefficient 〓 _B regarding the gap between the reinforcement roll and the work roll of the reinforcement roll is given by the following equation.

〓 _B = −f _B /fg=A _B w/(1+A _B w+Aw _B )
...... (15-10) In addition, the nonlinear load distribution correction coefficient 〓 regarding the gap between the reinforcing roll of the work roll and the work roll, which is necessary to find the work roll deflection, is given by the following formula.

〓=fw/fg=Aw _B /(1+A _B w+Aw _B )
...(15) Here, A _B w, Aw _B are given by the following formula.

A _B w=K _B w/〓(l _B w/D _B ) ² {29/210 1/E(l _B w
/D _B ) ² +7/45 1/G}...(16) Aw _B =K _B w/〓(l _B w/Dw) ² {29/210 1/E(l _B w/
Dw) ² +7/45 1/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 of point (x, y) due to any distributed load q(〓,〓) is given by the following equation based on the principle of superposition. It will be done.

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 flattening amount Wc of the work roll at the center of the plate at the exit of the roll bite and the flattening amount W of the work roll at a position further from the edge of the plate at the exit of the roll bite are given by the following equations.

Wc=1−ν ² /〓E P/b{b/Lln√b ² +4L ² +2L/
b＋2ln√b ² +4L ² +b/2L}... (19-1) W〓=1−ν ² /〓E P/b〓〓〓〓〓 ² +L ² +
L/〓+ln√〓 ² +L ² +〓/L}+{b-〓/Lln√(
b-〓) ² L ² +L/b-〓+ln
√(b−〓) ² +L ² +b−〓/L}〕……19-2) The influence Cf of work roll flattening on the mechanical plate crown can be calculated as Cf=Wc−W〓, so it is given by the following formula. .

Cf=1−〓 ² /〓E P/b [{b/Lln√b ² +4L ² +2
L/b+2ln√b ² +4L ² +b/2L} −{〓/Lln√〓 ² +L ² +L/〓+ln√〓 ² +L ² +〓
/L}−{b−〓/Lln√(b−〓) ² +L ² +L/b−
〓＋ln
√(b-〓) ² +L ² +b-〓/L}] ...(20) However, P: Rolling load b: Plate width L: Projected contact arc length 〓: Distance from the plate edge of the plate crown definition point 〓: Poisson's ratio.

Equation (20) is expressed by Fujisawa et al. (Fujisawa, Komatsu: Plasticity and Processing,
It is essentially the same as the formula derived by Tozawa et al. (Tozawa, Ueda: Plasticity and Processing, Vo1.11, No.108 (1970) p.29). ) can be said to be a simplified model of the numerical analysis performed. However, this calculation method that uses equation (18) as a starting point has the property that when the plate width becomes infinite, the displacement determined by equation (19) becomes infinite, so it is difficult to solve the problem of contact between infinitely long cylinders. It contains an obvious contradiction with the two-dimensional solution of .

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

In the method of Nakajima et al., equation (19) is corrected as shown in the following equation, and the solution is obtained by performing numerical integration.

However, d=Dw/e (e=2.718282...) Here, a model equation for Cf was derived based on equation (21). By making the same assumption as that used to obtain equation (20) from equation (19), (2
1) Execute the integration of the formula and calculate Wc, W〓, Cf=Wc
−W〓 is used, Cf is given by the following formula.

Equation (22) is somewhat complicated, but in general L/b≪
Using the fact that 1, L/(b-〓)≪1,
Further simplifications are possible.

The above equation (14) is academically unresolved.
The values of and Cf can be determined, and the mechanical plate crown model formula 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. The formula can be easily extended and applied. Since the working roll shift, reinforcing roll shift, or sleeve shift type rolling mill is basically a four-high rolling mill, formula (14) can be applied, but when calculating C _B w, the back up roll ~ The load distribution in the body length direction between the work rolls is generally a linear load distribution with a slope as shown in FIG. 5, which makes calculations somewhat complicated. However, since C _B w can be determined in advance within the scope of material mechanics, this calculation will be 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 for the gap between the reinforcement roll and the intermediate roll of the reinforcement roll〓 _BI

Claims (1)

[Claims] 1. In a shape/crown control setting method in a rolling mill, in which a rolled plate of a predetermined thickness is obtained by rolling an original rolled plate multiple times using a rolling mill equipped with a device that can control the thickness distribution of the rolled plate in the width direction. , after the target value of the exit plate thickness of each rolling pass is determined, the relationship between the widthwise plate thickness distribution and rolling conditions that would be achieved when the widthwise load distribution between the rolling plate and the work rolls is uniform is determined. The model formula shown, the widthwise plate thickness distribution calculated by substituting the rolling conditions into the model formula, and the widthwise plate thickness distribution of the rolled plate on the rolling mill entry side, which is configured as a linear combination of the rolling machine outlet side. Using a calculation formula for the thickness distribution in the width direction of the rolled plate and a calculation formula for estimating the plate shape from the difference between the inlet side thickness distribution and the outlet side thickness distribution, the plate shape on the exit side of each rolling pass is determined as the passing limit shape. Among the width direction plate thickness distributions on the outlet side of each rolling pass that can achieve the target width direction plate thickness distribution and plate shape of the finished product from the width direction plate thickness distribution of the rolled original plate without exceeding the above width direction plate Within the capabilities of the thickness distribution control device,
In addition, as the process progresses toward the second half of the pass, the end elongation limit schedule for the second half of the pass that maximizes the end elongation control capability of the control device within a predetermined limit is determined, and furthermore, the end elongation limit schedule is determined within the capability of the width direction plate thickness distribution control device. In the latter half of the pass, a maximum elongation schedule during the second half pass that maximizes the mid-elongation control capability of the control device within a predetermined limit is determined, and the maximum elongation schedule during the second half pass and the maximum elongation schedule during the second half pass are calculated. The target value of the thickness distribution in the width direction at the exit side of each rolling pass is determined as the internal division point of
Based on the set target value, a linear combination of the widthwise thickness distribution and the widthwise thickness distribution of the rolled plate on the entrance side of the rolling machine, which is realized when the widthwise load distribution between the rolled plate and the work rolls is uniform, is calculated. Using the above calculation formula for the thickness distribution in the width direction of the rolled plate on the exit side of the rolling mill, the thickness distribution in the width direction is calculated as follows: The target value of the thickness distribution is calculated backwards, and the above model formula is used to express the relationship between the thickness distribution in the width direction and the rolling conditions, which is achieved when the load distribution in the width direction between the rolled plate and the work roll is uniform. , a method for setting shape/crown control in a rolling mill, characterized in that setting values of the widthwise plate thickness distribution control device are determined by back calculation.