JPS6320109A - Measuring method for thermal crown of rolling roll - Google Patents

Abstract

PURPOSE:To remarkably reduce a computation time and to quickly measure thermal crowns with high accuracy by classifying the body length of a rolling roll into prescribed 6 elements and finding a roll surface temp. distribution based on those elements. CONSTITUTION:The roll body length of a rolling mill is classified into a rolling zone L1 for a rolled stock ST and zones L2, L3 of an element (1) different from L1; the rolling zone L1 is further classified into both end parts LE1, LE2 of an element (2) and an intermediate part Lc of an element (3). The temp. distribution of the element (1) and the temp. distribution of the element (3) are found by approximation using an about 6th function based on the contact temp. of a roll end and the element (2) and the contact temp. of the elements (2) and (3) and the roll center temp., respectively. The temp. distribution of the element (2) is found by use of a linear function based on the contact temp. of the elements (1) and (3). Therefore, the computation time is remarkably reduced in comparison with a conventional classification into 40 pieces and thermal crowns are quickly measured.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a method for measuring the thermal crown of a rolling roll, which improves the accuracy of crown control, plate thickness control, etc. in rolling steel plates.

(Prior Art) As a conventional thermal crown calculation model for a rolling roll, there is a method shown below.

(1) For example, as shown in Japanese Unexamined Patent Publication No. 80-238017, the amount of thermal crown of a roll is assumed to be symmetrical with respect to the center in the axial direction of the roll in the length direction and expressed by a quadratic equation. A model has been proposed in which the amount of thermal crown at the center of the roll axis after reassembly is expressed by an exponential function.

(2) Also, as a method to solve the change in roll temperature due to heating and cooling during rolling as an axisymmetric two-dimensional heat conduction equation, (i) Direct difference method (Naoi et al.: Showa Bθ Spring Plastic Working Lecture Collected Papers, P3?) (ii) Using the finite element method (Hamazu et al.: Spring 1981 Plastic Processing Lecture Proceedings, l) 301).

(Problems to be Solved by the Present Invention) Therefore, in the method (1) described above, since approximation is performed using a quadratic function, the width direction thermal crown profile cannot be accurately expressed.

On the other hand, since method (2) above directly solves the two-dimensional heat conduction equation, it can be expected to improve accuracy even when shifting work rolls, but in both methods, the number of division elements in the roll body length direction is about 40. Therefore, the calculation time is long and the computer load is high and it is not practical to use online.

(Means for Solving the Problems) The present invention is intended to solve the above problems, and its means are based on the thermal crown of the roll roll during rolling based on the temperature distribution in the longitudinal direction of the roll body during rolling. When making predictions, the roll body length of the roll is divided into a rolling area for the material to be rolled and other areas, and the rolling area is further divided into both sides and an intermediate area, and the contact position of each section is calculated. Measuring the roll temperature and the center temperature in the longitudinal direction of the roll body at the intermediate portion,
A method for measuring a thermal crown of a mill roll is characterized in that the temperature distribution in the longitudinal direction of the roll body is determined based on this and the thermal crown is calculated.

(Function) When the present inventors measure the profile of the thermal crown during rolling of a rolling roll, various experiments and studies have been carried out regarding changes in temperature distribution in the rolling region and other regions of the rolled material, which are determined in advance. As a result of the overlapping, as shown in FIG. 1, the central portion Lc within the rolling zone L1 of the rolled material ST of the rolling rolls and both side areas L2 of the several zones Ll. L3 changes slowly, but both sides LEI and LE□ in the region L1 change rapidly, and the temperature distribution at both sides LEI and LE2 is a linear function, and the temperature distribution at both sides LEI and LE2 is a linear function. L outside the rolling area of the rolled material
We found that 2 + L 3 can be approximated by a function of about 6th order.

That is, the present invention now covers the area L2. shown in FIG. As shown in FIG. 2 (a), L3 is the element ■, Lr/.

L and 2 are element ■, Lc is element ■, and since the temperature changes of elements ■ and ■ are always gradual, the temperature distribution of element ■ is based on the contact temperature between the long end of the rolling roll body and element ■, and The temperature distribution of element ■ is approximated by a 6th-order function based on the temperature at the contact point with element ■ and the temperature at the center of the roll body length of element ■, and the roll temperature distribution of element This approximation is performed using a linear function based on the measured temperature value. As a result, the thermal crown profile in the length direction of the roll body, which is calculated by solving a two-dimensional heat conduction equation, can be quickly and accurately performed using the minimum necessary number of rolling roll I4 longitudinal division elements.

Based on this clarification, the present invention defines an element division method for calculating a thermal crown profile from a two-dimensional heat conduction equation, thereby significantly reducing the calculation time for calculating a thermal crown profile.

This point will be specifically explained with reference to FIGS. 2(a) and 2(0).

Now consider the temperature distribution on either the right or left side of the center of the rolling roll body length as follows. Also, assuming that the temperature distribution in the radial direction of the roll is uniform, only the average temperature is considered as shown in Figure 2 (0).
As shown in , the temperature distribution in the longitudinal direction of the roll cylinder is approximated as follows.

Temperature distribution of element ■ θ-(1ft) θ1 +ft (+2 ・
... (1) Temperature distribution θ of element ■ = (1-I2) θ2 + f2 θ3 ... (2) Temperature distribution θ of element ■ = (1-I3) θ3 + f3 θ4 ... (3) However, fl is within element ■ A parameter that represents temperature distribution.

I2 is a parameter that represents the temperature distribution within element ■, and f2 = C4□...
・Represented by (5).

I3 is a parameter representing the temperature distribution within element
-'V13)"+c3(1-"43)2...
...It is expressed as (8).

Furthermore, θl, θ2. θ3. θq is the temperature at the long end of the rolling roll body, θ2 is the contact temperature between elements ■ and ■, and
03 is the contact point temperature of elements (2) and (2), and 04 is the center temperature of element (2) in the roll body length direction.

1 is the length of the roll body of element (2), i3 is the length of the roll body of element (2), and l l + fL 3 changes depending on the plate 11 value of the material to be rolled. , 1lL2 is the roll body length of element (2) and is a constant value.

al+ bIn cl+ J+ b3+ 03 is a constant and satisfies the following relationship.

X+= A-ite f1= 1, X1= O and fl-
0”f+ ”X-+=o = 0
Therefore, in order to obtain the temperature distribution in the roll body length direction, 01. Find only θl, '3+09, and the other parts are (+)~
Calculate by interpolating from equation (6).

Next, 01,0, θ3. θ9 is determined by solving an axisymmetric two-dimensional heat conduction model equation on one side in the roll axis direction using the finite element method by introducing the principle of virtual work. The solution is shown below. The axisymmetric two-dimensional heat conduction model formula for one side in the roll body length direction is shown below.

P, 970. r, (person 7.n, 42, (xv%)
”・(7) However, ρ: specific gravity, c: specific heat, input: thermal conductivity, θ: hot water temperature t: time, r: distance in the roll radial direction, X: distance in the roll body length direction, boundary condition r=0. λ=”'/ −0−=(8) r r=R, “θ Otsu, −−hB(θ−θa) −(9
) However, R: Roll radius, 08 Ambient temperature on the long surface of the two rolls, hB: Heat transfer coefficient on the long surface of the roll x=o
, λ8θ/ax-hA(θ-0A) ・”(10)x
=L, enter aθrux = o
11. (11) However, O
A: Ambient temperature at the long end surface of the roll body, hA: Heat transfer coefficient at the long end surface of the roll body.
11) Equation is also multiplied by another arbitrary variation δθ', integrated within the region, and further set δθ=δθ'', then Rf:f,,'pCa
80 F d r d x+R,, t f: Enter, j
θrue S Umoa 〒 d〒 48+RJ. 'hA(o
-oA)δθ〒drg,”h8(0-08)δ(J
dx=0...(12) is obtained. However, since the equation (12) derived from the principle of 〒=7° virtual work is δθ=δθ4, it is a necessary condition to simultaneously satisfy the equations (7) to (11).

Therefore, a partial differential equation can be converted into an ordinary differential equation by approximating the temperature θ using equations (1) to (8), and substituting it into equation (12) and integrating it.

[P] (δ) + (H) (θ) = (g)...
(13) Equation (13) is the model equation to be found.

Here, (θ)=(θ1.θU, θ3.θJ, (o)−(
θ1. θ2. θyo, θ4), T on the right shoulder of the right side represents the arrangement matrix, and δ7. δ2+ a3. Each figure is θ
,.

θyu, θ3. It represents the time differential of θl. Furthermore CP)(
H) is a 4-element trinomial diagonal matrix, and (g) is a quartic vector.

This ordinary differential equation can be solved as a four-dimensional simultaneous linear equation using, for example, the central difference method, and can be solved at time T during rolling or idling. (θ)=(θ
1. θ2. θ3. θ9) can be determined by the method described below.

Now, if T' is divided by a positive integer N greater than or equal to 1 and that value is the time step Δτ, then (δ) (0) is converted to (14
), replace it as shown in equation (15).

(0) =(' Z +al (' r
...(14)Δτ Here, (θ6) is T. (θ) = (θ9
．． θ2. θ3,0<t), ('1:+aゎ) is T. +Δ
tt le time 6 (0) = (0,, 0,,,
0, OJ"c. Using equations (14) and (15), equation (13) becomes a four-dimensional simultaneous linear equation like equation (1B).

Δ τ ([P] + TCH]) (O, r446) − ((P) −
(H))(0τ) 1Δτ(g) ・・・・・・(16
) (16) is further solved for (06, □), Δ
τ (θ□+,,wa) = ((P)+-(H)l=(CP
)---(H)) (0τ) +Δτ([P]+-[H]) (g) ......(17). This (θτ 6.1:) is newly set as (θτ) and (1
7) Find the time sound after time T+2Δτ based on the formula. Thereafter, by repeating this process N times, the temperature (θ) at time T, T, is obtained.

Note that the calculation target time T. When the boundary conditions shown in Figure 2 (a) change within the equation (13), (P), (H) (
g) needs to be recalculated.

In addition, in the above dividing method, the lengths if and fL3 of the roll body lengths of elements 2 and 3 shown in Fig. 2 change depending on the width value of the material to be rolled, so the width value of the material to be rolled is different from that of the old material. In this case, the temperature θ2, θ3 at the contact point of the element ■■■ determined by the plate width value of the rolled material is the temperature distribution of the rolled material just before rolling determined at the element division position determined by the mid-plate value of the old material, and ( It is determined by interpolation using equations 1) to (6).

Furthermore, in this calculation method, the axial center of the rolling roll coincides with the center of the rolled material in the l] direction, so the left and right regions from the axial center of the rolling roll show symmetrical identical profiles. The thermal crown profile is calculated only from the temperature distribution of one side of the roll, but even when the work roll is shifted, that is, the position of the rolled material relative to the work roll is not symmetrical with respect to the center in the longitudinal direction of the roll body. By changing the apparent width value for each side of the roll according to the shift position and calculating the value separately, the average value of the temperature θ4 at the center in the longitudinal direction of the roll body is calculated, thereby achieving a temperature distribution with sufficient accuracy over the entire roll. can be calculated.

(Embodiment) An embodiment of the present invention will be described with reference to an example of a crown control device using a bending device shown in FIG.

Device l in the figure is a contact position calculation device, and when calculating the temperature change of the rolling roll after a predetermined time during rolling based on the tracking information of the rolled material ST,
, input the shift position Si, and divide the rolling roll body length from the work side S to the drive side OS into six elements as shown in FIG. , discussion.

fJ-? <,! :L E /', l3<' is output. Here, W on the right shoulder indicates the work side on one side of the roll, and D indicates the drive side. Further, the subscript t at the lower right indicates the stand number, and the numbers 1 to 3 indicate the elements 1 to 2, which are assigned the same number. same as below. Device 2
is the roll temperature information storage area and contains long text 70 for each element of the rolling roll immediately before the calculation start time. LD, gob.

Love education 0. Official τㅅ0. Cross 7. D. Look! A and the corresponding contact temperature (θ)! , (θ), are stored. When calculating the temperature change of the rolling roll after a predetermined time during idling, use the divided element long sentence 1i5 sentence 7 immediately before the calculation start time. ．． Interchange 3j + history, i, see vt + see. 7 to device 2
input and output as each element length.

Device 3 is a contact position temperature calculation device that calculates the divisional elements. S, S', ), ('l S,
KL70. which was inputted from the device 2 and the corresponding temperature distribution just before the calculation start target time was inputted from the device 2. L.D.

17, D, A, W7', l? %'+l''
r'i' 1 N %'i" and he (0) 4"'qt
θj? Calculated based on LD and formulas (1) to (8), (o'
Output as t'Z > (O)2.

Device 4 is a matrix vector calculation device that calculates the divided element length and roll cooling water temperature θ-1. Input the temperature of the rolled material θO, the ambient temperature θAi, the roll radius, and the roll material. 11) Matrix CP), , CP) in formula 11)
, :, (H), :, (H), , and vector (g)
';, (g) ♀ is calculated and output under rolling or cooling boundary conditions based on tracking information.

Device 5 is a contact temperature calculation device that calculates the contact temperature (θ)b,<o)' immediately before the calculation start time based on the board tracking information.
; and the matrix CP)γ, CP)',.

(H), [H)? and vector (g), (gB and calculation target rolling time THi or calculation target cooling time TCi
17) Based on equation 17), the contact temperature (0) i: and (θ) i at a predetermined time corresponding to THi or TCi are calculated. The obtained (O), -, (θ)7 are the dividing element lengths, each degree, Ai, 4. Official 311 sentences 91. look? H, chin and V
A/, W', D.

Both are in the roll information storage area (θ) yoLD
.

(θ)　　　　　　　　　　　　　,　　　　　　　　　　　　　
.

In the device 6, the contact temperature (θ)t at a predetermined time.

(θ) o: F″”, contact temperature (θ) w, Ivx, (θ ) i
and corresponding requirements mjV2 wlv2 WI
VI p+2z [)IA/2 111A
71 long sentences, 4. Ai 2 □ 2 sentences, □ 7 sentences, 42 sentences, A, See, A. Based on 1) to (6), calculate the temperature distribution in the longitudinal direction of the rolling roll body at the predetermined time and at the time of installation, and calculate the A thermal crown profile Ct is output using the model formula.

In addition, at the time of roll rearranging, the contents of the roll initial information storage area are determined based on the temperature distribution of the incorporated rolls (θ)i7(θ
) Ding゛7. See γr, intersection 7'go 4i''go 2 sentences?Two intersection Sl,
VZ and fLSI:Z, and at the same time, the contents of the role information storage area are made to match these.

Further, the device 8 is a wear amount calculation device, which includes the plate width B, work roll shift amount Si, rolling length Li, rolling load Pi, and roll diameter Dw.
i. Input the roll material and output the axial wear profile C7 of the rolling roll using a known wear amount calculation model.

The device 9 inputs these thermal crown profile C7, wear profile C, lotus schedule H1, predicted rolling load P,..., work roll shift amount Si, and mill dimension to obtain a predetermined crown target value CArh and shape target value 371z. Output the pending force F of each stand that obtains /-I.

As shown in JP-A No. 58-76H5, for example, the method for calculating F is to calculate the target plate from the plate thickness distribution of the rolled original plate without the plate shape at the exit side of each rolling pass exceeding the sheet passing limit shape. Among the plate thickness distributions at the exit side of each rolling pass that can achieve the thickness distribution and plate shape, the edge elongation control ability side of the bending apparatus is set in advance to a predetermined limit that is within the capability of the bending apparatus and in the later passes. Find a limit elongation schedule for the end of the bending device that maximizes the end extension within the second half of the pass, and ask X et al. A maximum elongation schedule during the second half pass that is utilized to the maximum is determined, and a set target value for the thickness distribution on the exit side of each rolling pass is determined as an internal division point between the second half pass end elongation maximum schedule and the second half pass mid-elongation maximum schedule, and the set target value is determined. There is a method of determining the setting value FAj''I of the bending control device according to the following.

The pending force p9/-1 thus calculated is sent to the bending control device 10 to control the pending force.

FIGS. 5(a) and 5(b) show examples of thermal crown profiles calculated and measured by the thermal crown profile calculating device 6, together with profiles of comparative examples, conventional examples, and actual measurements.

In each of the above measurements, the rolling roll had a plate surface temperature of 860°C;
In the process of hot rolling a hot strip with a plate width of 10100O and a plate thickness of 21 to a plate thickness of 1.2tx■, 16
The test was carried out immediately after coil rolling [FIG. 5(a)] and immediately after rolling the 31st coil [FIG. 5(b)]. (However, 1 coil rolling time = 83 seconds, idle time between coils: 16 seconds) In the figure, 1 curve C1 + C2 is the actual measurement profile, Ctr-r
.

C-2 is the measurement profile according to the above-mentioned embodiment of the present invention, Ctr-t, Cl5-2 is the measurement profile according to the above-mentioned conventional method (2)
The measurement profile Co-a+co-b is a measurement profile [comparative example] calculated by classifying element (■■) and element (■■) into the same category in the example of the present invention described above. As is clear from FIGS. 5(a) and 5(b), the measurement profile C:-1I C4-2 according to the method of the present invention is
Both methods approximated the measured profile to the same extent as the time-consuming conventional method (2), and the accuracy of the comparative example was significantly lower.

In other words, the measurement profile c=-,,C,! In the conventional example (2), the 40-divided elements normally used can be substantially replaced with 6-divided elements, so if the same computer capacity is used, the productivity will be significantly improved. Since the computer capacity was installed with productivity in mind, the required scale was reduced to about 1/100, and the computer cost, which accounts for about 1/40 of the equipment cost for the rolling process, was significantly reduced.

(Effect of the invention) By applying the present invention, approximately 1/+00 of the conventional technology
With this computer capacity, the thermal crown profile of the work roll during rolling can be measured quickly and accurately on-line, regardless of changes in the plate 11 and the presence or absence of work roll shifts, in the same manner as in the prior art.

From this, it has become possible to significantly improve the productivity of processes involving crown control or plate thickness control in rolling metal materials, or to reduce equipment costs by a large amount.

[Brief explanation of the drawing]

FIG. 1 shows an example of thermal crown measurement results. Second
Figures (a) and (0) show an example of element division of the roll body length in the present invention (a) and the roll cross-sectional average temperature (0) of each element and the contact point between the elements to measure the thermal crown based on this. shows. FIG. 3 is a block diagram showing an example of a crown control device for implementing the uninvented method υ,
FIG. 4 is an explanatory diagram showing an element division aspect of the roll body length in the example shown in FIG. Figures 5 (a) and (b) show the thermal crown profile of a roll that was determined to be A11 by the measuring method of the present invention, and the thermal crown profiles of the same roll that were measured by the conventional method and a comparative example are also shown together with the actually measured profile. This is what I did.

Claims (1)

[Claims] When predicting the thermal crown of a roll during rolling based on the temperature distribution in the roll body length direction during rolling, the roll body length of the roll is divided into a rolling area of the material to be rolled and other areas, and The rolling zone is divided into both side parts and an intermediate part, and the roll temperature at the contact point of each division and the central temperature in the body length direction of the intermediate part are measured, and based on this, the temperature distribution in the roll body length direction is determined. A method for measuring thermal crown of a rolling roll, characterized by calculating a desired thermal crown.