JPH01306002A - Method for hot rolling steel stock - Google Patents

Abstract

PURPOSE:To improve the accuracy, quality, and yield of products by finding a parameter (m) representing a shape of a stock based on a stock surface area, typical outside radius, and stock volume at each stand and predicting a stock temp. by substituting the parameter (m) in an equation giving a stock temp. after cooling. CONSTITUTION:As for predictive calculation of a stock temp. after cooling at each stand, a stock shape is set by use of a parameter (m) obtained by (m)= stock surface areaXtypical outside radiusdivided by stock volume. Then, the (m) is substituted in the equation giving a stock temp. thetan+1' after cooling and the stock temp. is predicted. A billet 2 heated to a prescribed temp. by a heating furnace 1 is formed by a group of rolling mills 5, 6, 7 and a product 3 is rolled in on-line based on the predictive temp. after cooling. The accuracy, quality, and yield of the product 3 are improved because of use of the parameter (m) found based on the stock surface area, typical outside radius, and stock volume.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to a method for hot rolling steel materials, and more specifically, even if the cross-sectional shape of the material differs from rolling stand to rolling stand, it is possible to The present invention relates to a hot rolling method that can quickly and accurately predict the temperature of a material after cooling a group of stands.

Conventional technology In general, in the rolling of metal materials, (1) improvement of material dimensional accuracy and surface quality, (2) structure control, (3) required power and material strength evaluation for determining mill specifications, and (
4) Due to the requirements of controlled rolling and controlled cold FA, highly accurate material temperature prediction calculations are essential. Among them, (1)
, (2), and (4), on-line calculations with limited calculation time are also required, and this necessity is greater in the hot rolling process. In addition, more precise calculations are required in hole hot rolling of steel bars and wire rods, which handle square and round cross-sectional shapes that are more complex than flat plates. The following is an explanation.

Conventionally, in offline design calculations, the so-called difference method [for example, in addition to food products, the 74th Rolling Theory Subcommittee 74-2N1983-3] has been used, partly because the calculation time is not limited.
] is applied. This finite difference method divides the cross section of the material into fine sections, establishes a heat conduction equation within each domain, and calculates the boundary conditions between adjacent domains by simultaneously setting a number of algebraic equations to be equal. A method,
As shown in Figure 1, even if the cross-sectional shape of the material changes repeatedly as the rolling process progresses, such as square, diamond, circle, or oval, this change in cross-sectional shape of the material must be handled strictly. Therefore, highly accurate material temperature calculations are possible.

However, it is difficult to apply it to actual rolling, especially online, due to time constraints.

In other words, when rolling is performed by predicting the material temperature using the differential method in actual rolling, the actual values measured at the actual rolling site, such as the material temperature on the heating furnace exit side or the material temperature on the rough pass exit side, etc. Based on this, taking into account the amount of temperature drop due to various refrigerants in the rough pass process, predict the temperature of the material at the entrance of each rolling stand after the rough pass, estimate the rolling load, The distance between the upper and lower work rolls of each rolling stand is determined, and rolling is performed sequentially.

However, in so-called online calculations of material temperature, the more you use a bonded rolling stand, the less calculation time is allowed. For the reason,
Even if it can be adopted as an exact calculation offline, it cannot be applied online.

Therefore, for online prediction calculation of material temperature, instead of the difference method, it is convenient to use the equivalent cross-sectional area circular conversion method [e.g.
Square size, 34th Plastic Working Federation (1983-111)
, 169]. Although this method only changes the cross-sectional shape of the material as the rolling process progresses, it treats all the edges as circles with equal cross-sectional areas, making it impossible to perform highly accurate calculations.

To explain more specifically, the following two problems arise due to the use of the equivalent cross-sectional area circular conversion method instead of the difference method that takes into account changes in the cross-sectional shape of the material at the online calculation stage.

(1) Occurrence of error due to the simplified formula, (2) Occurrence of error when converting to a perfect circular cross-sectional shape.In other words, looking at item (1), with this simple formula, the material temperature θnn after cooling is , appears as shown in equation (1).

θn++ = f (θ., 6%℃)...(1
) However, θn+1: Average material temperature after cooling θn = Average material temperature before cooling d: Material outer diameter t: Cooling time In other words, material temperature after cooling 8 ports + 1
Heat transfer coefficient, rolling material, refrigerant; M
The cross-sectional shape of the material is fixed in a specific manner, and as shown in Figure 1, θ
. , d, as a function of [, and linearly approximated flJ
It is calculated in a table as an easy formula. For this reason,
- It is non-lethal, and the application period is limited to a very narrow range,
If the fixed conditions are deviated from, the calculation error will become extremely large.

Regarding item (2), for example, as shown in Figure 2, even if the cross-sectional shape of the material is rhombic 1 during the rolling process, it is converted into a circular 2 with the same cross-sectional area, so the radius of the material is the original. The radius will be larger than the radius of the shape. In such a case, due to the so-called mass effect caused by the increased wall thickness, fundamental defects arise such as ('a) underestimating the core temperature and overestimating the full average surface temperature.

Problems to be Solved by the Invention The present invention aims to solve the above-mentioned drawbacks.Specifically, the so-called differential method is a method for measuring the temperature of a material in m-density by incorporating changes in the cross-sectional shape of the material during the rolling process. However, the calculation time is too long and it cannot be applied online.On the other hand, the simple formula based on the circular conversion method can be applied online, but it cannot take into account changes in the material cross section during the rolling process. The aim is to solve problems.

Means for solving the problem and its effect, namely, the method of the present invention predicts and measures the temperature of the material after cooling for each stand during hot rolling of steel materials such as square bars and round bars,
Based on this predicted temperature, the rolling load at that stand is estimated, and when setting the upper and lower work roll spacing, the parameter expressing the shape of the material is set for each stand (m).
= Material surface area x representative outer radius ÷ material volume, and this parameter m is calculated using the material temperature formula after cold W. Ohn
= f (υ11θL, d, t, a, a, λ, l
11) to predict the temperature of the material online.

However, bn: average material temperature before cooling, θI-: refrigerant temperature, d
: Material outer diameter, t: Cooling time, α: Refrigerant heat transfer coefficient, a: Temperature propagation coefficient, λ: Thermal conductivity Therefore, with the method of the present invention, it is possible to achieve high precision dimensions, high quality, etc. of the product. Hot rolling of steel materials is possible.

In addition, it is now possible to conduct strict evaluation of hot rolling using exactly the same formula both online and offline, which not only enables advanced product manufacturing but also improves the reliability of equipment specifications and quality design J1 by designing more accurate process conditions. You can enhance your sexuality.

Therefore, more specific details are as follows.

First, Fig. 1 is a flow sheet of an example of a steel bar rolling line, where 1 is a heating furnace, 4 is a boring reeler, 5 is a rough rolling stand group, 6 is an intermediate rolling stand group, and 7 is a finishing rolling stand group. , 8 is tilter, 9 is descaler, 10
12 indicates a water cooling zone between the stands, and a winding thermometer. After the material bit 1/t2 is cooled in the heating furnace 1, it is transferred to each rolling stand group 5.
．． The steel rod 3 is formed into a desired shape through steps 6.7 and 6.7, and is wound into a boring reeler 4 as a coiled product.At this time, the material temperature is predicted in each rolling stand group 5.6.7. The rolling conditions are determined based on this predicted temperature, and the billet material 2 initially has a square cross section 1a, but is formed into a diamond cross section 5a during rough rolling, an oval cross section 6a during intermediate rolling, and a small circular cross section 7a during finish rolling.

Therefore, in each rolling stand group 5.6.7, the cross-sectional shape of the material that changes as described above, for example, square, diamond, circle, oval, is taken as the parameter m shown in (1) below, and this parameter m is (2) to predict the material temperature after being cooled by the refrigerant.On-+=r(θns θL, d,
t, α, alλ, 1111---
・--(2 squares, θn, 1: Material temperature after cooling θn; Material temperature before cooling d: Material outer diameter 1: Cooling time α: Refrigerant heat transfer coefficient a: Temperature propagation coefficient λ: Heat The conductivity, that is, the temperature of the material after cooling, is determined as an analytical solution of unsteady heat conduction based on heat conduction theory, and is given as the following equation (2').

θn++ = f(θn, 0L%d, t, a, λ
, a, X)-・-<2') However, θIl+1, θ
rI = Material temperature before and after cooling θL = Temperature of refrigerant d : Outer diameter of material α : Refrigerant heat transfer coefficient λ : Heat conduction chamber a : Temperature propagation coefficient X : Parameter Furthermore, in equation (2'), parameter X is infinite The solutions of different hypergeometric equations are given as equations (3-a), (3-b), and (3-c) for a long plate, an infinitely long cylinder, and a sphere, respectively.

However, these equations (3-a), (3-b), and (3-C) cannot be solved algebraically. Therefore, as approximate solutions, for example, (4-a), (4-b), (4
-C1 can also be given as shown in each formula.

However, when this approximate solution is used, the error becomes large when the heat transfer coefficient α or the material outer diameter d is large, and it is only applicable when the material outer diameter is small or the cooling capacity of the refrigerant is small. However, even if the range of application is expanded by correcting the outer diameter of the material, there is a limit.

From this point, the present inventors (3-a), (3-b)
, (3-c) algebraically and to find a formula for the solution X that can be expressed uniformly for a flat plate, cylinder, and sphere. I tried to obtain a calculation formula.

To explain in more detail, the shape of the material is taken as a shape factor m, and this is used as the parameter shown in equations (1) and (5).

S・(d/2) m= □ ・・・・・・(5) ■ S: Surface area of material V: Volume of material d: Outer diameter of material When viewed in this way, a flat plate, cylinder, and sphere are Zohm=
1.2.3, (4-a), +4-b), (4-C
Each equation of 1 can be expressed uniformly by equation (6).

However, for diamond-shaped and oval-shaped cross-section materials, m=
(Y, 1<m<2, and both take values between a flat plate (m=1+) and a cylinder (m=2). In particular, in the case of an oval shape, depending on the degree of flatness, ) lia tot
t le. Jutte, (3-a), (3-b), (3-C)
We came up with the idea that if we derive the solution X of each equation as a unified function form of .

In short, as mentioned above, when determining the material temperature after cold indium before analysis, (al (b) If this solution
It was necessary to be able to strictly handle oval cross sections.

Therefore, in order to embody these two conditions, the present invention is configured as follows to quickly and accurately calculate the average and surface temperature of a material with an arbitrary cross-sectional shape, as well as the temperature at an arbitrary depth position.

(1) Give the material average temperature equation after cooling as shown in equation (2) using the shape factor m as a parameter; (2) In the case of a rhombic or oval cross-sectional shape, give a formula for determining the representative outer diameter d; ( 3) Giving the temperature distribution formula in the material depth direction, (4)
(1) To express the average material temperature θn++ after cooling as the formula (2); In general, before analyzing unsteady heat conduction, as shown in Table 1, <、
After determining the M and P values, the formula (1) θn++=(θ.−θL
) Σ M-P-c-"' +OL・Song・(7)K
It is given by X=□·x2, and the temperature at any position β in the depth direction of the material can be calculated as shown in Table 1. In other words, equation (7) is β=
By applying 1.0, the surface temperature can be calculated. However, it is impossible to determine the average temperature because the position of the average temperature position β cannot be specified, and the average temperature is often required for things such as average evaluation of materials and rolling load calculations.
This is one problem.

Table 1 β: Material radial depth position coefficient Ji (X): First type ε-th Bessel function Therefore, as mentioned above in section (4), the present inventors calculated the average temperature position β expression (8 ), β-f(n+, d
, α, λ, θL) (8) Appeared as a function with the shape factor m as a parameter.

As a result, when β obtained from equation (8) is substituted for β in equation (7), the relationship ΣM-P=1.0 is obtained, and the material average temperature equation after cooling On÷1 is (
9) As a formula, θn++ = (θ.-θL)-C-KX' ・
・－・－・(91 hail.

Furthermore, in equation (9), the function kX is expressed as shown in equation (10).

kX=□・×2 ・・・・・・(10)(10)
In the formula, X is a parameter, and this parameter
is expressed by equation (11) as a representative function.

X=f(m%N)=r(a+, a, d, λ)...
- (111 As mentioned above, in the rolling process, if the cross-sectional shape of the material of each stand is taken as the shape factor m,
(9), (10) and (11), and using these equations (9), (10) and (11), the outer radius d of the material, thermal conductivity λ, temperature propagation rate a, material average temperature before cooling θ. By determining the heat transfer coefficient α, temperature θL, and cooling time t of the refrigerant, and giving these values, the material temperature θn and 1 after cooling can be determined instantaneously and accurately. For,
Online application becomes possible.

(3) Regarding the temperature distribution in the depth direction of the material, if the cross-sectional shape of the material is taken as the shape factor m, the ratio φβj of the material temperature θβ at an arbitrary depth position and the average material temperature θ is determined by the depth As a function of the position coefficient β and the shape number m, ψpfi=r(β, information, d, a, λ, θL)
--It can be induced as in (12a).

Therefore, the material temperature θβ at an arbitrary depth position is determined by equation (12).

θβ −φβj・θ (12) Also, when β = 1.0 in equation (12), we get
Surface: 3 degrees is required.

(2) Determining the representative outer diameter d of a rhombus, etc. For a rhombus or oval cross-sectional shape, the representative outer diameter d is, for example, Fig. 3 <
It is determined as shown in a) and (b). For example, in the case of an ellipse shown in Fig. 3(a) or a rhombus shown in Fig. 3(b), the four half-sections of the same shape, for example, the line segment OC that bisects the area of [1lTh OAB or h OAB. The shape factor m can be calculated by multiplying by twice.

As mentioned above, one of the features of the present invention is the general analytical solution equations (3-a), (3-b), (3-
The purpose is to derive the solution X for c) in a unified and algebraic manner, and to make this possible. Therefore, the prealgebraic derivation of x will be explained in more detail as follows.

(3-a), (3-1)), (3-c) The trigonometric function in each equation, Bessel function JL , (13-c
), (13-dJ equation).

By substituting this into each equation (3-at, +3-b) and (3-c), it can be expressed uniformly as shown in equation (14).

However, (2k)! ! =(2kl・(2(k−1)
))・(2(k-2))・・・・・・・・・2, N=α
- By deriving the d/λ formula (14) as in the formula (15) and applying the recurrence formula of the infinite series ΦL to the formula (15), the formula (16') can be derived.

In formula (16'), ΦQ-17Φ9 is an infinite series term, but as E becomes larger, it approaches 1.0, and as a result of logical examination by numerical calculation, for a finite number l = 6, Φ6 2-X2 An approximate solution of /(m+14) is obtained. This approximate solution is only 0.06% or less, which is sufficient accuracy for practical use, and as an algebraic solution for N,
Equation (16″) was obtained.

+16=1 formula allows you to immediately calculate N with high precision by substituting m and X, but on the other hand, from formula (16=)
By deriving the expression, the initial purpose of deriving an algebraic solution to X can be achieved.

For analytical processing, replace Y =
%N) was given by regression of the true value by series calculation. (1
The approximation error of formula 7) is 0.496 or less, which poses no practical problem. The solution Y of equation (17) was obtained as the root of an ordinary quadratic equation, and the parameter X was obtained as an algebraic solution of equation (18) as a function of thermal conductivity λ.

In short, by making it possible to calculate the average and surface temperature of a material with an arbitrary cross-sectional shape with high precision and speed, it is also possible to calculate rolling load with high precision based on strict online material temperature calculation in hot rolling of steel bars.

Example First, in FIG. 1, a billet material 2 is held at a predetermined temperature in a heating furnace 1 for a predetermined period of time, and in the case of a square billet, the billet material 2 is heated to a height of 90" by a tilter 8.
It is rotated, then descaled by a descaler 9, and enters the rough rolling stand group 5. Then, it is appropriately water-cooled by the inter-stand water cooling zone 10 and descaled by the descaler 9, sequentially rolled by the intermediate stand group 6 and finishing stand group 7, and coiled by the boring reeler 4. A line thermometer 11 appropriately installed on the exit side of the stand during rolling measures the surface temperature of the material in a state where reheating is completed, and finally the temperature is measured and recorded as the coiling temperature by a thermometer 12 immediately before the boring reeler. rod gi with circular cross section
! When finishing a product, a square material billet is usually used, and in the rough rolling stand group 5, it is square → diamond → square → diamond → square → diamond → square repeating, and in the intermediate rolling stand group 6, it is square → hexagon → circle → Oval →
Convert from circular to oval to circular and oval to circular types.

In the finishing rolling stand group 7, the process is repeated in the following order: circular → oval → circular → oval → circular → oval → perfect circle. In these series of changes in cross-sectional shape, the rhombus and oval are designed to have an arbitrary length/breadth axis ratio, so that the so-called shape factor takes on various values.

Therefore, in the hot rolling line shown in Figure 1, φ17-3
A 17-3C steel bar billet is extracted from the heating furnace at 1150°C and rolled at the lowest finishing speed of 8.4 m/s (0.51 m/s at the exit side of the 6th pass). When the temperature was actually measured and the measured temperature was compared with the conventional technology and the predicted temperature predicted by the present invention,
It was as shown in Table 2.

These material temperatures were measured using a radiation thermometer installed on the line at the exit of the 6.8.12.18 stand and immediately before winding.

In Table 2, in the conventional technology, the cross-sectional shape of the material is a perfect circle in terms of equal cross-sectional area, and it is determined based on the rolling results of high-speed rolled materials, and the atmospheric equivalent heat transfer coefficient αa for each stand is determined at the finishing material rolling speed level. It is divided into three stages, and in this example, it is predicted and calculated as the lowest speed level. In this case, in the conventional technology, each predicted calculated temperature is 3 times higher than the measured value.
The temperature is 5 to 45 degrees Celsius, and it is predicted to be 1! The error was clearly too large.

In addition, φ42-550CI 1M billet was heated to 1130℃.
The highest finishing speed is 5.51 m/s.
(1.42 m/S at the exit of the 6th pass) Measured temperature and each predicted calculated temperature of the prior art and the present invention <Effects of the Invention> As explained in detail above, the method of the present invention has the following advantages: The temperature of the material after cooling is predicted and calculated using a general analytical solution. At this time, the shape of the material is derived algebraically using a shape factor consisting of material surface area x representative outside radius ÷ material volume as a parameter. Therefore, the present invention can capture the transition of the cross-sectional shape of the material during the rolling process, and accurately calculate the temperature of the material online, thus achieving high-accuracy dimensions, high quality, etc. of the product.

Further, since the method of the present invention allows prediction and calculation of material temperature quickly and with high accuracy, the accuracy of prediction of rolling load and torque is increased, and rolling capacity can be accurately grasped. Furthermore, dynamic set-up is possible for online highly accurate dimensional control, and accurate prediction of rolling characteristics is made possible, resulting in improved yield by reducing the number of test strips.

The present invention can be applied not only to old wire rods, but also to plate materials, spheres, and cubes, and can be applied not only to hot rolling but also at all material temperature levels.

[Brief explanation of the drawing]

Fig. 1 is an explanatory diagram of a steel bar rolling line consisting of 18 stands as an example of equipment for carrying out the method of the present invention, and Fig. 2 is an explanatory diagram showing a rhombus-shaped actual cross section and a perfect circle equivalent to the equivalent area. ,
FIGS. 3(a) and 3(b) are explanatory diagrams showing representative diameters of an oval and a rhombus, respectively. Code 1... Heating furnace 2... Material billet 3... Coiled bar 1 (BIC) 4...
Boring reeler 5... Rough rolling stand group 6... Intermediate rolling stand group 7... Finishing rolling stand group 8... Tilter 9...・Descaler 10... Water cooling zone between stands 11... Rolling machine outlet thermometer 12... Winding thermometer 13... Rhombic cross-sectional actual shape 14.・・・・・・Replacement W perfect circular shape

Claims (1)

[Claims] 1) During hot rolling of steel materials such as square bars and round bars, the temperature of the material after cooling is predicted and calculated for each stand, and the rolling load at that stand is estimated based on this predicted temperature. Then, top
When setting the lower work roll interval, find the parameter that expresses the shape of the material for each stand using the formula m = material surface area x representative outside radius ÷ material volume, and use this parameter m as the material temperature formula after cooling @ θ@_n_+_1=f(@θ
A method for hot rolling a steel material, characterized in that the temperature of the material is predicted online by giving the following values: @_n, θ_L, d, t, α, a, λ, m). However, @θ@_n: average material temperature before cooling, θ_L: refrigerant temperature, d: material outer diameter, t: cooling time, α: refrigerant heat transfer coefficient, a: temperature propagation coefficient, λ: thermal conductivity 2) Claim 1. A method for hot rolling a steel material, which comprises adjusting the amount of reduction of the rolls in accordance with the predicted and calculated temperature of the material when hot rolling the steel material by the method set forth in item 1. 3) When performing hot rolling by the method according to claim 1, the heat transfer coefficient of the heating medium or cooling medium is estimated with high accuracy based on the predicted and calculated material temperature, and the amount of the heating medium or cooling medium is adjusted. A method for hot rolling steel materials, characterized by: