JPH07102362B2 - Hot rolling method for steel - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a hot rolling method for steel products, and more specifically, even if the cross-sectional shape of the material differs for each rolling stand, this change in cross-sectional shape is taken into consideration. The present invention relates to a hot rolling method capable of quickly and highly accurately predicting a material temperature after cooling a group of stands.

Conventional technology Generally, in rolling metal materials, (1) improvement of material dimensional accuracy and surface quality, (2) microstructure control, (3) required power for determining mill specifications, material strength evaluation and (4) controlled rolling In order to meet the demands for cooling, controlled cooling, etc., highly accurate predictive calculation of material temperature is essential. Above all,
For the items (1), (2), and (4), online calculation whose calculation time is limited is also required, and the necessity is higher in the hot rolling process. In addition, more rigorous calculations are required for hole type hot rolling of steel bars and wire rods that handle square and round cross-sectional shapes that have more complicated material cross-sectional shapes than flat plates.
The prior art will be described below by taking hole hot rolling of steel bars and the like as an example.

Conventionally, so-called difference [for example, Moritaka, 74th Rolling Theory Subcommittee 74-21 (1983-3)] has been applied in offline design calculation because the calculation time is not restricted. In this difference method, the material cross section is appropriately subdivided,
A method of making a heat conduction equation in each domain and calculating a number of simultaneous algebraic equations with the boundary conditions between adjacent domains being equal to each other, as shown in FIG. With the progress of
For example, even when the shape changes repeatedly such as a square, a rhombus, a circle, and an ellipse, the change in the material cross-sectional shape can be handled precisely, so that the material temperature can be calculated with high accuracy.

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

That is, when predicting the material temperature by the difference method in actual rolling and rolling, the measured value in the actual rolling field, for example, the measured value of the material temperature on the outlet side of the heating furnace or the material temperature on the rough pass outlet side, etc. Taking this into account, the inlet side material temperature of each rolling stand after the rough pass is predicted and calculated by taking into account the temperature drop due to various refrigerants in the processor after the rough pass, and the rolling load is estimated and each rolling is estimated. The interval between the upper and lower work rolls of the stand is determined, and the rolling is sequentially performed.

However, such a predictive calculation of the material temperature is so-called online, the calculation time allowed for the second-stage rolling stand becomes shorter, and moreover, the calculation time allowed for the rolling speed increase year by year decreases. ,
Even if it can be adopted as an exact calculation offline, it cannot be applied online.

Therefore, for the online calculation of the material temperature, for example, instead of the difference method, the equivalent cross-section circular conversion method of replacing the equivalent cross-section with a perfect circular section is a convenient process [eg,
Noguchi et al., 34th Plastic Working Federation (1983-11), 169]
Has been adopted as. This method treats all of them as circles having an equivalent cross-sectional area regardless of that the material cross-sectional shape changes as the rolling process progresses, and therefore high-precision calculation is impossible.

More specifically, in the online calculation stage, the equivalent cross-sectional area circular conversion method is adopted instead of the difference method that takes in the change in the material cross-sectional shape, so that the following two problems occur.

(1) Occurrence of error by the simple formula, (2) Occurrence of error when converting into a perfect circular cross-sectional shape, that is, regarding the item (1), this simple formula shows that the material temperature θ _n after cooling ₊₁ is represented as shown in equation (1).

θ _{n + 1} = f (θ _n , d, t) (1) where θ _{n + 1} : average material temperature after cooling θ _n : average material temperature before cooling d: material outer diameter t: cooling time That is, the material temperature θ _{n + 1} after cooling is the heat transfer coefficient, rolling material, refrigerant temperature,
With the material cross-sectional shape fixed, as shown in FIG. 1, θ _n ,
It is expressed as a function of d and t, and is obtained as a table as a simple expression that is approximated by a straight line. For this reason, it has no generality, the application range is limited to a very narrow range, and when it deviates from the fixed condition, the calculation error becomes extremely large.

Further, regarding the item (2), for example, as shown in FIG. 2, even when the material cross-sectional shape is a rhombus 1 in the rolling process, it is converted into a circle 2 having an equivalent cross-sectional area, so that the radius of the material is It will be handled larger than the radius of the shape.
In such a case, there are fundamental defects such as (a) underestimating the temperature decrease amount and (b) overestimating the average / surface temperature difference due to the so-called mass effect of increased wall thickness.

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention An object of the present invention is to solve the above-mentioned drawbacks. Specifically, the so-called difference method can accurately calculate the material temperature by taking in the transition of the material cross-sectional shape in the rolling process. However, it takes a long time to calculate and cannot be applied to online. On the other hand, the simple formula based on the circular conversion method can be applied to online, but it is not possible to take in changes in the material cross section during the rolling process. The purpose is to do.

Means for solving the problem and its action That is, the method of the present invention, during hot rolling of steel materials such as square bar, round bar, predictive calculation of the material temperature after cooling for each stand,
When the rolling load at the stand is estimated based on the predicted temperature and the upper and lower work roll intervals are set, the parameter expressing the shape of the material for each stand is m = material surface area × representative outer radius ÷ Obtained from the form of material volume, this parameter m is the material temperature formula after cooling _{n + 1} =
f ( _n , θ _L , d, t, α, a, λ, m) to predict the material temperature online.

However, _n : average material temperature before cooling, θ _L : refrigerant temperature, d: material outer diameter, f: cooling time, α: refrigerant heat transfer coefficient, a: temperature transfer coefficient,
[lambda]: Thermal conductivity Therefore, according to the method of the present invention, it is possible to hot-roll a steel material capable of realizing high-precision dimensions, high quality and the like of products.

At the same time, it is possible to perform a strict evaluation of hot rolling using the same formula online and offline, and not only high-precision product manufacturing but also more accurate process condition design
The reliability of equipment specification determination and quality design can be improved.

Therefore, more concretely, it is as follows.

First, FIG. 1 is a flow sheet of an example of a steel bar rolling line, wherein reference numeral 1 is a heating furnace, 4 is a pouring ring reel, 5 is a rough rolling stand group, 6 is an intermediate rolling stand group, and 7 is a finishing rolling stand group. , 8 is a tilter, 9 is a descaler, 10 is a water cooling zone between stands, and 12 is a winding thermometer. The material billet 2 is cooled in the heating furnace 1 and then each rolling stand group 5, 6,
After being molded into a desired shape through 7, the steel bar 3 is wound as a coiled product on the pore ring reeler 4, and at this time,
In each rolling stand group 5, 6, 7 the material temperature is predicted, and the rolling conditions are determined by this predicted temperature. The material billet 2 initially has a square cross section 1a, but rough rolling has a rhombus cross section 5a and intermediate rolling. A circular cross section 6a is formed into a small circular cross section 7a by finish rolling.

Therefore, in each of the rolling stand groups 5, 6, and 7, the cross-sectional shape of the material that changes as described above, for example, a square, a rhombus, or an ellipse is regarded as a parameter m shown in (1) below, and this parameter m is set to (2 ) To predict the material temperature after cooling with the refrigerant.

_{n + 1} = f ( _n , θ _L , d, t, α, a, λ, m) ...
(2) where _{n + 1} : material temperature after cooling θ _n : material temperature before cooling d: material outer diameter t: cooling time α: refrigerant heat transfer coefficient a: temperature transfer coefficient λ: heat transfer coefficient The material temperature after cooling is determined as an analytical solution for unsteady heat conduction based on the heat conduction theory, which is given by the following equation (2 ').

θ _{n + 1} = f (θ _n , θ _L , d, t, α, λ, a, X) ...
(2 ′) where θ _{n + 1} , θ _n : Material temperature before and after cooling θ _L : Temperature of refrigerant d: Outer diameter of material α: Heat transfer coefficient of refrigerant λ: Thermal conductivity a: Temperature transfer coefficient X: Parameter Further, in the equation (2 ′), the parameter X is the solution of the different hypergeometric equations for the infinite-length plate, the infinite-length cylinder and the sphere, respectively (3-a), (3-b), (3-c) Given as each formula.

However, these expressions (3-a), (3-b), and (3-c) cannot be solved algebraically so far. Therefore, as an approximate solution, for example, (4-a), (4-b),
It can also be given as shown in each formula of (4-c).

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 can be applied only when the material outer diameter is small or the cooling capacity of the refrigerant is small. However, there is a limit in itself even if the range of application is expanded by adding the correction of the material outer diameter.

From this point, the present inventors have found that (3-a) and (3-
Examine the point of finding the expression of the solution X that can be expressed algebraically and uniformly on the flat plate, cylinder, and sphere in b) and (3-c), which enables rigorous and rapid heat conduction calculation. I tried to obtain a different temperature calculation formula.

More specifically, the shape of the material is regarded as the shape factor m, and this is set as the parameter m shown in the equations (1) and (5).

S: surface area of the material V: volume of the material d: outer diameter of the material
1, 2, 3 and (4-a), (4-b), (4-
Each expression in c) can be expressed in a unified manner by expression (6).

However, for rhombus and oval cross-section materials, 1 <m <2, and both take values between the flat plate (m = 1) and the cylinder (m = 2), and in particular, in the case of an ellipse, it becomes an arbitrary value depending on the degree of flatness. . Therefore,
The solution X of each equation of (3-a), (3-b), and (3-c) is X.
It was conceived that strict temperature calculation of a material having an arbitrary cross-sectional shape becomes possible by deriving it as a unified function form of = f (m, d, α, λ).

In short, when the material temperature after cooling is obtained as an analytical solution as described above, the solution X of the equations (a), (3-a), (3-b), and (3-c) is used.
By deriving the equation (1) as an algebraic function, it becomes possible to calculate temperature precisely and promptly. (B) This solution X has a form factor m determined by the major axis / minor axis as a parameter. If so, a diamond,
Strict handling of elliptical cross sections was necessary.

Therefore, in order to embody these two conditions, the present invention is configured as follows, and the average and surface of the material having an arbitrary cross-section and the arbitrary depth position temperature are calculated quickly and with high accuracy.

(1) give the material average temperature formula after cooling as the formula (2) with the shape factor m as a parameter, (2) give the representative outer diameter determining formula in the case of a rhombus or elliptical cross-sectional shape, (3) ) Give a temperature distribution formula in the material depth direction, (4) Give a formula for determining the average temperature position in the material depth direction, (1) Show the average material temperature θ _{n + 1} after cooling as the formula (2). Generally, the analytical solution of unsteady heat conduction is as shown in Table 1.
When M and P values are defined, formula (7) The temperature at the position β in the arbitrary depth direction of the material can be calculated as shown in Table 1. That is, the equation (7) is β =
The surface temperature can be calculated by applying 1.0. However, the average temperature is not possible because the position of the average temperature position cannot be specified, and since the average temperature is often required, such as the average evaluation of the material and the rolling load calculation,
This is one problem.

x: Radial distance from the material center Ji (X): I-th order i-th order Bessel function Then, as described above in the item (4), the present inventors define the average temperature position expression as the expression (8). , = F (m, d, α, λ, θ _L ) (8) It is expressed as a function with the shape coefficient m as a parameter.

As a result, by substituting the value obtained from Eq. (8) into β in Eq. (7), the relationship of ΣM · P = 1.0 is obtained, and the material average temperature formula _{n + 1} after cooling is given as Eq. (9). _{n + 1 = (n -θ L} ) · e -KXt t ...... (9) represented.

Further, in the equation (9), the function kx is represented as the equation (10).

In the equation (10), X is a parameter, and this parameter X is the shape factor m and the Nusselt number N = α, which is a dimensionless number.
It is represented by the equation (11) as a typical function by d / λ.

X = f (m, N) = f (m, α, d, λ) (11) As described above, in the rolling process, if the sectional shape of the material of each stand is regarded as the shape factor m, (9) ,
It can be expressed as in the equations (10) and (11). Using these equations (9), (10) and (11), the outer radius d of the material, the thermal conductivity λ, the temperature propagation coefficient a, before cooling The material average temperature _{n 1} , the heat transfer coefficient α and the temperature θ _L of the refrigerant, and the cooling time t are obtained, and by giving these values, the material temperature _{n + 1} after cooling can be instantly and accurately obtained.
Above all, it is possible to apply online because it is instantly requested.

(3) Regarding the temperature distribution in the material depth direction, if the cross-sectional shape of the material is taken as the shape factor m, as in the above, the ratio φ _β between the material temperature θ _β at the arbitrary depth position and the average material temperature is As a function of the depth position coefficient β and the shape number m, φ _β = f (β, m, d, α, λ, θ _L ) (12a) can be derived.

Therefore, the material temperature θ _β at the arbitrary depth position can be obtained by the equation (12).

θ _β = φ _β ··· (12) Further, when β = 1.0 is calculated in the equation (12), the surface temperature can be calculated.

(2) Obtaining a representative outer diameter of a rhombus, etc. For a rhombus or an elliptical cross-sectional shape, a representative outer diameter is obtained, for example, as shown in FIGS. 3 (a) and 3 (b).
For example, in the case of the ellipse shown in FIG. 3 (a) and the rhombus shown in FIG. The shape factor m can be calculated by doubling the area of ∘ into the line segment ∇.

As described above, one of the features of the present invention is that the equations (3-a), (3-b), (3-
The solution X in c) is derived in a unified and algebraic manner and made possible. Therefore, the derivation of the algebraic solution of X will be described more specifically as follows.

The trigonometric function and the Bessel function Ji (X) in the equations (3-a), (3-b), and (3-c) are represented by general series expressions (13-a), (13-b), (13-c), (13-
It is given as in d).

By substituting this into the equations (3-a), (3-b), and (3-c), it can be expressed uniformly as in the equation (14).

However, (2k) !! = (2k) ・ (2 (k-1)) ・ (2
(K-2)) ······· 2, N = α · d / λ (14) Equation (15) And the recurrence formula of infinite series Φi When is applied to Eq. (15), Eq. (16 ') can be derived.

In equation (16 '), Φ _l-1 / Φ _l is an infinite series term, but when l becomes large, it approaches 1.0, and as a result of logical examination by numerical calculation, for a finite number l = 6, An approximate solution of is obtained. This approximate solution is only 0.06% or less, and has sufficient accuracy for practical use. As an algebraic solution of N, (1
6 ″) was obtained.

In the equation (16 ″), N can be immediately calculated with high precision by substituting m and X. On the other hand, if the expression of X is derived from the equation (16 ″), the initial algebraic solution of X is derived. The purpose is achieved.

Equation (17) is used to replace equation (16 ″) with a quadratic equation of Y by substituting Y = X ^{2 for} analysis processing. As described above, f (m, N) is given by regressing the true value by series operation. The approximation error of equation (17) is 0.4% or less, and there is no problem in practical use. The solution Y of equation (17) is obtained as the root of a normal quadratic equation, and the parameter X is (1
8) Formula X = f (m, N) = f (m, α, d, λ) (18) as a function of shape factor m, heat transfer coefficient α, material outer diameter d, and heat conductivity λ. Was obtained as an algebraic solution.

In short, by making it possible to calculate the average and surface temperature of a material having an arbitrary cross-section with high accuracy and speed, it is possible to perform highly accurate rolling load calculation based on strict online material temperature calculation in hot rolling of steel bars.

Example First, as shown in FIG. 1, the material billet 2 is held in the heating furnace 1 at a predetermined temperature for a predetermined time. In the case of a square billet, the heated material billet 2 is rotated 90 ° by the tilter 8. Then, it is descaled by Descaler 9,
Enter the rough rolling stand group 5. Then, water cooling by the inter-stand water cooling zone 10 and descaling by the descaler 9 are appropriately performed, and the intermediate stand group 6 and the finishing stand group 7 are sequentially subjected.
And is coiled by the porer reel 4. Line thermometer installed on the exit side of the stand during rolling
The surface temperature of the material in the reheat complete state is measured by 11 and finally measured and recorded as the winding temperature by the thermometer 12 immediately before the porering reel. When finishing a steel bar product with a circular cross section, normally, using a square material billet, the rough rolling stand group 5 repeats square → rhombus → square → rhombus → square → rhombus → square, and the intermediate rolling stand group 6 square → 6 Convert from polygonal → circular → elliptical → circular → elliptical → circular and elliptical → circular type. Then, in the finishing rolling stand group 7, a circle → an ellipse → a circle →
Repeated as oval → circle → ellipse → perfect circle. In the series of changes in the cross-sectional shape, the rhombus and the ellipse are designed so that the major axis / minor axis ratio is arbitrarily designed, so that the so-called shape factor has various values.

Therefore, in the hot rolling line shown in Fig. 1, φ17-SCM4
35 steel bar billet was extracted from the heating furnace at 1150 ° C and rolled at the lowest level finishing speed of 8.4 m / s (0.51 m / s on the exit side of the sixth pass), and the material temperature after cooling was measured at this time. The measured temperature is shown in Table 2 in comparison with the predicted temperature predicted by the prior art and the present invention.

The temperatures of these materials were measured by using a radiation thermometer installed on a line, immediately before the outlet of the sixth, eighth, twelfth and eighteenth stands and immediately before winding.

In Table 2, in the prior art, the cross-sectional shape of the material is the equivalent cross-sectional area converted to a perfect circle, which is determined based on the rolling results of the high-speed rolled material, and the atmospheric equivalent heat transfer rate α _a of each stand is set as the finishing material rolling speed. It is divided into three stages according to the level, and in this embodiment, it is predicted and calculated as the lowest speed level. In this case, in the prior art, each predicted calculated temperature is 35% less than the measured value.
It was higher than ~ 45 ℃, and the prediction error was too large.

In addition, φ42-S50C steel bar billet was extracted at 1130 ℃, and the finishing speed of 5.51m / s (1.42m at the exit of the 6th pass) at the highest speed level.
Table 3 shows the measured temperatures and the respective predicted calculation temperatures of the prior art and the present invention in the case of rolling at / st).

<Effects of the Invention> As described in detail above, the method of the present invention predicts and calculates the material temperature after cooling of each stand group using a general analytical solution.
At this time, the material shape is algebraically derived by using the shape coefficient of material surface area × representative outer radius / material volume as a parameter. Therefore, the present invention can take in the transition of the material cross-sectional shape in the rolling process, can calculate the exact material temperature online, and in this way, it is possible to realize high-accuracy dimensions and high quality of the product.

Further, since the material temperature can be predicted and calculated quickly and accurately by the method of the present invention, the rolling load and torque can be predicted with high accuracy, and the rolling functional force can be correctly grasped. Further, it is possible to perform dynamic setup for high-precision dimensional control online, and to accurately predict rolling characteristics, thereby improving yield by reducing the number of pressure members.

INDUSTRIAL APPLICABILITY The present invention can be applied not only to steel bars and wire rods but also to plate materials, balls and cubes, and is applicable not only to hot rolling but also to any material temperature level.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory view of a steel bar rolling line consisting of a total of 18 stands in one row of an apparatus for carrying out the method of the present invention, and FIG. 3 is an actual cross section of a rhombus shape and a conversion cross section of the equivalent cross sectional area. FIGS. 3 (a) and 3 (b) are explanatory diagrams showing circles, and FIG. 3 (a) and FIG. Reference numeral 1 ... heating furnace 2 ... material billet 3 ... coiled steel bar (BIG) 4 ... pore ring 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 …… Roller exit side thermometer 12 …… Rolling thermometer 13 …… Rhombus cross-section actual shape 14 …… Converted circular shape

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification code Internal reference number FI Technical indication location B21B 37/74 (56) References JP 62-45419 (JP, A) JPB 51- 25432 (JP, B2) JP-B-59-41805 (JP, B2)

Claims (3)

[Claims] 1. When hot rolling a steel material such as a square bar or a round bar, the material temperature after cooling is predicted and calculated for each stand, and the rolling load at the stand is estimated based on the predicted temperature, When setting the interval between the upper and lower work rolls, the parameter expressing the shape of the material for each stand is obtained from the format m = material surface area × representative outer radius ÷ material volume, and this parameter m is the material temperature after cooling. Formula _{n + 1} = f ( _n , θ
_L , d, t, α, a, λ, m) to predict the material temperature online to provide a hot rolling method for steel products. However, _n : average material temperature before cooling, θ _L : refrigerant temperature, d: material outer diameter, t: cooling time, α: refrigerant heat transfer coefficient, a: temperature transfer coefficient,
λ: thermal conductivity 2. When hot rolling by the method according to claim 1,
A method for hot rolling a steel material, characterized in that the amount of roll reduction is adjusted in accordance with the predicted and calculated material temperature. 3. When hot rolling by the method according to claim 1,
A method for hot rolling a steel material, which comprises highly accurately estimating a heat transfer coefficient of a heat medium or a refrigerant on the basis of the predicted and calculated material temperature, and adjusting the amount of the heat medium or the refrigerant.