JP4460493B2 - Calculation method of thermal crown of work roll in rolling mill - Google Patents

Description

  A method for calculating the heat transfer coefficient in the roll bite used for the prediction model with high accuracy, regarding the calculation method for calculating the thermal crown prediction used for calculating the plate crown and plate shape in hot rolling with high accuracy. About.

  In order to realize highly accurate sheet crown shape control in hot rolling, it is important to increase the accuracy of work roll thermal crown prediction that directly affects the thickness direction thickness distribution of the rolled material. Until now, as for thermal crown prediction, as shown in Patent Document 1 and Patent Document 2, for example, models have been proposed that perform prediction with high accuracy in practical calculation time in hot rolling.

  The heat transfer coefficient related to heat input to and extraction from the work roll, which is indispensable when calculating the thermal crown with the above prediction model, is set in advance so that the amount can be expressed from changes in the thermal crown amount and work roll temperature. It is given as a value. It is known that the heat input to the work roll varies depending on the rolling conditions (sheet thickness schedule, rolling speed, etc.) and the work roll temperature, and if the heat transfer coefficient related to this is treated as a set value, it is necessary to predict the thermal crown. An error is generated.

  On the other hand, as shown in Patent Document 3, for example, a prediction method is proposed in which a heat transfer coefficient in a roll bit is given as a function of a contact arc length and reflected in a thermal crown prediction model.

  According to Patent Document 3, the heat transfer coefficient in the roll bite is calculated from the relationship between the surface temperature in the circumferential direction of the rolled work roll and the work roll temperature, which is statistically processed under the rolling conditions, and the heat in the roll bite. Modeling of transfer coefficient.

  In the roll bite, the work roll and the rolled material are in intimate contact, and when evaluating the heat input to the work roll, that is, in order to accurately calculate the heat transfer coefficient in the roll bite, rolling is performed. It is necessary to calculate the heat transfer coefficient in the roll bite after accurately calculating the amount of heat transfer from the material to the work roll.

  However, in the case of Patent Document 3, it is difficult to say that the heat transfer amount from the rolled material to the work roll is accurately evaluated by paying attention only to the temperature of the work roll surface alone. There was a problem.

On the other hand, since the contact time between the work roll and the rolled material in the roll bite is extremely short, the heat transfer amount change (temperature change) in the work roll and the rolled material is, for example, Non-Patent Document 1 (Steel and Steel). As shown in Chapter 6 of the Association's “Theory and Practice of Sheet Rolling”, it is sufficient to ignore or calculate the heat conduction in the circumferential direction for work rolls and in the longitudinal direction for rolled materials. It is known that it is accurate, and from this, it is described that the unsteady one-dimensional heat conduction calculation is sufficient for the heat transfer amount calculation (temperature calculation) in the work roll radial direction and the rolled sheet thickness direction. Has been.
Japanese Unexamined Patent Publication No. 07-80517 JP 07-32041 A Japanese Patent Laid-Open No. 2002-346620 "Theory and practice of plate rolling", published by Japan Iron and Steel Institute, 1984

  An object of the present invention is to solve the above-described problems of the prior art and to provide a calculation method for calculating a thermal crown prediction used for calculating a plate crown and a plate shape with high accuracy.

In order to achieve the above object, the gist of the present invention is as follows.

(1) In the method for calculating the thermal crown of a work roll in a rolling mill,
The heat transfer coefficient of the contact part (in the roll bite) between the work roll and the rolled material used in the prediction model is assumed to be in a contact state between the work roll and the rolled material, and from the rolled material in the roll bite to the work roll. Calculate the amount of heat transfer (temperature distribution in the roll radial direction), and then the amount of change in heat transfer in the work roll radial direction (change in temperature distribution in the roll) on the entry side and exit side of the roll tool based on the calculated heat transfer amount. It is a method for calculating a thermal crown of a work roll in a rolling mill.

  (2) The amount of heat transferred from the rolled material to the work roll in the roll bite (roll radial direction temperature distribution), the frictional heat generation at the boundary between the work roll and the rolled material, the rolling material scale layer, the rolling material processing heat generation, And calculating the thermal crown of the work roll in the rolling mill according to the above (1), which is calculated in consideration of the thermal property value of the work roll and the rolled material, and the time during which the work roll and the rolled material are in contact.

  As described above, in the case of the present invention, the heat transfer coefficient in the roll bite during rolling can be calculated with high accuracy in a practical calculation time, and a highly accurate thermal crown can be predicted. The plate crown and shape of the rolled material inside can be stably produced.

  The present invention provides a method for accurately calculating a heat transfer coefficient related to heat input to a work roll in order to improve the accuracy of thermal crown prediction.

  Therefore, regarding the thermal crown prediction model, for example, as shown in Patent Document 1, the temperature distribution in the roll of a work roll composed of two layers having different physical property values, that is, a core material and an outer layer material, during the rolling operation. When calculating, as a mathematical expression of the temperature distribution in the roll radial direction, the temperature gradient in the roll radial direction inevitably generated from the continuity of the heat flux due to the difference in thermal conductivity between the core material and the outer layer material at the boundary. A model that performs thermal crown calculation using a polynomial that can express discontinuities may be used, and the heat transfer coefficient of the contact portion (in the roll bite) between the work roll and the rolled material used at that time is set in the present invention. It may be replaced with a calculated value based on the above.

  In addition, the heat transfer coefficient of the contact portion (within the roll bite) between the work roll and the rolled material calculated in the present invention is not limited to the thermal crown prediction model shown above, and other prediction models This calculation method can also be applied.

  As described in the above [Background Art], when the heat input to the work roll is evaluated in the roll bite, it is necessary to accurately calculate the amount of heat transfer from the rolled material to the work roll.

  Further, since the contact time between the work roll and the rolled material in the roll bite is extremely short, the change in the amount of heat transfer (temperature change) in the work roll and the rolled material is, for example, the first in Non-Patent Document 1. As shown in Chapter 6, it is known that the work roll is sufficiently accurate even if it ignores the heat conduction in the circumferential direction and the rolled material even if it ignores the heat conduction in the longitudinal direction. Further, it is described that unsteady one-dimensional heat conduction calculation is sufficient for calculating the amount of heat transfer (temperature calculation) in the work roll radial direction and the rolled sheet thickness direction.

  The amount of heat transfer to the work roll according to the present invention is calculated by adopting unsteady one-dimensional heat conduction calculation between the work roll and the rolled material. At this time, since the work roll and the rolled material are in contact with each other at a high pressure in the present invention, the heat transfer amount calculation is performed assuming that the work roll and the rolled material are completely in contact with each other.

  The calculation procedure performed in the present invention is shown below. FIG. 2 shows a schematic diagram showing a contact state between a work roll and a rolled material in a roll bite during rolling, and a diagram for explaining a calculation method of the present invention. At this time, when the unsteady one-dimensional heat conduction calculation is performed, the line 1 indicated by reference numeral 1 on the roll bite entry side shown in FIG. The calculation to be a line may be performed.

  At this time, the contact time Δt between the work roll and the rolled material shown in FIG. 2B can be calculated from the rolling conditions, and is expressed by the following equation, for example.

Here, R '(m) is the roll flat radius of the hitchcock, V _R (m / sec) is the peripheral speed of the work roll, R (m) is the work roll radius, H and h (m) are the input / output side plate thickness, p (kgf / m) is the rolling line load, E (kgf / m ² ), and ν is the Young's modulus and Poisson's ratio of the work roll.

  The unsteady one-dimensional heat conduction equation based on FIG. 2 (b) is shown in Equation (1), and the boundary condition is shown in Equation (2).

Where ρ (y) (kg / m ³ ) is density, c (y) (J / (kg · ° C)) is specific heat, λ (y) (W / (m · ° C)) is thermal conductivity, T (° C) is temperature, t (sec) is time, q _f (W / m ² ) is per unit time, frictional heat generation per unit area, q _p (W / m ³ ) is per unit time, per unit volume Y is the work roll radius and the thickness direction of the rolled material, where y ≧ 0 means the work roll, and y <0 means the rolled material.

Here, R is the work roll radius, H (t) is the plate thickness that changes with rolling time, and λ _R and λ _S are the roll side thermal conductivity at the interface (y = 0) between the work roll and the rolled material. Further, the rolled material side thermal conductivity, T _R , T _S are temperatures at the above-mentioned boundary surfaces.

In equations (1) and (2), ρ (y) c (y) and λ (y) are
Thermal property value of work roll when y ≧ 0,
What is necessary is just to use the thermophysical value of a rolling material by y <0.

Further, when there is a scale layer at the boundary between the work roll and the rolled material, the thermophysical value may be calculated at the position of y = 0 to −h _s (h _s is the scale thickness).

Furthermore, q _f and q _p in equation (2) can be calculated by the method described in Chapter 6 of Non-Patent Document 1, for example, and can be expressed by the following equation, for example.

q _f = k _f · In (H / h) / Δt (5)
q _p = μ · k _f · V _r (6)
Here, k _f is a two-dimensional deformation resistance, μ is a friction coefficient, and V _r is an average value of absolute values of relative speeds of the work roll and the rolled material.

  Moreover, the rolling material side of the roll bite inlet side temperature of 1 line | wire shown with the code | symbol 1 in FIG. 2 (a) is the rolling material plate | board thickness direction from the existing model described in Chapter 6 of a nonpatent literature 1, for example. The calculated value of the temperature distribution, the work roll side, for example, the temperature distribution in the work roll radial direction at the end of idling calculated in Patent Document 1 (the calculated value of Patent Document 1 immediately before the work roll and the rolled material come into contact). Use it. If the above heat conduction equation, boundary conditions, initial temperature conditions on the roll bite entry side, and the like are used, the temperature distribution in the work roll radial direction and the rolled material sheet thickness direction on the roll bite exit side can be calculated. Here, although finite element analysis is used for temperature calculation in the present invention, a method capable of performing heat conduction such as a difference method may be used. FIG. 2 (c) shows the calculation results of the work roll radius and the roll thickness direction temperature distribution on the roll bite entry and exit sides.

  At this time, in order to simplify the explanation, the time division in FIG. 2B is set to 4, but in order to maintain the calculation accuracy, at least 20 divisions are preferable.

Next, from the calculation result of the heat transfer amount (temperature distribution) to the work roll, the heat transfer coefficient α _R (W / (m ² · ° C.)) of the contact portion (within the roll bite) between the work roll and the rolled material is If the change amount of the heat transfer in the work roll radial direction (change amount of the temperature distribution in the roll) on the entry side and the exit side of the roll bite shown in FIG. 2C is used, it can be calculated by the following equation. At this time, since the work roll radial direction temperature distribution is performed by finite element analysis in the present invention, it is calculated in the form of n divisions in the roll radial direction. The heat transfer coefficient may be calculated using the calculation result.

Here, T _R ^e (y) and T _R ^d (y) are radial temperature distributions on the work roll inlet and outlet sides, ρ _R and c _R are the work roll density and specific heat, T _S ^e and T _R ^e is the surface temperature of the rolled material and the work roll at the entrance side of the roll bite, Δy _i is the element length of the I-th division, and Δt is the contact time between the work roll and the rolled material shown in Equation (1). Further, the amount of change in the heat transfer in the work roll radial direction on the entry side and the exit side of the roll bite may correspond to the term (T _R ^d (y) _i -T _R ^e (y) _i ) in Equation (7). Recognize.

  If the heat transfer coefficient in the roll bite is calculated using the present invention, the rapid heat transfer amount in the roll bite as shown in FIG. 2 (c) can be accurately expressed. It can be seen that the heat transfer coefficient in the roll bite inevitably generated from the rolling reduction, rolling material temperature, material (deformation resistance, etc.) can be expressed accurately.

  Specific embodiments of the present invention will be described in detail in (Examples).

  FIG. 3 shows a calculation flow of the thermal crown calculation to which the present invention is applied. Specifically, as shown in FIG. 3, as described in the best mode for carrying out the invention, the calculation result of the heat transfer amount to the work roll by the unsteady one-dimensional heat conduction calculation in the roll bite. From this, the heat transfer coefficient in the roll bite is calculated. Next, in the present invention, for example, thermal crown calculation is performed by replacing the heat transfer coefficient in the roll bite, which is the boundary condition of the thermal crown prediction model shown in Patent Document 1, with the heat transfer coefficient calculated from the present invention. become.

  FIG. 1 (a) shows the transition of the heat transfer coefficient in the roll bite when the present invention is applied to an F4 stand (F4-stand) of a hot finish rolling mill. Fig. 1 (b) shows the result of comparison between the actual value (calculated from the F4 outlet thickness gauge) and the predicted result of applying the present invention for the transition of the thermal expansion amount at the work roll center position, and after the end of rolling. The comparison result of the actual value of the thermal crown amount in the work roll body length direction after 4 minutes and the thermal crown prediction to which the present invention is applied is shown. From the difference in rolling conditions (FIG. 1 (c)), as shown in FIG. 1 (a), it can be seen that the heat transfer coefficient in the roll bite calculated in the present invention is greatly different. If the present invention is applied, the difference in the heat transfer coefficient in the roll bite caused by the different rolling conditions as described above can be reflected in the thermal crown prediction model, as shown in FIG. 1 (b). It can be seen that the thermal expansion amount of the work roll center can be expressed with high accuracy from the beginning to the end of rolling, and can be predicted with high accuracy even as a result of comparison as a work roll body length profile. That is, the present invention can accurately represent the heat transfer coefficient in the roll bite that inevitably arises from differences in rolling conditions (plate thickness, rolling reduction, rolled material temperature, material (deformation resistance), etc.). Recognize.

  Although the results of applying the embodiment of the present invention to a hot finish rolling mill have been shown, it goes without saying that the present invention is also applicable to thick plate rolling and cold rolling.

The figure which shows the thermal crown prediction (calculation) result at the time of applying this invention The figure used to explain the calculation procedure of the present invention The figure which shows the calculation flow of embodiment of this invention

Claims (2)

In the method for calculating the thermal crown of a work roll in a rolling mill,
The heat transfer coefficient of the contact part (in the roll bite) between the work roll and the rolled material used in the prediction model is assumed to be in a contact state between the work roll and the rolled material, and from the rolled material in the roll bite to the work roll. Calculate the amount of heat transfer (temperature distribution in the roll radial direction), and then the amount of change in heat transfer in the work roll radial direction (change in temperature distribution in the roll) on the entry side and exit side of the roll tool based on the calculated heat transfer amount. A method for calculating the thermal crown of a work roll in a rolling mill. The amount of heat transferred from the rolled material to the work roll in the roll tool (temperature distribution in the radial direction of the roll), the frictional heat generation at the boundary between the work roll and the rolled material, the rolled material scale layer, the rolled material processing heat generation, and the work roll 2. The method for calculating a thermal crown of a work roll in a rolling mill according to claim 1, wherein the calculation is performed in consideration of a thermal property value of the rolled material and a time during which the work roll is in contact with the rolled material.

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