KR101105900B1 - Method of roll force prediction in hot plate rolling - Google Patents

Abstract

In the present invention, it is possible to calculate the load distribution and pass schedule by direct calculation of the reduction ratio without repeated calculation, and the calculation time is short, and the productivity is high, but the accuracy is high and the learning is reflected by reflecting the influence of the rolling shape and the high temperature deformation characteristics of the rolling material. It is an object of the present invention to provide a method for predicting the rolling load of thick plate rolling with low dependence on the correction factor, and to achieve this, it is proportional to the 0.5 power of the ratio of the side thickness and the rolling reduction, and at the same time, the simplified Q ( h ₀ ) step of obtaining the rolling shape influence factor, characterized in that it is proportional to, and the reference strength, temperature influence factor, speed influence factor derived from the high temperature flow stress data measured for each rolled material in the rolling shape influence factor obtained by the above method And rolling load prediction method for calculating the rolling load by multiplying the reduction ratio and the material width. Provide the law.

Description

Method of roll force prediction in hot plate rolling}

The present invention relates to a rolling load prediction method applied to a steel plate rolling process of steel materials, and in more detail, the rolling load prediction value is set by smoothly performing the distribution for each pass of the total rolling load and accurately setting a roll gap to obtain a desired rolling thickness. The present invention relates to a thick plate rolling load prediction method that is accurately calculated and supplied to a control system.

In general, in order to meet the target thickness during the manufacture of the thick plate to determine the amount of reduction for each pass, for this purpose is to predict the rolling load. The basic form of a general rolling load prediction equation based on the rolling theory in hot rolling including thick plate rolling is as shown in Equation 1 below.

Where F _c is the calculated rolling load and K _m is the plane strain deformation resistance (hereinafter referred to as strain resistance) that represents the average flow stress of the material in the roll gap in the plane deformation state, and the material temperature (T) and strain rate (ε). And the reduction ratio r. B is the width of the rolled sheet and L _d is the projection length of the contact arc between the roll and the material, more precisely the contact arc projection length considering the elastic deformation of the roll. Q _P is a rolling reduction function that compensates for the effect of the rolling shape, and mainly uses the Sims equation or several types of equations that simplify the Sims equation. In Equation 1, the deformation resistance, the contact arc projection length, and the reduction force function are all functions of the reduction ratio, the side thickness (h ₀ ), and the roll radius (R). As a result, the calculated rolling load is a higher-order polynomial or exponent for the reduction ratio. It takes the form of complex equations such as logarithmic functions.

Many techniques are known for obtaining the strain resistance Km and the reduction force function Qp. For example, Korean Patent KR 10-0711402 provides a method for obtaining strain resistance Km and a reduction force function Qp in the basic form of Equation 1, and KR 1998-049291 provides a reduction force function Qp, KR 2002-0050886 and KR 2000-. 80842, JP JP-A 10-109106 provides a method for obtaining Km.

However, the above known techniques based on the basic form of Equation 1 have a disadvantage in that load distribution calculation is not smooth and productivity is low due to the following reason.

The rolling load calculation formula is used not only for setting the roll gap for rolling to the target thickness but also for distributing loads between rolling passes. The load distribution means the pass by appropriately calculating the appropriate rolling reduction ratio for each pass in order to properly distribute the total rolling load for rolling the first rolled material to the desired final thickness according to the pre-determined rolling load allowable range for each pass. This is a calculation process to set up a schedule.

The calculation of the reduction ratio for the load distribution is performed by repeatedly calculating the reduction ratio of the above-mentioned Equation 1 while varying the reduction ratio until the specified rolling load range is reached, and the equation 1 above. It can be performed by a direct calculation method to directly obtain the solution of the reduction ratio for the specified rolling load in.

In the case of thick plate rolling, the width, thickness and length of the rolled material are much more diverse than the hot rolling of the strip. In the case of rough rolling, cross rolling must be performed and shape control must be performed. The variation of rolling operation variables such as non-uniformity is very large, and the calculation of load distribution before rolling takes a lot of calculation load. The above-described iterative calculation method has a problem in that the productivity of the facility is generally lowered because it takes a lot of time to calculate the load distribution online.

In order to maximize productivity in thick plate rolling equipment, direct load calculation method is adopted. To this end, Equation 1, which is a complex equation for rolling reduction ratio, should be greatly simplified. The simplest form of rolling load is a rolling load expressed as a linear form of rolling rate, for example:

Where Ko is a constant representing the reference strength, C _T is the coefficient of temperature influence of the deformation resistance, C _V is the rolling speed dependence coefficient, and C _H is the thickness dependence coefficient. L _rf is a compensation value for roll elastic deformation.

Each term of Equation 2 is derived from a rolling result and used as a regression model on the premise that the terms are independent without mutual interaction.

When using a simple rolling load prediction equation having a linear relationship to the rolling reduction as shown in Equation 2 above, since it is possible to directly distribute the rolling reduction from the rolling load in a short time without repeat calculations online, Productivity can be maintained.

However, when the basic form of Equation 2 is used, the factor (C _H ) related to the rolling shape is excessively simplified as a function of the side thickness only, and the accuracy of the rolling load prediction is greatly lowered. Also, as the factors related to the rolling shape are inaccurate, the regression analysis results of factors related to the deformation resistance of the material (Ko, C _T , C _V ) also give values far from the high temperature deformation characteristics of the actual material. Because it makes it impossible to predict the deformation resistance from the measured value of the characteristic, it is a big obstacle to rolling the new developed steel grade or improving the accuracy of rolling load prediction of special steel grades such as stainless steel, which does not accumulate much more learning coefficient than ordinary steel. Acts as.

Therefore, in order to maintain high productivity, how to increase the accuracy of the rolling shape factor and the material strain resistance factor while using a simple form of the load load equation as shown in Equation 2 is an important technical problem.

However, well-known techniques for predicting load by the basic type of Equation 2 are methods of deriving correction coefficients for each term from regression analysis from rolling performance data, such as Korean Patent KR 1999-0057388 or KR 2001-0063533 and KR. 2004-0049623 provides a method of correcting the prediction error from the rolling performance data, such as the method of learning-correcting the difference between the predicted value and the measured value, and does not lead to improving the accuracy of the shape influence factor and the deformation resistance factor of the model. .

An object of the present invention is to calculate the load distribution by direct calculation of rolling reduction, and to predict the rolling load based on the high temperature deformation characteristics of the rolled material, which has high productivity and high prediction accuracy and low dependence on the learning correction coefficient. It is intended to provide a rolling load prediction method of rolling.

In order to achieve the above object, the first aspect of the present invention is to identify a rolling shape influence factor proportional to Q (h ₀ ) corresponding to the 0.5 power of the ratio of the side thickness and the content rate and the theoretical Q _P corresponding to the function of the side thickness. The rolling load prediction equation calculated by calculating the rolling shape influence factor, the reference strength and the temperature influence factor, the speed influence factor, the reduction ratio, the material width, the roll radius, and the roll elastic deformation factor obtained in the first step and the first step. It is to provide a thick plate rolling load prediction method comprising a second step of calculating the rolling load by substitution.

According to the heavy plate rolling load prediction method according to the present invention, the load prediction method according to the present invention improves the error rate by improving the dimensions, shape, internal quality of the thick plate product and reduce the defects, and also for new developed steel or special steel grade Stabilization of rolling operations within a short period of time, and because it is not necessary to repeat calculation when setting the pass schedule by the load distribution calculation before rolling, it is possible to quickly calculate the productivity of the rolling equipment.

Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

1 is a flowchart showing a method for calculating a thick plate rolling load according to the present invention. Referring to Figure 1, the heavy plate rolling load calculation method is a first step (ST 100) for calculating the rolling shape factor, a second step (ST 110) for calculating the reference strength and the third step for calculating the temperature influence factor (ST 120) and a fourth step (ST 130) of calculating the speed ovality factor and a fifth step (ST 140) of calculating the heavy plate rolling load using the factors calculated in the above step.

First, in the first step ST 100, the rolling factor factor C _H is calculated by the following equation (3).

Here, C is a constant, Q (h _o ) is a simplified Qp as a function of the side thickness, and is obtained by regression analysis of the theoretical Qp value calculated from actual rolling performance data according to the side thickness.

In addition, the second step ST 110 may be obtained by using Equation 4 below.

는 기준온도와 기준변형속도에서의 최대유동응력 으로서 압연소재별로 고온압축시험이나 고온비틀림시험, 고온인장시험 등 고온유동응력 시험을 통해서 실험실적으로 측정할 수 있는 재료상수 값이다. Here, k is a constant and applies the reference value of the roll radius.

Is the maximum flow stress at the reference temperature and the strain rate, and is a material constant that can be measured experimentally through high temperature flow stress tests such as high temperature compression test, high temperature torsion test and high temperature tensile test for each rolled material.

In addition, the temperature influence factor in the third step ST 120 may be obtained by Equation 5 below.

는 기준변형속도에서 온도가 변화함에 따른 최대유동응력의 변화를 나타내는 함수로서 압연소재별 고온유동응력 시험을 통해서 실험적으로 결정할 수 있는 매개변수이다.Where F (X) is the ratio of average flow stress to maximum flow stress (hereinafter referred to as flow stress ratio), which is a coefficient that depends on the work hardening properties and the recrystallization degree of the rolled material.

Is a function representing the change of the maximum flow stress with temperature at the standard strain rate, and it is a parameter that can be determined experimentally through the high temperature flow stress test for each rolled material.

In addition, in the fourth step ST 130, the speed modeling factor C _V may be calculated by Equation 6 below.

는 기준온도에서 변형속도가 변화함에 따른 최대유동응력의 변화를 나타내는 함수로서 압연소재별 고온유동응력 시험을 통해서 실험적으로 결정할 수 있는 매개변수이다. here,

Is a function representing the change of the maximum flow stress as the strain rate changes at the reference temperature, and is a parameter that can be determined experimentally through the high temperature flow stress test for each rolled material.

Substituting Equation 2 using the respective factors obtained as described above, a fifth step (ST 140) of calculating a rolling load is performed.

Hereinafter, the configuration of the present invention in more detail.

Equation 1 accurately predicts the rolling load, but has a disadvantage in that the calculation process is complicated and iterative calculation is required when calculating the load distribution.However, the coefficient regressed from the rolling record data as in the conventional method while using Equation 2 is used. In this case, the rolling load calculation is quick and the load distribution calculation is easy, but the error is generated because it is not based on the rolling theory and the high temperature characteristics of the material. Therefore, the present invention proposes a method that can reflect the high-temperature characteristics of the rolling theory and the material while using the basic form of Equation 2 above to secure the productivity.

It can be reconfigured as in Equation 7 of Equation 1 based on the rolling theory.

는 롤갭 내에서 소재의 평균유동응력이고, R₀는 롤반경의 기준값, △h는 압하량이다. here

Is the average flow stress of the material within the roll gap, R ₀ is the reference value of the roll radius, and Δh is the rolling reduction.

Here, if the factors related to the rolling shape are extracted, C _H in Equation 2 may be defined as Equation 8 below.

The rolling force function Q _p in the above Equation 8 is strictly a function of the side thickness, the roll radius, the rolling reduction rate, and the analysis results of the present inventors on the actual plate rolling operation data. , effects of fluctuations in the reduction rate even it is possible to simplify in function only inlet thickness by regression analysis of small rolling performance data to the end C _H is organized in the form of equation (3).

When the rolling shape factor of Equation 3 is substituted into the rolling load prediction equation of Equation 2, the rolling shape variation according to the reduction in rolling ratio may be additionally reflected compared to the conventional method of obtaining C _H as a function of the side thickness only. Therefore, the prediction error of the rolling load can be greatly reduced.

In addition, in the method of substituting the rolling shape factor of Equation 3 into the rolling load prediction equation of Equation 2, it is possible to directly calculate the reduction ratio in the form of the following Equation 9 without repeated calculations in the load distribution calculation so that the fast load is achieved. The high productivity of the installation can be maintained by the distribution calculation.

The average flow stress of the material in Equation 7 based on the rolling theory is strictly a function of temperature, strain rate, rolling reduction, recrystallization degree, or load distribution calculation of the direct calculation method according to Equation 9 above. It is necessary to change the function form irrespective of the reduction ratio, which is possible by using Equation 10 below.

는 롤갭 입측에서의 변형율,

는 롤갭 출측에서의 변형율,

는 변형율속도이다. here

Is the strain at the roll gap entry,

Is the strain at the roll gap exit,

Is the strain rate.

Hereinafter, the concept of Equation 10 will be described with reference to the drawings.

Figures 2a to 2c shows the stress-strain relationship appearing when deformation of the steel at high temperature. Referring to FIGS. 2A to 2C, generally, during high temperature deformation of steel, as the strain increases, the flow stress increases as the strain increases, but when the strain increases more than a certain degree, the flow stress does not increase any more. Flow stress (or saturated flow stress) is reached. This maximum flow stress depends on temperature and strain rate based on the high temperature deformation theory, and various types of equations have been proposed for the specific relationship.

인 롤갭 출측까지의 영역에서의 유동응력의 평균치로 정의되는데, 실제 후판압연실적의 분석을 통하여 살펴보면 이 평균유동응력과 최대유동응력의 비가 압하율보다는 압연소재의 특성과 재결정정도에 더욱 크게 의존한다. 이를 토대로 평균유동응력을 상기 수학식 10에서와 같이 압연소재와 재결정정도에 의존하는 매개변수(F(X))와 최대유동응력의 곱으로 파악한다. In rolling, the average flow stress was changed from the roll gap inlet where the strain was zero.

It is defined as the average value of the flow stress in the area up to the exit of the in-roll gap, and from the analysis of the actual plate rolling performance, the ratio of the average flow stress and the maximum flow stress depends more on the properties of the rolled material and the degree of recrystallization than on the reduction ratio. . Based on this, the average flow stress is determined as the product of the maximum flow stress and the parameter (F (X)) depending on the rolled material and the degree of recrystallization as in Equation 10 above.

만큼의 누적잔류변형이 있기 때문에 평균유동응력과 최대유동응력의 비는 도 2a에서의 완전재결정 조건에 비해 커지게 되고 그 정도는 온도에 의존하게 된다. For example, in the case of austenitic stainless steels with high work hardening in the rolling section in steel (complete recrystallization), as shown in FIG. 2A, the average flow stress is about 70% of the maximum flow stress under normal thick rolling conditions. In the case of two-phase stainless steel that maintains a constant flow stress level after reaching the maximum flow stress at, the average flow stress is almost equal to the maximum flow stress as shown in FIG. 2B. In addition, as shown in FIG. 2C, when the temperature at the end of the finish rolling decreases considerably in the austenitic stainless steel (unrecrystallized), the recrystallization softening does not occur sufficiently during the holding time between the rolling passes.

Because of the cumulative residual strain, the ratio of average flow stress to maximum flow stress becomes larger than that of the complete recrystallization condition in FIG. 2A, and the degree depends on the temperature.

By applying the above results, the average flow stress can be expressed as the product of the flow stress ratio and the maximum flow stress, thereby eliminating the dependence on the reduction ratio, which results in a simple load distribution by Equation (9).

The flow stress ratio can be determined as a constant value for each steel type by measuring the high-temperature flow stress curve for each rolled material.In the low temperature region where recrystallization is not complete, unrecrystallization according to temperature through two or more multistage high temperature compression tests or multistage high temperature torsion tests It can also be expressed as a function of temperature for steel grades through formulating the degree.

The maximum flow stress can be divided into a maximum flow stress at a reference temperature and a reference strain rate, a temperature influence factor and a speed influence factor on the maximum flow stress as shown in Equation 10. Therefore, when the maximum flow stress is measured for each steel type under various temperature and strain rate conditions, the temperature influence factor may be configured by using the relationship of Equation 5 and the speed influence factor of Equation 6, respectively. However, in the construction of the submodel using Equation 6, the strain rate is strictly a function of the reduction rate, the rolling speed, and the roll radius, but an approximate regression model between the strain rate and the rolling speed within the general sheet rolling operation range is given. The construction method can eliminate the dependence on the reduction ratio.

The maximum flow stress, flow stress ratio, temperature influence factor, and velocity influence factor at the reference conditions obtained by the above method show the deformation resistance based on the properties of the rolled material, and the rolling shape factors based on the above-described rolling theory By substituting for, it is possible to construct a rolling load prediction equation with a high load accuracy but simple load distribution calculation.

In addition, Denton and Crane's Qp equation (Journal of Iron and Steel Institute, 1972, August, shown in Equation 11 below) is obtained from the actual plate rolling performance data of 9,500 stainless steels in order to obtain the rolling shape factor C _H shown in Equation 3. Theoretical Qp calculated by p.606) was regressed according to the side thickness.

Where h _av is the average of the entry and exit thicknesses.

FIG. 3 shows that as a result of the above regression analysis, the theory Qp can be converted into a simple logarithmic regression model having a high suitability of the coefficient of determination (R ² ) 0.95 for the entrance thickness.

Applying this regression analysis result, C _H is represented by Equation 12 below.

In order to find K ₀ , C _T , and C _V , the high-temperature flow stress was measured for each rolled material by the high temperature compression test method. Figure 4a shows a low temperature flow capacity measurement example for 304 and stainless steel, Figure 4b shows a high temperature flow stress measurement example for 316 stainless steel.

After the maximum flow stress was determined from the measured high-temperature flow stress curve, the maximum flow stress value for each steel type was derived under the condition that the reference condition was set at 1000 ° C and the strain rate was 10 sec ^-1 , and the reference strength (Ko) ) Was calculated. At this time, the reference value of the roll radius was applied to 500mm.

Obtain the ratio of the maximum flow stress value at any temperature to the maximum flow stress value in the reference condition measured by Equation 5, and regression analysis according to the temperature to obtain a submodel of the temperature influence coefficient Configured.

The constant m for each steel type was derived by regression analysis.

The ratio of the maximum flow stress value at an arbitrary strain rate to the maximum flow stress value under the reference condition measured by Equation 6 is obtained, and the regression analysis is performed according to the strain rate. The model was constructed.

Here, using the regression model for the correlation between the strain rate and the rolling speed shown in Figure 5 from the rolling record data was used to convert the speed effect factor (C _V ) as a function of the rolling speed only.

The heavy plate rolling load predicted value obtained by substituting C _H , K ₀ , C _T , and C _V obtained through the above process into Equation 2 is shown in FIG. 6A and the thick plate rolling load actual value is shown in FIG. 6B. As can be seen in Figure 6a and 6b the rolling load predicted by the present invention can be seen that the accuracy is very improved compared to the existing method.

7A and 7B, the predicted value and the measured value for the measured thickness are shown, respectively, and the predicted value and the measured value for the temperature are shown in FIGS. 8B and 8B, respectively. 9A and 9B show the predicted value and the measured value for the rolling speed, respectively.

As shown in FIGS. 7A, 7B, 8B, 8B, 9A, and 9B, in the present invention, structural errors due to changes in rolling conditions such as thickness, temperature, and speed do not appear, and thus the predictability of the rolling load is increased. It can be seen.

In the rolling load prediction equation according to the present invention, the rolling load factor is inversely proportional to the 0.5 power of the rolling reduction factor, the rolling reduction factor, and the reference strength and temperature influence factor independent of the rolling reduction factor. In conclusion, the rolling load is proportional to the 0.5 power of the rolling reduction because it is calculated as the product of the speed factor and the material width. It is not necessary to repeat the calculation because the rolling reduction is directly calculated in a form proportional to the square of the rolling load when calculating the load distribution before rolling.

While preferred embodiments of the present invention have been described using specific terms, such description is for illustrative purposes only and it is understood that various changes and modifications may be made without departing from the spirit and scope of the following claims. Should be done.

1 is a flowchart showing a method for calculating a thick plate rolling load according to the present invention.

Figures 2a to 2c shows the stress-strain relationship appearing when deformation of the steel at high temperature.

3 is a graph showing the correlation between the theoretical reduction force function Qp and the side material thickness.

4A and 4B are stress-strain graphs showing high temperature flow stresses measured in stainless 304 and 316 steels.

5 is a graph showing the correlation between the strain rate and the rolling speed.

6A and 6B are graphs comparing the correlation between the predicted load and the actual load predicted by the conventional technique and the present invention.

7A and 7B are graphs showing the ratios of actual loads to predicted loads predicted by the conventional technique and the present invention with respect to the entrance thickness.

8A and 8B are graphs showing the ratio of actual loads to predicted loads predicted by the conventional technique and the present invention with respect to temperature.

9A and 9B are graphs showing the ratio of the actual load to the predicted load predicted by the conventional technique and the present invention with respect to the rolling speed.

Claims (9)

0.5 power of the ratio of lateral thickness to ration and the theory Q _P A first step of determining a rolling shape influence factor proportional to Q (h ₀ ) corresponding to a function of the side thickness; And Rolling loads were substituted into the rolling load prediction equations calculated from the rolling shape influence factor, the reference strength and temperature influence factor, the velocity influence factor, the reduction ratio, the material width, the roll radius, and the roll elastic deformation factor identified in the first step. Thick plate rolling load prediction method comprising the step of calculating the second. The method of claim 1, The rolling shape influence factor is

Plate rolling load prediction method corresponding to the. Where C is a constant and Q (h _o ) is a simplified Qp as a function of the side thickness. The method of claim 1, The load prediction formula is

Plate rolling load prediction method corresponding to the. (Where Ko is a constant indicating a reference intensity, C _T is the temperature influence coefficient, C _V in deformation resistance is a linear expression for the rolling velocity dependent coefficient, C _H is inlet thickness as the thickness dependence coefficient is used. L _rf rolls Compensation for elastic deformation.) The method of claim 1, And the reference strength is proportional to the maximum flow stress ratio at the reference temperature and the reference strain rate derived from the high temperature flow stress data measured for each rolled material. The method of claim 1, The temperature influencer

Plate rolling load prediction method corresponding to the. Where F (X) is the ratio of average flow stress to maximum flow stress,

Is a function representing the change of maximum flow stress with temperature at the standard strain rate.) The method of claim 1, The speed influencer

Plate rolling load prediction method corresponding to the. (

Is a function representing the change of maximum flow stress as the strain rate changes at the reference temperature.) The method of claim 4, wherein The maximum flow stress ratio is grasped as a function of temperature in all or part of the temperature range, and the thick plate rolling load prediction method for compensating for the increase in load due to the re-determination at the end of finishing rolling. The method according to any one of claims 1 to 7, The heavy plate rolling load prediction method for grasping the reduction ratio in the form of a function proportional to the square of the rolling load. The method of claim 8, The heavy plate rolling load prediction method for grasping the reduction ratio in the form of a function proportional to the square of the rolling load.

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