Method for calculating rolling force when negative forward slip occurs in reversible cold rolling process
By correcting the E-Fink front slip formula and calculating the neutral angle value, the problem of rolling force calculation failure caused by negative front slip during reversible cold rolling is solved, and a more accurate rolling force calculation is achieved.
Patent Information
- Application Number
- CN202510410540.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-02
- Publication Date
- 2025-05-30
AI Technical Summary
In the reversible cold rolling process, the prior art cannot effectively calculate the rolling force when negative forward slip occurs.
By correcting the E-Fink front slip formula, the corrected neutral angle value is calculated using the relationship between the movement speed of the rolling piece on the neutral surface and the circumferential speed of the rolling roll, and the friction coefficient and rolling force are recalculated.
It realizes the accurate calculation of neutral angle and friction coefficient under negative front slip, improves the accuracy of rolling force calculation, and solves the problem of rolling force calculation failure caused by negative front slip.
Smart Images
Figure CN120067495A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of metal rolling process optimization methods, and particularly relates to a method for calculating rolling force when negative forward slip occurs during reversible cold rolling. Background Art
[0002] The iron and steel industry is the material basis for the development of the national economy and national defense construction, and is also a symbol to measure a country's industrialization. With the rapid development of the global manufacturing industry, the demand for high-standard and high-quality steel is increasing continuously. Therefore, studying the establishment of mathematical models in the strip cold rolling process has very important practical significance for parameter setting and prediction in the rolling process. In theoretical research, the rolling force can be predicted through forward slip formulas, rolling force calculation formulas, etc. This method is usually used normally when the forward slip value is greater than zero.
[0003] However, in the actual production process of a reversible cold rolling mill, due to process lubrication, roll roughness or other reasons, negative forward slip often occurs, but the rolling process still proceeds normally. In the friction coefficient model obtained by back-calculating using the Stone rolling force formula, the off-line calculation formula of the friction coefficient is derived based on the theory that the forward slip is greater than zero. Therefore, once the production data shows a negative forward slip, this calculation model will fail. Summary of the Invention
[0004] The purpose of the present invention is to provide a method for calculating rolling force when negative forward slip occurs during reversible cold rolling, which can accurately calculate the rolling force when negative forward slip occurs during reversible cold rolling.
[0005] The technical solution adopted by the present invention is that the method for calculating rolling force when negative forward slip occurs during reversible cold rolling is specifically implemented according to the following steps: Step 1: Determine the forward slip calculation formula according to the definition of forward slip; Step 2: Use the relationship between the moving speed of the rolled piece at the neutral plane and the circumferential speed of the roll, the relationship between the thickness of the rolled piece at the exit and the thickness at the neutral plane, and the principle of constant volume of the second flow rate to obtain the relationship between the exit speed of the rolled piece and the circumferential speed of the roll; Step 3: According to the forward slip calculation formula obtained in Step 1 and the relationship obtained in Step 2, obtain the relationship between forward slip and neutral angle, that is, the modified E-Fink forward slip formula, and simplify it to the D-Dresden forward slip formula; Step 4: Calculate the modified new neutral angle value according to the E-Fink forward slip formula obtained in Step 3; Step 5: Calculate the modified friction coefficient and rolling force according to the new neutral angle value obtained in Step 4.
[0006] The characteristics of the present invention also lie in: In Step 1, the forward slip calculation formula is:
[0007] where is the forward slip value, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll.
[0008] The relationship between the speed of the rolled piece at the exit and the circumferential speed of the roll obtained in Step 2 is:
[0009] where is the neutral angle, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll, is the roll diameter, is the thickness of the rolled piece at the exit.
[0010] Step 3 is specifically: Substitute the relational expression obtained in Step 2 into the forward slip calculation formula obtained in Step 1 to obtain the modified E-Fink forward slip formula:
[0011] where is the forward slip value, is the neutral angle, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll, is the roll diameter, is the thickness of the rolled piece at the exit.
[0012] The modified E-Fink forward slip formula is simplified to: .
[0013] Step 4 is specifically: According to the modified E-Fink forward slip formula, reverse-derive the calculation formula for the neutral angle, transpose the terms, and organize the terms containing the neutral angle to obtain:
[0014] where is the roll diameter, is the neutral angle, is the forward slip value, is the thickness of the rolled piece at the exit; Substitute Regarding the items as a whole, the above equation is a quadratic equation of one variable. Solving this quadratic equation of one variable can obtain two solutions. Select the solution with a negative angular value as the new neutral angle corresponding to the negative forward slip phenomenon. 。
[0015] Step 5 is specifically as follows: Substitute the new neutral angle value calculated in Step 4 into the D-Dresden forward slip formula to re-correct the original negative forward slip value, and then use the friction coefficient model deduced by the Stone rolling force formula to calculate the magnitude of the friction coefficient μ, and further calculate the rolling force.
[0016] The calculation formula for the friction coefficient μ is:
[0017] Among them, the reduction is the difference between the entrance thickness of the rolled piece after rolling and the exit thickness of the rolled piece; is the flattened radius; the reduction rate is the percentage of the reduction to the entrance thickness.
[0018] The beneficial effects of the present invention are: The method of the present invention utilizes the mechanical principles in the rolling process, based on the deformation behavior of the metal between the rolls, the dynamic changes of the friction conditions, and the kinematic relationship between the rolls and the rolled piece. By deriving the neutral angle in the deformation zone during the rolling process from the known forward slip data, recalculating the forward slip value, and then using the Stone formula to inversely calculate the friction coefficient, and further calculating the rolling force, it solves the problem that the negative forward slip cannot be theoretically calculated, enables the calculation of the value of the neutral angle and the reliable value of the friction coefficient 𝜇 even when the forward slip is negative, thereby effectively correcting the negative forward slip problem and ensuring the accuracy of the rolling force calculation. Description of the Drawings
[0019] Figure 1 is a schematic diagram of the rolling mill and the rolling deformation zone during the rolling process; Figure 2 is a schematic diagram of the rolling area; Figure 3 is a flow chart of the method of the present invention; Figure 4 is a comparison chart of the forward slip values before and after correction in Embodiment 1 of the present invention. Specific Embodiments
[0020] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.
[0021] According to the definition of forward slip, the phenomenon that the speed of the rolled piece at the exit is greater than the linear speed of the roll is the forward slip phenomenon. The forward slip value obtained theoretically is not negative, that is, the forward slip value must be greater than 0. However, in actual production, the situation of negative forward slip is very common, that is, the exit speed of the rolled piece is less than the circumferential speed of the roll, and the rolling mill can still roll stably.
[0022] However, when problems occur in production, such as the slipping phenomenon of the strip, negative forward slip is often the potential cause. Some scholars believe that when the slipping phenomenon of the rolling mill occurs, it must be caused by negative forward slip, while the occurrence of negative forward slip does not necessarily lead to the slipping phenomenon. From the perspective of rolling principle, the reason for the generation of negative forward slip may be that the rear tension of the strip is too large, resulting in the exit speed of the rolled piece at the roll being less than the circumferential speed of the roll.
[0023] By analyzing the theory of the rolling process, it can be known that the friction coefficient and the forward slip , the rolling force are mutually functional relationships. When the rolling force is known, through the reverse derivation of the known forward slip formula, rolling force calculation formula, etc., the exact solution of the friction coefficient 𝜇 can be solved, and the exact value of the friction coefficient obtained by off-line calculation can be used as a sample of the coefficient of the rolling force prediction model.
[0024] Usually, the friction coefficient model is inversely derived using the Stone rolling force formula. Only by knowing the forward slip value f , the actual rolling force F and the inlet and outlet thicknesses of the rolled piece , the magnitude of the friction coefficient μ can be calculated:
[0025] Among them, the reduction is the difference between the inlet thickness of the rolled piece after rolling and the outlet thickness of the rolled piece; the reduction ratio represents the degree of deformation of the rolled piece.
[0026] From this model, it can be seen that the derivation of the off-line calculation formula of the friction coefficient is based on the theory that the forward slip is greater than zero, which leads to the failure of this calculation model once the production data shows a negative forward slip. The existing technology's treatment method for this problem is: if the situation of negative forward slip only accounts for a small number, the value of negative forward slip is approximately taken as zero and substituted into the calculation, but this is not advisable.
[0027] Because the neutral angle and the forward slip value are mutually functional relationships in the simple rolling process, the definition and concept of the neutral angle are often used when calculating the friction coefficient using the forward slip value. For example Figure 1As shown in the figure, due to the existence of forward slip and backward slip phenomena (the roll linear speed is not equal to the workpiece speed) during the cold rolling process, the rolling area is divided into three categories: the forward slip area, the backward slip area, and the plastic deformation area. Both the forward slip area and the backward slip area are elastic deformation areas. There must be a point in the plastic deformation area where the horizontal linear speed of the work roll is equal to the moving speed of the workpiece, which is called the neutral point. The plane composed of the neutral points is called the neutral plane, as Figure 2 shown. The neutral angle refers to the angle between the neutral plane and the perpendicular line of the roll center line, and is often used to derive the forward slip value.
[0028] The calculation method of the rolling force when negative forward slip occurs during the reversible cold rolling process of the present invention, as Figure 3 shown, is specifically implemented according to the following steps: Step 1: Determine the forward slip calculation formula according to the definition of forward slip; The definition of forward slip is: at the rolling exit, the percentage of the speed difference between the workpiece and the roll linear speed, that is, the forward slip definition formula is:
[0029] Among them, is the forward slip value, is the speed of the workpiece at the roll exit, is the circumferential speed of the roll.
[0030] Step 2: Utilize the relationship between the moving speed of the workpiece at the neutral plane and the circumferential speed of the roll, and the relationship between the thickness of the workpiece at the exit and the thickness at the neutral plane . In addition, according to the principle of constant volume of the second flow rate during the rolling process, it can be known that the second flow rate of the metal at the rolling deformation zone exit should be equal to the second flow rate of the metal at the neutral plane: . The relationship between and and can be obtained:
[0031] Among them, is the neutral angle, is the speed of the workpiece at the roll exit, is the roll diameter.
[0032] Step 3: Substitute the relational expression obtained in Step 2 into the forward slip definition formula obtained in Step 1, and the relational expression between the forward slip and the neutral angle can be obtained, that is, the modified E-Fink forward slip formula:
[0033] Since the neutral angle is very small and is much greater than 1, so the above formula can be simplified to the D - Dresden forward slip formula:
[0034] where R is the roll radius.
[0035] Step 4: According to the corrected E - Fink forward slip formula, inversely deduce the calculation formula of the neutral angle. Transpose the terms and organize the terms containing the neutral angle γ to get:
[0036] Regarding as a whole, the above formula is a quadratic equation in one variable. By solving the above quadratic equation in one variable, two solutions can be obtained, and the solution with a negative angle value is selected as the neutral angle corresponding to the negative forward slip phenomenon.
[0037] Let the coefficients of the quadratic equation in one variable be , when , let:
[0038] According to the quadratic formula for the roots of a quadratic equation in one variable, we can get:
[0039] Let be the two solutions of the quadratic equation in one variable, and let . At this time, is used as the new neutral angle value corresponding to the negative forward slip phenomenon.
[0040] Step 5: Substitute the new neutral angle calculated in Step 4 into the D - Dresden forward slip formula, and the original negative forward slip value can be corrected again. Then, using the friction coefficient model inversely deduced from the Stone rolling force formula, as long as the forward slip value f and the inlet and outlet thicknesses of the rolled piece are known, the magnitude of the friction coefficient μ can be calculated, and then the rolling force can be calculated: .
[0041] where is the reduction, that is, the difference between the inlet thickness and the outlet thickness; is the flattened radius, is the reduction ratio, that is, the percentage of the reduction to the inlet thickness.
[0042] Example 1 In this example, the effectiveness of the method of the present invention is verified by dealing with the negative forward slip phenomenon in the actual production data of a certain factory.
[0043] A series of data related to the cold rolling process were obtained from the actual production records of a certain factory, including the exit speed of the rolled piece at different times, the circumferential speed of the roll, the thickness of the rolled piece at the entrance and exit, etc. These data cover multiple rolling passes, and in some of the data, the forward slip value is negative.
[0044] Initial data calculation: According to the obtained original data, the forward slip value was calculated according to the traditional forward slip definition formula. Record all the sample data with negative forward slip and their corresponding working condition parameters, such as roll diameter, the thickness of the rolled piece at the neutral plane and the exit, etc.
[0045] The corrected forward slip value was calculated according to the method of the present invention, and a comparison chart of the forward slip values before and after correction was drawn. As Figure 4 shown, it can be intuitively seen that after being corrected by the method of the present invention, the originally negative forward slip values have been reasonably corrected and all become positive values, meeting the theoretical requirement that the forward slip value must be greater than 0, and the corrected forward slip value is more consistent with the rolling situation in actual production. From the data trend, it can better reflect the speed relationship between the rolled piece and the roll.
[0046] Based on the corrected forward slip value and the calculated friction coefficient, substitute them into the rolling force calculation formula for calculation. Compare the calculated rolling force with the rolling force recorded in actual production, and it is found that the error between the rolling force calculated by the method of the present invention and the actual value is significantly smaller than the result calculated by using the traditional approximate processing method. This shows that the method of the present invention significantly improves the accuracy of rolling force calculation by effectively correcting the negative forward slip problem, and has important guiding significance for the setting and control of rolling parameters in actual production.
[0047] In summary, the solution strategy proposed by the present invention for the negative forward slip phenomenon in the rolling force calculation process is effective and reliable, can play an important role in actual production, and ensure the stability of the rolling process and product quality.
[0048] Example 2 The calculation method of the rolling force when negative forward slip occurs in the reversible cold rolling process of this embodiment is specifically implemented according to the following steps: Step 1: Determine the forward slip calculation formula according to the forward slip definition; Step 2: Use the relationship between the moving speed of the rolled piece at the neutral plane and the circumferential speed of the roll, the relationship between the thickness of the rolled piece at the exit and the thickness at the neutral plane, and the principle of constant volume of the second flow rate to obtain the relationship between the exit speed of the rolled piece and the circumferential speed of the roll; Step 3: According to the forward slip calculation formula obtained in Step 1 and the relationship obtained in Step 2, obtain the relationship between the forward slip and the neutral angle, that is, the corrected E-Fink forward slip formula, and simplify it to the D-Dresden forward slip formula; Step 4: Calculate the corrected new neutral angle value according to the E-Fink forward slip formula obtained in Step 3; Step 5: Calculate the corrected friction coefficient and rolling force according to the new neutral angle value obtained in Step 4.
[0049] Example 3 On the basis of Example 2, in Step 1, the forward slip calculation formula is:
[0050] Wherein, is the forward slip value, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll.
[0051] Example 4 On the basis of Example 3, the relationship between the rolled piece exit speed and the roll circumferential speed obtained in Step 2 is:
[0052] Wherein, is the neutral angle, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll, is the roll diameter, is the thickness of the rolled piece at the exit.
[0053] Example 5 On the basis of Example 4, Step 3 is specifically: Substitute the relationship obtained in Step 2 into the forward slip calculation formula obtained in Step 1 to obtain the corrected E-Fink forward slip formula:
[0054] Wherein, is the forward slip value, is the neutral angle, is the speed of the rolled piece at the roll exit, is the circumferential speed of the roll, is the roll diameter, is the thickness of the rolled piece at the exit.
[0055] The corrected E-Fink forward slip formula is simplified to: .
[0056] Example 6 On the basis of Example 5, Step 4 is specifically: According to the corrected E-Fink forward slip formula, inversely deduce the calculation formula of the neutral angle, move the terms, and put the terms containing the neutral angle Sort the terms to get:
[0057] Among them, is the roll diameter, is the neutral angle, is the forward slip value, is the thickness of the rolled piece at the exit; Regarding the term as a whole, the above equation is a quadratic equation of one variable. Solving this quadratic equation of one variable can obtain two solutions. Select the solution with a negative angle value as the new neutral angle corresponding to the negative forward slip phenomenon .
Claims
1. A method for calculating rolling force when negative forward slip occurs during reversible cold rolling, characterized in that: Follow the steps below to implement it: Step 1, determine the forward slip calculation formula according to the forward slip definition; Step 2, using the relationship between the moving speed of the rolled piece on the neutral plane and the circumferential speed of the roll, the relationship between the thickness of the rolled piece at the exit and the thickness at the neutral plane, and the principle that the volume per second flow rate is constant, the relationship between the exit speed of the rolled piece and the circumferential speed of the roll is obtained; Step 3: According to the forward slip calculation formula obtained in step 1 and the relationship formula obtained in step 2, a relationship formula between the forward slip and the neutral angle is obtained, that is, a modified E-Fink forward slip formula, and simplified to a D-Dresden forward slip formula; Step 4: Calculate the corrected new neutral angle value according to the E-Fink forward sliding formula obtained in step 3; Step 5: Calculate the corrected friction coefficient and rolling force according to the new neutral angle value obtained in step 4.
2. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 1, characterized in that: In step 1, the forward slip calculation formula is: in, is the forward slip value, is the speed of the workpiece at the roller exit, is the circumferential speed of the roller.
3. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 1, characterized in that: The relationship between the workpiece exit speed and the roller circumferential speed obtained in step 2 is: in, is the neutral angle, is the speed of the workpiece at the roller exit, is the circumferential speed of the roller, is the roller diameter, It is the thickness of the rolled product at the exit.
4. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 1, characterized in that: Step 3 is as follows: Substitute the relationship obtained in step 2 into the forward slip calculation formula obtained in step 1 to obtain the modified E-Fink forward slip formula: in, is the forward slip value, is the neutral angle, is the speed of the workpiece at the roller exit, is the circumferential speed of the roller, is the roller diameter, It is the thickness of the rolled product at the exit.
5. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 4, characterized in that: The revised E-Fink forward sliding formula is simplified to: 。 6. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 1, characterized in that: Step 4 is as follows: According to the modified E-Fink forward sliding formula, the calculation formula of the neutral angle is deduced, and the term containing the neutral angle is shifted. The items are sorted to get: in, is the roller diameter, is the neutral angle, is the forward slip value, is the thickness of the rolled product at the exit; Will The above formula is a quadratic equation. Solving the quadratic equation can give two solutions. The solution with a negative angle value is selected as the new neutral angle corresponding to the negative forward slip phenomenon. .
7. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 1, characterized in that: Step 5 is as follows: Substitute the new neutral angle value calculated in step 4 into the D-Dresden forward slip formula, correct the original negative forward slip value, and then use the friction coefficient model obtained by reverse deduction using the Stone rolling force formula to calculate the size of the friction coefficient μ, and then calculate the rolling force.
8. The method for calculating rolling force when negative forward slip occurs during reversible cold rolling according to claim 7, characterized in that: The calculation formula of friction coefficient μ is: Among them, the pressure , which is the entrance thickness of the rolled piece after rolling The outlet thickness of the rolled product difference; is the flattening radius; , which is the percentage of the reduction amount to the entrance thickness.