Method and apparatus for designing an axially displaced crowning roll profile

Abstract

The application discloses a method and device for designing an axially shifted variable crown roll shape, and relates to the technical field of roll shape design.According to a1, a2 and a3 in a roll shape equation, a roll diameter difference equation at both ends of a roll body and a maximum roll diameter difference equation in the middle of the roll body are constructed; according to an adjustment coefficient, the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle of the roll body, a comprehensive roll diameter difference equation is constructed; and a1 that makes the comprehensive roll diameter difference minimum is obtained according to the comprehensive roll diameter difference equation.The maximum roll diameter difference in the middle of the roll body of the designed roll shape is small, the linear velocities of each point in the middle of the roll body of the roll can be consistent, and the plate shape quality is ensured; on the basis, the roll diameter difference at both ends of the roll body is small, the radial grinding amount is reduced while the product quality is ensured, and the service life of the roll is prolonged; that is, the roll shape with consistent linear velocities of each point in the middle of the roll body and small radial grinding amount can be designed, and the plate shape quality and the roll life are considered.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of roll shape design, in particular to an axial displacement variable crown roll shape design method and device. BACKGROUND

[0002] Continuous variable crown roll shape has become one of the most important shape control means in the field of strip rolling. Continuous variable crown roll shape can replace conventional roll shape and meet the requirements of shape control under different rolling parameters (rolling force, strip width, etc.), and the roll shifting of work roll makes the roll wear more uniform, the in-plant service life is significantly prolonged, the roll changing frequency is greatly reduced, and the rolling schedule design is more flexible. Continuous variable crown roll shape can improve the flexibility of rolling schedule and production plan, thereby improving the utilization rate of rolling mill.

[0003] In the conventional design method, due to the principle limitation, it is impossible to design a roll shape with uniform linear speed at each point of the middle roll body and small radial grinding amount, so that the plate shape quality and roll life cannot be considered. SUMMARY

[0004] The present application provides an axial displacement variable crown roll shape design method and device, which solves the technical problem that the roll shape designed by the prior art cannot consider the plate shape quality and roll life.

[0005] In one aspect, the embodiments of the present application provide the following technical solutions:

[0006] An axial displacement variable crown roll shape design method comprises the following steps:

[0007] constructing a roll shape equation R(x) = R0 + a1x + a2x 2 +a3x 3 , wherein x is the roll body coordinate, R0 is the roll shape radius when x = 0, a1, a2 and a3 are roll shape coefficients, and R(x) is the roll shape radius;

[0008] calculating a2 and a3 in the roll shape equation;

[0009] constructing a roll diameter difference equation at both ends of the roll body and a maximum roll diameter difference equation in the middle of the roll body according to a1, a2 and a3;

[0010] obtaining an adjustment coefficient, and constructing a comprehensive roll diameter difference equation according to the adjustment coefficient, the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle of the roll body;

[0011] obtaining a1 that makes the comprehensive roll diameter difference minimum according to the comprehensive roll diameter difference equation.

[0012] Preferably,

[0013] Sm is the roll shifting limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shifting limit-sm in the roll shifting stroke, and C2 is the roll crown corresponding to the positive roll shifting limit-sm in the roll shifting stroke.

[0014] Preferably, the roll diameter difference equation at both ends of the roll body is:

[0015] ΔD1 = 2a1L - 2a2L 2 - 2a3L 3 ; ΔD1 is the roll diameter difference at both ends of the roll body.

[0016] The maximum roll diameter difference equation in the middle part of the roll body is:

[0017] ΔD2 is the maximum roll diameter difference in the middle part of the roll body.

[0018] Preferably, the comprehensive roll diameter difference equation is:

[0019] ΔD is the comprehensive roll diameter difference, and k is the adjustment coefficient.

[0020] In another aspect, the embodiments of the present application also provide the following technical solutions:

[0021] An axial displacement variable crown roll shape design device comprises:

[0022] An equation construction module is configured to construct a roll shape equation R(x) = R0 + a1x + a2x 2 + a3x 3 , x is a roll body coordinate, R0 is the roll shape radius when x = 0, a1, a2, and a3 are roll shape coefficients, and R(x) is a roll shape radius.

[0023] A coefficient calculation module is configured to calculate a2 and a3 in the roll shape equation.

[0024] The equation construction module is further configured to construct a roll diameter difference equation at both ends of the roll body and a maximum roll diameter difference equation in the middle part of the roll body according to a1, a2, and a3.

[0025] The equation construction module is further configured to obtain an adjustment coefficient, and construct a comprehensive roll diameter difference equation according to the adjustment coefficient, the roll diameter difference equation at both ends of the roll body, and the maximum roll diameter difference equation in the middle part of the roll body.

[0026] The coefficient calculation module is further configured to obtain a1 that minimizes the comprehensive roll diameter difference according to the comprehensive roll diameter difference equation.

[0027] Preferably,

[0028] Sm is the roll shifting limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shifting limit-sm in the roll shifting stroke, and C2 is the roll crown corresponding to the positive roll shifting limit-sm in the roll shifting stroke.

[0029] Preferably, the roll diameter difference equation at both ends of the roll body is:

[0030] ΔD1=2a1L-2a2L 2 -2a3L 3 ; ΔD1 is the roll diameter difference at both ends of the roll body;

[0031] The maximum roll diameter difference equation in the middle part of the roll body is:

[0032] ΔD2 is the maximum roll diameter difference in the middle part of the roll body.

[0033] Preferably, the comprehensive roll diameter difference equation is:

[0034] ΔD is the comprehensive roll diameter difference, and k is the adjustment coefficient.

[0035] In another aspect, the embodiments of the present application also provide the following technical solutions:

[0036] An electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor implements any of the above-mentioned axial displacement variable crown roll shape design methods when executing the program.

[0037] In another aspect, the embodiments of the present application also provide the following technical solutions:

[0038] A computer readable storage medium has a computer program stored thereon, and the computer program implements any of the above-mentioned axial displacement variable crown roll shape design methods when executed by a processor.

[0039] The one or more technical solutions provided by the present application have at least the following technical effects or advantages:

[0040] The present application constructs the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle part of the roll body according to a1, a2 and a3 in the roll shape equation, constructs the comprehensive roll diameter difference equation according to the adjustment coefficient, the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle part of the roll body, and obtains a1 that makes the comprehensive roll diameter difference minimum according to the comprehensive roll diameter difference equation. The maximum roll diameter difference in the middle part of the roll body of the designed roll shape is small, the linear speed of each point in the middle part of the roll body can be consistent, and the plate shape quality is ensured. On this basis, the roll diameter difference at both ends of the roll body is small, the radial grinding amount is reduced while the product quality is ensured, and the service life of the roll is prolonged. The roll shape with consistent linear speed of each point in the middle part of the roll body and small radial grinding amount is designed, and the plate shape quality and the roll life are considered. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort.

[0042] Figure 1 A flow chart of the axial displacement variable crown roll shape design method in the embodiment of the present application;

[0043] Figure 2 A schematic diagram of the axial displacement variable crown roll shape performing axial displacement in the embodiment of the present application;

[0044] Figure 3 A schematic diagram of the axial displacement variable crown roll shape finally designed in the embodiment of the present application;

[0045] Figure 4 A structural schematic diagram of the axial displacement variable crown roll shape design device in the embodiment of the present application. DETAILED DESCRIPTION

[0046] The axial displacement variable crown roll shape design method and device provided by the embodiment of the present application solve the technical problem that the roll shape designed by the prior art cannot balance the plate shape quality and the roll life.

[0047] In order to better understand the technical solutions of the present application, the technical solutions of the present application will be described in detail below in combination with the drawings of the specification and specific embodiments.

[0048] Firstly, the term "and / or" appearing in this paper is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents an "or" relationship between the front and rear associated objects.

[0049] As shown in the formula (1), the axial displacement variable crown roll shape design method of the embodiment of the present application comprises: Figure 1 Step S1, constructing a roll shape equation R(x) = R0 + a1x + a2x 2 +a3x 3 , x is the roll body coordinate, R0 is the roll shape radius when x = 0, a1, a2, a3 are roll shape coefficients, and R(x) is the roll shape radius;

[0050] Step S2, calculating a2 and a3 in the roll shape equation;

[0051]

[0052] ​Step S3, constructing a roll body two-end roll diameter difference equation and a roll body middle part maximum roll diameter difference equation according to a1, a2 and a3;

[0053] Step S4, obtaining an adjustment coefficient, and constructing a comprehensive roll diameter difference equation according to the adjustment coefficient, the roll body two-end roll diameter difference equation and the roll body middle part maximum roll diameter difference equation;

[0054] Step S5, obtaining a1 that makes the comprehensive roll diameter difference minimum according to the comprehensive roll diameter difference equation.

[0055] In step S1, the unit of x is mm, the value range is 0-L, L is the roll length; the unit of R(x) is mm; a1 has no unit, the unit of a2 is mm-1, and the unit of a3 is mm-2.

[0056] In step S2, the formula for calculating a2 is:

[0057]

[0058] The formula for calculating a3 is:

[0059]

[0060] Sm is the roll shifting limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shifting limit-sm in the roll shifting stroke, and C2 is the roll crown corresponding to the positive roll shifting limit-sm in the roll shifting stroke.

[0061] According to the actual crown control requirement, the limit range [Sm, -Sm] of the roll shifting value s and the regulation range [C1, C2] of the corresponding roll crown C are determined.

[0062] In step S3, the roll body two-end roll diameter difference equation is:

[0063] ΔD1=2a1L-2a2L 2 -2a3L 3 ; ΔD1 is the roll body two-end roll diameter difference, with the unit of mm;

[0064] The roll body middle part maximum roll diameter difference equation is:

[0065] ΔD2 is the roll body middle part maximum roll diameter difference, with the unit of mm.

[0066] In step S4, the comprehensive roll diameter difference equation is:

[0067] ΔD is the integrated roll diameter difference, unit: mm; k is the adjustment coefficient, dimensionless, the value range is 0 to 1, k is determined according to the on-site roll usage. According to the on-site roll usage requirements, it is necessary to reduce the maximum roll diameter difference in the middle of the roll body to promote the line speed of each point of the roll body in the middle of the roll to be consistent, so as to ensure the plate shape quality; on this basis, the roll diameter difference at both ends of the roll body is reduced as much as possible, so as to ensure the product quality, reduce the radial grinding amount, and prolong the service life of the roll.

[0068] In step S5, the integrated roll diameter difference equation is regarded as a functional relationship between the integrated roll diameter difference ΔD and the first-order term coefficient a1 of the axial displacement variable crown roll shape, and the first-order partial derivative of ΔD with respect to a1 is obtained:

[0069]

[0070] The second-order partial derivative of the above equation is:

[0071]

[0072] It is known from the second-order partial derivative greater than 0 that the first-order partial derivative is an increasing function, and the first-order partial derivative formula has a zero solution, so the monotonicity of the integrated roll diameter difference equation is first decreasing and then increasing, that is, when the first-order partial derivative formula is zero, the integrated roll diameter difference is the minimum, which is the optimal result obtained by considering the maximum roll diameter difference in the middle of the roll body and the roll diameter difference at both ends of the roll body, and a1 can be obtained by setting the first-order partial derivative formula to zero.

[0073] In this way, after a1, a2 and a3 are obtained, the roll shape equation R(x) = R0 + a1x + a2x 2 +a3x 3 is obtained.

[0074] This embodiment illustrates the axial displacement variable crown roll shape design method:

[0075] According to the variable crown roll shape rolled strip specifications, steel grades and crown control requirements, the best crown control range is determined to be [-1.3, 1.1], that is, C1 =-1.3 and C2 = 1.1; the roll length provided on site is L = 2550 mm, the work roll roll shifting limit is Sm = 150 mm, a2 =-3.1065E-06 and a3 = 8.20197E-10 are calculated, k is 0.3, a1 = 3.187307E-03 is obtained, and the final roll shape curve is shown in Figure 3 .

[0076] From the above, the embodiment constructs the roll body two-end roll diameter difference equation and the roll body middle part maximum roll diameter difference equation according to a1, a2, a3, constructs the comprehensive roll diameter difference equation according to the adjustment coefficient, the roll body two-end roll diameter difference equation and the roll body middle part maximum roll diameter difference equation, and obtains a1 that makes the comprehensive roll diameter difference minimum according to the comprehensive roll diameter difference equation. The roll shape designed has small roll body middle part maximum roll diameter difference, can make the linear velocity of each point of the roll body middle part of the roll consistent, and ensures the plate shape quality. On this basis, the roll body two-end roll diameter difference is small, the radial grinding amount is reduced while the product quality is ensured, and the service life of the roll is prolonged. That is, the roll shape that has consistent linear velocity of each point of the roll body middle part and small radial grinding amount is designed, and the plate shape quality and the roll life are considered.

[0077] As shown in Figure 4 , the embodiment also provides a kind of axial displacement variable crown roll shape design device, comprising:

[0078] Equation construction module, for constructing roll shape equation R (x) = R0+a1x+a2x 2 +a3x 3 , x is roll body coordinate, R0 is the roll shape radius when x=0, a1, a2, a3 are roll shape coefficients, and R (x) is roll shape radius;

[0079] Coefficient calculation module, for calculating a2, a3 in roll shape equation;

[0080] Equation construction module is also used for constructing roll body two-end roll diameter difference equation and roll body middle part maximum roll diameter difference equation according to a1, a2, a3;

[0081] Equation construction module is also used for obtaining adjustment coefficient, and constructing comprehensive roll diameter difference equation according to adjustment coefficient, roll body two-end roll diameter difference equation and roll body middle part maximum roll diameter difference equation;

[0082] Coefficient calculation module is also used for obtaining a1 that makes comprehensive roll diameter difference minimum according to comprehensive roll diameter difference equation.

[0083] Wherein,

[0084] Sm is the roll shifting limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shifting limit-sm in the roll shifting stroke, and C2 is the roll crown corresponding to the positive roll shifting limit sm in the roll shifting stroke.

[0085] Wherein, roll body two-end roll diameter difference equation is:

[0086] ΔD1=2a1L-2a2L 2 -2a3L 3 ; ΔD1 is roll body two-end roll diameter difference;

[0087] Roll body middle part maximum roll diameter difference equation is:

[0088] ΔD2 is the maximum roll diameter difference in the middle of the roll body.

[0089] wherein the comprehensive roll diameter difference equation is:

[0090] ΔD is the comprehensive roll diameter difference, and k is the adjustment coefficient.

[0091] In this embodiment, the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle of the roll body are constructed according to a1, a2 and a3, the comprehensive roll diameter difference equation is constructed according to the adjustment coefficient, the roll diameter difference equation at both ends of the roll body and the maximum roll diameter difference equation in the middle of the roll body, and a1 that makes the comprehensive roll diameter difference minimum is obtained according to the comprehensive roll diameter difference equation, so that the roll shape designed has small maximum roll diameter difference in the middle of the roll body, the linear speed of each point of the roll body in the middle of the roll can be consistent, and the plate shape quality is ensured; on this basis, the roll diameter difference at both ends of the roll body is small, the radial grinding amount is reduced while the product quality is ensured, and the service life of the roll is prolonged; that is, the roll shape with consistent linear speed of each point of the roll body in the middle of the roll and small radial grinding amount can be designed, and the plate shape quality and the roll life are considered.

[0092] Based on the same inventive concept as the axial displacement variable crown roll shape design method described above, the embodiment also provides an electronic device, which includes a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the steps of any method of the axial displacement variable crown roll shape design method described above when executing the program.

[0093] Wherein, the bus architecture (represented by a bus), the bus can include any number of interconnected buses and bridges, the bus links various circuits including one or more processors represented by a processor and a memory represented by a memory together. The bus can also link various other circuits such as peripheral devices, voltage stabilizers and power management circuits, which are well known in the art, and therefore, they will not be further described herein. The bus interface provides an interface between the bus and the receiver and the transmitter. The receiver and the transmitter can be the same element, i.e. the transceiver, which provides a unit for communicating with various other devices on the transmission medium. The processor is responsible for managing the bus and general processing, while the memory can be used to store data used by the processor in performing operations.

[0094] Since the electronic device introduced in the embodiment is the electronic device used in the design method of the axial displacement variable crown roll shape, the specific implementation of the electronic device and various changes thereof can be understood by those skilled in the art based on the design method of the axial displacement variable crown roll shape introduced in the embodiment, and therefore, how the electronic device realizes the method in the embodiment will not be introduced in detail. As long as the electronic device used in the design method of the axial displacement variable crown roll shape in the embodiment is implemented by those skilled in the art, it belongs to the scope of the present application.

[0095] Based on the same inventive concept as the design method of the axial displacement variable crown roll shape, the present application also provides a computer readable storage medium, which stores a computer program, and the computer program realizes any of the design methods of the axial displacement variable crown roll shape when executed by a processor.

[0096] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0097] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system), and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general purpose computer, a special purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices produce a device that implements the flowcharts and / or block diagrams. Figure 1 The function specified in one or more flows and / or blocks. Figure 1 The function specified in one or more blocks or multiple blocks.

[0098] These computer program instructions can also be stored in a computer readable storage medium that can guide the computer or other programmable data processing devices to work in a specific way, so that the instructions stored in the computer readable storage medium produce a product including instruction devices, which implement the flowcharts and / or block diagrams. Figure 1 The function specified in one or more flows and / or blocks. Figure 1 The function specified in one or more blocks or multiple blocks.

[0099] These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 Figure 1

[0100] Although preferred embodiments of the application have been described herein, it will be apparent to those skilled in the art that various modifications and changes can be made to the embodiments without departing from the spirit and scope of the application. Accordingly, it is intended that all claims be interpreted to include all such modifications and changes as fall within the true spirit and scope of the application.

[0101] Obviously, numerous modifications and variations of the present application are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described herein.​​

Claims

1. A method for designing an axially displaced variable crown roller, characterized in that, include: Constructing the Roller Equation , For the roller body coordinates, for The radius of the roller at that time, , , The roll shape coefficient, The radius of the roller; Calculate the roller shape equation , ; according to , , Construct equations for the difference in roll diameter at both ends of the roll body and for the maximum difference in roll diameter at the middle of the roll body; Obtain the adjustment coefficient, and construct a comprehensive roller diameter difference equation based on the adjustment coefficient, the roller diameter difference equation at both ends of the roller body, and the maximum roller diameter difference equation at the middle of the roller body; The equation for the combined roll diameter difference is used to find the value that minimizes the combined roll diameter difference. ,include: Take the first and second partial derivatives of the comprehensive roll diameter difference equation with respect to the comprehensive roll diameter difference ΔD with respect to a1, and set the first partial derivative to zero to find the value that minimizes the comprehensive roll diameter difference. ; in, , ; Sm is the roll shift limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shift limit -sm in the roll shift stroke, and C2 is the roll crown corresponding to the positive roll shift limit sm in the roll shift stroke. The equation for the difference in roller diameter at both ends of the roller body is as follows: ΔD1 is the difference in roller diameter between the two ends of the roller body; The equation for the maximum roller diameter difference in the middle of the roller body is: ΔD2 is the maximum difference in roll diameter at the center of the roll body; The equation for the combined roller diameter difference is: ΔD is the combined roller diameter difference, and k is the adjustment coefficient.

2. A roller shape design device for axial displacement and variable convexity, characterized in that, include: The equation building module is used to construct the roller equation. , For the roller body coordinates, for The radius of the roller at that time, , , The roll shape coefficient, The radius of the roller; The coefficient calculation module is used to calculate the coefficients in the roller shape equation. , ; The equation construction module is also used to, according to , , Construct equations for the difference in roll diameter at both ends of the roll body and for the maximum difference in roll diameter at the middle of the roll body; The equation construction module is also used to obtain the adjustment coefficient, and construct a comprehensive roller diameter difference equation based on the adjustment coefficient, the roller diameter difference equation at both ends of the roller body, and the maximum roller diameter difference equation in the middle of the roller body. The coefficient calculation module is also used to determine the coefficient that minimizes the overall roll diameter difference based on the overall roll diameter difference equation. ,include: Take the first and second partial derivatives of the comprehensive roll diameter difference equation with respect to the comprehensive roll diameter difference ΔD with respect to a1, and set the first partial derivative to zero to find the value that minimizes the comprehensive roll diameter difference. ; in, , ; Sm is the roll shift limit, L is the roll length, C1 is the roll crown corresponding to the negative roll shift limit -sm in the roll shift stroke, and C2 is the roll crown corresponding to the positive roll shift limit sm in the roll shift stroke. The equation for the difference in roller diameter at both ends of the roller body is as follows: ΔD1 is the difference in roller diameter between the two ends of the roller body; The equation for the maximum roller diameter difference in the middle of the roller body is: ΔD2 is the maximum difference in roll diameter at the center of the roll body; The equation for the combined roller diameter difference is: ΔD is the combined roller diameter difference, and k is the adjustment coefficient.

3. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the axial displacement variable convexity roller design method of claim 1.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the axial displacement variable convexity roller design method of claim 1.

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