Roll profile design method for variable crown work roll with mid-wave control capability

Abstract

The present invention discloses a roll profile design method for a variable-crown work roll with mid-wave control capability. The method comprises the following steps: setting a coordinate origin on the work roll, setting a conventional cubic CVC curve within the secondary crown range of the work roll and an M-shaped quartic curve symmetrical about the midpoint of the roll surface; based on the conventional cubic CVC curve, superimposing an M-shaped quartic curve symmetrical about the midpoint of the roll surface on the roll gap to compensate for the crown of the unloaded roll gap at the internal width position of the work roll, thereby obtaining a roll profile curve for the variable-crown work roll with mid-wave control capability; calculating the roll profile coefficients of each roll of the roll profile curve for the variable-crown work roll with mid-wave control capability, thereby ultimately determining the roll profile curve for the variable-crown work roll with mid-wave control capability. The present invention increases the roll gap crown at different strip width positions without changing the secondary crown range of the unloaded roll gap in the continuous variable-crown section or the plate shape control model, thereby achieving the purpose of mid-wave control.

Description

Technical Field

[0001] The present invention relates to the technical field of plate and strip rolling, and in particular to a roll shape design method for a variable crown working roll with mid-wave control capability. Background Art

[0002] In the late 1970s, SMS of Germany pioneered the development of the continuously variable crown (CVC) roll profile. Currently, CVC roll profile is still one of the most important plate shape control methods in the field of plate and strip rolling. This technology can continuously change the crown of the unloaded roll gap through the relative axial movement of the rolls to achieve plate shape control, such as Figure 1 shown.

[0003] like Figure 2 As shown, the upper roller radius function equation of the cubic CVC roller curve is y t (x) = R0 + a1x + a2x 2 +a3x 3 The function equation for the lower roll radius can be derived based on the antisymmetric properties of the upper and lower rolls. The advantages of this roll shape in plate shape control are: the roll shape and control characteristics are relatively simple. If the reduction in effective roll gap length caused by axial roll shifting is not considered, and the effects of rolling force and bending roll force are not considered, the secondary crown of the unloaded roll gap is strictly linearly related to the amount of roll shifting. This characteristic is very beneficial to the design and processing of the roll shape and the plate shape control during the production process.

[0004] Generally speaking, strip waves often appear at the mill exit. Roll bending technology is often used to address this issue, providing real-time control. However, for common strip waves within a certain width range, controlling the waves significantly increases the operator's workload, making it difficult to implement.

[0005] If the three-stage CVC roller shape is used to control the mid-wave, the following problems will occur:

[0006] First, the three-dimensional CVC roll shape mainly controls the secondary crown of the roll gap, but does not have the ability to control the fourth-order crown. It has no control ability for the fourth-order flatness defects that occur during the rolling process of wide and thin strips.

[0007] Second, the ability of the tertiary CVC roll shape to control crown is proportional to the square of the strip width. Adjusting the overall secondary crown range to solve the wave problem at a certain width position may cause the crown control range to be too large, affecting the uniform wear of the working roll, which is not conducive to the plate shape control and rolling stability of wide-specification strip steel. Summary of the Invention

[0008] In response to the shortcomings of the existing technology, the present invention proposes a roll shape design method for a variable-convex working roll with the ability to control middle waves. Without changing the secondary convexity range of the no-load roll gap in the continuous variable-convexity section, the roll shape of the working roll is flexibly designed according to the degree of middle-wave control required, thereby achieving effective control of the middle edge waves of plates and strips of different widths.

[0009] To achieve the above-mentioned purpose, the present invention provides a roll profile design method for a variable crown work roll with mid-wave control capability, which is particularly characterized in that it includes the following steps:

[0010] S1) setting the coordinate origin on the work roll, setting the conventional cubic CVC curve within the quadratic crown range of the work roll and the M-shaped quartic curve symmetrical about the midpoint of the roll surface;

[0011] The conventional cubic CVC curve is expressed as follows

[0012] y t1 (x) = R0 + A1x + A2x 2 +A3x 3

[0013] Where,

[0014] y t1 (x) is the working roll shape with continuously variable crown,

[0015] R0 is the initial radius of the roller,

[0016] A1 is the roll shape coefficient,

[0017] A2 is the roll shape coefficient,

[0018] A3 is the roll shape coefficient,

[0019] x is the coordinate of the roller body, and the value range of x is [0, L].

[0020] L is the length of the roller body;

[0021] The M-shaped quartic curve symmetrical about the midpoint of the roller surface is expressed as follows

[0022] y t2 (x) = e2(xL / 2) 2 +e4(xL / 2) 4 -(e2L 2 / 4+e4L 4 / 16)

[0023] Where,

[0024] y t2 (x) is the work roll shape that is symmetrical about the midpoint of the roll surface,

[0025] e2 is the roll shape coefficient,

[0026] e4 is the roll shape coefficient,

[0027] x is the coordinate of the roller body, and the value range of x is [0, L].

[0028] L is the length of the roller body;

[0029] S2) Based on the conventional cubic CVC curve, in order to meet the need for no-load roll gap crown compensation at the internal width position of the work roll, an M-shaped quartic curve symmetrical about the midpoint of the roll surface is superimposed on the roll gap to obtain a variable crown work roll profile curve with the ability to control mid-wave. This achieves a positive offset of the secondary crown at different strip width positions, increases the roll gap crown at the same roll shifting position and different strip width positions, and achieves the purpose of controlling mid-wave at the stand exit;

[0030] The roll profile curve of the variable crown work roll with mid-wave control capability is shown as follows:

[0031] y t (x) = R0 + a1x + a2x 2 +a3x 3 +a4x 4

[0032] Where,

[0033] y t (x) is the roll shape of the variable crown work roll with the ability to control the middle wave.

[0034] R0 is the initial radius of the roller,

[0035] a1 is the roll shape coefficient,

[0036] a2 is the roll shape coefficient,

[0037] a3 is the roll shape coefficient,

[0038] a4 is the roll shape coefficient,

[0039] x is the coordinate of the roller body, and the value range of x is [0, L].

[0040] L is the length of the roller body;

[0041] S3) determining the roll body length, the maximum roll shifting amount of the roll, the secondary convexity adjustment range of the no-load roll gap in the continuous variable convexity section of the roll shape, the strip width that generates medium waves, the no-load roll gap convexity compensation amount at the strip width position that generates medium waves, and the normal rolling width when the roll diameter difference is 0; by calculating the roll shape coefficients of the conventional cubic CVC curve in step S1) and the M-shaped quartic curve symmetrical about the midpoint of the roll surface, the roll shape coefficients of the variable convexity work roll roll shape curve with medium wave control capability in step S2) are obtained, thereby finally determining the variable convexity work roll roll shape curve with medium wave control capability.

[0042] Furthermore, in step S2), if the middle waves generated at the frame outlet are large, a larger no-load roll gap crown compensation amount needs to be given during roll shape design; if the middle waves generated at the frame outlet are small, a smaller no-load roll gap crown compensation amount needs to be given during roll shape design; if no middle waves are generated at the frame outlet, the no-load roll gap crown compensation amount given during roll shape design is 0.

[0043] Furthermore, in step S3), the roll shape coefficients of the conventional cubic CVC curves are calculated as follows:

[0044] The roll shape coefficient A3 is expressed as

[0045]

[0046] The roll shape coefficient A2 is expressed as

[0047]

[0048] The roll shape coefficient A1 is expressed as

[0049] A1=-A2L-3A3(L / 2) 2 -A3b 2 / 4

[0050] Where,

[0051] L is the length of the roller body,

[0052] s m is the maximum roll shifting amount of the roll,

[0053] C1 is the roller-shaped negative electrode line position -s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is

[0054] C2 is the roller-shaped positive electrode line position s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is

[0055] b is the normal rolling width when the roller diameter difference is 0.

[0056] Furthermore, in step S3), the calculated roll shape coefficients of the M-shaped quartic curve are expressed as follows:

[0057] The roll shape coefficient e2 is expressed as

[0058]

[0059] The roll shape coefficient e4 is expressed as

[0060]

[0061] Where,

[0062] L is the length of the roller body,

[0063] s m is the maximum roll shifting amount of the roll,

[0064] B is the width of the strip that produces the middle wave,

[0065] △C B It is the no-load roll gap convexity compensation amount at the strip width that produces medium waves.

[0066] Furthermore, in step S3), the roll shape coefficients of the roll shape curve of the variable crown work roll with the ability to control the middle wave are calculated and expressed as follows:

[0067] The roll shape coefficient a4 is expressed as

[0068]

[0069] The roll shape coefficient a3 is expressed as

[0070]

[0071] The roll shape coefficient a2 is expressed as

[0072]

[0073] The roll shape coefficient a1 is expressed as

[0074] a1=-e2L-e4L 3 / 2+A1=-a2L-3a3(L / 2) 2 -a3b 2 / 4-4a4(L / 2) 3 -a4(L / 2)b 2

[0075] Where,

[0076] e2 and e4 are the roll shape coefficients of the M-shaped quartic curve symmetrical about the midpoint of the roll surface,

[0077] A1, A2, and A3 are the roll shape coefficients of the basic cubic CVC curve.

[0078] L is the length of the roller body,

[0079] s m is the maximum roll shifting amount of the roll,

[0080] C1 is the roller-shaped negative electrode line position -s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is

[0081] C2 is the roller-shaped positive electrode line position s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is

[0082] B is the width of the strip that produces the middle wave,

[0083] △C B is the no-load roll gap crown compensation amount at the strip width position where the middle wave is generated,

[0084] b is the normal rolling width when the roller diameter difference is 0.

[0085] Furthermore, in step S3), for the final determined variable crown work roll profile with mid-wave control capability, the no-load roll gap crown compensation value ΔC at any strip width B1 position is B1 The no-load roll gap crown compensation △C at the strip width B position where the middle wave is generated B The relationship between

[0086]

[0087] Where,

[0088] △C B1 is the no-load roll gap crown compensation at any strip width B1 position,

[0089] B1 is the width of any strip,

[0090] L is the length of the roller body,

[0091] △C B It is the no-load roll gap convexity compensation amount at the strip width B position where the middle wave is generated, and B is the strip width where the middle wave is generated.

[0092] The advantages of the present invention are:

[0093] 1. Based on the conventional cubic CVC curve with the same nominal quadratic crown range, the present invention superimposes an M-shaped quartic curve symmetrical about the midpoint of the roll surface on the roll gap to compensate for the roll gap crown at a specific width position. This method obtains a variable-crown work roll profile curve with the ability to control mid-roll in the form of a quartic polynomial function, achieving a positive offset of the quadratic crown at different strip width positions, increasing the roll gap crown at the same roll shifting position and different strip width positions, and achieving the purpose of controlling mid-roll at the stand exit.

[0094] 2. The present invention calculates partial roll shape coefficients of a conventional cubic CVC curve and an M-shaped quartic curve based on the adjustment range of the no-load roll gap quadratic crown and the roll gap crown compensation amount at a specific width position. Other roll shape coefficients are then obtained based on the principle of minimum roll diameter difference under normal rolling width. Finally, the above data are substituted into the work roll quartic polynomial function to obtain the variable crown work roll roll shape curve with mid-roll control capability.

[0095] 3. The present invention utilizes the corresponding relationship between the roller shape coefficients provided, and can flexibly design the roller shape according to the degree of control required for the middle wave, thereby achieving effective control of the side waves in the middle of strips of different widths.

[0096] The roll shape design method of the variable crown working roll with the ability to control the middle wave of the present invention can adjust the middle wave at any strip width position. Compared with the ordinary three-dimensional CVC roll shape, it does not change the secondary crown range of the no-load roll gap in the continuous variable crown section and does not change the plate shape control model. The roll gap crown at different strip width positions is increased, which not only achieves the purpose of middle wave control, but also ensures the overall expression of the roll shape of the variable crown working roll with the ability to control the middle wave. It is suitable for CNC grinding machines that use the overall polynomial method to enter the roll shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 This is the working principle diagram of the continuously variable crown roller control technology;

[0098] Figure 2 Schematic diagram of axial movement of continuously variable crown roller;

[0099] Figure 3 Schematic diagram of a variable crown roller with mid-wave control capability according to the present invention;

[0100] Figure 4 Three variable crown roller curves with mid-wave control capabilities designed to meet different mid-wave control requirements;

[0101] Figure 5 This is a comparison chart of three M-shaped curves with mid-wave control capabilities;

[0102] Figure 6The roller gap formed by three variable crown roller curves with mid-wave control capability when s = -100 mm;

[0103] Figure 7 The roller gap formed by three variable crown roller curves with mid-wave control capability when s=0mm;

[0104] Figure 8 The roller gap formed by three variable crown roller curves with mid-wave control capability when s=100mm;

[0105] Figure 9 The roll gap formed by three variable crown roll curves with mid-wave control capability when s = -100 mm and B = 1250 mm;

[0106] Figure 10 The roll gap formed by three variable crown roll curves with mid-wave control capability when s = 0 mm and B = 1250 mm;

[0107] Figure 11 The roller gap formed by three variable convex roller curves with mid-wave control capability when s=100mm and B=1250mm. DETAILED DESCRIPTION

[0108] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0109] In the description of the present invention, it should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the invention.

[0110] The present invention provides a roll profile design method for a variable crown work roll with mid-wave control capability, comprising the following steps:

[0111] S1) Set the coordinate origin on the working roll, set the conventional cubic CVC curve within the quadratic crown range of the working roll and the M-shaped quartic curve symmetrical about the midpoint of the roll surface.

[0112] In this embodiment, the operating side end of the working roll is the coordinate origin, and the conventional cubic CVC curve is expressed as follows:

[0113] y t1 (x) = R0 + A1x + A2x 2 +A3x 3

[0114] Where,

[0115] y t1 (x) is the work roll shape with continuously variable crown, in mm.

[0116] R0 is the initial radius of the roller, in mm,

[0117] A1 is the roll shape coefficient, no unit,

[0118] A2 is the roll shape coefficient, unit is mm -1 ,

[0119] A3 is the roll shape coefficient, unit is mm -2 ,

[0120] x is the coordinate of the roller body, the value range of x is [0, L], the unit is mm,

[0121] L is the length of the roller body, in mm.

[0122] The M-shaped quartic curve symmetrical about the midpoint of the roller surface is expressed as follows

[0123] y t2 (x) = e2(xL / 2) 2 +e4(xL / 2) 4 -(e2L 2 / 4+e4L 4 / 16)

[0124] Where,

[0125] y t2 (x) is the work roll shape that is symmetrical about the midpoint of the roll surface, in mm.

[0126] e2 is the roll shape coefficient, unit is mm -1 ,

[0127] e4 is the roll shape coefficient, unit is mm -3 ,

[0128] x is the coordinate of the roller body, the value range of x is [0, L], the unit is mm,

[0129] L is the length of the roller body, in mm.

[0130] S2) On the basis of the conventional cubic CVC curve, in order to meet the need for compensation of the no-load roll gap crown at the internal width position of the working roll, an M-shaped quartic curve symmetrical about the midpoint of the roll surface is superimposed on the roll gap to obtain a variable-crown work roll profile curve with the ability to control mid-waves. This achieves a positive offset of the secondary crown at different strip width positions, increases the roll gap crown at the same roll shifting position and different strip width positions, and achieves the purpose of controlling the mid-waves at the stand outlet.

[0131] The roll shape curve of the variable crown working roll with the ability to control middle waves in the present invention is a continuous quartic curve. It is a cubic curve with an M-shaped quartic curve symmetrical about x=L / 2 superimposed on it, so as to achieve the purpose of keeping the nominal roll gap convexity of the entire length unchanged and increasing the roll gap convexity of the middle width, thereby solving the middle waves at the frame outlet without changing the control model.

[0132] Specifically, in step S2), if the middle waves generated at the frame outlet are large, a larger no-load roll gap convexity compensation amount needs to be given when designing the roll shape; if the middle waves generated at the frame outlet are small, a smaller no-load roll gap convexity compensation amount needs to be given when designing the roll shape; if no middle waves are generated at the frame outlet, the no-load roll gap convexity compensation amount given when designing the roll shape is 0, and at this time the roll shape of the present invention is a conventional three-time variable convexity roll shape.

[0133] The roll profile curve of the variable crown work roll with mid-wave control capability is shown as follows:

[0134] y t (x) = R0 + a1x + a2x 2 +a3x 3 +a4x 4

[0135] Where,

[0136] y t (x) is the roll shape of the variable crown work roll with the ability to control the middle wave, the unit is mm,

[0137] R0 is the initial radius of the roller, in mm,

[0138] a1 is the roll shape coefficient, no unit,

[0139] a2 is the roll shape coefficient, unit is mm -1 ,

[0140] a3 is the roll shape coefficient, unit is mm -2 ,

[0141] a4 is the roll shape coefficient, unit is mm -3 ,

[0142] x is the coordinate of the roller body, the value range of x is [0, L], the unit is mm,

[0143] L is the length of the roller body, in mm.

[0144] S3) determining the roll body length, the maximum roll shifting amount of the roll, the secondary convexity adjustment range of the no-load roll gap in the continuous variable convexity section of the roll shape, the strip width that generates medium waves, the no-load roll gap convexity compensation amount at the strip width position that generates medium waves, and the normal rolling width when the roll diameter difference is 0; by calculating the roll shape coefficients of the conventional cubic CVC curve in step S1) and the M-shaped quartic curve symmetrical about the midpoint of the roll surface, the roll shape coefficients of the variable convexity work roll roll shape curve with medium wave control capability in step S2) are obtained, thereby finally determining the variable convexity work roll roll shape curve with medium wave control capability.

[0145] like Figure 3 The figure shows a schematic diagram of the roll shape of the variable crown working roll with the ability to control mid-waves according to the present invention.

[0146] Specifically, in step S3), the calculated roll shape coefficients of the conventional cubic CVC curve are expressed as follows:

[0147] The roll shape coefficient A3 is expressed as

[0148]

[0149] The roll shape coefficient A2 is expressed as

[0150]

[0151] The roll shape coefficient A1 is expressed as

[0152] A1=-A2L-3A3(L / 2) 2 -A3b 2 / 4

[0153] Where,

[0154] L is the length of the roller body, in mm,

[0155] s m The maximum roller shifting amount of the roller, in mm,

[0156] C1 is the roller-shaped negative electrode line position -s m The secondary crown of the roll gap in the continuous crowning section of the roll shape is in mm.

[0157] C2 is the roller-shaped positive electrode line position s m The secondary crown of the roll gap in the continuous crowning section of the roll shape is in mm.

[0158] b is the normal rolling width when the roller diameter difference is 0, in mm.

[0159] According to the definition of the positive and negative roll shifting directions of the rollers, C1>C2.

[0160] Specifically, in step S3), the calculated roll shape coefficients of the M-shaped quartic curve are expressed as follows:

[0161] The roll shape coefficient e2 is expressed as

[0162]

[0163] The roll shape coefficient e4 is expressed as

[0164]

[0165] Where,

[0166] L is the length of the roller body, in mm,

[0167] s m The maximum roller shifting amount of the roller, in mm,

[0168] B is the width of the strip that produces the middle wave, in mm.

[0169] △C B It is the no-load roll gap convexity compensation amount at the strip width that produces medium waves, in mm.

[0170] Specifically, in step S3), the roll shape coefficients of the roll shape curve of the variable crown work roll with the ability to control the middle wave are calculated and expressed as follows:

[0171] The roll shape coefficient a4 is expressed as

[0172]

[0173] The roll shape coefficient a3 is expressed as

[0174]

[0175] The roll shape coefficient a2 is expressed as

[0176]

[0177] The roll shape coefficient a1 is expressed as

[0178] a1=-e2L-e4L 3 / 2+A1=-a2L-3a3(L / 2) 2 -a3b 2 / 4-4a4(L / 2) 3 -a4(L / 2)b2

[0179] Where,

[0180] e2 and e4 are the roll shape coefficients of the M-shaped quartic curve symmetrical about the midpoint of the roll surface,

[0181] A1, A2, and A3 are the roll shape coefficients of the basic cubic CVC curve.

[0182] L is the length of the roller body,

[0183] s m is the maximum roll shifting amount of the roll,

[0184] C1 is the roller-shaped negative electrode line position -s m The secondary crown of the roll gap in the continuous crowning section of the roll shape is in mm.

[0185] C2 is the roller-shaped positive electrode line position s m The secondary crown of the roll gap in the continuous crowning section of the roll shape is in mm.

[0186] B is the width of the strip that produces the middle wave, in mm.

[0187] △C B The no-load roll gap crown compensation amount at the strip width position where the middle wave is generated is in mm.

[0188] b is the normal rolling width when the roller diameter difference is 0, in mm.

[0189] The roller profile of this invention relies on superimposing an M-shaped curve to achieve mid-wave control. The effectiveness of this control depends on the effective roll gap formed by the M-shaped curve within the strip width. The resulting integrated roller profile is presented as a quartic curve, while ensuring continuous crown control for varying widths. Regardless of strip width, the crown control range remains unchanged, resulting in a positive offset within the control range.

[0190] In this embodiment, when the mill design parameters are: L = 2000 mm, the maximum roll shifting amount s m =100mm and the no-load roll gap secondary crown adjustment range of the roller shape continuously variable crown section is [C1, C2] = [0.55mm, -0.05mm], the rolled strip width range is 1000mm ~ 1600mm, according to the design of the present invention, when the strip width B that produces the middle wave is 1250mm, the no-load roll gap crown compensation amount △C B The roller shape curves when the diameters of the working rolls are 0mm, 0.02mm and 0.04mm respectively and the roller diameter difference at both ends of the working roll is the same are as follows: Figure 4 shown.

[0191] Figure 4 Middle △CB When it is 0mm, it is a conventional cubic curve. When the strip width B that produces the middle wave is 1250mm, △C B When the diameters are 0 mm, 0.02 mm and 0.04 mm respectively, the M-shaped quartic curves symmetrical about the midpoint of the roller surface superimposed on the conventional cubic curve are as follows: Figure 5 As shown. B As the value increases, the difference between the roller edge control section and the three-dimensional CVC roller shape gradually increases, and its effect of compensating for mid-waves also gradually increases.

[0192] like Figures 6-8 The figure shows the roller gap comparison diagram formed by the three roller curves designed according to the present invention at the three roller shifting positions of s = -100mm, s = 0mm and s = 100mm. Figures 6-8 It can be seen that:

[0193] First, as the roll shifting position moves from the negative limit to the positive limit, the roll gap crown gradually decreases;

[0194] Second, the roll gap shape can be adjusted within the strip width without affecting the overall no-load roll gap crown;

[0195] Third, as the compensation amount ΔC B As the roll gap increases, the difference between the roll gap and the conventional three-stage CVC roll shape at nearly 1 / 4 becomes greater, and the difference in the crown of the no-load roll gap under the rolling width gradually increases;

[0196] Fourth, under different roller shifting positions, the crown compensation amount under the same width remains basically the same. At the positive limit roller shifting position s m and negative limit roller position s m The crown compensation amount is the same when the strip width is B1, and the no-load roll gap crown compensation amount △C at any strip width B1 position is B1 The no-load roll gap crown compensation △C at the strip width B position where the middle wave is generated B The relationship between

[0197]

[0198] Where,

[0199] △C B1 is the no-load roll gap crown compensation amount at any strip width B1 position, in mm,

[0200] B1 is the width of any strip, in mm,

[0201] L is the length of the roller body, in mm,

[0202] △C BThe no-load roll gap crown compensation amount at the strip width B position where the middle wave is generated, in mm.

[0203] B is the width of the strip that produces the middle wave, in mm.

[0204] The strip width will not exceed the roll width, and for all specifications of strip, the roll gap convexity within the strip width range at the same roll shifting position will be increased. The strip convexity compensation amount is the largest.

[0205] Depend on Figure 6 and Figure 8 It can be seen that when s = -100mm and s = 100mm, the nominal roll gap crown of the variable crown roll with mid-roll control capability and different triple CVC roll profiles is the same. For the same width, the increase in the unloaded roll gap crown is the same at the positive and negative extreme roll shifting positions, and the crown control range shifts. Without changing the roll shifting mode, it is beneficial to increase the roll gap crown under the same strip width at the same roll shifting position, thereby alleviating mid-roll at the stand exit.

[0206] Depend on Figure 7 It can be seen that at the non-roller shifting limit position, such as s=0, the full-length nominal roll gap convexity increases slightly; at the same roll shifting position, for the same width, the roll gap convexity under the strip width is increased to alleviate the waves at the frame outlet.

[0207] The core of the wave control adjustment of the roller curve of the present invention is to adjust the convexity compensation amount ΔC under the width B. B , while keeping the no-load convexity unchanged over the entire length range, adjust the convexity under the rolling width.

[0208] ΔC 1250 =0.02mm and ΔC 1250 =0.04mm roller curve as an example, for B = 1250mm, the roller gaps at the three roller shifting positions of s = -100mm, s = 0mm and s = 100mm are as follows: Figures 9-11 As shown, according to the convexity compensation amount △C under width B B When the rollers are in the same shifting position and the roller gap convexity at the same strip width position increases, the regulating ability is positively offset, which is beneficial to the control of the waves at the frame outlet.

[0209] If the middle wave is large, a larger △C is given when optimizing the roller shape design. B If the middle wave is small, a smaller △C is given when designing the roller shape. B If there is no middle wave, then △C B =0, at this time the roller shape of the present invention is a conventional three-times crowned roller shape.

[0210] The roll shape design method of the variable crown working roll with the ability to control the middle wave of the present invention can adjust the middle wave at any strip width position. Compared with the ordinary three-dimensional CVC roll shape, it does not change the secondary crown range of the no-load roll gap in the continuous variable crown section and does not change the plate shape control model. The roll gap crown at different strip width positions is increased, which not only achieves the purpose of middle wave control, but also ensures the overall expression of the roll shape of the variable crown working roll with the ability to control the middle wave. It is suitable for CNC grinding machines that use the overall polynomial method to enter the roll shape.

[0211] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A roll shape design method for a variable crown work roll with mid-wave control capability, characterized in that: The steps include: S1) setting the coordinate origin on the work roll, setting the conventional cubic CVC curve within the quadratic crown range of the work roll and the M-shaped quartic curve symmetrical about the midpoint of the roll surface; The conventional cubic CVC curve is expressed as follows y t1 (x)=R0+A1x+A2x 2 +A3x 3 Where, y t1 (x) is the working roll shape with continuously variable crown, R0 is the initial radius of the roller, A1 is the roll shape coefficient, A2 is the roll shape coefficient, A3 is the roll shape coefficient, x is the coordinate of the roller body, and the value range of x is [0, L]. L is the length of the roller body; The M-shaped quartic curve symmetrical about the midpoint of the roller surface is expressed as follows y t2 (x)=e2(x-L / 2) 2 +e4(x-L / 2) 4 -(e2L 2 / 4+e4L 4 / 16) Where, y t2 (x) is the working roll shape that is symmetrical about the midpoint of the roll surface, e2 is the roll shape coefficient, e4 is the roll shape coefficient, x is the coordinate of the roller body, and the value range of x is [0, L]. L is the length of the roller body; S2) Based on the conventional cubic CVC curve, in order to meet the need for no-load roll gap crown compensation at the internal width position of the work roll, an M-shaped quartic curve symmetrical about the midpoint of the roll surface is superimposed on the roll gap to obtain a variable crown work roll profile curve with the ability to control mid-wave. This achieves a positive offset of the secondary crown at different strip width positions, increases the roll gap crown at the same roll shifting position and different strip width positions, and achieves the purpose of controlling mid-wave at the stand exit; The roll profile curve of the variable crown work roll with mid-wave control capability is shown as follows: y t (x)=R0+a1x+a2x 2 +a3x 3 +a4x 4 Where, y t (x) is the roll shape of the variable crown work roll with the ability to control the middle wave. R0 is the initial radius of the roller, a1 is the roll shape coefficient, a2 is the roll shape coefficient, a3 is the roll shape coefficient, a4 is the roll shape coefficient, x is the coordinate of the roller body, and the value range of x is [0, L]. L is the length of the roller body; S3) determining the roll body length, the maximum roll shifting amount of the roll, the secondary convexity adjustment range of the no-load roll gap in the continuous variable convexity section of the roll shape, the strip width that generates medium waves, the no-load roll gap convexity compensation amount at the strip width position that generates medium waves, and the normal rolling width when the roll diameter difference is 0; by calculating the roll shape coefficients of the conventional cubic CVC curve in step S1) and the M-shaped quartic curve symmetrical about the midpoint of the roll surface, the roll shape coefficients of the variable convexity work roll roll shape curve with medium wave control capability in step S2) are obtained, thereby finally determining the variable convexity work roll roll shape curve with medium wave control capability.

2. The roll profile design method for a variable crown work roll with mid-wave control capability according to claim 1, characterized in that: In step S2), if the middle wave generated at the frame outlet is large, a larger no-load roll gap crown compensation amount needs to be given during roll shape design; if the middle wave generated at the frame outlet is small, a smaller no-load roll gap crown compensation amount needs to be given during roll shape design; if no middle wave is generated at the frame outlet, the no-load roll gap crown compensation amount given during roll shape design is 0.

3. The roll profile design method for a variable crown work roll with mid-wave control capability according to claim 2, characterized in that: In step S3), the calculated roll shape coefficients of the conventional cubic CVC curve are expressed as follows: The roll shape coefficient A3 is expressed as The roll shape coefficient A2 is expressed as The roll shape coefficient A1 is expressed as A1=-A2L-3A3(L / 2) 2 -A3b 2 / 4 Where, L is the length of the roller body, s m is the maximum roll shifting amount of the roll, C1 is the roller-shaped negative electrode line position -s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is C2 is the roller-shaped positive electrode line position s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is b is the normal rolling width when the roller diameter difference is 0.

4. The roll profile design method for a variable crown work roll with mid-wave control capability according to claim 3, characterized in that: In step S3), the calculated roll shape coefficients of the M-shaped quartic curve are expressed as follows: The roll shape coefficient e2 is expressed as The roll shape coefficient e4 is expressed as Where, L is the length of the roller body, s m is the maximum roll shifting amount of the roll, B is the strip width that produces the middle wave, △C B It is the no-load roll gap convexity compensation amount at the strip width that produces medium waves.

5. The roll profile design method for a variable crown work roll with mid-wave control capability according to claim 4, characterized in that: In step S3), the roll shape coefficients of the roll shape curve of the variable crown work roll with the ability to control the middle wave are calculated and expressed as follows: The roll shape coefficient a4 is expressed as The roll shape coefficient a3 is expressed as The roll shape coefficient a2 is expressed as The roll shape coefficient a1 is expressed as a1=-e2L-e4L 3 / 2+A1=-a2L-3a3(L / 2) 2 -a3b 2 / 4-4a4(L / 2) 3 -a4(L / 2)b 2 Where, e2 and e4 are the roll shape coefficients of the M-shaped quartic curve symmetrical about the midpoint of the roll surface, A1, A2, and A3 are the roll shape coefficients of the basic cubic CVC curve. L is the length of the roller body, s m is the maximum roll shifting amount of the roll, C1 is the roller-shaped negative electrode line position -s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is C2 is the roller-shaped positive electrode line position s m The roller shape continuously changes the crown section and the no-load roller gap secondary crown is B is the strip width that produces the middle wave, △C B is the no-load roll gap crown compensation amount at the strip width position where the middle wave is generated, b is the normal rolling width when the roller diameter difference is 0.

6. The roll profile design method for a variable crown work roll with mid-wave control capability according to claim 5, characterized in that: In step S3), for the final determined variable crown work roll profile with mid-wave control capability, the no-load roll gap crown compensation value ΔC at any strip width B1 position is B1 The no-load roll gap crown compensation △C at the strip width B position where the middle wave is generated B The relationship between Where, △C B1 is the no-load roll gap crown compensation at any strip width B1 position, B1 is the width of any strip, L is the length of the roller body, △C B The no-load roll gap crown compensation amount at the strip width B position where the middle wave is generated is: B is the width of the strip that produces the middle wave.

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