CN117574582B - Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling - Google Patents

Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling Download PDF

Info

Publication number
CN117574582B
CN117574582B CN202410056777.3A CN202410056777A CN117574582B CN 117574582 B CN117574582 B CN 117574582B CN 202410056777 A CN202410056777 A CN 202410056777A CN 117574582 B CN117574582 B CN 117574582B
Authority
CN
China
Prior art keywords
roll
coefficient
roll shape
beta
function
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202410056777.3A
Other languages
Chinese (zh)
Other versions
CN117574582A (en
Inventor
丁敬国
金利
孟令明
李刚
李旭
张殿华
Original Assignee
东北大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 东北大学 filed Critical 东北大学
Priority to CN202410056777.3A priority Critical patent/CN117574582B/en
Publication of CN117574582A publication Critical patent/CN117574582A/en
Application granted granted Critical
Publication of CN117574582B publication Critical patent/CN117574582B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B29/00—Counter-pressure devices acting on rolls to inhibit deflection of same under load, e.g. backing rolls ; Roll bending devices, e.g. hydraulic actuators acting on roll shaft ends
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention provides a support roller shape for fusing a sine function with a high-order curve for hot rolling and a design method thereof. In the process of the cooperation of the support roller and the convexity-changing working roller, the support roller is easy to generate serious uneven abrasion due to the special S-shaped curve of the working roller, so that the service life of the support roller is reduced, and the deformation of the roller generated in the service period affects the shape of the plate. In order to reduce the influence, the method comprehensively considers the curve characteristics of the working rolls, the adjusting capability of the supporting rolls to the shape and the uneven wear of the supporting rolls, and provides a method for designing the roll shape of the supporting rolls by fusing a sine function with a high-order curve for hot rolling. According to the method, the condition of uneven contact pressure distribution between the supporting roller and the variable convexity working roller is improved, when the supporting roller is matched with the variable convexity working roller, contact stress between the two ends of the supporting roller can be reduced, the phenomenon of stress concentration at the edge of the supporting roller is improved, uniform wear of the roller is realized, and the service life of the supporting roller is prolonged.

Description

Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling
Technical Field
The invention belongs to the technical field of plate and strip rolling, and relates to a supporting roller shape for fusing a sine function with a high-order curve for hot rolling and a design method thereof.
Background
The hot rolled strip is one of important steel materials necessary for national economy development, the level of the hot rolled strip product is also directly related to the whole level of the national steel industry, along with the development of the national industry, the hot rolled strip production has been from simple pursuing of yield to importance of product quality, the roll shape control technology plays an important role in the strip production, a reasonable roll shape curve is a precondition for obtaining a good sheet product, and the roll shape technology of a working roll and the roll shape technology of a supporting roll are also included, so that a schematic diagram of the cooperation of the supporting roll 1 and the working roll 2 in the rolling process is shown in fig. 1. In the field production, the theoretical service period of the support roller 1 is longer than that of the working roller 2, and the roller shape of the support roller is continuously changed in the whole service period due to continuous contact friction, so that the quality of the inner plate strip also fluctuates in the whole service period.
The variable convexity rolling mill developed by cimak in germany has good plate shape regulating capability, and the working roll shape curve is a cubic polynomial. Then scholars at home and abroad develop and research based on the roll shape curve of the working roll of the variable convexity rolling mill, and design an HVC working roll, wherein the roll shape curve of the working roll is a five-degree polynomial; smart Crown work rolls were designed, the roll shape curves of which are a polynomial and Sin function composite roll shape, and the curve forms of the work rolls are all S-shaped, as shown in FIG. 2. When the support rolls cooperate with these S-shaped work rolls 3, the most likely is a severe asymmetric wear condition. The special S-shaped curve of the variable convexity working roll enables contact stress between the rolls at the end part of the roll body of the supporting roll to be rapidly increased under the action of rolling force and the bending force of the working roll, so that micro cracks and even roll shoulder falling of the roll are generated. The supporting roller with the S-shaped curve is adopted in a general steel mill, and chamfers are added at the ends of the supporting roller to reduce the pressure of a stress concentration area where the supporting roller contacts with a working roller, the supporting roller curve combined by a plurality of sections of curves is not suitable for the integral polynomial type input roller-shaped numerical control grinding machine, and the field application effect is not ideal.
Disclosure of Invention
The invention aims to solve the technical problems of the prior art, and provides a high-order curve fused sine function support roller shape for hot rolling and a design method thereof, which change the contact mode of a working roller and a support roller of a rolling mill and reduce the peak stress of the end part of the support roller.
The high-order curve fusion sine function support roller shape for hot rolling is an octave polynomial fusion sine function curve, and the curve function of the support roller shape is shown in the following formula:
Wherein R (x) is a roll shape curve function equation of a support roll of the variable convexity rolling mill; r 0 is a basic roll shape radius coefficient, and the unit is mm; x is the axial coordinate of the supporting roller body of the rolling mill, the coordinate ranges [ (L w-Ls),2Ls];Lw and L s) are the length of the working roller half roller body and the length of the supporting roller half roller body respectively, the unit is mm, alpha is a characteristic angle, the value range is [360 DEG, 450 DEG ], A is a first roller shape coefficient, B is a second roller shape coefficient, C is a third roller shape coefficient, D is a fourth roller shape coefficient, E is a fifth roller shape coefficient, F is a sixth roller shape coefficient, G is a seventh roller shape coefficient, H is an eighth roller shape coefficient, beta 8 is a fourth basic roller shape coefficient, and the value range is [3.89744E-26,1.16923E-25].
Further, the second roll form factor B function is:
the third roll form factor C function is:
the fourth roll form factor D function is:
the fifth roll form factor E function is:
the eighth roll form factor H function is:
The basic roll shape radius coefficient R 0 is as follows:
R0＝Lw 2β2+Lw 4β4+Lw 6β6+Lw 8β8;
The sixth roll form factor F function is:
F＝β6+28Lw 2β8；
The seventh roll form factor G function is:
G＝-8Lwβ8；
Wherein C w1、Cw2 is the minimum secondary convexity regulating capability and the maximum secondary convexity regulating capability of the idle roll gap of the rolling mill respectively, and the unit mm; c h1、Ch2 is the minimum fourth convexity regulation and control capability and the maximum fourth convexity regulation and control capability of the idle roll gap of the rolling mill respectively, and the units are mm; lambda is the contact stress control coefficient; s m is the maximum roll lateral movement amount, and the unit is mm;2K is the width of the strip steel, the unit is mm, and DeltaC hk is the actual four-convexity regulating and controlling capability when the corresponding width of the strip steel is 2K; beta A is a first basic roll shape function, beta B is a second basic roll shape function, beta C is a third basic roll shape function, beta D is a fourth basic roll shape function, beta E is a fifth basic roll shape function, depending only on the backup roll basic roll shape factor and the work roll body length, as shown in the following formula:
Wherein, beta 2 is the first basic roll shape coefficient, beta 4 is the second basic roll shape coefficient, beta 6 is the third basic roll shape coefficient, beta 8 is the fourth basic roll shape coefficient, and the value range of beta 2 is [0,6.32099E-08]; the value range of beta 4 is [ -1.87289E-14, -7.49154E-14]; the value range of beta 6 is [9.8654E-20,1.97308E-19]; the value range of beta 8 is [3.89744E-26,1.16923E-25].
Further, the first roll form factor a function is:
Wherein, deltaD is the roller diameter difference, the unit is mm, and L w is the half roll length of the working roller, the unit is mm.
Further, the value range of the contact stress control coefficient lambda is [0.5,0.9], and the more seriously affected by the contact stress, the larger the contact stress control coefficient is selected.
The invention relates to a method for designing a roll shape of a support roll by fusing a sine function with a high-order curve for hot rolling, which is used for designing the roll shape of the support roll, and comprises the following steps:
Step 1: designing a curve function of the roller shape of the support roller;
Step 2: selecting design parameters according to the requirements of a rolling mill, wherein the design parameters comprise a first basic roll shape coefficient beta 2, a second basic roll shape coefficient beta 4, a third basic roll shape coefficient beta 6, a fourth basic roll shape coefficient beta 8 and a characteristic angle alpha;
Step 3: selecting a secondary convexity adjustment range [ C w1,Cw2 ] and a quaternary convexity adjustment range [ C h1,Ch2 ] of a rolling mill no-load roll gap according to the rolling mill requirement;
step 4: taking actual four convexity regulating and controlling capacity delta C hk when the corresponding strip steel width is 2K according to the requirement of a rolling mill;
Step 5: selecting a contact stress control coefficient lambda according to the contact stress peak values at the two ends of the supporting roller;
Step 6: calculating a second roll shape coefficient B, a third roll shape coefficient C, a fourth roll shape coefficient D, a fifth roll shape coefficient E, a sixth roll shape coefficient F, a seventh roll shape coefficient G, an eighth roll shape coefficient H and a basic roll shape radius coefficient R 0 according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll shape coefficients and the contact stress control coefficient;
step 7: and determining a roll shape coefficient and a basic roll shape coefficient obtained by combining the roll diameter difference according to the rolling mill requirement, and solving the first roll shape coefficient A.
Further, in the step 6, seven roll shape coefficients B, C, D, E, F, G, H and a base roll shape radius coefficient R 0 are calculated according to the following formula:
The second roll form factor B function is:
the third roll form factor C function is:
the fourth roll form factor D function is:
the fifth roll form factor E function is:
the eighth roll form factor H function is:
The initial radius R 0 of the supporting roller is as follows:
R0＝Lw 2β2+Lw 4β4+Lw 6β6+Lw 8β8;
The sixth roll form factor F function is:
F＝β6+28Lw 2β8；
The seventh roll form factor G function is:
G＝-8Lwβ8；
Wherein C w1、Cw2 is the minimum secondary convexity regulating capability and the maximum secondary convexity regulating capability of the idle roll gap of the rolling mill respectively, and the unit mm; c h1、Ch2 is the minimum fourth convexity regulation and control capability and the maximum fourth convexity regulation and control capability of the idle roll gap of the rolling mill respectively, and the units are mm; lambda is the contact stress control coefficient; s m is the maximum roll lateral movement amount, and the unit is mm;2K is the width of the strip steel, the unit is mm, and DeltaC hk is the actual four-convexity regulating and controlling capability when the corresponding width of the strip steel is 2K; beta A is a first basic roll shape function, beta B is a second basic roll shape function, beta C is a third basic roll shape function, beta D is a fourth basic roll shape function, beta E is a fifth basic roll shape function, depending only on the backup roll basic roll shape factor and the work roll body length, as shown in the following formula:
Wherein, beta 2 is the first basic roll shape coefficient, beta 4 is the second basic roll shape coefficient, beta 6 is the third basic roll shape coefficient, beta 8 is the fourth basic roll shape coefficient, and the value range of beta 2 is [0,6.32099E-08]; the value range of beta 4 is [ -1.87289E-14, -7.49154E-14]; the value range of [ beta 6 ] is [9.8654E-20,1.97308E-19]; the value range of beta 8 is [3.89744E-26,1.16923E-25].
Further, according to the seven roll form coefficients B, C, D, E, F, G and H and the basic roll form coefficient R 0, a first roll form coefficient A is solved, and the first roll form coefficient A function is as follows:
Wherein, deltaD is the roller diameter difference, the unit is mm, and L w is the half roll length of the working roller, the unit is mm.
The high-order curve fusion sine function support roller shape for hot rolling and the design method thereof have the following advantages:
The high-order support roller curve and the sine function are fused, the integral roller curve is improved, the condition of uneven pressure distribution between the working roller and the support roller is improved, the contact stress between the rollers at two ends of the support roller can be reduced, the phenomenon of stress concentration at the roller edge of the support roller is improved, the uniform wear of the roller is realized, and the service life of the support roller is prolonged.
Drawings
FIG. 1 is a schematic diagram of the cooperation of a backup roll and a work roll during rolling;
FIG. 2 is a schematic diagram of a variable crown work roll in the shape of an S;
FIG. 3 is a flow chart of a method of designing the shape of a backup roll of the high-order curve fusion sine function for hot rolling of the present invention;
FIG. 4 is a schematic view of a roller shape of a backup roller according to an embodiment of the present invention;
fig. 5 is a schematic diagram showing a comparison of the stress distribution curves between rollers according to an embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
The embodiment provides a support roller shape of a high-order curve fusion sine function for hot rolling, wherein the support roller shape is a curve of an octave polynomial fusion sine function, and the curve function of the support roller shape is shown in the following formula:
Wherein R (x) is a roll shape curve function equation of a support roll of the variable convexity rolling mill; r 0 is a basic roll shape radius coefficient, and the unit is mm; x is the axial coordinate of the roll body of the backup roll of the rolling mill, the coordinate ranges [ (L w-Ls),2Ls];Lw and L s) are the length of the half roll body of the working roll and the length of the half roll body of the backup roll respectively, the unit is mm, alpha is a characteristic angle, the value range is [360 DEG, 450 DEG ], A is a first roll shape coefficient, B is a second roll shape coefficient, C is a third roll shape coefficient, D is a fourth roll shape coefficient, E is a fifth roll shape coefficient, F is a sixth roll shape coefficient, G is a seventh roll shape coefficient, H is an eighth roll shape coefficient, beta 8 is a basic roll shape coefficient, and the value range is [3.89744E-26,1.16923E-25].
The roll shape coefficients B, C, D, E, F, G and H and the basic roll shape radius coefficient R 0 are related to the actual four-convexity regulation capability delta C hk under the corresponding strip steel width, the secondary and four-convexity regulation range [ C w1,Cw2]、[Ch1,Ch2 ] under the maximum roll traversing amount, the four basic roll shape coefficients beta 2、β4、β6、β8, the characteristic angle alpha and the contact stress control coefficient lambda.
In specific implementation, the second roll form factor B function is:
the third roll form factor C function is:
the fourth roll form factor D function is:
the fifth roll form factor E function is:
the eighth roll form factor H function is:
The basic roll shape radius coefficient R 0 is as follows:
R0＝Lw 2β2+Lw 4β4+Lw 6+β6+Lw 8β8;
The sixth roll form factor F function is:
F＝β6+28LLw 2β8；
The seventh roll form factor G function is:
G＝-8Lwβ8；
Wherein C w1、Cw2 is the minimum secondary convexity regulating capability and the maximum secondary convexity regulating capability of the idle roll gap of the rolling mill respectively, and the unit mm; c h1、Ch2 is the minimum fourth convexity regulation and control capability and the maximum fourth convexity regulation and control capability of the idle roll gap of the rolling mill respectively, and the units are mm; lambda is the contact stress control coefficient; s m is the maximum roll lateral movement amount, and the unit is mm;2K is the width of the strip steel, the unit is mm, and DeltaC hk is the actual four-convexity regulating and controlling capability when the corresponding width of the strip steel is 2K; beta A is a first basic roll shape function, beta B is a second basic roll shape function, beta C is a third basic roll shape function, beta D is a fourth basic roll shape function, beta E is a fifth basic roll shape function, depending only on the backup roll basic roll shape factor and the work roll body length, as shown in the following formula:
Wherein, beta 2 is the first basic roll shape coefficient, beta 4 is the second basic roll shape coefficient, beta 6 is the third basic roll shape coefficient, beta 8 is the fourth basic roll shape coefficient, and the value range of beta 2 is [0,6.32099E-08]; the value range of beta 4 is [ -1.87289E-14, -7.49154E-14]; the value range of beta 6 is [9.8654E-20,1.97308E-19]; the value range of beta 8 is [3.89744E-26,1.16923E-25].
Preferably, the contact stress control coefficient λ has a value in the range of [0.5,0.9], and the more severely affected by the contact stress, the larger the contact stress control coefficient is selected.
According to the second to seventh roll form coefficients and the four basic roll form coefficients, solving a first roll form coefficient A function, wherein the first roll form coefficient A function specifically comprises the following steps:
Wherein, deltaD is the roller diameter difference, the unit is mm, and L w is the half roll length of the working roller, the unit is mm.
As shown in fig. 3, an embodiment of the present invention provides a method for designing a roll shape of a backup roll for hot rolling by fusing a sinusoidal function with a higher order curve, where the method is used for designing the roll shape of the backup roll, and the method includes:
Step 1: designing a curve function of the roller shape of the support roller;
in specific implementation, a 2250mm rolling mill is adopted, the length of the working roll body is 2L w =2550 mm, the length of the supporting roll body is 2L s =2250 mm, and the roll lateral movement range is [ -150mm,150mm ], namely the maximum roll lateral movement amount s m =150 mm. The designed function of the roller shape curve of the support roller is shown in the following formula:
Step 2: selecting design parameters according to the requirements of a rolling mill, wherein the design parameters comprise a first basic roll shape coefficient beta 2, a second basic roll shape coefficient beta 4, a third basic roll shape coefficient beta 6, a fourth basic roll shape coefficient beta 8 and a characteristic angle alpha;
in practice, the base roll form factor β 2＝1.2642E-08、β4＝-3.12148E-14、β6＝1.08519E-19、β8 = 7.0154E-26; characteristic angle α=360°;
Step 3: selecting a secondary convexity adjustment range [ C w1,Cw2 ] and a quaternary convexity adjustment range [ C h1,Ch2 ] of a rolling mill no-load roll gap according to the rolling mill requirement;
In practice, C w1＝0.5,Cw2＝-0.5,Ch1＝-0.15,Ch2 = 0.15.
Step 4: taking actual four convexity regulating and controlling capacity delta C hk when the corresponding strip steel width is 2K according to the requirement of a rolling mill;
In specific implementation, the actual four-convexity regulating and controlling capability delta C hk =0.209 corresponding to the strip steel width of 2K=2000 mm is obtained according to the requirement of a rolling mill.
Step 5: selecting a contact stress control coefficient lambda according to the contact stress peak values at the two ends of the supporting roller;
in practice, λ=0.75.
Step 6: calculating a second roll shape coefficient B, a third roll shape coefficient C, a fourth roll shape coefficient D, a fifth roll shape coefficient E, a sixth roll shape coefficient F, a seventh roll shape coefficient G, an eighth roll shape coefficient H and a basic roll shape radius coefficient R 0 according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll shape coefficients and the contact stress control coefficient;
In the step 6, B, C, D, E, F, G and H and the basic roll radius coefficient R 0 are calculated according to the following formula:
The second roll form factor B function is:
the third roll form factor C function is:
the fourth roll form factor D function is:
the fifth roll form factor E function is:
the eighth roll form factor H function is:
The initial radius R 0 of the supporting roller is as follows:
R0＝Lw 2β2+Lw 4β4+Lw 6β6+Lw 8β8;
The sixth roll form factor F function is:
F＝β6+28Lw 2β8；
The seventh roll form factor G function is:
G＝-8Lwβ8；
Wherein C w1、Cw2 is the minimum secondary convexity regulating capability and the maximum secondary convexity regulating capability of the idle roll gap of the rolling mill respectively, and the unit mm; c h1、Ch2 is the minimum fourth convexity regulation and control capability and the maximum fourth convexity regulation and control capability of the idle roll gap of the rolling mill respectively, and the units are mm; lambda is the contact stress control coefficient; s m is the maximum roll lateral movement amount, and the unit is mm;2K is the width of the strip steel, the unit is mm, and DeltaC hk is the actual four-convexity regulating and controlling capability when the corresponding width of the strip steel is 2K; beta A is a first basic roll shape function, beta B is a second basic roll shape function, beta C is a third basic roll shape function, beta D is a fourth basic roll shape function, beta E is a fifth basic roll shape function, depending only on the backup roll basic roll shape factor and the work roll body length, as shown in the following formula:
Wherein, beta 2 is the first basic roll shape coefficient, beta 4 is the second basic roll shape coefficient, beta 6 is the third basic roll shape coefficient, beta 8 is the fourth basic roll shape coefficient, and the value range of beta 2 is [0,6.32099E-08]; the value range of beta 4 is [ -1.87289E-14, -7.49154E-14]; the value range of beta 6 is [3.89744E-26,1.16923E-25]; the value range of beta 8 is [9.8654E-20,1.97308E-19].
In practice, the seven roll form factors B, C, D, E, F, G, H and the base roll form radius factor R 0 are found as shown in table 1.
Table 1 roll form factor and base roll form radius factor tables.
Step 7: and determining seven roll form coefficients and four basic roll form coefficients obtained by combining the roll diameter differences according to the rolling mill requirements, and solving the roll form coefficient A.
In specific implementation, the first roll form factor a is solved by combining the seven roll form factors B, C, D, E, F, G and H and the basic roll form factor R 0, and the first roll form factor a function is:
Where Δd=0.296 is the roll diameter difference in mm and L w is the work roll half roll length in mm.
And finally, the eight roll shape coefficients are brought into a function formula of the roll shape curve of the support roll, so that the designed roll shape curve of the support roll can be obtained.
The roll profile of the backup roll, which is obtained by plotting the high-order curve for hot rolling and the sinusoidal function in accordance with the above parameters, is shown in fig. 4. In this embodiment, the obtained roller shape curves of the support roller are compared with the conventional roller shape curves of the support roller respectively matched with the working roller to simulate the hot rolling process, and the contact stress between the rollers is calculated and a distribution diagram is drawn in a finite element simulation mode, as shown in fig. 5, it can be seen from the diagram that the roller shape curves of the support roller determined by the method of the invention can really achieve the aims of reducing the contact stress between the rollers at two ends of the support roller, improving the stress concentration phenomenon at the edges of the support roller, realizing uniform wear of the roller and prolonging the service life of the support roller.
The foregoing description of the preferred embodiments of the invention is not intended to limit the scope of the invention, but rather to enable any modification, equivalent replacement, improvement or the like to be made without departing from the spirit and principles of the invention.

Claims (2)

1. The method for designing the roll shape of the support roll by fusing the higher-order curves for hot rolling is characterized by comprising the following steps of:
Step 1: designing a curve function of the roller shape of the support roller;
Step 2: selecting design parameters according to the requirements of a rolling mill, wherein the design parameters comprise a first basic roll shape coefficient beta 2, a second basic roll shape coefficient beta 4, a third basic roll shape coefficient beta 6, a fourth basic roll shape coefficient beta 8 and a characteristic angle alpha;
Step 3: selecting a secondary convexity adjustment range [ C w1,Cw2 ] and a quaternary convexity adjustment range [ C h1,Ch2 ] of a rolling mill no-load roll gap according to the rolling mill requirement;
step 4: taking actual four convexity regulating and controlling capacity delta C hk when the corresponding strip steel width is 2K according to the requirement of a rolling mill;
Step 5: selecting a contact stress control coefficient lambda according to the contact stress peak values at the two ends of the supporting roller;
Step 6: calculating a second roll shape coefficient B, a third roll shape coefficient C, a fourth roll shape coefficient D, a fifth roll shape coefficient E, a sixth roll shape coefficient F, a seventh roll shape coefficient G, an eighth roll shape coefficient H and a basic roll shape radius coefficient R 0 according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll shape coefficients and the contact stress control coefficient;
Step 7: determining a roll shape coefficient and a basic roll shape coefficient which are obtained by combining the roll diameter difference according to the rolling mill requirement, and solving a first roll shape coefficient A;
in the step 6, seven roll form coefficients B, C, D, E, F, G, H and a basic roll form radius coefficient R 0 are calculated according to the following formula:
The second roll form factor B function is:
the third roll form factor C function is:
the fourth roll form factor D function is:
the fifth roll form factor E function is:
the eighth roll form factor H function is:
The backup roll initial radius R 0 function:
R0＝Lw 2β2+Lw 4β4+Lw 6β6+Lw 8β8;
The sixth roll form factor F function is:
F＝β6+28Lw 2β8；
The seventh roll form factor G function is:
G＝-8Lwβ8；
Wherein C w1、Cw2 is the minimum secondary convexity regulating capability and the maximum secondary convexity regulating capability of the idle roll gap of the rolling mill respectively, and the unit mm; c h1、Ch2 is the minimum fourth convexity regulation and control capability and the maximum fourth convexity regulation and control capability of the idle roll gap of the rolling mill respectively, and the units are mm; lambda is the contact stress control coefficient; s m is the maximum roll lateral movement amount, and the unit is mm;2K is the width of the strip steel, the unit is mm, and DeltaC hk is the actual four-convexity regulating and controlling capability when the corresponding width of the strip steel is 2K; beta A is a first basic roll shape function, beta B is a second basic roll shape function, beta C is a third basic roll shape function, beta D is a fourth basic roll shape function, beta E is a fifth basic roll shape function, depending only on the backup roll basic roll shape factor and the work roll body length, as shown in the following formula:
Wherein, beta 2 is the first basic roll shape coefficient, beta 4 is the second basic roll shape coefficient, beta 6 is the third basic roll shape coefficient, beta 8 is the fourth basic roll shape coefficient, and the value range of beta 2 is [0,6.32099E-08]; the value range of beta 4 is [ -1.87289E-14, -7.49154E-14]; the value range of [ beta 6 ] is [9.8654E-20,1.97308E-19]; the value range of beta 8 is [3.89744E-26,1.16923E-25];
According to the seven roll form coefficients B, C, D, E, F, G and H and the basic roll form coefficient R 0, solving a first roll form coefficient A, wherein the first roll form coefficient A function is as follows:
Wherein, deltaD is the roller diameter difference, the unit is mm, and L w is the half roll length of the working roller, the unit is mm.
2. The method for designing a backup roll shape of a high-order curve fused sine function for hot rolling according to claim 1, wherein the value range of the contact stress control coefficient λ is [0.5,0.9], and the more severely affected the contact stress, the larger the contact stress control coefficient is selected.
CN202410056777.3A 2024-01-16 2024-01-16 Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling Active CN117574582B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202410056777.3A CN117574582B (en) 2024-01-16 2024-01-16 Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202410056777.3A CN117574582B (en) 2024-01-16 2024-01-16 Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling

Publications (2)

Publication Number Publication Date
CN117574582A CN117574582A (en) 2024-02-20
CN117574582B true CN117574582B (en) 2024-04-19

Family

ID=89864774

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202410056777.3A Active CN117574582B (en) 2024-01-16 2024-01-16 Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling

Country Status (1)

Country Link
CN (1) CN117574582B (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH1157821A (en) * 1997-08-27 1999-03-02 Kawasaki Steel Corp Intermediate roll of rolling and rolling shape control method
CN1743090A (en) * 2004-08-30 2006-03-08 宝山钢铁股份有限公司 Method for designing roller shape and milling roller for inhibiting higher-order wave shape
CN101758080A (en) * 2010-01-12 2010-06-30 北京科技大学 Strip-rolling variable contact support roller and processing method thereof
CN102688889A (en) * 2011-03-23 2012-09-26 宝山钢铁股份有限公司 Intermediate roll form of cold continuous mill
CN102716911A (en) * 2012-06-21 2012-10-10 首钢总公司 Composite supporting roll for hot-continuous rolling wide-strip-steel four-roll mill

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH1157821A (en) * 1997-08-27 1999-03-02 Kawasaki Steel Corp Intermediate roll of rolling and rolling shape control method
CN1743090A (en) * 2004-08-30 2006-03-08 宝山钢铁股份有限公司 Method for designing roller shape and milling roller for inhibiting higher-order wave shape
CN101758080A (en) * 2010-01-12 2010-06-30 北京科技大学 Strip-rolling variable contact support roller and processing method thereof
CN102688889A (en) * 2011-03-23 2012-09-26 宝山钢铁股份有限公司 Intermediate roll form of cold continuous mill
CN102716911A (en) * 2012-06-21 2012-10-10 首钢总公司 Composite supporting roll for hot-continuous rolling wide-strip-steel four-roll mill

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Axial Force Analysis and Roll Contour Configuration of Four-High CVC Mill;Guang-ming Liu et al.;Mathematical Problems in Engineering;20180104;全文 *
Investigation on contact pressure of backup roll with parabolic chamfer curve and intelligent modeling of plate crown in plate rilling process;Jingguo Ding et al.;The International Journal of Advanced Manufacturing Technology;20230718;全文 *
板带轧机通用变凸度板型控制技术;曹建国等;中南大学学报（自然科学版）;20201031;第51卷(第10期);全文 *

Also Published As

Publication number Publication date
CN117574582A (en) 2024-02-20

Similar Documents

Publication Publication Date Title
CN101229560B (en) Continuous variational convexity degree rolling mill back-up shaft
CN110202001B (en) Roll system preparation method for rolling ultrathin ultra-wide stainless steel product and rolling method
CN101811142B (en) Rolling control method of high-strength cold rolled steel strip
CN102728618B (en) Continuously variable crown (CVC) working roll contour and control method thereof
CN113319128B (en) Variable contact working roll and roll shape design method thereof
CN102744260A (en) Working roller considering both convexity and edge drop control of strip steel and design method for roller shape of working roller
CN112588838B (en) Asymmetric self-compensation rolling working roll suitable for short-stroke roll shifting and implementation method thereof
CN107052052A (en) Multi-model full duration board rolling Strip Shape Control working roll and design method
CN101486042A (en) Roll shape configuration method for whole-set precision rolling working roll
CN1062495C (en) Roller shape of axial movement capable of changing roll pass concavity and shape
CN113239494B (en) Design method of multistage working roll shape of HC cold rolling mill
CN113857265B (en) Method for designing roll shape of working roll of hot-rolled ultrathin strip based on multi-target cooperative control
CN117574582B (en) Method for designing roll shape of support roll by fusing high-order curves with sine functions for hot rolling
CN101211372A (en) Four-high mill plate control work roll curve design method for strip rolling
CN111881528B (en) Method for determining roll shape curve of CVC rolling mill backup roll with parabolic chamfer
CN101422785B (en) Method for adjusting middle-roller drunkenness in double cold reduction shadow-mask strip-steel machine
CN114700368A (en) Working roll shape for eliminating local high points of plate strip and design method
CN112588822B (en) Hot continuous rolling mill model and plate shape control method
CN111112343B (en) Secondary cold-rolled plate shape control method of six-roller UCM rolling mill
CN113688501B (en) Variable contact supporting roller shape design method considering rolling of plate strips with various widths
CN108435797B (en) Method for determining the surface profile of a roll and roll
CN110976518A (en) Method for prolonging roll period of 1250 hot continuous rolling finishing mill group
CN102335675B (en) Work roll capable of improving edge drop control capability
CN211027521U (en) Back-up roll capable of adapting to width change of strip steel
CN115475840A (en) Hot-rolled strip steel edge drop control method adaptive to deviation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant