CN117574582A - High-order curve fused sine function support roller shape for hot rolling and design method thereof - Google Patents
High-order curve fused sine function support roller shape for hot rolling and design method thereof Download PDFInfo
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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
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 roll shape control technology plays an important role in the production of the plate and strip, a reasonable roll shape curve is a precondition for obtaining a good plate product, and the roll shape control technology also comprises a work roll shape technology and a support roll shape technology, and as shown in fig. 1, a schematic diagram of the cooperation of a support roll 1 and a work roll 2 in the rolling process is shown. 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) A roll shape curve function equation of a support roll of the variable convexity rolling mill;R 0 the unit is mm for the radius coefficient of the basic roll shape;xthe axial coordinates of the roll body of the backup roll of the rolling mill are within the range of [ (], the coordinate range is shown as followsL w -L s )，2L s ]；L w AndL s the length of the working roller half roller body and the length of the supporting roller half roller body are respectively in mm;αis a characteristic angle, the value range is [360 DEG, 450 DEG ]]；AIs the first roll form factor of the roll,Bis the coefficient of the second roll shape,Cis the coefficient of the third roll shape,Dfor the fourth roll form factor,Eis the fifth roll form factor of the roll,Fis the coefficient of the shape of the sixth roller,Gfor the seventh roll form factor,His the eighth roll form factor;β 8 for the fourth basic roll shape coefficient, the value range is [3.89744E-26,1.16923E-25 ]]。
Further, the second roll form factorBThe function is:
；
the third oneRoll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the basic roll form radius coefficientR 0 The method comprises the following steps:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λIs a contact stress control coefficient;s m for maximum rollLateral movement amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll shape function, only the backup roll basic roll shape factor and the work roll body length are determined as follows:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；β 6 The value range is [9.8654E-20,1.97308E-19 ]]；β 8 The value range is [3.89744E-26,1.16923E-25 ]]。
Further, the first roll form factorAThe function is:
；
wherein delta isDIs the roll diameter difference, the unit ismm，L w Is the half length of the working roll, unitmm。
Further, the contact stress control coefficientλThe value range of (5) is [0.5,0.9 ]]The more severely affected by contact stress, the greater 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 the rolling mill, wherein the design parameters comprise a first basic roll shape coefficientβ 2 Form factor of second base rollβ 4 Form factor of third base rollβ 6 Form factor of fourth base rollβ 8 Characteristic angleα；
Step 3: selecting the secondary convexity regulating range of idle roll gap of rolling mill according to the requirement of rolling millC w1 ,C w2 ]And four convexity adjustment ranges [C h1 ,C h2 ]；
Step 4: the width of the corresponding strip steel is 2 according to the requirement of the rolling millKActual four convexity control ability delta at that timeC hk ；
Step 5: selecting a contact stress control coefficient according to the peak values of contact stress at two ends of the supporting rollerλ；
Step 6: calculating to obtain a second roll form coefficient according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll form coefficients and the contact stress control coefficientBForm factor of third rollerCFourth roll form factorDFifth roll form factorECoefficient of sixth roll shapeFSeventh roll form factorGAnd an eighth roll form factorHBasic roll form radius coefficientR 0 ；
Step 7: determining a roll shape coefficient and a basic roll shape coefficient obtained by combining roll diameter differences according to the requirements of a rolling mill, and obtaining a first roll shape coefficientAAnd solving.
Further, in the step 6, seven roll form coefficients are calculated according to the following formulaB、C、D、E、F、G、HBasic roll form radius coefficientR 0 ：
The second roll form factorBThe function is:
；
the third roll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the initial radius of the supporting rollerR 0 The method comprises the following steps:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λIs a contact stress control coefficient;s m for maximum roll traversing amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll shape function, only the backup roll basic roll shape factor and the work roll body length are determined as follows:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；[β 6 The value range is [9.8654E-20,1.97308E-19 ]]；β 8 The value range is [3.89744E-26,1.16923E-25 ]]。
Further, according to the seven roll form factorsB、C、D、E、F、GAndHbasic roll form factorR 0 For the first roll form factorASolving, namely, the first roll form coefficientAThe function is:
；
wherein delta isDIs the roll diameter difference, the unit ismm，L w Is the half length of the working roll, unitmm。
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) A roll shape curve function equation of a support roll of the variable convexity rolling mill;R 0 the unit is mm for the radius coefficient of the basic roll shape;xthe axial coordinates of the roll body of the backup roll of the rolling mill are within the range of [ (], the coordinate range is shown as followsL w -L s )，2L s ]；L w AndL s the length of the working roller half roller body and the length of the supporting roller half roller body are respectively in mm;αis a characteristic angle, the value range is [360 DEG, 450 DEG ]]；AIs the first roll form factor of the roll,Bis the coefficient of the second roll shape,Cis the coefficient of the third roll shape,Dis a fourth roller systemThe number of the product is the number,Eis the fifth roll form factor of the roll,Fis the coefficient of the shape of the sixth roller,Gfor the seventh roll form factor,His the eighth roll form factor;β 8 takes the basic roll shape coefficient as the basic roll shape coefficient, and the value range is [3.89744E-26,1.16923E-25 ]]。
Roll form factorB、C、D、E、F、GAndHbasic roll form radius coefficientR 0 Actual four-convexity regulation capability delta under the same corresponding strip steel widthC hk Secondary and four convexity adjusting range under maximum roll traversingC w1 ,C w2 ]、[C h1 ,C h2 ]Form factor of four basic rollsβ 2 、β 4 、β 6 、β 8 Characteristic angleαCoefficient of contact stress controlλThere is a relationship.
In particular implementation, the second roll form factorBThe function is:
；
the third roll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the basic roll form radius coefficientR 0 The method comprises the following steps:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λIs a contact stress control coefficient;s m for maximum roll traversing amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll shape function, only the backup roll basic roll shape factor and the work roll body length are determined as follows:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；β 6 The value range is [9.8654E-20,1.97308E-19 ]]；β 8 The value range is [3.89744E-26,1.16923E-25 ]]。
Preferably, the contact stress control coefficientλThe value range of (5) is [0.5,0.9 ]]The more severely affected by contact stress, the greater the contact stress control coefficient is selected.
Solving the first roll form factor according to the obtained second to seventh roll form factors and the four basic roll form factorsAThe function is specifically:
；
wherein delta isDIs the roll diameter difference, the unit ismm，L w Is the half length of the working roll, unitmm。
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, and the length of the working roll body is 2L w The length of the back-up roll is 2 =2550mmL s 2250mm, roll shift range [ -150mm,150mm]I.e. maximum roll-to-roll displacements m =150mm. 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 the rolling mill, wherein the design parameters comprise a first basic roll shape coefficientβ 2 Form factor of second base rollβ 4 Form factor of third base rollβ 6 Form factor of fourth base rollβ 8 Characteristic angleα；
In specific implementation, the basic roll form factorβ 2 =1.2642E-08、β 4 =-3.12148E-14、β 6 =1.08519E-19、β 8 = 7.0154E-26; characteristic angleα=360°；
Step 3: selecting the secondary convexity regulating range of idle roll gap of rolling mill according to the requirement of rolling millC w1 ,C w2 ]And four convexity adjustment ranges [C h1 ,C h2 ]；
In the case of a specific implementation of the method,C w1 =0.5，C w2 =-0.5，C h1 =-0.15，C h2 =0.15。
step 4: the width of the corresponding strip steel is 2 according to the requirement of the rolling millKActual four convexity control ability delta at that timeC hk ；
In specific implementation, the corresponding strip steel width 2 is obtained according to the requirements of a rolling millK=2000mmActual four convexity control ability delta at that timeC hk =0.209。
Step 5: selecting a contact stress control coefficient according to the peak values of contact stress at two ends of the supporting rollerλ；
In the case of a specific implementation of the method,λ=0.75。
step 6: calculating to obtain a second roll form coefficient according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll form coefficients and the contact stress control coefficientBForm factor of third rollerCFourth roll form factorDFifth roll form factorECoefficient of sixth roll shapeFSeventh roll form factorGEighth roll form factorHBasic roll form radius coefficientR 0 ；
In the step 6, the calculation is performed according to the following formulaB、C、D、E、F、GAndHbasic roll form radius coefficientR 0 ：
The second roll form factorBThe function is:
；
the third roll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the initial radius of the supporting rollerR 0 The method comprises the following steps:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λFor controlling contact stressPreparing coefficients;s m for maximum roll traversing amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll shape function, only the backup roll basic roll shape factor and the work roll body length are determined as follows:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；β 6 The value range is [3.89744E-26,1.16923E-25 ]]；β 8 The value range is [9.8654E-20,1.97308E-19 ]]。
In specific implementation, seven roll form coefficients are solvedB、C、D、E、F、G、HAnd a base roll form radius factorR 0 As shown in table 1.
Table 1 roll form factor and base roll form radius factor tables.
| Coefficients of | Calculated value |
| B | -3.76E-04 |
| C | -1.78E-08 |
| D | 1.58E-11 |
| E | -9.01E-15 |
| F | 3.30E-18 |
| G | 7.16E-22 |
| H | -3.22E-02 |
| R 0 | 8.94E-01 |
Step 7: determining seven roll form coefficients and four basic roll form coefficients obtained by combining roll diameter differences according to rolling mill requirements, and matching the roll form coefficientsAAnd solving.
In specific implementation, the seven roll form coefficients obtained are combinedB、C、D、E、F、GAndHbasic roll form factorR 0 For the first roll form factorASolving, namely, the first roll form coefficientAThe function is:
；
wherein delta isD=0.296 is the roll diameter difference in units ofmm，L w Is the half length of the working roll, unitmm。
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 (7)
1. The high-order curve fusion sine function support roll shape for hot rolling is characterized in that the support roll shape is a curve of eight-order polynomial fusion sine function, and the curve function of the support roll shape is shown in the following formula:
；
wherein,R(x) A roll shape curve function equation of a support roll of the variable convexity rolling mill;R 0 the unit is mm for the radius coefficient of the basic roll shape;xthe axial coordinates of the roll body of the backup roll of the rolling mill are within the range of [ (], the coordinate range is shown as followsL w -L s )，2L s ]；L w AndL s the length of the working roller half roller body and the length of the supporting roller half roller body are respectively in mm;αis a characteristic angle, the value range is [360 DEG, 450 DEG ]]；AIs the first roll form factor of the roll,Bis the coefficient of the second roll shape,Cis the coefficient of the third roll shape,Dfor the fourth roll form factor,Eis the fifth roll form factor of the roll,Fis the coefficient of the shape of the sixth roller,Gfor the seventh roll form factor,His the eighth roll form factor;β 8 for the fourth basic roll shape coefficient, the value range is [3.89744E-26,1.16923E-25 ]]。
2. The high-order curve fused sine function backup roll shape for hot rolling according to claim 1, wherein the second roll shape factorBThe function is:
；
the third roll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the basic roll form radius coefficientR 0 The method comprises the following steps:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λIs a contact stress control coefficient;s m for maximum roll traversing amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll shape function, only the backup roll basic roll shape factor and the work roll body length are determined as follows:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；β 6 The value range is [9 ].8654E-20，1.97308E-19]；β 8 The value range is [3.89744E-26,1.16923E-25 ]]。
3. The high-order curve fused sine function backup roll shape for hot rolling according to claim 2, wherein the first roll shape factorAThe function is:
；
wherein delta isDIs the roll diameter difference, the unit ismm，L w Is the half length of the working roll, unitmm。
4. The high-order curve fused sine function backup roll shape for hot rolling according to claim 1, wherein the contact stress control coefficientλThe value range of (5) is [0.5,0.9 ]]The more severely affected by contact stress, the greater the contact stress control coefficient is selected.
5. A method for designing a roll shape of a backup roll for hot rolling, which is a method for designing a roll shape of a backup roll according to any one of claims 1 to 4, comprising:
step 1: designing a curve function of the roller shape of the support roller;
step 2: selecting design parameters according to the requirements of the rolling mill, wherein the design parameters comprise a first basic roll shape coefficientβ 2 Form factor of second base rollβ 4 Form factor of third base rollβ 6 Form factor of fourth base rollβ 8 Characteristic angleα；
Step 3: selecting the secondary convexity regulating range of idle roll gap of rolling mill according to the requirement of rolling millC w1 ,C w2 ]And four convexity adjustment ranges [C h1 , C h2 ]；
Step 4: the width of the corresponding strip steel is 2 according to the requirement of the rolling millKActual four convexities at timeRegulatory capability deltaC hk ；
Step 5: selecting a contact stress control coefficient according to the peak values of contact stress at two ends of the supporting rollerλ；
Step 6: calculating to obtain a second roll form coefficient according to the actual fourth convexity regulation capability, the second convexity regulation range, the fourth convexity regulation range, the four basic roll form coefficients and the contact stress control coefficientBForm factor of third rollerCFourth roll form factorDFifth roll form factorECoefficient of sixth roll shapeFSeventh roll form factorGEighth roll form factorHBasic roll form radius coefficientR 0 ；
Step 7: determining a roll shape coefficient and a basic roll shape coefficient obtained by combining roll diameter differences according to the requirements of a rolling mill, and obtaining a first roll shape coefficientAAnd solving.
6. The method for designing a backup roll shape of a high-order curve fusion sine function for hot rolling according to claim 5, wherein seven roll shape coefficients are calculated in step 6 according to the following formulaB、C、D、E、F、G、HBasic roll form radius coefficientR 0 ：
The second roll form factorBThe function is:
；
the third roll form factorCThe function is:
；
the fourth roll form factorDThe function is:
；
the fifth roll form factorEThe function is:
；
the eighth roll form factorHThe function is:
；
the initial radius of the supporting rollerR 0 Function:
；
the sixth roll form factorFThe function is:
；
the seventh roll form factorGThe function is:
；
wherein the method comprises the steps ofC w1 、C w2 The minimum secondary convexity regulating and controlling capability and the maximum secondary convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；C h1 、C h2 The minimum fourth convexity regulating and controlling capability and the maximum fourth convexity regulating and controlling capability of the idle roll gap of the rolling mill are respectively provided with the unitsmm；λIs a contact stress control coefficient;s m for maximum roll traversing amount, unitmm；2KIs the width of the strip steel, the unit is mm, deltaC hk For the corresponding width of the strip steel is 2KActual four convexities regulation capability;β A as a function of the shape of the first base roll,β B as a function of the shape of the second base roll,β C as a function of the shape of the third base roll,β D as a function of the fourth basic roll shape,β E as a fifth basic roll-form functionOnly depends on the basic roll form factor of the supporting roll and the length of the roll body of the working roll, and the following formula is shown:
；
wherein,β 2 for the first basic roll form factor,β 4 is the second basic roll form factor of the roll,β 6 for the third basic roll form factor,β 8 for the fourth basic roll form factor,β 2 the value range is [0,6.32099E-08 ]]；β 4 The value range is [ -1.87289E-14, -7.49154E-14]；[β 6 The value range is [9.8654E-20,1.97308E-19 ]]；β 8 The value range is [3.89744E-26,1.16923E-25 ]]。
7. The method for designing a backup roll shape of a high-order curve fusion sine function for hot rolling according to claim 6, wherein the roll shape coefficients are determined based on seven roll shape coefficientsB、C、D、E、F、GAndHbasic roll form factorR 0 For the first roll form factorASolving, namely, the first roll form coefficientAThe function is:
；
wherein delta isDIs the roll diameter difference, the unit ismm，L w Is the half length of the working roll, unitmm。
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