CN117171904A - Roller system structure design method of stretch bending straightener based on elastic deformation of roller system - Google Patents

Abstract

The invention provides a roller system structure design method of a stretch bending straightener based on elastic deformation of a roller system, which comprises the following steps: selecting known parameters; setting an initial value: alpha = alpha ₀ ,β＝β ₀ ,γ＝γ ₀ The method comprises the steps of carrying out a first treatment on the surface of the Calculating the transverse distribution F of the elastic deformation of the upper roller system _1i (i＝1，2，…，n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the Calculating the transverse distribution F of the elastic deformation of the lower roller system _2i (i＝1，2，…，n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the Determination of the transverse distribution of the strip bending yieldAnd transverse distribution epsilon of elongation of strip _i (i＝1，2，…，n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the Calculating the maximum delta epsilon of the elongation difference of the strip _max The method comprises the steps of carrying out a first treatment on the surface of the Judgment discrimination type delta epsilon _max Whether the ratio is less than or equal to 0.0001; by the obtained maximum value delta epsilon of the elongation difference _max The structural design of the roller system of the stretch bending straightener is provided with a basis within the control precision of the elongation rate. According to the method, the influence of the elastic deformation of the roller system on the transverse distribution of the elongation of the strip is obtained by calculating the transverse distribution of the elastic deformation of the roller system. The design of a roller system mechanism of the stretching bending straightener can be guided, and the maximum value of the calculated elongation difference is within the elongation control precision, so that the transverse uniformity of the elongation and the flatness of the strip is improved, and the quality and the yield of the withdrawal and straightening products are greatly improved.

Description

Roller system structure design method of stretch bending straightener based on elastic deformation of roller system

Technical Field

The invention belongs to the technical field of strip steel finishing and processing, and particularly relates to a design method of a roller system structure of a stretching bending straightener based on elastic deformation of the roller system.

Background

The strip steel rolled by the cold rolling mill unit must be processed by finishing treatment to obtain high-quality qualified products. The finishing treatment is the last procedure of the finished strip steel, so that new defects cannot be generated, and scratch and plastic deformation cannot be generated on the surface of the strip steel. The finishing unit mainly performs the working procedures of splitting, withdrawal and straightening, rewinding, trimming, surface inspection, oiling and the like.

When the finishing machine set is used for withdrawal and straightening production, a stretching bending straightener is mainly used for eliminating bad plate shapes of the strip, such as double-side waves, single-side waves, middle waves, double-rib waves, warping, buckling, potential bad plate shapes and the like, so that the surface of the whole strip is smooth and clean.

The stretching-bending straightener is mainly of a two-bending one-straightening structure, and straightens the strip according to the elastic-plastic extension theory of the material. The straightening tension causes the strip to generate certain deformation, the deformation is elastic deformation, the strip continuously passes through the two bending units under the action of the straightening tension, the strip generates plastic deformation along the length direction and forms certain elongation, and the straightening units are used for compensating residual bending caused by the tension and the bending units, so that the non-uniformity of longitudinal internal stress distribution inside the strip is reduced, and the flatness of the strip is improved.

When the rigidity of the roller system is insufficient, the elastic deformation of the roller system can lead the rolling reduction of the bending unit to be distributed unevenly in the transverse direction, so that the plastic deformation generated by the strip along the length direction is distributed unevenly in the transverse direction, thereby affecting the uniformity of the transverse distribution of the elongation of the strip and affecting the transverse uniformity of the flatness of the strip.

Therefore, in order to improve the transverse uniformity of the elongation and flatness of the strip after the withdrawal and straightening, the roll system is required to have a certain rigidity, the elastic deformation is controlled in a certain range, and the development of a transverse division determination method of the elongation difference value of the stretch bending straightener based on the elastic deformation of the roll system is urgently required.

Disclosure of Invention

In order to solve the problem that when the rigidity of a roller system is insufficient, the elastic deformation of the roller system can cause uneven transverse distribution of rolling reduction of a bending unit, and uneven transverse distribution of plastic deformation generated by a strip along the length direction, thereby affecting the uniformity of transverse distribution of elongation of the strip and affecting the transverse uniformity of flatness of the strip, the invention provides a roller system structure design method of a stretching bending straightener based on the roller system elastic deformation.

The invention adopts the technical scheme that:

the design method of the roller system structure of the stretch bending straightener based on the elastic deformation of the roller system comprises the following steps:

first, selecting known parameters including the distance L between left and right pressing fulcrums _s Length of work roll L _w Diameter D of work roll _w Length of intermediate roll L _m Diameter D of intermediate roll _m Length L of backup roll _b Diameter D of backup roll _b Elastic modulus E of 1# roller ₁ Poisson's ratio v for roller # 1 ₁ Elastic modulus E of 2# roller ₂ Poisson's ratio v of roller # 2 ₂ Modulus of elasticity E of No. 4 roller ₄ Poisson's ratio v for roller # 4 ₄ Modulus of elasticity E of 5# roller ₅ Poisson's ratio v of roller # 5 ₅ Modulus of elasticity E of strip _s Poisson's ratio v of strip _s Yield of strip materialStrength sigma _s The thickness h of the plate and the width b of the plate and the roll gap t of the plate;

setting an initial value for an included angle alpha between the connecting line of the cross section central point of the working roll and the middle roll, an included angle beta between the connecting line of the cross section central point of the middle roll and the support roll and the horizontal direction, and an included angle gamma between the connecting line of the cross section central point of the middle roll and the middle support roll and the horizontal direction: alpha = alpha ₀ ,β＝β ₀ ,γ＝γ ₀ ；

Third, calculating the transverse distribution F of the elastic deformation of the upper roller system according to the known parameters in the first step and the second step _1i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The upper roll system is divided into n ₀ The number of units, i is the unit number;

Fourth, calculating the lateral distribution F of the elastic deformation of the lower roll system according to the known parameters in the first and second steps _2i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The lower roll system is divided into n ₀ The number of units, i is the unit number;

fifthly, determining the transverse distribution of the reverse bending rate of the strip according to the calculation results of the third step and the fourth stepThe upper and lower roller systems are divided into n ₀ The number of units, i is the unit number;

sixth, calculating the transverse distribution epsilon of the elongation of the strip _i (i＝1,2,…,n ₀ ) The upper and lower roller systems are divided into n ₀ The number of units, i is the unit number; calculating the maximum delta epsilon of the elongation difference of the strip _max ；

Seventh, according to the maximum value delta epsilon of the elongation difference of the strip obtained in the sixth step _max To make a determination of delta epsilon _max If the elongation difference is less than or equal to 0.0001, the qualification can be judged, and if the elongation difference is the maximum value delta epsilon of the strip _max > 0.0001, let α=ζ _α α ₀ ,β＝ξ _β β ₀ ,γ＝ξ _γ γ ₀ ，ξ _α ,ξ _β ,ξ _γ To adjust the coefficient, the third step is returned, and the third step is repeated to the seventh step until the difference of the elongation values of the strip material is the maximum value delta epsilon _max ≤0.0001；

Eighth stepStep, the obtained maximum value delta epsilon of the elongation difference _max The structural design of the roller system of the stretch bending straightener is provided with a basis within the control precision of the elongation rate.

In the third step, the transverse distribution F of the elastic deformation of the upper roller system is calculated by adopting a segmentation model influence function method _1i (i＝1,2,…,n ₀ ) In the fourth step, the method for transversely distributing the elastic deformation of the lower roller system is the same as the method for calculating the transverse distribution of the elastic deformation of the upper roller system.

Transverse distribution F of elastic deformation of upper roll system _1i (i＝1,2,…,n ₀ ) The specific method of (a) is as follows: the adopted stretch bending straightener roller system comprises a working roller, two middle rollers and three supporting rollers, wherein the working roller is arranged between the middle roller on the left side and the middle roller on the right side, and the middle part of the working roller is higher than the tops of the two middle rollers; the three support rollers are supported below the two middle rollers, the middle support roller is supported between the two middle rollers, the left support roller is supported on one side of the left middle roller, and the right support roller is supported on one side of the right middle roller;

then, assume that: assuming that the bending deflection of the first supporting roller is equal to 0, only the extrusion deformation of the supporting roller is considered; assume two, a plurality of short support rollers are equivalent to one long roller; the following steps are then carried out:

1) Cell division

Dividing the strip into n sections; the middle roller is divided into m in the length range of the supporting roller body ₀ A segment; the working rolls are divided into n in the length range of the middle roll body ₀ A segment;

2) Deflection solving

Deflection f of the ith unit of the 1# roller in the direction of the line connecting the 1# roller and the 2# roller section center point _1i The method comprises the following steps:

wherein alpha is _1ij -bending influence coefficient of the 1 st roll i-th element caused by straightening stress of the j-th element or inter roll pressure;

When y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₁ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₁ ,G ₁ Elastic modulus and shear elastic modulus of roller # 1, < -> Is the moment of inertia of the roll body of the roll No. 1, < + >> Is the cross section area of the roller body of the No. 1 roller, +.>

y _i Coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _w is the length of the working roll; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₁ poisson's ratio for roller # 1; d (D) _w Is the diameter of the working roll;

-rigid displacement of the axis of the ith unit of roller # 1;

wherein C is ₇ ，C ₈ The left end and the right end of the roller body of the No. 1 roller are rigidly displaced in the vertical direction;

Δy _j is the width of the j-th cell;

p _j straightening stress for a unit width of a j-th unit between the strip and the 1# roll;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller;

deflection f of ith unit of No. 2 roller in the direction of connecting center point of No. 1 roller and No. 2 roller section _2i The method comprises the following steps:

wherein alpha is _2ij -bending influence coefficient of the jth unit of the 2# roll ith unit caused by inter-roll pressure of the jth unit;

when y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₂ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₂ ,G ₂ Elastic modulus and shear elastic modulus of roller # 2, < -> Is the moment of inertia of the roll body of the roll No. 2, < + >> Is the cross-sectional area of the roller body of the No. 2 roller, +. >

y _i Coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _m is the length of the middle roller; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₂ poisson's ratio for roller # 2; d (D) _m Is the diameter of the middle roller;

-rigid displacement of the axis of the ith unit of roller # 2;

wherein C is ₅ ，C ₆ The left end and the right end of the roller body of the No. 2 roller are rigidly displaced in the vertical direction; c (C) ₉ ，C ₁₀ The left end axis and the right end axis of the roller body of the No. 2 roller are rigidly displaced in the horizontal direction;

Δy _j is the width of the j-th cell;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller; q _24j Is the j-th unit between the No. 2 roller and the No. 4 rollerContact stress between the rollers per unit width; q _25j Contact stress between rolls per unit width of the j-th unit between the roll # 2 and the roll # 5;

3) Coordinate equation of deformation between rollers

Amount of elastic crush delta between rolls of the ith unit between roll # 1 and roll # 2 _12i (i＝1,2,…,n ₀ ) The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _12i Contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

-the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 1 and roll # 2;

wherein v ₁ 、ν ₂ Poisson ratio of 1# roller and 2# roller; b _i The inter-roller contact crush half width for the i-th unit between roller # 1 and roller # 2 is expressed as:

E ₁ 、E ₂ the elastic modulus of the 1# roller and the 2# roller;

D _w is the diameter of the working roll; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 1# roller and the 2# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _1i ＝f _2i +δ _12i +ΔD _12i (i＝1,2,…,n ₀ ) (4)

wherein DeltaD _12i -1 # roller and 2# rollerOriginal gap or convexity of the ith cell in between;

f _1i deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

the force and moment balance equation for roller # 1 is:

q _12i contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

Δy _i is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

p _i straightening stress for a unit width of an ith unit between the strip and the 1 st roll;

the force and moment balance equation for roller # 2 is:

q _12i single for the ith unit between roller 1 and roller 2Contact stress between the bit width rollers; q _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4; q _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

Δy _i is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 4 _24i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4;

φ _24i -the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 4;

wherein v ₂ 、ν ₄ Poisson ratio of the 2# roller and the 4# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₄ the elastic modulus of the roller # 2 and the roller # 4;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 4# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(α-β)＝δ _24i +ΔD _24i (i＝1,2,…,m ₀ ) (12)

wherein DeltaD _24i -the original gap or convexity of the ith unit between roller # 2 and roller # 4;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

Alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 5 _25i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

φ _25i -the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 5;

wherein v ₂ 、ν ₅ Poisson ratio of the 2# roller and the 5# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₅ the elastic modulus of the roller # 2 and the roller # 5;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 5# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(180°-α-γ)＝δ _25i +ΔD _25i (i＝1,2,…,m ₀ ) (14)

wherein DeltaD _25i -the original gap or convexity of the ith unit between roller # 2 and roller # 5;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

4) Simultaneous solving

Combined type (3) - (14), total n ₀ +2m ₀ +6 linear equations, unknowns q _12i (i＝1,2,…,n ₀ ),q _24i (i＝1,2,…,m ₀ ),q _25i (i＝1,2,…,m ₀ ),C ₅ ,C ₆ ,C ₇ ,C ₈ ,C ₉ ,C ₁₀ The number is also n ₀ +2m ₀ +6, can solve the unit width roller contact stress directly;

thereby solving and obtaining the transverse distribution F of the elastic deformation of the upper roller system in the vertical direction _1i (i＝1,2,…,n ₀ )：

F _1i ＝f _1i sin(α)(i＝1,2,…,n ₀ ) (15)

Wherein: f (f) _1i Deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

alpha is the included angle between the connecting line of the cross section central points of the working roll and the middle roll and the horizontal direction.

The transverse distribution F of the elastic deformation of the upper roller system in the step 4) _1i (i＝1,2,…,n ₀ ) The solving process of (2) is as follows:

step 1, straightening stress transverse distribution p (y) of a given unit width;

step 2, assume a contact stress distribution q between rolls per unit width ₁₂ (y)、q ₂₄ (y) and q ₂₅ (y) is uniformly distributed;

step 3, calculating elastic flattening between the rollersCoefficient of influence phi _12i 、φ _24i And phi _25i；

Step 4, solving a linear equation set to obtain a new unit width roller contact stress distribution And

step 5, judging and judgingIf not, turning to step 6; if so, go to step 7;

step 6, order

Turning to step (3);

step 7, orderCalculating to obtain transverse distribution F of elastic deformation of upper roller system in vertical direction _1i (i＝1,2,L,n ₀ )；

In the step, p (y) is the unit width straightening stress;

q ₁₂ (y) is the contact stress between the rollers per unit width between roller # 1 and roller # 2;

q ₂₄ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 4;

q ₂₅ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 5.

In the fifth step, the strip material is reversely bent and transversely distributedIs provided with (1)The body method comprises the following steps:

the strip reverse bending rate transverse distribution caused by the transverse distribution of the elastic deformation of the upper roller system and the lower roller system is as follows:

wherein: f (F) _1i The elastic deformation of the ith unit of the upper roller system;

F _2i the elastic deformation of the ith unit of the lower roller system;

t is the roll gap;

D _w is the work roll diameter.

In the sixth step, the elongation of the strip is distributed transversely epsilon _i (i＝1,2,…,n ₀ ) The calculation formula of (2) is as follows:

wherein:to feed the original curvature of the plate strip.

h is the thickness of the strip steel;

p _i straightening stress for a unit width of an ith unit between the strip and the 1 st roll;

σ _s is the yield strength of the strip;

is the reverse bending rate of the ith element of the strip.

Maximum value delta epsilon of strip elongation difference _max The calculation formula of (2) is as follows:

Δε _max ＝max(|ε _i -ε _j |)，i＝1,2，…，n ₀ ；j＝1,2，…，n ₀ (18)

wherein: epsilon _i Elongation for the ith cell of the strip;

ε _j the elongation of the jth cell of the strip.

The invention has the beneficial effects that:

according to the method, the influence of the elastic deformation of the roller system on the transverse distribution of the elongation difference of the strip is obtained by calculating the transverse distribution of the elastic deformation of the roller system. The method can guide the design of the rigidity of the roller system of the stretching bending straightener, and ensures that the calculated elongation difference value is transversely distributed within the elongation control precision, thereby improving the transverse uniformity of the elongation and the flatness of the strip and greatly improving the quality and the yield of the withdrawal and straightening products.

Drawings

The present invention will be described in further detail with reference to the accompanying drawings.

FIG. 1 is a flow chart of the calculation of the lateral distribution of elongation differences.

FIG. 2 is a layout of a roll system of a stretch-bending leveler.

FIG. 3 is a diagram of a roll train of a stretch bender.

Fig. 4 is an angular relationship between the work roll, intermediate roll and backup roll.

Fig. 5 is a flowchart of calculation of the lateral distribution of the elastic deformation amount of the roll system.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Various structural schematic diagrams according to the disclosed embodiments of the present invention are shown in the accompanying drawings. The figures are not drawn to scale, wherein certain details are exaggerated for clarity of presentation and may have been omitted. The shapes of the various regions, layers and their relative sizes, positional relationships shown in the drawings are merely exemplary, may in practice deviate due to manufacturing tolerances or technical limitations, and one skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions as actually required.

Example 1:

in order to solve the problems that when the rigidity of the roller system is insufficient, the elastic deformation of the roller system can lead the rolling reduction of the bending unit to be uneven, and the plastic deformation generated by the strip along the length direction is uneven in transverse distribution, so that the uniformity of the transverse distribution of the elongation percentage of the strip is influenced and the transverse uniformity of the flatness of the strip is influenced, the invention provides a roller system structure design method of a stretching bending straightener based on the roller system elastic deformation, which is shown in the figures 1-5.

In the invention, as shown in fig. 1, a method for designing a roller system structure of a stretch bending straightener based on elastic deformation of the roller system comprises the following steps:

the design method of the roller system structure of the stretch bending straightener based on the elastic deformation of the roller system comprises the following steps:

first, selecting known parameters including the distance L between left and right pressing fulcrums _s Length of work roll L _w Diameter D of work roll _w Length of intermediate roll L _m Diameter D of intermediate roll _m Length L of backup roll _b Diameter D of backup roll _b Elastic modulus E of 1# roller ₁ Poisson's ratio v for roller # 1 ₁ Elastic modulus E of 2# roller ₂ Poisson's ratio v of roller # 2 ₂ Modulus of elasticity E of No. 4 roller ₄ Poisson's ratio v for roller # 4 ₄ Modulus of elasticity E of 5# roller ₅ Poisson's ratio v of roller # 5 ₅ Modulus of elasticity E of strip _s Poisson's ratio v of strip _s Strip yield strength sigma _s The thickness h of the plate and the width b of the plate and the roll gap t of the plate;

setting an initial value for an included angle alpha between the connecting line of the cross section central point of the working roll and the middle roll, an included angle beta between the connecting line of the cross section central point of the middle roll and the support roll and the horizontal direction, and an included angle gamma between the connecting line of the cross section central point of the middle roll and the middle support roll and the horizontal direction: alpha = alpha ₀ ,β＝β ₀ ,γ＝γ ₀ ；

A third step of counting according to the known parameters of the first and second stepsCalculating the transverse distribution F of the elastic deformation of the roller system _1i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The upper roll system is divided into n ₀ The number of units, i is the unit number;

fourth, calculating the lateral distribution F of the elastic deformation of the lower roll system according to the known parameters in the first and second steps _2i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The lower roll system is divided into n ₀ The number of units, i is the unit number;

fifthly, determining the transverse distribution of the reverse bending rate of the strip according to the calculation results of the third step and the fourth stepThe upper and lower roller systems are divided into n ₀ The number of units, i is the unit number;

sixth, calculating the transverse distribution epsilon of the elongation of the strip _i (i＝1,2,…,n ₀ ) The upper and lower roller systems are divided into n ₀ The number of units, i is the unit number; calculating the maximum delta epsilon of the elongation difference of the strip _max ；

Seventh, according to the maximum value delta epsilon of the elongation difference of the strip obtained in the sixth step _max To make a determination of delta epsilon _max If the elongation difference is less than or equal to 0.0001, the qualification can be judged, and if the elongation difference is the maximum value delta epsilon of the strip _max > 0.0001, let α=ζ _α α ₀ ,β＝ξ _β β ₀ ,γ＝ξ _γ γ ₀ ，ξ _α ,ξ _β ,ξ _γ To adjust the coefficient, the third step is returned, and the third step is repeated to the seventh step until the difference of the elongation values of the strip material is the maximum value delta epsilon _max ≤0.0001；

Eighth step, the maximum value delta epsilon of the elongation difference is obtained _max The structural design of the roller system of the stretch bending straightener is provided with a basis within the control precision of the elongation rate.

According to the method, the influence of the elastic deformation of the roller system on the transverse distribution of the elongation of the strip is obtained by calculating the transverse distribution of the elastic deformation of the roller system. The roller system structure design of the stretching bending straightener can be guided, and the maximum value of the calculated elongation difference is within the elongation control precision, so that the transverse uniformity of the elongation and the flatness of the strip is improved, and the quality and the yield of the withdrawal and straightening products are greatly improved.

The data calculated by the method provided by the invention is applied to the actual roller system structure design of the straightener, so that the plate strip operated by the straightener has good withdrawal and straightening effects, the elongation control precision meets the requirements, the quality is completely qualified, and the yield of the plate strip is effectively improved.

The invention develops a roller system structure design method of a stretching bending straightener based on roller system elastic deformation, and proper roller system rigidity is obtained by designing the roller system structure, so that the transverse uniformity of the elongation and flatness of the straightened strip is improved, and the quality and the yield of the withdrawal and straightening products are greatly improved.

Example 2:

based on the embodiment 1, in the present embodiment, preferably, in the third step, the transverse distribution F of the elastic deformation of the upper roller system is calculated by using a split model influence function method _1i (i＝1,2,…,n ₀ ) In the fourth step, the method for transversely distributing the elastic deformation of the lower roller system is the same as the method for calculating the transverse distribution of the elastic deformation of the upper roller system.

In the process of withdrawal and straightening, the shape of a load roll gap is directly determined by the elastic deformation of the bending unit and the straightening unit, and the quality of the plate shape after withdrawal and straightening is influenced, so that the elastic deformation of the roll system is necessary to be calculated. Existing roller system elastic deformation calculations can be divided into three categories: an integral model analysis method, a segmentation model influence function method and a numerical calculation method. The invention adopts a segmentation model influence function method to calculate.

In the invention, as shown in fig. 2, reference numeral 1 in the drawing is a working roller and is also a 1# roller, reference numeral 2 is a middle roller at the left side in fig. 2 and is also a 2# roller; reference numeral 3 is a middle roller on the right in fig. 2, which is also a 3# roller; reference numeral 4 is a support roller on the right in fig. 2, also a 4# roller; reference numeral 5 is a supporting roller in the middle of fig. 2, also a 5# roller; reference numeral 6 is a support roller on the left in fig. 2, also a 6# roller.

In the invention, the roller system of the stretch bending straightener is arranged as shown in figure 2, the roller system is stressed as shown in figure 3, and the angles among the working roller, the middle roller and the supporting roller are closedAs shown in fig. 4. Number 1 is the work roll, numbers 2 and 3 are the intermediate rolls, and numbers 4, 5 and 6 are the backup rolls. Then the elastic deformation of the upper roll system is transversely distributed F according to the roll system layout of the stretch bending straightener as shown in figure 2 _1i (i＝1,2,…,n ₀ ) The specific method for calculating comprises the following steps:

as shown in fig. 2, the adopted stretch bending straightener roller system comprises a working roller 1, two middle rollers and three supporting rollers, wherein the working roller 1 is arranged between a left middle roller 2 and a right middle roller 3, and the middle part of the working roller 1 is higher than the tops of the two middle rollers; three support rollers are supported below the two intermediate rollers, a middle support roller 5 is supported between the two intermediate rollers, a left support roller 6 is supported on one side of the left intermediate roller 3, and a right support roller 4 is supported on one side of the right intermediate roller 2;

then, assume that: assuming that the bending deflection of the first supporting roller is equal to 0, only the extrusion deformation of the supporting roller is considered; assume two, a plurality of short support rollers are equivalent to one long roller; the following steps are then carried out:

1) Cell division

Dividing the strip into n sections; the middle roller is divided into m in the length range of the supporting roller body ₀ A segment; the working rolls are divided into n in the length range of the middle roll body ₀ A segment;

2) Deflection solving

Deflection f of the ith unit of the 1# roller in the direction of the line connecting the 1# roller and the 2# roller section center point _1i The method comprises the following steps:

wherein alpha is _1ij -bending influence coefficient of the 1 st roll i-th element caused by straightening stress of the j-th element or inter roll pressure;

when y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₁ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₁ ,G ₁ Elastic modulus and shear elastic modulus of roller # 1, < -> Is the moment of inertia of the roll body of the roll No. 1, < + >> Is the cross section area of the roller body of the No. 1 roller, +.>

y _i Coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _w is the length of the working roll; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₁ poisson's ratio for roller # 1; d (D) _w Is the diameter of the working roll;

-rigid displacement of the axis of the ith unit of roller # 1;

wherein C is ₇ ，C ₈ The left end and the right end of the roller body of the No. 1 roller are rigidly displaced in the vertical direction;

Δy _j is the width of the j-th cell;

p _j straightening stress for a unit width of a j-th unit between the strip and the 1# roll;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller;

Deflection f of ith unit of No. 2 roller in the direction of connecting center point of No. 1 roller and No. 2 roller section _2i The method comprises the following steps:

wherein alpha is _2ij -bending influence coefficient of the jth unit of the 2# roll ith unit caused by inter-roll pressure of the jth unit;

when y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₂ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₂ ,G ₂ Elastic modulus and shear elastic modulus of roller # 2, < -> Is the moment of inertia of the roll body of the roll No. 2, < + >> Is the cross-sectional area of the roller body of the No. 2 roller, +.>

y _i Coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _m is the length of the middle roller; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₂ poisson's ratio for roller # 2; d (D) _m Is the diameter of the middle roller;

-rigid displacement of the axis of the ith unit of roller # 2;

wherein C is ₅ ，C ₆ The left end and the right end of the roller body of the No. 2 roller are rigidly displaced in the vertical direction; c (C) ₉ ，C ₁₀ The left end axis and the right end axis of the roller body of the No. 2 roller are rigidly displaced in the horizontal direction; />

Δy _j Is the width of the j-th cell;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller; q _24j Contact stress between rolls per unit width of the j-th unit between the roll # 2 and the roll # 4; q _25j Contact stress between rolls per unit width of the j-th unit between the roll # 2 and the roll # 5;

3) Coordinate equation of deformation between rollers

Amount of elastic crush delta between rolls of the ith unit between roll # 1 and roll # 2 _12i (i＝1,2,…,n ₀ ) The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _12i Contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

-the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 1 and roll # 2;

wherein v ₁ 、ν ₂ Poisson ratio of 1# roller and 2# roller; b _i The inter-roller contact crush half width for the i-th unit between roller # 1 and roller # 2 is expressed as:

E ₁ 、E ₂ the elastic modulus of the 1# roller and the 2# roller;

D _w is the diameter of the working roll; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 1# roller and the 2# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _1i ＝f _2i +δ _12i +ΔD _12i (i＝1,2,…,n ₀ ) (4)

wherein DeltaD _12i -the original gap or convexity of the ith unit between roller # 1 and roller # 2;

f _1i deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

f _2i an ith unit of the No. 2 roller in the direction of connecting the No. 1 roller and the No. 2 roller section center pointIs used for the deflection of the unit;

the force and moment balance equation for roller # 1 is:

q _12i contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

Δy _i Is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

p _i straightening stress for a unit width of an ith unit between the strip and the 1 st roll;

the force and moment balance equation for roller # 2 is:

/>

q _12i contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2; q _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4; q _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

Δy _i is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 4 _24i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4;

-the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 4;

Wherein v ₂ 、ν ₄ Poisson ratio of the 2# roller and the 4# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₄ the elastic modulus of the roller # 2 and the roller # 4;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 4# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(α-β)＝δ _24i +ΔD _24i (i＝1,2,…,m ₀ ) (12)

in the formula deltaD _24i -the original gap or convexity of the ith unit between roller # 2 and roller # 4;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 5 _25i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein q is _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

-the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 5;

wherein v ₂ 、ν ₅ Poisson ratio of the 2# roller and the 5# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₅ the elastic modulus of the roller # 2 and the roller # 5;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 5# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(180°-α-γ)＝δ _25i +ΔD _25i (i＝1,2,…,m ₀ ) (14)

wherein DeltaD _25i -the original gap or convexity of the ith unit between roller # 2 and roller # 5;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

4) Simultaneous solving

Combined type (3) - (14), total n ₀ +2m ₀ +6 linear equations, unknowns q _12i (i＝1,2,…,n ₀ ),q _24i (i＝1,2,…,m ₀ ),q _25i (i＝1,2,…,m ₀ ),C ₅ ,C ₆ ,C ₇ ,C ₈ ,C ₉ ,C ₁₀ The number is also n ₀ +2m ₀ +6, can solve the unit width roller contact stress directly;

thereby solving and obtaining the transverse distribution F of the elastic deformation of the upper roller system in the vertical direction _1i (i＝1,2,…,n ₀ )：

F _1i ＝f _1i sin(α)(i＝1,2,…,n ₀ ) (15)

Wherein: f (f) _1i Deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

alpha is the included angle between the connecting line of the cross section central points of the working roll and the middle roll and the horizontal direction.

As shown in FIG. 5, the upper roll system elastic deformation amount in the step 4) is transversely distributed F _1i (i＝1,2,…,n ₀ ) The solving process of (2) is as follows:

step 1, straightening stress transverse distribution p (y) of a given unit width;

step 2, assume a contact stress distribution q between rolls per unit width ₁₂ (y)、q ₂₄ (y) and q ₂₅ (y) is uniformly distributed;

step 3, calculating the elastic flattening influence coefficient between the rollersAnd->

Step 4, solving a linear equation set to obtain a new unit width roller contact stress distribution And

step 5, judging and judgingIf not, turning to step 6; if so, go to step 7;

step 6, order

Turning to step (3);

step 7, orderCalculating to obtain transverse distribution F of elastic deformation of upper roller system in vertical direction _1i (i＝1,2,L,n ₀ )；

In the step, p (y) is the unit width straightening stress;

q ₁₂ (y) is the contact stress between the rollers per unit width between roller # 1 and roller # 2;

q ₂₄ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 4;

q ₂₅ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 5.

In the fourth step of the present invention, the lower roll is calculatedTransverse distribution F of elastic deformation _2i (i＝1,2,…,n ₀ ) And the third step calculates the transverse distribution F of the elastic deformation of the upper roller system _1i (i＝1,2,…,n ₀ ) The same method as in (a).

Preferably, in the fifth step, the strip has a transverse distribution of the rate of reverse bendingThe specific method of (a) is as follows:

the strip reverse bending rate transverse distribution caused by the transverse distribution of the elastic deformation of the upper roller system and the lower roller system is as follows:

wherein: f (F) _1i The elastic deformation of the ith unit of the upper roller system;

F _2i The elastic deformation of the ith unit of the lower roller system;

t is the roll gap;

D _w is the work roll diameter.

In the sixth step, the elongation of the strip is distributed transversely epsilon _i (i＝1,2,…,n ₀ ) The calculation formula of (2) is as follows:

wherein:to feed the original curvature of the plate strip.

h is the thickness of the strip steel;

p _i straightening stress for a unit width of an ith unit between the strip and the 1 st roll;

σ _s is the yield strength of the strip;

is the reverse bending rate of the ith element of the strip.

Maximum value delta epsilon of strip elongation difference _max The calculation formula of (2) is as follows:

Δε _max ＝max(|ε _i -ε _j |)，i＝1,2，…，n ₀ ；j＝1,2，…，n ₀ (18)

wherein: epsilon _i Elongation for the ith cell of the strip;

ε _j the elongation of the jth cell of the strip.

And calculating the transverse distribution of the elastic deformation of the roller system to obtain the influence of the elastic deformation on the transverse distribution of the elongation of the strip. The roller system structure design of the stretching bending straightener can be guided, and the maximum value of the calculated elongation difference is within the elongation control precision, so that the transverse uniformity of the elongation and the flatness of the strip is improved, and the quality and the yield of the withdrawal and straightening products are greatly improved.

If applied to a certain automobile plate finishing unit, the thickness h=1.5 mm of the strip steel and the yield strength sigma _s =400 MPa, straightening stress p _i Work roll diameter D =35 MPa _w =40 mm, intermediate roll diameter D _m Support roller diameter D =50mm _b Distance L between left and right depressing fulcrums =65 mm _s Length of work roll L =2150 mm _w =2110 mm, intermediate roll length L _m 2110mm, backing roll length L _b 2040mm, roll gap t=39 mm.

Through calculation, an included angle alpha=43.2 degrees between the connecting line of the cross section central point of the working roll and the middle roll and the horizontal direction is obtained, an included angle beta=21.08 degrees between the connecting line of the cross section central point of the middle roll and the support roll and the horizontal direction is obtained, an included angle gamma=60.92 degrees between the connecting line of the cross section central point of the middle roll and the middle support roll and the horizontal direction is obtained, the maximum value of the elastic variable of the roll system is 0.07535mm, and the maximum difference value of the generated elongation is 0.00009223. In the contract, the elongation control precision guarantee value is 0.01%, and the roll system rigidity meets the elongation precision requirement.

After the plate and strip tension leveler is applied on site, the plate and strip tension leveler has good tension leveler effect, the elongation control precision meets the requirement, and the quality is completely qualified.

The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

The above examples are merely illustrative of the present invention and are not meant to limit the scope of the present invention, and all designs that are the same or similar to the present invention are within the scope of the present invention. The device structure and method steps not described in detail in the present invention are all prior art, and will not be further described in the present invention.

Claims (7)

1. The design method of the roller system structure of the stretch bending straightener based on the elastic deformation of the roller system is characterized by comprising the following steps: the method comprises the following steps:

first, selecting known parameters including the distance L between left and right pressing fulcrums _s Length of work roll L _w Diameter D of work roll _w Length of intermediate roll L _m Diameter D of intermediate roll _m Length L of backup roll _b Diameter D of backup roll _b Elastic modulus E of 1# roller ₁ Poisson's ratio v for roller # 1 ₁ Elastic modulus E of 2# roller ₂ Poisson's ratio v of roller # 2 ₂ Modulus of elasticity E of No. 4 roller ₄ Poisson's ratio v for roller # 4 ₄ Modulus of elasticity E of 5# roller ₅ Poisson's ratio v of roller # 5 ₅ Modulus of elasticity E of strip _s Poisson's ratio v of strip _s Strip yield strength sigma _s The thickness h of the plate and the width b of the plate and the roll gap t of the plate;

setting an initial value for an included angle alpha between the connecting line of the cross section central point of the working roll and the middle roll, an included angle beta between the connecting line of the cross section central point of the middle roll and the support roll and the horizontal direction, and an included angle gamma between the connecting line of the cross section central point of the middle roll and the middle support roll and the horizontal direction: alpha = alpha ₀ ,β＝β ₀ ,γ＝γ ₀ ；

Third, calculating the transverse distribution F of the elastic deformation of the upper roller system according to the known parameters in the first step and the second step _1i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The upper roll system is divided into n ₀ The number of units, i is the unit number;

fourth, calculating the lateral distribution F of the elastic deformation of the lower roll system according to the known parameters in the first and second steps _2i (i＝1,2,…,n ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the The lower roll system is divided into n ₀ The number of units, i is the unit number;

fifthly, determining the transverse distribution of the reverse bending rate of the strip according to the calculation results of the third step and the fourth stepThe upper and lower roller systems are divided into n ₀ The number of units, i is the unit number;

sixth, calculating the transverse distribution epsilon of the elongation of the strip _i (i＝1,2,…,n ₀ ) The upper and lower roller systems are divided into n ₀ The number of units, i is the unit number; calculating the maximum delta epsilon of the elongation difference of the strip _max ；

Seventh, according to the maximum value delta epsilon of the elongation difference of the strip obtained in the sixth step _max To make a determination of delta epsilon _max If the elongation difference is less than or equal to 0.0001, the qualification can be judged, and if the elongation difference is the maximum value delta epsilon of the strip _max > 0.0001, let α=ζ _α α ₀ ,β＝ξ _β β ₀ ,γ＝ξ _γ γ ₀ ，ξ _α ,ξ _β ,ξ _γ To adjust the coefficient, the third step is returned, and the third step is repeated to the seventh step until the difference of the elongation values of the strip material is the maximum value delta epsilon _max ≤0.0001；

Eighth step, the maximum value delta epsilon of the elongation difference is obtained _max The structural design of the roller system of the stretch bending straightener is provided with a basis within the control precision of the elongation rate.

2. The roll system structural design method of the stretch bending straightener based on roll system elastic deformation as claimed in claim 1, wherein the method comprises the following steps: in the third step, the transverse distribution F of the elastic deformation of the upper roller system is calculated by adopting a segmentation model influence function method _1i (i＝1,2,…,n ₀ ) In the fourth step, the method for transversely distributing the elastic deformation of the lower roller system is the same as the method for calculating the transverse distribution of the elastic deformation of the upper roller system.

3. The roll system structural design method of the stretch bending straightener based on roll system elastic deformation as claimed in claim 2, wherein the method comprises the following steps: transverse distribution F of elastic deformation of upper roll system _1i (i＝1,2,…,n ₀ ) The specific method of (a) is as follows: the adopted stretch bending straightener roller system comprises a working roller (1), two middle rollers and three supporting rollers, wherein the working roller (1) is arranged between the middle roller (2) on the left side and the middle roller (3) on the right side, and the middle part of the working roller (1) is higher than the tops of the two middle rollers; the three support rollers are supported below the two middle rollers, the middle support roller (5) is supported between the two middle rollers, the left support roller (6) is supported on one side of the left middle roller (3), and the right support roller (4) is supported on one side of the right middle roller (2);

then, assume that: assuming that the bending deflection of the first supporting roller is equal to 0, only the extrusion deformation of the supporting roller is considered; assume two, a plurality of short support rollers are equivalent to one long roller; the following steps are then carried out:

1) Cell division

Dividing the strip into n sections; the middle roller is divided into m in the length range of the supporting roller body ₀ A segment; the working rolls are divided into n in the length range of the middle roll body ₀ A segment;

2) Deflection solving

Deflection f of the ith unit of the 1# roller in the direction of the line connecting the 1# roller and the 2# roller section center point _1i The method comprises the following steps:

wherein alpha is _1ij -bending influence coefficient of the 1 st roll i-th element caused by straightening stress of the j-th element or inter roll pressure;

when y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₁ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₁ ,G ₁ Elastic modulus and shear elastic modulus of roller # 1, < -> Is the moment of inertia of the roll body of the roll No. 1, < + >> Is the cross-sectional area of the roller body of the No. 1 roller,

y _i coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _w is the length of the working roll; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₁ poisson's ratio for roller # 1; d (D) _w Is the diameter of the working roll;

-rigid displacement of the axis of the ith unit of roller # 1;

wherein the method comprises the steps of，C ₇ ，C ₈ The left end and the right end of the roller body of the No. 1 roller are rigidly displaced in the vertical direction;

Δy _j is the width of the j-th cell;

p _j straightening stress for a unit width of a j-th unit between the strip and the 1# roll;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller;

deflection f of ith unit of No. 2 roller in the direction of connecting center point of No. 1 roller and No. 2 roller section _2i The method comprises the following steps:

wherein alpha is _2ij -bending influence coefficient of the jth unit of the 2# roll ith unit caused by inter-roll pressure of the jth unit;

when y is _i ≤y _j At the time, there are

When y is _i ≥y _j At the time, there are

Wherein C is ₂ As the coefficient of the light-emitting diode,α _Q is the section coefficient alpha _Q ＝1.11；E ₂ ,G ₂ Elastic modulus and shear elastic modulus of roller # 2, < -> Is the moment of inertia of the roll body of the roll No. 2, < + >> Is the cross-sectional area of the roller body of the No. 2 roller, +.>

y _i Coordinates of the ith unit; y is _j Coordinates of the j-th cell;

L _m is the length of the middle roller; l (L) _s The distance between the left and right pressing fulcrums is set;

v ₂ poisson's ratio for roller # 2; d (D) _m Is the diameter of the middle roller;

-rigid displacement of the axis of the ith unit of roller # 2;

wherein i=1, 2, …, m ₀ Wherein C is ₅ ，C ₆ The left end and the right end of the roller body of the No. 2 roller are rigidly displaced in the vertical direction; c (C) ₉ ，C ₁₀ The left end axis and the right end axis of the roller body of the No. 2 roller are rigidly displaced in the horizontal direction;

Δy _j is the width of the j-th cell;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

q _12j a unit width roller contact stress of a j-th unit between the 1# roller and the 2# roller; q _24j Contact stress between rolls per unit width of the j-th unit between the roll # 2 and the roll # 4; q _25j Unit width roller indirect for the j-th unit between roller # 2 and roller # 5Touch stress;

3) Coordinate equation of deformation between rollers

Amount of elastic crush delta between rolls of the ith unit between roll # 1 and roll # 2 _12i (i＝1,2,…,n ₀ ) The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

wherein i=1, 2, …, n ₀ (3)

Wherein q is _12i Contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

-the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 1 and roll # 2;

wherein v ₁ 、ν ₂ Poisson ratio of 1# roller and 2# roller; b _i The inter-roller contact crush half width for the i-th unit between roller # 1 and roller # 2 is expressed as:

E ₁ 、E ₂ the elastic modulus of the 1# roller and the 2# roller;

D _w is the diameter of the working roll; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 1# roller and the 2# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _1i ＝f _2i +δ _12i +ΔD _12i wherein i=1, 2, …, n ₀ (4)

Wherein DeltaD _12i Ith unit between roller # 1 and roller # 2Is a raw gap or convexity of (c);

f _1i deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

the force and moment balance equation for roller # 1 is:

q _12i Contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2;

Δy _i is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction;

p _i straightening stress for a unit width of an ith unit between the strip and the 1 st roll;

the force and moment balance equation for roller # 2 is:

q _12i contact stress between rollers per unit width of the i-th unit between roller 1 and roller 2; q _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4; q _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

Δy _i is the width of the ith cell; y is _i Coordinates of the ith unit;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 4 _24i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

δ _24i ＝φ _24i q _24i wherein i=1, 2, …, m ₀ (11)

Wherein q is _24i Contact stress between rollers per unit width of the i-th unit between the roller # 2 and the roller # 4;

φ _24i -the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 4;

wherein v ₂ 、ν ₄ Poisson ratio of the 2# roller and the 4# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₄ the elastic modulus of the roller # 2 and the roller # 4;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 4# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(α-β)＝δ _24i +ΔD _24i wherein i=1, 2, …, m ₀ (12)

Wherein DeltaD _24i -the original gap or convexity of the ith unit between roller # 2 and roller # 4;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; beta is an included angle between the connecting line of the central points of the cross sections of the intermediate roller and the supporting roller and the horizontal direction;

amount of elastic collapse delta between rolls of the ith unit between roll # 2 and roll # 5 _25i The approach quantity of the center lines of the two rollers is obtained by analyzing and solving according to a half-plane body model under the plane strain condition:

δ _25i ＝φ _25i q _25i wherein i=1, 2, …, m ₀ (13)

Wherein q is _25i Contact stress between rollers per unit width of the i-th unit between the 2# roller and the 5# roller;

φ _25i -the coefficient of influence of the elastic collapse between the rolls of the ith unit between roll # 2 and roll # 5;

wherein v ₂ 、ν ₅ Poisson ratio of the 2# roller and the 5# roller; b _i For the inter-roll contact crush half width, expressed as:

E ₂ 、E ₅ the elastic modulus of the roller # 2 and the roller # 5;

D _b is the diameter of the supporting roller; d (D) _m Is the diameter of the middle roller;

the deformation coordination equation between the 2# roller and the 5# roller in the connecting line direction of the center points of the two roller sections is as follows:

f _2i cos(180°-α-γ)＝δ _25i +ΔD _25i wherein i=1, 2, …, m ₀ (14)

Wherein DeltaD _25i -the original gap or convexity of the ith unit between roller # 2 and roller # 5;

f _2i the deflection of the ith unit of the No. 2 roller in the direction of connecting the center points of the sections of the No. 1 roller and the No. 2 roller;

alpha is an included angle between a connecting line of the cross section center points of the working roll and the middle roll and the horizontal direction; gamma is the included angle between the connecting line of the central points of the cross sections of the middle roller and the middle supporting roller and the horizontal direction;

4) Simultaneous solving

Combined type (3) - (14), total n ₀ +2m ₀ +6 linear equations, unknowns

q _12i (i＝1,2,…,n ₀ )，q _24i (i＝1,2,…,m ₀ )，q _25i (i＝1,2,…,m ₀ )，q _25i (i＝1,2,…,m ₀ )，C ₅ ,C ₆ ,C ₇ ,C ₈ ,C ₉ ,C ₁₀ The number is also n ₀ +2m ₀ +6, can solve the unit width roller contact stress directly;

thereby solving and obtaining the transverse distribution F of the elastic deformation of the upper roller system in the vertical direction _1i (i＝1,2,…,n ₀ )：

F _1i ＝f _1i sin (α) where i=1, 2, …, n ₀ (15)

Wherein: f (f) _1i Deflection of the ith unit of the 1# roller in the direction of connecting the center points of the sections of the 1# roller and the 2# roller;

alpha is the included angle between the connecting line of the cross section central points of the working roll and the middle roll and the horizontal direction.

4. The method for designing a roll train structure of a stretch bending straightener based on elastic deformation of a roll train as claimed in claim 3, wherein: transverse distribution F of elastic deformation of upper roll system in step 4) _1i (i＝1,2,…,n ₀ ) The solving process of (2) is as follows:

step 1, straightening stress transverse distribution p (y) of a given unit width;

step 2, assume a contact stress distribution q between rolls per unit width ₁₂ (y)、q ₂₄ (y) and q ₂₅ (y) is uniformly distributed;

step 3, calculating an influence coefficient phi of elastic flattening between the rollers _12i 、φ _24i And phi _25i；

Step 4, solving a linear equation set to obtain a new unit width roller contact stress distribution And

step 5, judging and judgingIf not, turning to step 6; if so, go to step 7;

step 6, order

Turning to step (3);

step 7, orderCalculating to obtain transverse distribution F of elastic deformation of upper roller system in vertical direction _1i (i＝1,2,L,n ₀ )；

In the step, p (y) is the unit width straightening stress;

q ₁₂ (y) is the contact stress between the rollers per unit width between roller # 1 and roller # 2;

q ₂₄ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 4;

q ₂₅ (y) is the contact stress between the rollers per unit width between the roller # 2 and the roller # 5.

5. The roll system structural design method of the stretch bending straightener based on roll system elastic deformation as claimed in claim 1, wherein the method comprises the following steps: in the fifth step, the strip material is reversely bent and transversely distributedThe specific method of (a) is as follows:

the strip reverse bending rate transverse distribution caused by the transverse distribution of the elastic deformation of the upper roller system and the lower roller system is as follows:

Wherein: f (F) _1i The elastic deformation of the ith unit of the upper roller system;

F _2i the elastic deformation of the ith unit of the lower roller system;

t is the roll gap;

D _w is the work roll diameter.

6. The roll system structural design method of the stretch bending straightener based on roll system elastic deformation as claimed in claim 1, wherein the method comprises the following steps: in the sixth step, the elongation of the strip is distributed transversely epsilon _i (i＝1,2,…,n ₀ ) The calculation formula of (2) is as follows:

wherein:to feed the original curvature of the plate strip.

h is the thickness of the strip steel;

p _i is a strip and a roller 1#Straightening stress per unit width of the ith unit;

σ _s is the yield strength of the strip;

is the reverse bending rate of the ith element of the strip.

7. The roll system structural design method of the stretch bending straightener based on roll system elastic deformation as claimed in claim 1, wherein the method comprises the following steps: maximum value delta epsilon of strip elongation difference _max The calculation formula of (2) is as follows:

Δε _max ＝max(|ε _i -ε _j i), where i=1, 2, …, n ₀ ；j＝1,2，…，n ₀ (18)

Wherein: epsilon _i Elongation for the ith cell of the strip;

ε _j the elongation of the jth cell of the strip.