CN110991078A - Working roll shape design method capable of reducing axial force - Google Patents

Working roll shape design method capable of reducing axial force Download PDF

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CN110991078A
CN110991078A CN201911301514.XA CN201911301514A CN110991078A CN 110991078 A CN110991078 A CN 110991078A CN 201911301514 A CN201911301514 A CN 201911301514A CN 110991078 A CN110991078 A CN 110991078A
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陈全忠
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Johnson Electric SA
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Abstract

The invention discloses a method for designing a roll shape of a working roll capable of reducing axial force, which comprises the following steps: constructing a curve equation of the roll shape of the working roll, wherein a in the equation1、a2、a3And s0Respectively, obtaining the roll shape coefficient of the working roll, obtaining the structural parameters and rolling parameters of the working roll, presetting the contour angle α of the roll, and calculating the roll shape coefficient s from the structural parameters and rolling parameters of the working roll0、a1And a3(ii) a Calculating the roll shape coefficient a by taking the reduction of the axial force of the working roll as a target2(ii) a The roll profile curve is formed by1、a2、a3And s0The roll form factors of the several work rolls are determined. The invention has the beneficial effects that: the design method provided by the invention obtains the roll shape coefficient by constructing a working roll shape curve equation, based on the working roll structure parameters and the rolling parameters and aiming at reducing the axial force of the working roll, and the working roll shape designed according to the roll shape coefficient can effectively reduce the axial force of the working roll when rolling a rolled piece with a larger width, thereby obviously prolonging the service life of a bearing of the working roll.

Description

Working roll shape design method capable of reducing axial force
Technical Field
The invention belongs to the technical field of rolling, and particularly relates to a method for designing a roll shape of a working roll capable of reducing axial force.
Background
The work roll profile is the most direct factor in rolled piece shape control. At present, the roller shape of a working roller which is applied more is a variable-crown roller shape, as shown in figure 1, the variable-crown roller shape is mainly characterized in that an upper working roller 1 and a lower working roller 2 are ground into the same S shape and are arranged in a reverse symmetry mode, the upper working roller and the lower working roller axially move in an equivalent reverse mode (namely the working rollers shift), the effective crown of the working rollers is continuously adjusted in an electrodeless mode, the shape adjustment of a no-load roller gap is achieved, and the plate shape of a rolled piece 3 is controlled most directly.
However, when rolling a rolled piece with a large width (such as a medium plate, a non-ferrous metal strip and the like), the convexity working roll has the problem that the service life of a bearing of the working roll is too short due to overlarge axial force. As shown in fig. 2, the unit force N between the work rolls and the rolled stock has a component in the axial direction of the work rolls, the cumulative sum of which over the width of the rolled stock is the axial force F, which is obviously mainly related to the width of the rolled stock when the rolling conditions are the same, the greater the width of the rolled stock, the greater the axial force. Therefore, it is important to design a work roll with a small axial force.
Disclosure of Invention
The invention aims to provide a working roll shape design method capable of reducing axial force aiming at the defects of the prior art, and solves the problem that the service life of a working roll bearing is low due to overlarge axial force when a variable-crown working roll rolls a rolled piece with a large width.
The technical scheme adopted by the invention is as follows: a method for designing a roll shape of a working roll capable of reducing axial force comprises the following steps:
step one, constructing a working roll shape curve equation, wherein the working roll shape curve equation is expressed by the axial radius distribution of a working roll, and the roll shape curve equation of an upper working roll is as follows:
Figure BDA0002321918250000011
the roll profile curve equation of the lower working roll is as follows:
Figure BDA0002321918250000012
in the above formula, a1、a2、a3And s0Are respectively the roll shape coefficient of the working roll without unit, α is the roll contour angle with the unit of degree, s is the roll shifting quantity with the unit of mm, x is the axial abscissa of the working roll with the unit of mm, y is the axial abscissa of the working rollu1(x)、yb1(x) The radius of the upper and lower working rolls at the axial abscissa x is respectively, and the unit is mm;
step two, obtaining working roll structure parameters and rolling parameters, wherein the working roll structure parameters comprise a nominal diameter D, a roll body length L and a roll shifting maximum stroke SmThe rolling parameters comprise roll shifting quantity s and roll gap secondary convexity range [ C ]1,C2]And width range of rolled piece [ Bmin,Bmax]The unit of each parameter is mm;
step three, presetting a roller contour angle α;
step four, calculating the roll shape coefficient s according to the structural parameters and the rolling parameters of the working roll0、a1And a3；
Step five, calculating the roll form coefficient a by taking the reduction of the axial force of the working roll as a target2The roller-shaped curve is formed by1、a2、a3And s0And (4) determining.
According to the scheme, in the fourth step, the roller type coefficient s0、a1And a3The specific calculation method comprises the following steps:
if C1≠0，C2Not equal to 0, then
Figure BDA0002321918250000021
Figure BDA0002321918250000022
If C1＝0，C2Not equal to 0, then s0＝sm，
Figure BDA0002321918250000023
If C1≠0，C2When the value is 0, s0＝-sm，
Figure BDA0002321918250000024
Figure BDA0002321918250000025
According to the scheme, in the step five, the roller type coefficient a is calculated2The specific method comprises the following steps:
(1) establishing a working roll axial force calculation model, wherein the working roll axial force can be expressed as
Figure BDA0002321918250000026
In the formula p0Rolling force per unit width, in KN/mm, processed as a constant in the design calculation, R-axial force coefficient,
Figure BDA0002321918250000027
(2) determining a2Value range (K) of1,K2) If a1If greater than 0, then
Figure BDA0002321918250000028
If a1If less than 0, then
Figure BDA0002321918250000029
(3) A is to2The value range of (a) is divided into N equal parts to obtain a series of a2Value, i th a2The value can be expressed as
Figure BDA0002321918250000031
(4) For each a2The value is in the range of roll shifting [ -s ]m,sm]And the width B of the stripmin,Bmax]Internally calculating the maximum value R of the corresponding axial force coefficient Rmax；
(5) Comparing differences a2Value (a)2(1)、a2(2)、a2(3)…a2(i)…a2(N-1)) the maximum value R of the axial force coefficient Rmax(Rmax(1)、Rmax(2)、Rmax(3)…Rmax(i)…Rmax(N-1)), finding out the smallest RmaxThe minimum RmaxCorresponding to a2The value is the result.
According to the scheme, in the step five (4), the maximum value R of the corresponding axial force coefficient R is calculatedmaxThe specific method comprises the following steps:
a. calculating extreme points and boundary value points, wherein the extreme points comprise:
Figure BDA0002321918250000032
and
Figure BDA0002321918250000033
wherein k is1、k2Is an integer, and B e [ B ∈ [ ]min,Bmax]，s∈[-sm,sm]；
The boundary value points include:
Figure BDA0002321918250000034
and
Figure BDA0002321918250000035
b. calculating the axial force coefficient R value corresponding to each group B and s value, and comparing the values, wherein the maximum R value is the value of the a2Value condition in roll shifting range [ -s ]m,sm]And strip width range [ Bmin,Bmax]Maximum value R of inner Rmax。
According to the scheme, in the third step, the value range of the preset roller profile angle α is 0-180 degrees.
The invention has the beneficial effects that: the design method provided by the invention obtains the roll shape coefficient by constructing the roll shape curve equation of the working roll, based on the structural parameters and the rolling parameters of the working roll and aiming at reducing the axial force of the working roll, and the working roll obtained according to the roll shape coefficient can effectively reduce the axial force of the working roll when rolling a rolled piece with larger width, thereby obviously prolonging the service life of the bearing of the working roll.
Drawings
FIG. 1 is a schematic view of a roll profile and roll shifting of a variable crown work roll.
FIG. 2 is a schematic view of the axial force of a variable crown work roll.
FIG. 3 is a flow chart of the present invention.
FIG. 4 shows the difference a of the embodiment calculated for the purpose of reducing the axial force of the work rolls2Value of RmaxAnd (6) comparing.
Fig. 5 is a graph showing the roll profile of the upper work roll calculated in this example.
Wherein: 1. an upper work roll; 2. a lower working roll; 3. and (5) rolling pieces.
Detailed Description
For a better understanding of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
A method for designing a roll shape of a work roll capable of reducing axial force as shown in fig. 3 comprises the following steps:
step one, constructing a working roll shape curve equation, wherein the working roll shape curve equation is expressed by the axial radius distribution of a working roll, and the roll shape curve equation of an upper working roll is as follows:
Figure BDA0002321918250000041
the roll profile curve equation of the lower working roll is as follows:
Figure BDA0002321918250000042
in the above formula, a1、a2、a3And s0Are respectively the roll shape coefficient of the working roll without unit, α is the roll contour angle with the unit of degree, s is the roll shifting quantityIn mm; x is the axial abscissa of the working roll and the unit is mm; y isu1(x)、yb1(x) The radii of the upper and lower work rolls, respectively, at the axial abscissa x, are in mm.
Step two, obtaining working roll structure parameters and rolling parameters, wherein the working roll structure parameters comprise a nominal diameter D, a roll body length L and a roll shifting maximum stroke SmThe rolling parameters comprise roll shifting quantity s and roll gap secondary convexity range [ C ]1,C2]And width range of rolled piece [ Bmin,Bmax](ii) a The units of the above parameters are mm.
And step three, presetting a roller profile angle α, wherein the roller profile angle is more than 0 and less than α and less than 180 degrees.
Step four, calculating the roll shape coefficient s according to the structural parameters and the rolling parameters of the working roll0、a1And a3The method specifically comprises the following steps:
if C1≠0，C2Not equal to 0, then
Figure BDA0002321918250000043
Figure BDA0002321918250000044
If C1＝0，C2Not equal to 0, then s0＝sm，
Figure BDA0002321918250000051
If C1≠0，C2When the value is 0, s0＝-sm，
Figure BDA0002321918250000052
Figure BDA0002321918250000053
Step five, calculating the roll form coefficient a by taking the reduction of the axial force of the working roll as a target2Is concretely provided with：
(1) Establishing a working roll axial force calculation model, wherein the working roll axial force can be expressed as:
Figure BDA0002321918250000054
in the above formula, p0The rolling force is the unit width, the unit is KN/mm, and the rolling force is processed according to a constant in the design calculation; r is the coefficient of axial force,
Figure BDA0002321918250000055
(2) a is determined2Value range (K) of1,K2) If a1If greater than 0, then
Figure BDA0002321918250000056
If a1If less than 0, then
Figure BDA0002321918250000057
(3)、a2The value range of (a) is divided into N equal parts to obtain a series of a2Value, i th a2The value can be expressed as
Figure BDA0002321918250000058
(4) Each a2The value is in the range of roll shifting [ -s ]m,sm]And the width B of the stripmin,Bmax]Internally calculating the maximum value R of the corresponding axial force coefficient Rmax：
a. Calculating extreme points and boundary value points, wherein the extreme points comprise:
Figure BDA0002321918250000059
and
Figure BDA00023219182500000510
wherein k is1、k2Is an integer, and B e [ B ∈ [ ]min,Bmax]，s∈[-sm,sm]；
The boundary value points include:
Figure BDA0002321918250000061
and
Figure BDA0002321918250000062
b. calculating the axial force coefficient R value corresponding to each group B and s value, and comparing the values, wherein the maximum R value is the value of the a2Value condition in roll shifting range [ -s ]m,sm]And strip width range [ Bmin,Bmax]Maximum value R of inner Rmax；
(5) Comparing a different2Value (a)2(1)、a2(2)、a2(3)…a2(i)…a2(N-1)) the maximum value R of the axial force coefficient Rmax(Rmax(1)、Rmax(2)、Rmax(3)…Rmax(i)…Rmax(N-1)), finding out the smallest RmaxThe minimum RmaxCorresponding to a2The value is the result; the roll profile curve is formed by1、a2、a3And s0The roll form factors of the several work rolls are determined.
Examples
In order to further illustrate the practicability of the method, the method is adopted to obtain the working roll profile curve meeting the site requirement of a certain steel mill.
The site requirements of a certain steel mill are as follows: the structural parameters of the working roll are that the nominal diameter D is 580mm, the roll body length L is 2200, and the maximum roll shifting stroke Sm225mm, and the rolling parameter condition is the lower limit C of the secondary crown of the roll gap10.4mm, upper limit C20.5mm, minimum width range B of rolled piecemin900mm, maximum width Bmax1600mm and a preset roll profile angle α of 90.
Roll shape coefficient s calculated by working roll structure parameter, rolling parameter and preset roll contour angle0＝-25.886、a1＝-0.713、a3＝290.026。
Calculating the roll shape coefficient a by taking the reduction of the axial force of the working roll as a target2The specific process is as follows:
1、a2has a value range of (0,0.00102), namely K1＝0，K20.00102, the range is divided into 10000 equal parts (N is 10000), and 9999 a are obtained2Value, i th a2The value can be expressed as a2-1(i)＝1.02×10-7i，i＝1、2、3...9999；
2. For each a2The value is in the range of roll-shifting [ -225,225]And strip width range [900,1600]Internally calculating the maximum value R of the corresponding axial force coefficient Rmax. For convenience of description, only the 5000 th a is used here2The values are illustrated as examples: a is2(5000)＝5.1×10-4The axial force coefficients R at the extreme point and the boundary point are 0.2384, 0.2329, 0.117, 0.131, 0.16 and 0.185 respectively, so a2(5000) Corresponding Rmax＝0.2384；
3. All a are2Value of RmaxCalculated and compared to find the smallest R among them, as shown in fig. 4maxCorresponding to a2The value is the result. The roll shape coefficient a thus calculated with the aim of reducing the axial force of the work rolls2A value of a2＝8.277×10-4At this time, the corresponding RmaxMinimum, 0.01202.
The overall roll profile factor a of the roll profile curve of the work roll satisfying the above-mentioned field requirements has been calculated1、a2、a3And s0The obtained upper work roll profile curve is shown in fig. 5, in which the actual roll shifting amount s is 0.
As can be seen from the above working roll axial force formula, the smaller the axial force coefficient R, the smaller the working roll axial force F2The smaller. For all the working roll profile curves, when the maximum value R of the axial force coefficient R corresponding to a certain working roll profile curvemaxAt the minimum, the working roll profile (in the embodiment, a) can be ensured for all rolling conditions (including roll shifting amount and rolled piece width)2＝8.277×10-4Corresponding curve) is small. The statistical data of field production shows that the working roll shape designed by the method of the embodiment of the invention has obviously prolonged service life of the working roll bearing because the axial force of the working roll is effectively reduced.
It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and the present invention is not limited thereto, and although the present invention has been described in detail with reference to the embodiments, it will be apparent to those skilled in the art that modifications can be made to the technical solutions described in the above-mentioned embodiments, or equivalent substitutions of some technical features, but any modifications, equivalents, improvements and the like within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (5)

1. A method for designing a roll shape of a working roll capable of reducing axial force is characterized by comprising the following steps:
step one, constructing a working roll shape curve equation, wherein the working roll shape curve equation is expressed by the axial radius distribution of a working roll, and the roll shape curve equation of an upper working roll is as follows:
Figure FDA0002321918240000011
the roll profile curve equation of the lower working roll is as follows:
Figure FDA0002321918240000012
in the above formula, a1、a2、a3And s0Are respectively the roll shape coefficient of the working roll without unit, α is the roll contour angle with the unit of degree, s is the roll shifting quantity with the unit of mm, x is the axial abscissa of the working roll with the unit of mm, y is the axial abscissa of the working rollu1(x)、yb1(x) The radius of the upper and lower working rolls at the axial abscissa x is respectively, and the unit is mm;
step two, obtaining the structural parameters of the working rollAnd rolling parameters, wherein the structural parameters of the working roll comprise a nominal diameter D, a roll body length L and a roll shifting maximum stroke SmThe rolling parameters comprise roll shifting quantity s and roll gap secondary convexity range [ C ]1,C2]And width range of rolled piece [ Bmin,Bmax]The unit of each parameter is mm;
step three, presetting a roller contour angle α;
step four, calculating the roll shape coefficient s according to the structural parameters and the rolling parameters of the working roll0、a1And a3；
Step five, calculating the roll form coefficient a by taking the reduction of the axial force of the working roll as a target2(ii) a The roll profile curve is formed by1、a2、a3And s0And (4) determining.
2. The method of claim 1, wherein in step four, the roll form factor s is0、a1And a3The specific calculation method comprises the following steps:
if C1≠0，C2Not equal to 0, then
Figure FDA0002321918240000013
Figure FDA0002321918240000014
If C1＝0，C2Not equal to 0, then s0＝sm，
Figure FDA0002321918240000021
If C1≠0，C2When the value is 0, s0＝-sm，
Figure FDA0002321918240000022
Figure FDA0002321918240000023
3. The method as claimed in claim 1, wherein in step five, the roll form coefficient a is calculated2The specific method comprises the following steps:
(1) establishing a working roll axial force calculation model, wherein the working roll axial force can be expressed as
Figure FDA0002321918240000024
In the formula p0Rolling force per unit width, in KN/mm, processed as a constant in the design calculation, R-axial force coefficient,
Figure FDA0002321918240000025
(2) determining a2Value range (K) of1,K2) If a1If greater than 0, then
Figure FDA0002321918240000026
If a1If less than 0, then
Figure FDA0002321918240000027
(3) A is to2The value range of (a) is divided into N equal parts to obtain a series of a2Value, i th a2The value can be expressed as
Figure FDA0002321918240000028
(4) For each a2The value is in the range of roll shifting [ -s ]m,sm]And the width B of the stripmin,Bmax]Internally calculating the maximum value R of the corresponding axial force coefficient Rmax；
(5) Comparing differences a2Value (a)2(1)、a2(2)、a2(3)…a2(i)…a2(N-1)) the maximum value R of the axial force coefficient Rmax(Rmax(1)、Rmax(2)、Rmax(3)…Rmax(i)…Rmax(N-1)), finding out the smallest RmaxThe minimum RmaxCorresponding to a2The value is the result.
4. The method of claim 3, wherein in step five (4), the maximum value R of the corresponding axial force coefficient R is calculatedmaxThe specific method comprises the following steps:
a. calculating extreme points and boundary value points, wherein the extreme points comprise:
Figure FDA0002321918240000031
and
Figure FDA0002321918240000032
wherein k is1、k2Is an integer, and B e [ B ∈ [ ]min,Bmax]，s∈[-sm,sm]；
The boundary value points include:
Figure FDA0002321918240000033
and
Figure FDA0002321918240000034
b. calculating the axial force coefficient R value corresponding to each group B and s value, and comparing the values, wherein the maximum R value is the value of the a2Value condition in roll shifting range [ -s ]m,sm]And strip width range [ Bmin,Bmax]Maximum value R of inner Rmax。
5. The method of claim 1, wherein in step three, the preset roll profile angle α is in the range of 0-180 °.
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