CN109732022B - Optimization method for movement track of holding roller of ring rolling mill - Google Patents
Optimization method for movement track of holding roller of ring rolling mill Download PDFInfo
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Abstract
An optimization method of a looping mill looping roll movement track comprises the following steps of firstly determining influence factors of the looping roll movement track and a value range of the influence factors; secondly, establishing an evaluation index of the motion track of the holding roller; then designing an experimental scheme and establishing a correlation model of the evaluation index of the movement track of the holding roller and the influence factor by using a finite element simulation test; further establishing a mathematical model for optimizing the motion trail of the holding roller; and finally, acquiring an optimized value of the influence factors of the movement track of the contracting roll by using a mathematic tool MATLAB to realize the optimization of the movement track of the contracting roll. The invention can realize the optimization of the movement locus of the holding roller aiming at different ring rolling equipment and sizes of rolled ring pieces, reduces the design cost of the movement locus of the holding roller, shortens the design period of the movement locus of the holding roller, solves the problems of high cost, low efficiency and the like caused by designing or optimizing the movement locus of the holding roller by a trial and error or experience method, and provides important reference for the process design and equipment development of ring piece rolling.
Description
Technical Field
The invention belongs to the field of ring rolling forming processing, and particularly relates to an optimization method for a looping roller movement track of a looping mill.
Background
In the whole process of ring rolling forming, the holding roller rotates around the axis of the holding roller under the action of friction force of the ring on the holding roller, and simultaneously moves along the circumference track around the fixed hinge point of the connecting rod along with the diameter of the ring. The rotating center of the circumferential motion of the holding roller is determined by the position of a connecting rod fixed hinge point, the motion radius is related to the contact position of the holding roller and the ring blank and is determined by an initial holding roller angle, and the position of the connecting rod fixed hinge point and the initial holding roller angle jointly determine the circular arc motion track of the holding roller. In the actual ring rolling equipment development and ring rolling process design, the movement locus of the holding roller is an important parameter which needs to be reasonably designed, and the quality of the movement locus of the holding roller determines whether the holding roller mechanism can play an effective role or not, so that the stability of the ring rolling process and the roundness of a formed ring are greatly influenced. However, in the past, the movement track of the holding roller is designed or optimized by experience or trial and error, so that the cost is high, the efficiency is low, the action effect of the holding roller mechanism is poor, the applicability of the ring rolling machine for different sizes is poor, and the stability of the ring rolling process and the roundness of a formed ring cannot be fully ensured. A calculation method [ J ] of a roll holding motion trail in a ring radial-axial bidirectional rolling process of [ Lishu, Liudong, Mayiwei ] Lishu and the like [ 2010, 39(11) ]: 48-52 ] a calculation method of the motion track of the holding roller is established on the basis of the change rule of the instantaneous outer diameter of the ring, but the optimization related research of the motion track of the holding roller is not reported yet. In view of the above, the invention provides a method for optimizing the roll embracing motion track of the ring rolling mill by optimizing the position of the connecting rod fixed hinge and the initial roll embracing angle, and provides reference for design optimization of the actual roll embracing mechanism of the ring rolling mill and planning of the ring rolling process.
Disclosure of Invention
The invention provides an optimization method of a looping roller motion track of a looping mill, aiming at overcoming the defects that in the prior art, the looping roller motion track is designed by relying on experience and a trial and error method, so that the cost is high, the efficiency is low, the action effect of a looping roller mechanism is poor, and the applicability is poor for different loop piece sizes.
The method comprises the following specific steps:
the influence factors of the motion trail of the holding roller comprise an initial holding roller angle α0A fixed hinge point horizontal coordinate x and a fixed hinge point vertical coordinate z;
calculating the value range of the influence factors of the roll holding motion trail according to the roll size of the ring rolling mill and the size of a ring blank, wherein the roll size of the ring rolling mill comprises the radius R of a main roll of the ring rolling mill1Radius R of core roll of ring rolling mill2Radius R of wrap roll of ring rolling mill3The size of the ring blank comprises the outer radius R of the ring blank0；
Initial wrap angle α0The value range of (A):
the value range of the abscissa x of the connecting rod fixed hinge point is as follows:
[1.2R1,1.7R1](4)
the value range of the vertical coordinate z of the connecting rod fixed hinge point is as follows:
the evaluation indexes of the movement track of the holding roller comprise ring rolling stability evaluation indexes and ring roundness evaluation indexes; calculating a ring rolling stability evaluation index and a ring roundness evaluation index according to coordinate values of different nodes on the ring section at different moments in the rolling process, wherein the ring section is a ring section on a symmetrical plane vertical to the axis of the ring;
calculating a ring rolling stability evaluation index by the formula (9):
wherein:
wherein z isMSEFor the ring rolling stability evaluation index, m is the number of times of acquiring coordinates of nodes on the excircle and the inner circle of the section of the ring piece in the rolling process, n is the total number of nodes on the inner circle or the excircle of the section of the ring piece, and zojThe z coordinate value of the geometric center of the section of the ring piece, z, is obtained by the j-th calculation based on the excircle of the section of the ring pieceijZ coordinate value, zo, of geometric center of cross section of the ring member obtained by the j-th calculation based on the inner circle of cross section of the ring memberjkZ coordinate value of kth node on the excircle of the cross section of the ring at the j-th calculationijkIs the z coordinate value of the kth node on the inner circle of the cross section of the ring at the j-th calculation,
calculating an ideal value of a z coordinate value of the geometric center of the section of the ring piece based on the excircle and the inner circle of the section of the ring piece;
calculating a ring roundness evaluation index by the formula (13):
wherein
(Reo)j＝max|Δrojk|-min|Δrojk| (14)
(Rei)j＝max|Δrijk|-min|Δrijk| (15)
Wherein (R)e)MSEFor the roundness evaluation index of the ring piece, m is the number of times of acquiring coordinates of nodes on the outer circle and the inner circle of the section of the ring piece in the rolling process, (R)eo)jFor the jth roundness error obtained by calculation based on the excircle of the section of the ring member, (R)ei)jAnd calculating the roundness error obtained based on the inner circle of the section of the ring piece for the jth time, wherein the roundness error is calculated by adopting a least square method. x is the number ofojThe x coordinate value, z coordinate value of the geometric center of the section of the ring piece is calculated and obtained for the jth time based on the excircle of the section of the ring pieceojCalculating a z-coordinate value of the geometric center of the section of the ring piece for the jth time based on the excircle of the section of the ring piece; x is the number ofijThe x coordinate value, z coordinate value of the geometric center of the section of the ring piece is obtained for the jth time based on the calculation of the inner circle of the section of the ring pieceijCalculating a z-coordinate value of the geometric center of the section of the ring piece for the jth time based on the inner circle of the section of the ring piece; x is the number ofojkThe x coordinate value, z, of the kth node on the excircle of the cross section of the ring at the jth calculationojkThe z coordinate value of the kth node on the outer circle of the cross section of the ring piece in the j-th calculation; x is the number ofijkThe x coordinate value, z, of the kth node on the inner circle of the cross section of the ring at the j-th calculationijkThe z coordinate value of the kth node on the inner circle of the cross section of the ring piece in the j-th calculation; Δ rokjFor the jth calculation, the distance from the kth node on the outer circle of the section of the ring to the geometric center of the section of the ring obtained by calculation of the outer circle of the section of the ring, max | delta rokj|、min|Δrokj| represents Δ r, respectivelyokjMaximum and minimum values of; Δ rikjFor the distance from the kth node on the inner circle of the cross section of the ring part at the jth calculation to the geometric center of the cross section of the ring part obtained by calculation of the inner circle of the cross section of the ring part, max | delta rikj|、min|Δrikj| represents Δ r, respectivelyikjMaximum and minimum values of;
theory of roundness error obtained by calculation based on outer circle and inner circle of section of ring pieceA desired value;
designing a test scheme by a center combination design method in a value range of the influence factors of the movement track of the holding roller, carrying out finite element simulation test on each group of parameter combination, obtaining coordinate values of k nodes on the outer circle and k nodes on the inner circle of the cross section of the ring for m times, calculating according to test results to obtain the central offset displacement of the ring and the root-mean-square error of the roundness of the ring, and respectively establishing a ring rolling stability evaluation index model f by regression analysis1(x) And ring roundness evaluation index model f2(x)；
The ring rolling stability evaluation index model f1(x) The method is a quadratic polynomial mathematical model of ring rolling stability evaluation indexes and influence factors of the roll holding motion track; ring piece roundness evaluation index model f2(x) The method is characterized in that a quadratic polynomial mathematical model of influence factors of a ring roundness evaluation index and a roller holding motion track is as follows:
f1(x)＝a1α0+a2x+a3z+a4α0x+a5α0z+a6xz+a7α0 2+a8x2+a9z2+a10(21)
f2(x)＝b1α0+b2x+b3z+b4α0x+b5α0z+b6xz+b7α0 2+b8x2+b9z2+b10(22)
wherein x represents the combined vector of the influencing factors of the motion trail of the holding roller, and x is [ α ]0,x,z]，α0Is an initial roll holding angle; x is the abscissa value of the fixed hinge point of the connecting rod; z is a connecting rod fixed longitudinal coordinate value; f. of1(x) Model representing evaluation index of Ring Rolling stability, a1、a2、a3Respectively represents variables α in the ring rolling stability evaluation index model0The first order coefficient of the variable x and the variable z; a is4、a5、a6Are respectively provided withVariable α in the evaluation index model representing the stability of ring rolling0And x, variable α0Interaction term coefficients between z and the variables x and z; a is7、a8、a9Respectively represents variables α in the ring rolling stability evaluation index model0The coefficients of the quadratic terms of the variable x and the variable z; a is10Constant items in a ring rolling stability evaluation index model are represented; f. of2(x) Model representing evaluation index of roundness of ring member, b1、b2、b3Respectively representing variables α in the index model of the ring roundness evaluation index0The first order coefficient of the variable x and the variable z; b4、b5、b6Respectively representing variations α in the evaluation index model of the roundness of the ring0And x, variable α0Interaction term coefficients between z and the variables x and z; b7、b8、b9Respectively representing variations α in the evaluation index model of the roundness of the ring0The coefficients of the quadratic terms of the variable x and the variable z; b10Representing a constant term in the ring roundness evaluation index model;
and 4, establishing a mathematical model for optimizing the motion track of the holding roller.
Based on the established association model of the evaluation index of the movement track of the contracting roll and the influence factors, the mathematical model for optimizing the movement track of the contracting roll is established
The specific steps of establishing the optimized mathematical model of the motion track of the holding roller are as follows:
i obtaining ring rolling stability evaluation index model f1(x) The optimal solution vector of (2);
the optimal solution vector refers to a combined vector of the influence factors of the motion trail of the holding roller when the evaluation index reaches an optimal value. The smaller the ring rolling stability evaluation index in the rolling process is, the better the ring rolling stability is, and the better the movement track of the holding roller is. Obtaining the motion track of the holding roller by using a mathematic tool MATLABThe influence factors enable the ring rolling stability evaluation index z to be in a value rangeMSEObtaining the optimal solution vector of the minimum value:
minf1(x)＝f1(x1 *) (25)
in the formula, x1 *For ring rolling stability evaluation index model f1(x) The optimal solution vector of (2).
II obtaining ring roundness evaluation index model f2(x) The optimal solution vector of (2);
the smaller the evaluation index of the roundness of the ring piece in the rolling process is, the better the roundness of the ring piece is, and the better the movement track of the holding roller is. Obtaining a ring roundness evaluation index (R) by using a mathematic tool MATLAB to enable the influence factors of the motion track of the holding roller to be in a value rangee)MSEObtaining the optimal solution vector of the minimum value:
minf2(x)＝f2(x2 *) (26)
in the formula, x2 *For ring roundness evaluation index model f2(x) The optimal solution vector of (2).
III determination of ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) A vector of weight coefficients;
the weight coefficient vector refers to a weight coefficient omega of a ring rolling stability evaluation index model1And the weight coefficient omega of the ring roundness evaluation index model2The composed vector ω:
ω＝[ω1,ω2](27)
wherein, the weight coefficient omega of the ring rolling stability evaluation index model1And the weight coefficient omega of the ring roundness evaluation index model2Determined by equation (28):
in the formula, ω1The weight coefficient omega of the ring rolling stability evaluation index model2And the weight coefficient is the evaluation index model of the roundness of the ring piece.
IV, establishing a mathematical model for optimizing the motion track of the holding roller;
a mathematical model for optimizing the motion trail of the holding roller can be obtained by a linear weighting method:
in the formula (I), the compound is shown in the specification,
i.e. a mathematical model for optimizing the motion trail of the holding roller, omega is a ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) The vector of weight coefficients.
the method can obtain the influence factor of the motion track of the holding roller within the value range
To a minimum
Optimal solution vector of (2):
x*＝[α0 *,x*,z*](35)
α0 *for an optimized initial wrap angle, (x)*,z*) The optimized fixed hinge point position is determined as the optimized holding roller motion track;
therefore, the optimization of the roll embracing motion track of the encircling mill is completed.
In order to solve the optimization problem of the movement track of the holding roller of the encircling mill, firstly, determining the influence factors of the movement track of the holding roller and the value range of the influence factors; secondly, establishing an evaluation index of the motion track of the holding roller; then designing an experimental scheme and establishing a correlation model of the evaluation index of the movement track of the holding roller and the influence factor by using a finite element simulation test; further establishing a mathematical model for optimizing the motion trail of the holding roller; most preferablyAnd then, acquiring an optimized value of the influence factors of the motion trail of the holding roller by using a mathematic tool MATLAB to realize the optimization of the motion trail of the holding roller, wherein in the process, an initial holding roller angle α can be used0The fixed hinge point horizontal coordinate value x and the fixed hinge point vertical coordinate value z are in the optimal combined vector [ α ] within the value range0 *,x*,z*]To show the optimal motion trajectory of the wrap rollers.
The invention relates to a mathematical model optimized by establishing a motion track of a holding roller
Namely ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) To obtain the optimal solution vector x of the combined vector x of the influence factors of the motion trail of the holding roller*To obtain the optimal initial wrap angle α0 *And optimum fixed hinge point position (x)*,z*) Therefore, the optimization of the motion track of the holding roller is realized. According to the invention, a three-dimensional finite element simulation test is adopted to establish a mathematical model for optimizing the movement locus of the contracting roll, the error between the simulation value of the simulation test and the predicted value of the mathematical model is not more than 2%, and the model can accurately describe the influence rule of the influence factors of the movement locus of the contracting roll on the evaluation index of the movement locus of the contracting roll; the method can realize optimization of the movement track of the holding roller aiming at different ring rolling equipment and sizes of rolled rings without trial rolling of the rings on a ring rolling mill, reduces the design cost of the movement track of the holding roller, shortens the design period of the movement track of the holding roller, and solves the problems of high cost, low efficiency and the like caused by designing or optimizing the movement track of the holding roller by a trial and error or experience method in the prior art; the optimized movement locus of the holding roller can improve the stability of the ring and the roundness of the formed ring in the ring rolling process, and the effect of the holding roller mechanism in the ring rolling process can be fully exerted. The invention provides a new method for optimizing the motion trail of the holding roller, and provides important reference for the process design and equipment development of ring rolling.
Drawings
FIG. 1 is a schematic view of a ring rolling system in an initial ring rolling state, and FIG. 1a is a top view in the x-z plane; FIG. 1b is a cross-sectional view in the x-y plane.
Fig. 2 is a simplified schematic diagram of the motion trajectory of the wrap rollers, where VV 'is the x-axis direction and WW' is the z-axis direction.
FIG. 3 is a schematic view of a value range of an influence factor of a motion track of a wrap roll.
FIG. 4 is a cross-sectional view of the ring at the plane of symmetry perpendicular to the axis of the ring
FIG. 5 is a schematic diagram of an optimized hugging roller motion track.
FIG. 6 is a schematic diagram of the optimization of the motion track of the wrap rollers.
FIG. 7 is a flow chart of the present invention.
In the figure:
1. a main roller; 2. carrying out roller holding; 3. a core roll; 4. ring blank; 5. a conical roller; 6. a first link; 7. a second link; 8. a third link; 9. a connecting rod fixes a hinge point; 10. a hydraulic cylinder; 11. fixing a hinge point by a hydraulic cylinder; 12. and (5) optimizing the motion track of the holding roller.
Detailed Description
The implementation example is an optimization method of the looping mill looping roll motion track, and firstly, the influence factors and the value range of the looping mill looping roll motion track are determined; then, establishing an evaluation index of the motion track of the holding roller; secondly, establishing a correlation model of the evaluation index of the motion track of the holding roller and the influence factors; thirdly, establishing a mathematical model for optimizing the motion track of the holding roller; and finally, obtaining an optimized value of the influence factors of the movement track of the contracting roll, and realizing the optimization of the movement track of the contracting roll.
The method comprises the following specific steps:
FIG. 1 is a schematic diagram of an annular rolling system in an initial ring rolling state, the annular rolling system comprises a main roll 1, a holding roll 2, a core roll 3, an annular blank 4 and a conical roll 5, and the center of the main roll 1 is O1The center of the main roller 1 refers to the circle center of a circular section on a symmetrical plane vertical to the axis of the main roller; the center of the ring blank 4 is O2The center of the ring blank 4 refers to the ring center of the ring section at the symmetrical plane perpendicular to the axis of the ring blank. The outer side surface of the ring blank 4 is simultaneously in close contact with the side surface of the holding roller 2 and the side surface of the main roller 1, and the inner side surface of the ring blank is in close contact with the side surface of the main roller 1The sides of the core roller 3 are in close contact. Establishing a three-dimensional rectangular coordinate system of the ring rolling system, and enabling the origin O of the three-dimensional coordinate system to be positioned at the center O of the main roll 11. Three-dimensional coordinate system with origin O pointing to center O of ring blank2The linear direction of the three-dimensional coordinate system is the x axis of the three-dimensional coordinate system; the axis direction of the main roller 1 is the y axis of the three-dimensional coordinate system; and a straight line direction which passes through the origin O of the three-dimensional coordinate system and is perpendicular to the xOy plane is taken as the z axis of the three-dimensional coordinate system.
FIG. 2 is a simplified schematic diagram of the motion trajectory of the contracting roller, and in FIG. 2, a Z-shaped link mechanism is formed by a first link 6, a second link 7 and a third link 8; wherein: one end of the first connecting rod is hinged with the center of the end face of one end of the holding roller 2, and the center of the end face is a hinge point A; the other end of the first connecting rod is fixedly connected with one end of the second connecting rod 7, and the fixed connection point is B; the other end of the second connecting rod is fixedly connected with one end of a third connecting rod 8, the fixed connection point is C, the other end of the third connecting rod is hinged with a piston rod of a hydraulic cylinder, and the hinged point is D; the fixed connection point C of the second connecting rod 7 and the third connecting rod 8 is hinged with a connecting rod fixed hinge point 9, and the hinge point is E. The coordinate of the point E in the coordinate system is (x, z), the coordinate system is an x-z two-dimensional plane rectangular coordinate system of the ring rolling system, the coordinate systems are all plane coordinate systems, and the coordinate value of a certain point is the coordinate value of the point in the coordinate system. The holding roller 2 is connected with a connecting rod fixed hinge point 9 through a first connecting rod 6 and a second connecting rod 7, and can rotate around the fixed hinge point, and the fixed hinge point is a hinge point E between a fixed connection point C of the second connecting rod 7 and a third connecting rod 8 and the connecting rod fixed hinge point 9.
FIG. 3 is a schematic diagram of a value range of an influence factor of a motion track of a holding roller, and a ring rolling system is symmetrical about an x axis of a coordinate system. In FIG. 3, the ring blank 4 has an outer radius R0Inner radius of r0The radius of the main roller 1 is R1The radius of the core roll 3 is R2The radius of the holding roller 2 is R3When the initial wrap angle takes the minimum value, it is called the minimum initial wrap angle α0minThe center of the holding roll is A', and the maximum initial holding roll angle α is defined when the initial holding roll angle is maximum0maxThe center of the holding roller is A' at the moment, and the initial holding roller angle α0Is referred to as the beginning of rollingCenter O of stage main roller 11The central line of the core roller 3 and the center of the holding roller 2 and the center O of the ring blank 42The center of the core roller 3 refers to the circle center of a circular section on the symmetrical plane vertical to the axis of the core roller, and the center of the holding roller 2 refers to the circle center of a circular section on the symmetrical plane vertical to the axis of the holding roller. Value lower limit x of fixed hinge point horizontal coordinate value xminThe determined straight line x ═ xminValue lower limit z of longitudinal coordinate value z of fixed hinge pointminThe determined straight line x ═ zminHas an intersection point of E1The value upper limit x of the fixed hinge point abscissa value xmaxThe determined straight line x ═ xmaxValue lower limit z of longitudinal coordinate value z of fixed hinge pointminZ is the determined straight lineminHas an intersection point of E2The value upper limit x of the fixed hinge point abscissa value xmaxThe determined straight line x ═ xmaxUpper limit z of longitudinal coordinate value z of fixed hinge pointmaxZ is the determined straight linemaxHas an intersection point of E3The value lower limit x of the fixed hinge point abscissa value xminThe determined straight line x ═ xminUpper limit z of longitudinal coordinate value z of fixed hinge pointmaxZ is the determined straight linemaxHas an intersection point of E4，E1E2E3E4And determining the rectangular value range of the position of the fixed hinge point. Value lower limit x of fixed hinge point horizontal coordinate value xminThe determined straight line x ═ xminThe intersection point of the X axis of the coordinate system is M, and the value upper limit x of the abscissa value x of the fixed hinge pointmaxThe determined straight line x ═ xmaxThe intersection with the x-axis of the coordinate system is N.
Determining the influence factors of the motion track of the holding roller and the value range of the influence factors:
i, determining influence factors of a moving track of a holding roller;
in the whole process of ring rolling and forming, the holding roller 2 moves along with the diameter of the ring around the fixed hinge point in a circular track, as shown in fig. 2. The rotation center of the circular motion of the holding roller is determined by the position of the fixed hinge point, and the motion radius is related to the initial contact position of the holding roller and the ring blank and is determined by the initial holding roller angle. Influence of the influence on the movement track of the holding rollerFactors include initial wrap angle α0The abscissa value x of the fixed hinge point and the ordinate value z of the fixed hinge point.
Defining a combined vector of the influence factors of the motion trail of the holding roller:
x＝[α0,x,z](1)
formula (III) α0Is the initial holding roll angle, x is the abscissa value of the fixed hinge point, and z is the ordinate value of the fixed hinge point.
Calculating the value range of the influence factors of the roll holding motion trail according to the roll size of the ring rolling mill and the size of a ring blank, wherein the roll size of the ring rolling mill comprises the radius R of a main roll of the ring rolling mill1Radius R of core roll of ring rolling mill2Radius R of wrap roll of ring rolling mill3The size of the ring blank comprises the outer radius R of the ring blank0。
II determining an initial wrap angle α0The value range of (a);
during the ring rolling process, the holding roll rotates clockwise around the fixed hinge point and keeps contact with the ring at the same time, as shown in figure 3, when the holding roll is tangent to the main roll and the ring blank at the same time, the minimum initial holding roll angle α is obtained0minThe center of the holding roller is A' at △ O1A'O2In, O1O2Denotes the distance, O, from the center of the main roll to the center of the ring blank1A' and O2A' represents that when the holding roller is tangent to the main roller and the ring blank at the same time, the minimum initial holding roller angle α is taken0minAnd the distance from the center of the main roller and the center of the ring blank to the center of the holding roller. As can be seen from the figure, O1O2＝R1+R0，O2A'＝R0+R3，O1A'＝R1+R3The minimum initial wrap angle α is obtained by the cosine law0minComprises the following steps:
take the maximum initial wrap angle α0maxAt 90 °, the tuck roll center is a ". accordingly, the initial tuck roll angle α is0The value range is as follows:
III, determining the value range of a longitudinal coordinate value z of the fixed hinge point;
in order to ensure the compact structure of the ring rolling mill equipment, the value lower limit z of the longitudinal coordinate value z of the fixed hinge point is takenmin＝1.2R1Upper limit z of the longitudinal coordinate value z of the fixed hinge pointmax＝1.7R1. Therefore, the value range of the fixed hinge point ordinate value z is as follows:
[1.2R1,1.7R1](4)
IV, determining the value range of the fixed hinge point abscissa value x;
in order to ensure enough installation space of the roller holding mechanism, the value of the x value of the abscissa value of the fixed hinge point is taken as the lower limit xmin＝-0.5R1. X value upper limit x of fixed hinge point horizontal coordinate valuemaxIs determined by the following method:
at △ O2NE3In (3), according to the trigonometric function in combination with equation (2), one can obtain:
wherein, α0minAt a minimum initial wrap angle, R1Radius of main roll of ring rolling mill, R2Radius of ring rolling mill core roll, R3For the diameter of the holding roll of the ring rolling mill, R0The outer radius of the ring blank.
At △ O2NE3In the middle, the value upper limit x of the fixed hinge point abscissa value xmaxThe determined straight line x ═ xmaxDistance NE from the x-axis of the coordinate system3＝1.7R1Therefore, the value of the fixed hinge point abscissa value x is limited to the upper limit xmaxThe determined straight line x ═ xmaxAnd the center O of the ring blank2Distance NO of2Can be expressed as:
distance O between center of main roller and center of ring blank1O2＝R1+R0So that the x value of the abscissa value of the fixed hinge point is limited to xmaxThe determined straight line x ═ xmaxCan be expressed as:
therefore, the range of the fixed hinge point abscissa value x is:
in the present embodiment, α is used as the initial wrap angle0The coordinates of the fixed hinge point are expressed by (x, z), and the influence factors of the motion track of the holding roller comprise the initial holding roller angle α0The abscissa value x of the fixed hinge point, the ordinate value z of the fixed hinge point and the combined vector x of the influencing factors of the motion trail of the holding roller are [ α ]0,x,z]L. Outer radius R of ring blank0250.15mm, main roll radius R1550mm, core roll radius R2130mm, radius of the wrap roll R3100mm, thus determined initial wrap angle α0Has a value range of [52.6 DEG, 90 DEG ]]The value range of the longitudinal coordinate value z of the fixed hinge point is [660, 935 ]]The value range of the fixed hinge point abscissa value x is [ -275,85 [)]。
And 2, establishing an evaluation index of the motion track of the holding roller.
The evaluation indexes of the movement locus of the holding roller comprise ring rolling stability evaluation indexes and ring roundness evaluation indexes. The optimization of the motion trail of the holding roller aims to find a group of parameter values of the influence factors of the motion trail of the holding roller, so that the evaluation index of the motion trail of the holding roller reaches the optimum. In the whole ring rolling process, the movement locus of the holding roller mainly affects the stability of the rolling process and the roundness of the ring, and corresponding indexes are required to be established for evaluating the effect of different movement loci of the holding roller on the ring rolling forming aiming at the rolling stability and the roundness of the ring, so as to judge the quality of the movement locus of the holding roller.
FIG. 4 is a sectional view of the ring at a symmetrical plane perpendicular to the axis of the ring, a certain number of nodes are uniformly selected on the inner circle and the outer circle of the section of the ring, and the ring rolling stability evaluation index and the ring roundness evaluation index are calculated by coordinate values of different nodes on the section of the ring in a coordinate system at different moments in the rolling process. The ring section refers to the ring section at the symmetrical plane perpendicular to the axis of the ring.
I, establishing a ring rolling stability evaluation index;
the ring rolling stability evaluation index of the invention is defined by the formula (9):
wherein:
wherein z isMSEFor the evaluation index of the ring rolling stability, m is the number of times of acquiring coordinates of nodes on the excircle and the inner circle of the section of the ring piece in the rolling process, n is the total number of nodes on the inner circle or the excircle of the section of the ring piece, and z is the total number of the nodes on the excircle and the inner circle of the section of the ring pieceojThe z coordinate value of the geometric center of the section of the ring piece, z, is obtained by the j-th calculation based on the excircle of the section of the ring pieceijThe z coordinate value of the geometric center of the section of the ring piece, z, is obtained by the j-th calculation based on the inner circle of the section of the ring pieceojkZ coordinate value of kth node on the excircle of the cross section of the ring at the j-th calculationijkIs the z coordinate value of the kth node on the inner circle of the cross section of the ring at the j-th calculation,
and calculating an ideal value of the z coordinate value of the geometric center of the section of the ring piece based on the excircle or the inner circle of the section of the ring piece. The smaller the ring rolling stability evaluation index is, the stability of the rolling process isThe better the movement track of the holding roller is.
II, establishing a roundness evaluation index of the ring piece;
the ring roundness evaluation index of the invention is defined by the formula (13):
wherein:
(Reo)j＝max|Δrojk|-min|Δrojk| (14)
(Rei)j＝max|Δrijk|-min|Δrijk| (15)
wherein (R)e)MSEFor the roundness evaluation index of the ring piece, m is the number of times of acquiring coordinates of nodes on the outer circle and the inner circle of the section of the ring piece in the rolling process, (R)eo)jFor the jth roundness error obtained by calculation based on the excircle of the section of the ring member, (R)ei)jFor the jth roundness error obtained by calculation based on the inner circle of the cross-section of the ring, the roundness error is the least square evaluation study of the roundness error [ Liyantian ] calculated by the least square method [ J]Journal of North China university of electric Power, 1992(4):59-67.]。xojThe x coordinate value, z coordinate value of the geometric center of the section of the ring piece is calculated and obtained for the jth time based on the excircle of the section of the ring pieceojCalculating a z-coordinate value of the geometric center of the section of the ring piece for the jth time based on the excircle of the section of the ring piece; x is the number ofijThe x coordinate value, z coordinate value of the geometric center of the section of the ring piece is obtained for the jth time based on the calculation of the inner circle of the section of the ring pieceijFor the jth time based on the calculation of the inner circle of the section of the ring pieceObtaining a z coordinate value of the geometric center of the section of the ring piece; x is the number ofojkThe x coordinate value, z, of the kth node on the excircle of the cross section of the ring at the jth calculationojkThe z coordinate value of the kth node on the outer circle of the cross section of the ring piece in the j-th calculation; x is the number ofijkThe x coordinate value, z, of the kth node on the inner circle of the cross section of the ring at the j-th calculationijkThe z coordinate value of the kth node on the inner circle of the cross section of the ring piece in the j-th calculation; Δ rokjFor the jth calculation, the distance from the kth node on the outer circle of the section of the ring to the geometric center of the section of the ring obtained by calculation of the outer circle of the section of the ring, max | delta rokj|、min|Δrokj| represents Δ r, respectivelyokjMaximum and minimum values of; Δ rikjFor the distance from the kth node on the inner circle of the cross section of the ring part at the jth calculation to the geometric center of the cross section of the ring part obtained by calculation of the inner circle of the cross section of the ring part, max | delta rikj|、min|Δrikj| represents Δ r, respectivelyikjMaximum and minimum values of;
and calculating an ideal value of the roundness error obtained based on the excircle or inner circle of the section of the ring piece. The smaller the evaluation index of the roundness of the ring piece is, the better the roundness of the ring piece is and the better the motion track of the holding roller is.
To sum up, defining the combination vector of the evaluation indexes of the motion track of the holding roller:
M＝[zMSE,(Re)MSE]T(19)
and 3, establishing a correlation model of the evaluation index of the motion trail of the holding roller and the influence factors.
The correlation model of the embracing roller motion trail evaluation index and the influence factor comprises a ring rolling stability evaluation index model and a ring roundness evaluation index model, wherein the ring rolling stability evaluation index model is a quadratic polynomial mathematical model of the ring rolling stability evaluation index and the embracing roller motion trail influence factor; the ring roundness evaluation index model is a quadratic polynomial mathematical model of ring roundness evaluation indexes and influence factors of the roller holding motion track. Designing a test scheme by a center combination design method in the value range of the influence factors of the movement locus of the holding roller, carrying out finite element simulation test on each group of parameter combination, obtaining coordinate values of n nodes on the outer circle and n nodes on the inner circle of the cross section of the ring for m times, calculating by using the formulas (9) and (13) to obtain a ring rolling stability evaluation index and a ring roundness evaluation index, and then establishing an associated model of the movement locus evaluation index of the holding roller and the influence factors by regression analysis:
M＝[f1(x),f2(x)](20)
wherein the content of the first and second substances,
f1(x)＝a1α0+a2x+a3z+a4α0x+a5α0z+a6xz+a7α0 2+a8x2+a9z2+a10(21)
f2(x)＝b1α0+b2x+b3z+b4α0x+b5α0z+b6xz+b7α0 2+b8x2+b9z2+b10(22)
wherein M represents a combined vector of the evaluation indexes of the motion trail of the holding roller and is defined by a formula (14), and x represents a combined vector of the influence factors of the motion trail of the holding roller and is defined by a formula (1) α0Is an initial roll holding angle; x is the horizontal coordinate value of the fixed hinge point; z is a fixed ordinate value. f. of1(x) Model representing evaluation index of Ring Rolling stability, a1、a2、a3Respectively represents variables α in the ring rolling stability evaluation index model0The first order coefficient of the variable x and the variable z; a is4、a5、a6Respectively represents variables α in the ring rolling stability evaluation index model0And x, variable α0Interaction term coefficients between z and the variables x and z; a is7、a8、a9Respectively represents variables α in the ring rolling stability evaluation index model0The coefficients of the quadratic terms of the variable x and the variable z; a is10And constant items in the ring rolling stability evaluation index model are shown. f. of2(x) Model representing evaluation index of roundness of ring member, b1、b2、b3Respectively representing variations α in the evaluation index model of the roundness of the ring0The first order coefficient of the variable x and the variable z; b4、b5、b6Respectively representing variations α in the evaluation index model of the roundness of the ring0And x, variable α0Interaction term coefficients between z and the variables x and z; b7、b8、b9Respectively representing variations α in the evaluation index model of the roundness of the ring0The coefficients of the quadratic terms of the variable x and the variable z; b10And constant terms in the ring roundness evaluation index model are shown.
In the embodiment, the value range of the influence factors of the motion trajectory of the wrap rollers determined in the step 1 is the initial wrap roller angle α0Has a value range of [52.6 DEG, 90 DEG ]]The value range of the longitudinal coordinate value z of the fixed hinge point is [660, 935 ]]The value range of the fixed hinge point abscissa value x is [ -275,85 [)]Using the center combination test method, α0And the value ranges of x and z are respectively input into Design-Expert software, and the combined vector x of the influence factors of the motion trail of the holding roller is obtained according to the test scheme shown in the test scheme in the table 1 by the formula (1). And performing finite element numerical simulation, outputting coordinate values of the 24 nodes on the outer circle of the ring section and the 24 nodes on the inner circle of the ring section for 114 times, and calculating by using the formulas (9) and (13) to obtain a ring rolling stability evaluation index z under each group of test dataMSEAnd ring roundness evaluation index (R)e)MSE. And (3) obtaining a combined vector M of the embrace roller motion track evaluation index corresponding to the combined vector x of the influence factors of the embrace roller motion track of each group by the formula (19), wherein the combined vector M is shown in the test result of the table 1.
TABLE 1 test protocol and test results
According to the combined vector x of the influence factors of the motion trail of the holding roller and the combined vector M of the evaluation indexes of the motion trail of the holding roller under the test scheme designed in the table 1, the two times are carried outRegression analysis is carried out to establish a ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) Respectively, formula (23) and formula (24):
after the ring rolling stability evaluation index model and the ring roundness evaluation index model are established, the significance and the reliability of the ring rolling stability evaluation index model and the ring roundness evaluation index model are checked. The significance of the ring rolling stability evaluation index model and the ring roundness evaluation index model is usually checked by variance analysis, and the prediction capabilities of the ring rolling stability evaluation index model and the ring roundness evaluation index model are evaluated according to data under non-test conditions.
Table 2 shows the variance analysis of the ring rolling stability evaluation index model, and it can be seen that the P value of the ring rolling stability evaluation index model<0.0001, which shows that the function model is significant. The correction value of the model decision coefficient is 0.9991, which indicates that the model can explain the change of 99.91% response value, and only 0.09% of the total variation can not be explained by the model; model decision coefficient R2The value is 0.9994, which shows that the model has high correlation between the predicted value and the simulated value, and the fitting effect of the model is good; meanwhile, the predicted value of the model judgment coefficient is reasonably consistent with the correction value of the judgment coefficient, so that the fitting degree of the established ring rolling stability evaluation index model is good.
TABLE 2 analysis of variance of ring rolling stability evaluation index model
TABLE 3Is the variance analysis of the ring roundness evaluation index model, and can see the P value of the ring roundness evaluation index model<0.0001, which shows that the function model is significant. The corrected value of the model decision coefficient is 0.9931, which indicates that the model can explain the change of 99.31% response value, and only 0.69% of the total variation can not be explained by the model; determination coefficient R of model2The correlation between the model predicted value and the simulation value is 0.9949, so that the model has good fitting effect; meanwhile, the predicted value of the model judgment coefficient is reasonably consistent with the correction value of the judgment coefficient, so that the fitting degree of the established ring roundness evaluation index model is good.
TABLE 3 analysis of variance of ring roundness evaluation index model
According to the analysis, the established ring rolling stability evaluation index model and the ring roundness evaluation index model are obvious, but the prediction capability of the models needs to be evaluated according to data under non-experimental conditions, wherein the model is determined according to the α determined in the step I0And the value ranges of x and z, randomly selecting 5 groups of non-test data to obtain corresponding embracing roller motion track influence factor combination vectors x, calculating by using a formula (9) and a formula (13) to obtain simulation values of a ring rolling stability evaluation index and a ring roundness evaluation index, and calculating by using a formula (23) and a formula (24) to obtain predicted values of the ring rolling stability evaluation index and the ring roundness evaluation index as shown in tables 4 and 5. Through comparison, the differences between the predicted values and the simulation values of the ring rolling stability evaluation index and the ring roundness evaluation index are very small, and the error is not more than 2%. Therefore, the established ring rolling stability evaluation index model and the ring roundness evaluation index model have better prediction capability.
TABLE 4 comparison of predicted values and simulated values of ring rolling stability evaluation indexes
TABLE 5 comparison of the predicted value of the evaluation index of the roundness of the ring piece with the simulated value
And 4, establishing a mathematical model for optimizing the motion track of the holding roller.
Based on the established correlation model of the looping roller motion track evaluation index and the influence factor, an evaluation function of a double-evaluation index optimization problem is further established by using a linear weighting method [ Chen Li, Sun Bao, Jianglinqi ] comparison analysis of a multi-target linear weighting evaluation model and a membership degree evaluation model [ J ]. Industrial technology economy, 1994(2):44-45 ], namely a mathematical model for looping roller motion track optimization, wherein the double-evaluation indexes are a looping stability evaluation index and a loop roundness evaluation index.
The method comprises the following specific steps:
i obtaining ring rolling stability evaluation index model f1(x) The optimal solution vector of (2);
and the optimal solution vector refers to a combined vector of the influence factors of the motion trail of the holding roller when the evaluation index reaches an optimal value. The smaller the ring rolling stability evaluation index in the rolling process is, the better the ring rolling stability is, and the better the movement track of the holding roller is. The method comprises the steps of utilizing a mathematic tool MATLAB to obtain a ring rolling stability evaluation index z of the roll embracing motion track influence factors in a value rangeMSEObtaining the optimal solution vector of the minimum value:
minf1(x)＝f1(x1 *) (25)
in the formula, x1 *For ring rolling stability evaluation index model f1(x) The optimal solution vector of,.
II obtaining ring roundness evaluation index model f2(x) The optimal solution vector of (2);
the smaller the evaluation index of the roundness of the ring piece in the rolling process is, the better the roundness of the ring piece is, and the better the movement track of the holding roller is. Obtaining a ring roundness evaluation index (R) by using a mathematic tool MATLAB to enable the influence factors of the motion track of the holding roller to be in a value rangee)MSEObtaining the optimal solution vector of the minimum value:
minf2(x)＝f2(x2 *) (26)
in the formula, x2 *For ring roundness evaluation index model f2(x) The optimal solution vector of (2).
III determination of ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) A vector of weight coefficients;
the weight coefficient vector refers to a weight coefficient omega of a ring rolling stability evaluation index model1And the weight coefficient omega of the ring roundness evaluation index model2The composed vector ω:
ω＝[ω1,ω2](27)
wherein, the weight coefficient omega of the ring rolling stability evaluation index model1And the weight coefficient omega of the ring roundness evaluation index model2Determined by equation (28):
in the formula, ω1The weight coefficient omega of the ring rolling stability evaluation index model2And the weight coefficient is the evaluation index model of the roundness of the ring piece.
IV, establishing a mathematical model for optimizing the motion track of the holding roller;
a mathematical model for optimizing the motion trail of the holding roller can be obtained by a linear weighting method:
in the formula (I), the compound is shown in the specification,
i.e. a mathematical model for optimizing the motion trail of the holding roller, omega is a ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) The vector of weight coefficients.
In the present embodiment, the ring rolling stability evaluation index model f1(x) Is (23)And obtaining the optimal solution vector of the ring rolling stability evaluation index model through a mathematic tool MATLAB:
x1 *＝[90.0,85.0,935.0](30)
ring piece roundness evaluation index model f2(x) And (3) solving an optimal solution vector of the ring roundness evaluation index model by a mathematic tool MATLAB as shown in the formula (24):
x2 *＝[59.8,-275.0,660.0](31)
the formula (30) and the formula (31) are respectively substituted into the formula (28) to obtain the weight coefficient omega of the ring rolling stability evaluation index model10.464 and weight coefficient omega of ring roundness evaluation index model20.536, resulting in a weight coefficient vector:
ω＝[0.464,0.536](32)
and (3) respectively substituting the formulas (32), (23) and (24) into the formula (29) to obtain a mathematical model for optimizing the motion track of the holding roller:
wherein the content of the first and second substances,
mathematical model optimized for the path of the rollers1(x) Is a ring rolling stability evaluation index model, f2(x) As an index model for evaluating the roundness of a ring member, α0Is the initial holding roll angle, x is the abscissa value of the fixed hinge point, and z is the ordinate value of the fixed hinge point.
And 5, obtaining an optimized value of the influence factors of the movement track of the wrap roll and an optimal wrap roll movement track.
The mathematical model for optimizing the motion trail of the holding roller is a linear weighting model of a ring rolling stability evaluation index model and a ring roundness evaluation index model, and the influence of the motion trail of the holding roller on the ring rolling stability and the ring roundness is considered. The smaller the ring rolling stability evaluation index is, the better the ring rolling stability is; the smaller the evaluation index of the roundness of the ring piece is, the better the roundness of the ring piece is, and the better the motion track of the holding roller is. The optimization target of the movement track of the holding roller is the mathematics for optimizing the movement track of the holding rollerModel (model)
Obtaining a minimum value:
in the formula, x*Mathematical model for representing optimization of motion trail of holding roller
The optimal solution vector of (a) is,
the influence factor of the motion track of the holding roller is shown in a value range so that
And obtaining the minimum value of the combined vector of the influence factors of the motion trail of the holding roller.
The mathematic tool MATLAB is used for acquiring the influence factors of the motion trail of the holding roller in the value range
To a minimum
Optimal solution vector of (2):
x*＝[α0 *,x*,z*](35)
α0 *for an optimized initial wrap angle, (x)*,z*) The optimized position of the fixed hinge point and the optimized position of the fixed hinge point determine the movement track of the holding roller, and the movement track of the holding roller and the movement track of the ring piece can reach the minimum value under the condition of considering the ring rolling stability and the roundness of the ring piece, namely the optimal movement track of the holding roller.
In the embodiment, the mathematical model for optimizing the motion trail of the wrap roll is shown as formula (33), and the value range of the influence factors of the motion trail of the wrap roll is the initial wrap roll angle α0Has a value range of [52.6 DEG, 90 DEG ]]Is fixed toThe value range of the longitudinal coordinate value z of the hinge point is [660, 935 ]]The value range of the fixed hinge point abscissa value x is [ -275,85 [)]Obtained using the mathematical tool MATLAB
Optimal solution vector x of mathematical model for optimizing motion track of holding roller*＝[71.7,85.0,935.0]. That is, it is explained that the optimum initial wrap roll angle is 71.7 ° in the present embodiment, and the coordinate of the optimum fixed hinge point is (85.0,935.0), so the optimum wrap roll movement locus is a circular locus centered on point (85.0,935.0) and the initial wrap roll position is at wrap roll angle 71.7 °, as shown in fig. 5.
Therefore, the optimization of the roll embracing motion track of the encircling mill is completed.
Claims (4)
1. The optimization method of the looping mill roller holding motion trail is characterized by comprising the following specific steps of:
step 1, determining influence factors and value ranges of the movement track of the holding roller:
the influence factors of the motion trail of the holding roller comprise an initial holding roller angle α0A fixed hinge point horizontal coordinate x and a fixed hinge point vertical coordinate z;
calculating the value range of the influence factors of the roll holding motion trail according to the roll size of the ring rolling mill and the size of a ring blank, wherein the roll size of the ring rolling mill comprises the radius R of a main roll of the ring rolling mill1Radius R of core roll of ring rolling mill2Radius R of wrap roll of ring rolling mill3The size of the ring blank comprises the outer radius R of the ring blank0；
Initial wrap angle α0The value range of (A):
the value range of the abscissa x of the connecting rod fixed hinge point is as follows:
[1.2R1,1.7R1](4)
the value range of the vertical coordinate z of the connecting rod fixed hinge point is as follows:
step 2, establishing an evaluation index of the motion track of the holding roller:
the evaluation indexes of the movement track of the holding roller comprise ring rolling stability evaluation indexes and ring roundness evaluation indexes; calculating a ring rolling stability evaluation index and a ring roundness evaluation index according to coordinate values of different nodes on the ring section at different moments in the rolling process, wherein the ring section is a ring section on a symmetrical plane vertical to the axis of the ring;
step 3, establishing a correlation model of the evaluation indexes of the motion trail of the holding roller and the influence factors:
designing a test scheme by a center combination design method in a value range of the influence factors of the movement track of the holding roller, carrying out finite element simulation test on each group of parameter combination, obtaining coordinate values of k nodes on the outer circle and k nodes on the inner circle of the cross section of the ring for m times, calculating according to test results to obtain the central offset displacement of the ring and the root-mean-square error of the roundness of the ring, and respectively establishing a ring rolling stability evaluation index model f by regression analysis1(x) And ring roundness evaluation index model f2(x)；
Step 4, establishing a mathematical model for optimizing the motion track of the holding roller:
based on the established association model of the evaluation index of the movement track of the contracting roll and the influence factors, the mathematical model for optimizing the movement track of the contracting roll is established
Step 5, obtaining an optimized value of the influence factors of the motion trail of the holding roller and an optimal holding roller motion trail:
the method can obtain the influence factor of the motion track of the holding roller within the value range
To a minimum
Optimal solution vector of (2):
x*＝[α0 *,x*,z*](35)
α0 *for an optimized initial wrap angle, (x)*,z*) The optimized fixed hinge point position is determined as the optimized holding roller motion track;
therefore, the optimization of the roll embracing motion track of the encircling mill is completed.
2. The optimization method of the roll embracing motion trail of the ring rolling mill according to claim 1, wherein in the step 2, the ring rolling stability evaluation index is calculated through a formula (9):
wherein:
wherein z isMSEFor the evaluation index of the ring rolling stability, m is the number of times of acquiring coordinates of nodes on the excircle and the inner circle of the section of the ring piece in the rolling process, n is the total number of nodes on the inner circle or the excircle of the section of the ring piece, and z is the total number of the nodes on the excircle and the inner circle of the section of the ring pieceojThe z coordinate value of the geometric center of the section of the ring piece, z, is obtained by the j-th calculation based on the excircle of the section of the ring pieceijThe j-th ring section obtained based on the calculation of the inner circle of the ring sectionZ-coordinate value of which center, zojkZ coordinate value of kth node on the excircle of the cross section of the ring at the j-th calculationijkIs the z coordinate value of the kth node on the inner circle of the cross section of the ring at the j-th calculation,
calculating an ideal value of a z coordinate value of the geometric center of the section of the ring piece based on the excircle and the inner circle of the section of the ring piece;
calculating a ring roundness evaluation index by the formula (13):
wherein
(Reo)j＝max|Δrojk|-min|Δrojk| (14)
(Rei)j＝max|Δrijk|-min|Δrijk| (15)
Wherein (R)e)MSEFor the roundness evaluation index of the ring piece, m is the number of times of acquiring coordinates of nodes on the outer circle and the inner circle of the section of the ring piece in the rolling process, (R)eo)jFor the jth roundness error obtained by calculation based on the excircle of the section of the ring member, (R)ei)jCalculating a roundness error obtained based on the inner circle of the section of the ring piece for the jth time, wherein the roundness error is calculated by adopting a least square method; x is the number ofojFor the j-th time of geometric centre of ring section obtained based on calculation of outer circle of ring sectionx coordinate value, zojCalculating a z-coordinate value of the geometric center of the section of the ring piece for the jth time based on the excircle of the section of the ring piece; x is the number ofijThe x coordinate value, z coordinate value of the geometric center of the section of the ring piece is obtained for the jth time based on the calculation of the inner circle of the section of the ring pieceijCalculating a z-coordinate value of the geometric center of the section of the ring piece for the jth time based on the inner circle of the section of the ring piece; x is the number ofojkThe x coordinate value, z, of the kth node on the excircle of the cross section of the ring at the jth calculationojkThe z coordinate value of the kth node on the outer circle of the cross section of the ring piece in the j-th calculation; x is the number ofijkThe x coordinate value, z, of the kth node on the inner circle of the cross section of the ring at the j-th calculationijkThe z coordinate value of the kth node on the inner circle of the cross section of the ring piece in the j-th calculation; Δ rokjFor the jth calculation, the distance from the kth node on the outer circle of the section of the ring to the geometric center of the section of the ring obtained by calculation of the outer circle of the section of the ring, max | delta rokj|、min|Δrokj| represents Δ r, respectivelyokjMaximum and minimum values of; Δ rikjFor the distance from the kth node on the inner circle of the cross section of the ring part at the jth calculation to the geometric center of the cross section of the ring part obtained by calculation of the inner circle of the cross section of the ring part, max | delta rikj|、min|Δrikj| represents Δ r, respectivelyikjMaximum and minimum values of;
and calculating an ideal value of the roundness error based on the outer circle and the inner circle of the section of the ring piece.
3. The optimization method of the roll embracing motion trail of the ring rolling mill according to claim 1, wherein an evaluation index model f of ring rolling stability1(x) The method is a quadratic polynomial mathematical model of ring rolling stability evaluation indexes and influence factors of the roll holding motion track; ring piece roundness evaluation index model f2(x) The method is characterized in that a quadratic polynomial mathematical model of influence factors of a ring roundness evaluation index and a roller holding motion track is as follows:
f1(x)＝a1α0+a2x+a3z+a4α0x+a5α0z+a6xz+a7α0 2+a8x2+a9z2+a10(21)
f2(x)＝b1α0+b2x+b3z+b4α0x+b5α0z+b6xz+b7α0 2+b8x2+b9z2+b10(22)
wherein x represents the combined vector of the influencing factors of the motion trail of the holding roller, and x is [ α ]0,x,z]，α0Is an initial roll holding angle; x is the abscissa value of the fixed hinge point of the connecting rod; z is a connecting rod fixed longitudinal coordinate value; f. of1(x) Model representing evaluation index of Ring Rolling stability, a1、a2、a3Respectively represents variables α in the ring rolling stability evaluation index model0The first order coefficient of the variable x and the variable z; a is4、a5、a6Respectively represents variables α in the ring rolling stability evaluation index model0And x, variable α0Interaction term coefficients between z and the variables x and z; a is7、a8、a9Respectively represents variables α in the ring rolling stability evaluation index model0The coefficients of the quadratic terms of the variable x and the variable z; a is10Constant items in a ring rolling stability evaluation index model are represented; f. of2(x) Model representing evaluation index of roundness of ring member, b1、b2、b3Respectively representing variables α in the index model of the ring roundness evaluation index0The first order coefficient of the variable x and the variable z; b4、b5、b6Respectively representing variations α in the evaluation index model of the roundness of the ring0And x, variable α0Interaction term coefficients between z and the variables x and z; b7、b8、b9Respectively representing variations α in the evaluation index model of the roundness of the ring0The coefficients of the quadratic terms of the variable x and the variable z; b10And constant terms in the ring roundness evaluation index model are shown.
4. The method for optimizing the roll embracing motion trail of the encircling mill according to claim 1, wherein the specific steps of establishing the mathematical model for optimizing the roll embracing motion trail are as follows:
i obtaining ring rolling stability evaluation index model f1(x) The optimal solution vector of (2);
the optimal solution vector refers to a combined vector of the influence factors of the motion trail of the holding roller when the evaluation index reaches an optimal value; the smaller the ring rolling stability evaluation index in the rolling process is, the better the ring rolling stability is, and the better the movement track of the holding roller is; the method comprises the steps of utilizing a mathematic tool MATLAB to obtain a ring rolling stability evaluation index z of the roll embracing motion track influence factors in a value rangeMSEObtaining the optimal solution vector of the minimum value:
minf1(x)＝f1(x1 *) (25)
in the formula, x1 *For ring rolling stability evaluation index model f1(x) The optimal solution vector of (2);
II obtaining ring roundness evaluation index model f2(x) The optimal solution vector of (2);
the smaller the evaluation index of the roundness of the ring piece in the rolling process is, the better the roundness of the ring piece is, and the better the movement track of the holding roller is; obtaining a ring roundness evaluation index (R) by using a mathematic tool MATLAB to enable the influence factors of the motion track of the holding roller to be in a value rangee)MSEObtaining the optimal solution vector of the minimum value:
minf2(x)＝f2(x2 *) (26)
in the formula, x2 *For ring roundness evaluation index model f2(x) The optimal solution vector of (2);
III determination of ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) A vector of weight coefficients;
the weight coefficient vector refers to a weight coefficient omega of a ring rolling stability evaluation index model1And the weight coefficient omega of the ring roundness evaluation index model2The composed vector ω:
ω＝[ω1,ω2](27)
wherein the ring rolling stabilityEvaluation index model weight coefficient ω1And the weight coefficient omega of the ring roundness evaluation index model2Determined by equation (28):
in the formula, ω1The weight coefficient omega of the ring rolling stability evaluation index model2The weight coefficient is used as the evaluation index model of the roundness of the ring piece;
IV, establishing a mathematical model for optimizing the motion track of the holding roller;
a mathematical model for optimizing the motion trail of the holding roller can be obtained by a linear weighting method:
in the formula (I), the compound is shown in the specification,
i.e. a mathematical model for optimizing the motion trail of the holding roller, omega is a ring rolling stability evaluation index model f1(x) And ring roundness evaluation index model f2(x) The vector of weight coefficients.
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