CN102500640B - Technique optimization method of cage roll forming machine set of longitudinal welded pipe - Google Patents

Abstract

The invention discloses a technique optimization method of a cage roll forming machine set of a longitudinal welded pipe, belonging to the technical field of mechanical forming, wherein forming technique parameters are obtained by coordinate transformation and iterative process; the invention aims at solving the problem that the current welded pipe manufacturing enterprises basically rely on experience and a cut and try method to obtain the forming technique parameters of cage roll forming machine sets of welded pipes; and the technique optimization method disclosed by the invention has the advantages of providing a better theoretical reference for design methods of cage roll forming technique parameters, shortening the development periods of products with new specifications, decreasing raw material waste and reducing the production cost of longitudinal welded pipes.

Description

The technique optimization method of welded pipe cage forming unit

Technical field

What the present invention relates to is the method for a kind of mechanical molding technical field, specifically a kind of technique optimization method of welded pipe cage forming unit.

Background technology

ERW production is generally to adopt roll forming technique.Roll forming technique is the multi-step forming roll by arranged in order, metal plate and belt is bent to gradually to a kind of Technology of Plastic Processing of particular cross section from straightened condition.The structure of early stage conventional roll o ing unit is plain-barreled roll and edger roll arranged crosswise, mainly for the production of small-diameter welded pipes, afterwards through updating, early stage shaping unit starts to develop becomes form flat, edger roll+edger roll group, can produce also diameter in minor diameter develops into of caliber, after this in order to overcome edge deformation in the conventional roll o ing and resilience is excessive and shaping edger roll sharing nature is poor shortcoming, and then develop into row roller forming.

Row roller forming is also named cage shaping (cage roll forming), refer to that band is rolled into the roll-type forming technology of socket by some groups of passive pony roll Curved Continuous of two rows, in the continuous row roller forming process of skelp, utilize the three-point bending principle, at the adjustable passive little roller frame in essence shaping one or more groups position of (closed type) front employing, the some active horizontal frames and the passive standing roller frame that replace common roll-type to be shaped, band can be deformed into socket by designed pass schedule.Typical welded pipe cage forming unit model as shown in Figure 1.Because row roller forming technique has, the strip resilience is little, the edge shaping quality is good and the large characteristics of roll sharing nature strong three, also all numerous and confused transformation roll-type shapings in a row of the not only intermediate diameters welded tube unit of the new operation all row's of employing roll-type shapings mostly in the world, and in the past traditional roll-type shaping unit at present.Row roller forming technique is considered to the trend of current welded tube production technology development.For the ERW shaping unit that adopts row roller forming technique, its forming parameters has directly determined the shaping position attitude of roll in space, is the direct factor that affects forming quality.Reasonably forming parameters can be distributed the transverse curvature distortion of differing formed section lower strip preferably, thereby reduces in theory the probability that the product shaping defect occurs, and significantly improves the forming quality of distortion pipe.

The passage that respectively is shaped in welded tube conventional roll o ing unit mostly adopts plain-barreled roll or edger roll to realize the transverse curvature of sheet material, in unit, the free degree of forming rolls is regulated relatively simple, the forming parameters of its each passage roll only needs to carry out simple computation according to determined band steel shaping bottom line and flower type figure and can obtain, correspondingly, the translation adjustment that in the unit of production scene, each forming rolls also only need to be done upper and lower (plain-barreled roll) or left and right (edger roll) can put in place, so that the forming parameters of welded tube conventional roll o ing unit is determined is relatively easy.But, for the welded tube unit that adopts row roller forming technique, because the float roller of installing on frame is to do as a whole the adjustment, and its each row's roller Duan Junyou nearly 5 adjust the free degree (translation of entry and exit width and height and around the rotation of roller beam), the forming parameters that therefore will calculate according to the colored type design drawing of strip respective row roller section also just becomes very difficult.The domestic and international research definite for the forming parameters of welded pipe cage forming unit is substantially in blank at present, the welded tube manufacturing enterprise of the overwhelming majority adopts empirical method or trial and error procedure to obtain the forming parameters of row's roller section, it is not only wasted time and energy, increase production cost, and the theoretical foundation of the science of shortage, be difficult to reach quantification and the optimization of forming parameters.

Summary of the invention

The present invention is directed to the prior art above shortcomings, a kind of technique optimization method of welded pipe cage forming unit is provided, for current welded tube manufacturing enterprise, substantially rely on experience and trial and error procedure to obtain this present situation of forming parameters of welded tube row roller forming unit, in order to make the row roller forming technological parameter there is better theoretical foundation, shorten the construction cycle of new spec product simultaneously, reduce waste of raw materials, reduce the ERW production cost.By this method can science, realize that the wounded in the battle type figure of slave plate obtains to welded pipe cage forming unit forming parameters accurately, fast and efficiently, have dependable with function preferably, by it, definite forming parameters can be directly used in production and the manufacture of on-the-spot ERW.

The present invention is achieved by the following technical solutions, the present invention includes following steps:

The first step, row's roller roll centre of take is initial point, sets up the first local coordinate system;

Described the first local coordinate system, i.e. X ₃y ₃z ₃refer to: row's roll axis is X ₃axle, the Z of the first local coordinate system ₃axle is consistent with the Z-direction under global coordinate system, according to the cross section profile shape of row's roller, sets up corresponding cross section profile parametric equation, establishes P for a bit (x on row's running roller profile ₃, y ₃, z ₃), at the initial point O of the first local coordinate system ₃, arrange under the roller roll centre, according to the contour shape of float roller, the parametric equation of the row's of writing out running roller profile

Wherein: R _pfor the profile radius of float roller, the footpath, the end that R is the float roller.

Second step, take that to cross the roller beam cross section center of circle arrange roll axis be initial point, sets up the second local coordinate system and construct the initial static row roller curved surface of all row's running roller profiles.

Described the second local coordinate system, i.e. X ₂y ₂z ₂in X ₂axle is consistent with the X-direction under global coordinate system, Z ₂axle is consistent with the Z-direction under global coordinate system, and the rule of arranging according to row's roller group in space obtains the direction that longitudinally is shaped and respectively arranges the first primary dip (S of roll axis in space _wqs=0 o'clock), and then constructed the initial static row roller curved surface of all row's running roller profiles

:

Wherein: P is at local coordinate system O ₂under coordinate be (x ₂, y ₂, z ₂), the roll centre O of row's roller ₃at local coordinate system X ₂y ₂z ₂under coordinate position be ²o ₃=(x ₃₂, y ₃₂, z ₃₂) ^t, work as S _wqs=0, when roller beam axis is parallel to the shaping direction, ²o ₃position according to row roller group, in the rule of arranging in space, determine:

Write formula (2) as homogeneous form, can be constructed the initial static row roller curved surface of all row's running roller profiles

homogeneous form:

$\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_3^2\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e1,\mathrm{\α})& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_3^2\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_3+x_{32}\\ y_3+y_{32}\\ z_3+z_{32}\\ 1\end{array}\right)---\left(3\right)$

Wherein: α controls parameter S for rotation _wqs=0 o'clock, the first primary dip value of row's roller section, e1=(0,0,1) ^t.

The 3rd step adopts the mode of inclination correction to arrange after the roller curved surface is revised and obtain the relevant row of forming parameters roller curved surface initial static under the second local coordinate system.

Described inclination correction refers to: obtaining initial static row roller curved surface

basis on, control parameter S according to rotation _wqsthe correction value θ at the row's of calculating roller inclination angle _z(S _wqs), at the second local coordinate system X ₂y ₂z ₂under, can obtain revised and forming parameters S through a rotation transformation _wqsrelevant row's roller curved surface homogeneous form:

$\left(\begin{array}{c}{x}_{2z}\\ y_{2z}\\ z_{2z}\\ 1\end{array}\right)=\left[\begin{array}{cc}R(e2,{\mathrm{\θ}}_z\left(S_{\mathrm{wqs}}\right))& 0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)---\left(4\right)$

Wherein: e2=(0,0,1) ^t.

The 4th step, the reference point of arranging roller frame of take is initial point, be the cylinder boss axis of entrance side slide block and the intersection point of round hole axial, set up the 3rd local coordinate system, and be transition and conversion to the row's roller curved surface under global coordinate system by the relevant row of forming parameters roller curved surface with the 3rd local coordinate;

Described the 3rd local coordinate system, i.e. X ₁y ₁z ₁middle X ₁axle is consistent with the X-direction under global coordinate system, Z ₁axle is consistent with the Z-direction under global coordinate system, and the axis of roller beam is parallel to strip be shaped longitudinally direction, i.e. X _iqs=X _oqs, Y _iqs=Y _oqs, row's roller curved surface now is only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, first will arrange the roller curved surface convert at local coordinate system O ₁under curved surface again according to an O ₁and the relative distance relation between O, utilize translation transformation, again by curved surface

convert the curved surface under global coordinate system O to

curved surface

be under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant curved surface.

Described is that transition and conversion refers to the 3rd local coordinate: the coordinate system X of section sets a trap ₂y ₂z ₂initial point O ₂at local coordinate system X ₁y ₁z ₁under coordinate be (x ₂₁, y ₂₁, z ₂₁) ^t, consider that now the axis of roller beam is parallel to the strip direction that is shaped longitudinally, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, by local coordinate system X ₂y ₂z ₂under row's roller curved surface

convert local coordinate system X to ₁y ₁z ₁under row's roller curved surface

Wherein: local coordinate system X ₁y ₁z ₁initial point O ₁coordinate under global coordinate system XYZ is (x ₁₀, y ₁₀, z ₁₀) ^t, due to initial point O ₁for the axis of row's reference point of roller frame and roller beam is parallel to strip be shaped longitudinally direction, i.e. X _oqs=X _iqs, Y _oqs=Y _iqsso, initial point O ₁coordinate position only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined, according to an O ₁and the relative distance relation between an O, utilize translation transformation again, by local coordinate system X ₁y ₁z ₁under row's roller curved surface

convert the row's roller curved surface under global coordinate system XYZ to

The 5th step, be rotated correction by the row's roller curved surface under global coordinate system, obtains the forming parameters correlation surface;

Described forming parameters correlation surface refers to:

5.1) under global coordinate system O, if Y _iqs≠ Y _oqs, X _iqs=X _oqs, mean curved surface

understood the reference point O that arranges roller frame ₁rotate θ around X-axis _x, θ _xcan be by according to Y _iqs, Y _oqsdifference and the spacing of chute calculate, therefore arrange the roller curved surface

the reference point O of the row's of mistake roller frame ₁rotate θ around X-axis _xafter curved surface

can be tried to achieve by the complex transformation of coordinate:

$\left(\begin{array}{c}{x}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e3,{\mathrm{\θ}}_x)& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_z\\ y_z\\ z_z\\ 1\end{array}\right)---\left(7\right)$

Wherein: e3=(1,0,0) ^t, curved surface

under global coordinate system, cross row's running roller profile and with 4 forming parameters S _wqs, X _iqs, Y _iqsand Y _oqsrelevant curved surface;

5.2) at the row's of trying to achieve roller curved surface

basis on, consider under global coordinate system O Y _iqs≠ Y _oqs, and X _iqs≠ X _oqs, this means curved surface

the further reference point O of the row's of walking around roller frame ₁and direction cosines are (0, cos θ _x, sin θ _x) ^tstraight line rotation, the anglec of rotation is according to Y _iqsand Y _oqsbetween difference, X _iqsand X _oqsbetween difference and chute the distance calculate, finally according to the complex transformation of coordinate, can obtain:

$\left(\begin{array}{c}{x}_{\mathrm{zxy}}\\ y_{\mathrm{zxy}}\\ z_{\mathrm{zxy}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(\mathrm{<figure-callout\; id="4"\; label="e"\; filenames="HDA0000099966050000012.png"\; state="\{\{state\}\}">e</figure-callout>}4,{\mathrm{\&alpha;}}_2)& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\\ 1\end{array}\right)---\left(8\right)$

So far curved surface

be under global coordinate system, cross row's running roller profile and with 5 forming parameters S _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsrelevant dynamic row's roller curved surface.

The 6th step, utilize flower type method for designing to calculate the colored type figure of strip under the row differing formed position of roller section, thereby obtain the shape of cross section of row roller section entry and exit side plate band, the forming parameters correlation surface obtained in conjunction with geometrical constraint boundary condition and the 5th step, can be regarded as to obtain S _wqs, X _iqsand Y _iqsinitial parameter;

Described geometrical constraint boundary condition refers to:

(a) row roller section porch strip edge end points D _iwith certain 1 P on row's running roller profile _ioverlap, and

(b) contact point P on float running roller profile _iwith the tangential direction of shaping pipe EDGE CONTACT end points, be consistent, specific as follows:

Investigation under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant row's roller curved surface

equation, by geometrical constraint boundary condition (a), can be obtained:

X _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)＝X _d(θ _i，z _i) (9)

Y _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)＝Y _d(θ _i，z _i) (10)

Wherein: X _zand Y _zon the row's of being running roller profile, the XY of contact point, can be according to row's roller curved surface to coordinate figure

solving Equations obtain; X _dand Y _dcan calculate according to flower type method for designing;

By geometrical constraint boundary condition (b), can be obtained:

T _pi(s _wqs，x _iqs，y _iqs，θ _i，z _i)＝T _di(θ _i，z _i) (11)

Wherein: T _pifor the tangent line direction vector at contact point place on row's running roller profile, can be according to row's roller curved surface

solving Equations obtain; T _difor the tangent line direction vector of strip flower type at the contact terminal place, can try to achieve according to flower type method for designing.

The 7th step, construct, strip edge, porch end points along the width X under global coordinate system and height Y-direction to dynamic row's roller curved surface apart from functional ∏, then substitution initial parameter after the iteration of several times, calculate all forming parameters S that meet particular requirement apart from functional ∏ _wqs, X _iqs, Y _iqs, Y _oqsand X _oqs, concrete steps are as follows:

7.1) try to achieve rotation control parameter S _wqsand initial translation parameters X _iqs0, Y _iqs0basis on, in order further to try to achieve the forming parameters X of final entrance and exit side height and width _iqs, Y _iqs, Y _oqsand X _oqs, structure outlet and strip edge, porch end points D _oand D _ialong width (X) and height (Y) direction to row's roller curved surface apart from functional:

I＝∏(f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)，f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _o，z _o))

＝f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)+f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _o，z _o) (12)

Wherein:

$f_i(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs},}{s}_{\mathrm{wqs}},{\mathrm{\&theta;}}_i{z}_i)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-X_{\mathrm{di}})}^2{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-Y_{\mathrm{di}})}^2}$

$f_o(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs},}{s}_{\mathrm{wqs}},{\mathrm{\&theta;}}_o{z}_o)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-X_{\mathrm{do}})}^2{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-Y_{\mathrm{do}})}^2}$

7.2) initialize the control parameter of outlet side width and short transverse, get x _oqs0=x _iqs0, y _oqs0=y _iqs0; By X _iqs, Y _iqs, X _oqs, Y _oqsand S _wqssubstitution row roller curved surface

equation (8) formula obtain arranging roller curved surface entrance side contact point coordinate x _zxyi, y _zxyiwith outlet side contact point coordinate x _zxyo, y _zxyo, then according to flower type method for designing, calculate row's roller section entrance side strip marginal end point coordinates X _di, Y _diand outlet side strip marginal end point coordinates X _do, Y _do, then by (12) formula, calculate apart from functional I value and revise step-length d _xi, d _yi, d _xoand d _yo; Whether judging distance functional I value satisfies condition simultaneously, if meet, exports current each forming parameters; If do not meet, according to revising current each forming parameters of step-length correction, and recalculate apart from functional I, until meet stopping criterion for iteration apart from functional I value, corresponding each forming parameters X while can be regarded as to such an extent that dynamically arrange the meeting the demands apart from functional ∏ of roller curved surface _iqs, Y _iqs, X _oqs, Y _oqsand S _wqsvalue.

In the solution procedure of described iteration, the corrected Calculation formula of outlet and each forming parameters of porch is:

x _iqs＝x _iqs-dx _i，y _iqs＝y _iqs-dy _i，x _oqs＝x _oqs-dx _o，y _oqs＝y _oqs-dy _o。

According to above-mentioned computational methods, the initial forming parameters of substitution, after the several times iteration, corresponding each forming parameters S while can be regarded as to such an extent that dynamically arrange the meeting the demands apart from functional ∏ of roller curved surface _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsvalue.

The 8th step, according to calculating determined forming parameters S _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsvalue, be used directly in float roller on production scene adjustment row roller section shaping unit and, at the shaping position in space, carry out production and the manufacture of ERW.

The present invention can be for optimizing the forming parameters of welded pipe cage forming unit, realize the leap to " theory " by " experience " of row roller forming process parameters design, breaking external industry blocks and technical monopoly, have that theoretical property is strong, accuracy good, reliability is high, efficiency is high and the characteristics such as practicality, while being specially adapted to develop new spec welded tube product, the theory of forming parameters is calculated.If when exploitation new spec welded tube, relying on traditional trial and error procedure to form technological parameter to complicated welded pipe cage forming unit obtains, often need to carry out repetition test and adjustment (reaching month) for the forming parameters under each row roller forming section on production line, it not only expends the time of a large amount of preciousnesses, increase the construction cycle of new product, and waste a large amount of examination rolling sheets, improve the cost of new product development; Yet the forming parameters that realizes the welded pipe cage forming unit by the present invention is obtained, not only design time is foreshortened to 1 hour with interior (the efficiency raising reaches more than 700 times), and overcome traditional trial and error procedure and adjusting and limitation during designing and arranging roller forming parameters, both greatly shorten the design cycle, improved well again reliability and the theoretical property of design.

The accompanying drawing explanation

Fig. 1 welded pipe cage forming unit schematic diagram;

In figure: 1. for pinch passage, 2. for the crimp passage, 3. for the preform section, 4. for the line shaped segment, 5. for smart shaped segment.

Fig. 2 arranges roller section frame schematic diagram;

In figure: 1 for being equipped with the roller beam of float roller, for integrally-regulated all float rollers, also can be under the driving of motor around self axis rotation, with this, regulate the spatial arrangement angle of float roller, 2 is the support be connected with the roller beam, for associated roller beam, go out, the motion of entrance side, the 3rd, row's roller section entrance side vertical slipper, be responsible for the entrance side height of control roll beam 1, the 4th, row's roller section outlet side vertical slipper, be responsible for the outlet side height of control roll beam 1, 5 guide posts that are entrance side slide block 3, 6 guide posts that are outlet side slide block 4, 7 is row's roller section entrance side transverse slider, be responsible for the entrance side width of control roll beam 1, 8 is row's roller section outlet side transverse slider, be responsible for the outlet side width of control roll beam 1, the 9 fixedly chutes for row's roller section entrance side, the 10 fixedly chutes for row's roller section outlet side.

Fig. 3 arranges the free degree of roller section and adjusts schematic diagram.

Fig. 4 arranges the flow chart of roller section forming parameters design.

The schematic diagram of each coordinate system of Fig. 5.

Fig. 6 row roller forming position affect schematic diagram.

Fig. 7 geometrical constraint boundary condition schematic diagram.

The flow chart of Fig. 8 forming parameters iterative computation.

The passage place relative curvature integrated value that respectively is shaped under the new forming parameters of Fig. 9 and production scene forming parameters distributes and compares schematic diagram.

The shaping geometric representation of preform section strip under the forming parameters of Figure 10 production scene.

The roll off the production line shaping geometric representation of shaped segment strip of Figure 11 production scene forming parameters.

The shaping geometric representation of preform section strip under the new forming parameters of Figure 12.

The roll off the production line shaping geometric representation of shaped segment strip of the new forming parameters of Figure 13.

The specific embodiment

Below embodiments of the invention are elaborated, the present embodiment is implemented take technical solution of the present invention under prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Embodiment 1

As shown in Figure 2, for arranging the frame mechanism abstract schematic of roller section.Consider that all float rollers are installed in above the roller beam, move with the roller beam, so the adjusting free degree of all row's rollers of row roller forming section has 5, as shown in Figure 3: around the rotation (S of roller beam axis _w), entrance side vertical height (Y _i) and transverse width (X _i) translation and outlet side vertical height (Y _o) and the translation (X of transverse width _o), its corresponding 5 forming parameters are respectively that parameter S is controlled in rotation _wqs, the entrance side height controls parameter Y _iqs, the entrance side width controls parameter X _iqs, the outlet side height controls parameter Y _oqsand the outlet side width is controlled parameter X _oqs.

The datum mark O of row's roller unit of take is initial point (be positioned at and pinch passage), and the strip direction that vertically is shaped is Z axis, and the transverse horizontal direction is X-axis, sets up global coordinate system XYZ.

As shown in Figure 4, the present embodiment comprises the following steps:

The first step, with row's roller roll centre O ₃for initial point, set up local coordinate system X ₃y ₃z ₃, wherein arranging roll axis is X ₃axle, Z ₃axle is consistent with the Z-direction under global coordinate system, according to the cross section profile shape of row's roller, sets up corresponding cross section profile parametric equation.As shown in Figure 5, establish P for a bit (x on row's running roller profile ₃, y ₃, z ₃), at local coordinate system O ₃under, according to the contour shape of float roller, the parametric equation of the row's of writing out running roller profile

Wherein: R _pprofile radius for the float roller;

The footpath, the end that R is the float roller.

Second step, to cross the roller beam cross section center of circle O that arranges roll axis ₂for initial point, set up local coordinate X ₂y ₂z ₂, X wherein ₂axle is consistent with the X-direction under global coordinate system, Z ₂axle is consistent with the Z-direction under global coordinate system, and the rule of arranging according to row's roller group in space obtains the direction that longitudinally is shaped and respectively arranges the first primary dip (S of roll axis in space _wqs=0 o'clock), and then constructed the initial static row roller curved surface of all row's running roller profiles if P is at local coordinate system O ₂under coordinate be (x ₂, y ₂, z ₂), have:

The roll centre O of order row roller ₃at local coordinate system O ₂under coordinate position be ²o ₃=(x ₃₂, y ₃₂, z ₃₂) ^t, work as S _wqs=0, when roller beam axis is parallel to the shaping direction, ²o ₃position can in the rule of arranging in space, determine according to row roller group.Write formula (2) as homogeneous form, can be constructed the initial static row roller curved surface of all row's running roller profiles homogeneous form:

$\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_3^2\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e1,\mathrm{\&alpha;})& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_3^2\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_3+x_{32}\\ y_3+y_{32}\\ z_3+z_{32}\\ 1\end{array}\right)---\left(3\right)$

Wherein: α controls parameter S for rotation _wqs=0 o'clock, the first primary dip value of row's roller section;

e1＝(0，0，1) ^T。

The 3rd step, on the basis that obtains initial static row roller curved surface, further at local coordinate system X ₂y ₂z ₂under, control parameter S according to rotation _wqsthe inclination angle value that the row's of calculating roll axis need to be revised, the initial static row roller curved surface before then revising, thus obtain forming parameters S _wqsrelevant row's roller curved surface

obtaining initial static row roller curved surface

basis on, control parameter S according to rotation _wqsthe correction value θ at the row's of calculating roller inclination angle _z(S _wqs), at local coordinate system X ₂y ₂z ₂under, can obtain revised and forming parameters S through a rotation transformation _wqsrelevant row's roller curved surface

homogeneous form:

$\left(\begin{array}{c}{x}_{2z}\\ y_{2z}\\ z_{2z}\\ 1\end{array}\right)=\left[\begin{array}{cc}R(e2,{\mathrm{\&theta;}}_z\left(S_{\mathrm{wqs}}\right))& 0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)---\left(4\right)$

Wherein: e2=(0,0,1) ^t.

The 4th step, with the reference point O of row's roller frame ₁(the cylinder boss axis of entrance side the slide block 3 and intersection point of round hole axial) is initial point, sets up local coordinate system X ₁y ₁z ₁, X wherein ₁axle is consistent with the X-direction under global coordinate system, Z ₁axle is consistent with the Z-direction under global coordinate system, when the axis of roller beam is parallel to the strip direction that is shaped longitudinally, (is X _iqs=X _oqs, Y _iqs=Y _oqs), row's roller curved surface now is only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, first will arrange the roller curved surface

convert at local coordinate system O ₁under curved surface

again according to an O ₁and the relative distance relation between O, utilize translation transformation, again by curved surface

convert the curved surface under global coordinate system O to curved surface

be under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant curved surface.

The coordinate system X of section sets a trap ₂y ₂z ₂initial point O ₂at local coordinate system X ₁y ₁z ₁under coordinate be (x ₂₁, y ₂₁, z ₂₁) ^t, consider that now the axis of roller beam is parallel to the strip direction that is shaped longitudinally, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, by local coordinate system X ₂y ₂z ₂under row's roller curved surface

convert local coordinate system X to ₁y ₁z ₁under row's roller curved surface

The coordinate system X of section sets a trap ₁y ₁z ₁initial point O ₁coordinate under global coordinate system XYZ is (x ₁₀, y ₁₀, z ₁₀) ^t, due to initial point O ₁for the axis of row's reference point of roller frame and roller beam is parallel to the strip direction (X that is shaped longitudinally _oqs=X _iqs, Y _oqs=Y _iqs), so initial point O ₁coordinate position only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined.According to an O ₁and the relative distance relation between an O, utilize translation transformation again, by local coordinate system X ₁y ₁z ₁under row's roller curved surface

convert the row's roller curved surface under global coordinate system XYZ to

The 5th step, under global coordinate system O, if Y _iqs≠ Y _oqs, X _iqs=X _oqs, mean curved surface

understood the reference point O that arranges roller frame ₁rotate θ around X-axis _x, θ _xcan be by according to Y _iqs, Y _oqsdifference and chute 9 and 10 s' spacing calculate, therefore arrange the roller curved surface

the reference point O of the row's of mistake roller frame ₁rotate θ around X-axis _xafter curved surface

can be tried to achieve by the complex transformation of coordinate:

$\left(\begin{array}{c}{x}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e3,{\mathrm{\&theta;}}_x)& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_z\\ y_z\\ z_z\\ 1\end{array}\right)---\left(7\right)$

Wherein, e3=(1,0,0) ^t.

Curved surface

under global coordinate system, cross row's running roller profile and with 4 forming parameters S _wqs, X _iqs, Y _iqsand Y _oqsrelevant curved surface.

The 6th step, at the row's of trying to achieve roller curved surface

basis on, consider under global coordinate system O Y _iqs≠ Y _oqs, and X _iqs≠ X _oqs, this means curved surface

the further reference point O of the row's of walking around roller frame ₁and direction cosines are (0, cos θ _x, sin θ _x) ^tstraight line rotate to an angle, this angle can be by according to Y _iqsand Y _oqsbetween difference, X _iqsand X _oqsbetween difference and chute 9 and 10 s' distance calculate, finally according to the complex transformation of coordinate, can obtain:

$\left(\begin{array}{c}{x}_{\mathrm{zxy}}\\ y_{\mathrm{zxy}}\\ z_{\mathrm{zxy}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(\mathrm{<figure-callout\; id="4"\; label="e"\; filenames="HDA0000099966050000012.png"\; state="\{\{state\}\}">e</figure-callout>}4,{\mathrm{\&alpha;}}_2)& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\\ 1\end{array}\right)---\left(8\right)$

So far curved surface

be under global coordinate system, cross row's running roller profile and with 5 forming parameters S _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsrelevant dynamic row's roller curved surface.

The 7th step, utilize flower type method for designing, the colored type figure of strip under the differing formed position of the row's of calculating roller section, thereby the shape of cross section of the row's of acquisition roller section entry and exit side plate band;

The 8th step, according to row's roller curved surface

equation and the section expression of corresponding row roller section entry and exit side plate band, in conjunction with the geometrical constraint boundary condition, can be regarded as to obtain S _wqs, X _iqsand Y _iqsinitial parameter; Consider in the actual production of ERW; if the angle α of float roll axis and shaping pipe EDGE CONTACT end points place tangent line excessive (seeing Fig. 6 (a)); usually can make the wedge angle limit of strip limit section directly with the forming rolls Surface Contact; this local stress that will cause contact area too concentrate and the strip edge deformation excessive, thereby produce the forming defectses such as limit wave and bulge.In order to guarantee the stability of Welded Pipe Production Process strip edge shaping quality, when forming the technological parameter adjustment, should reduce the angle α of row's roll axis and shaping pipe EDGE CONTACT end points place tangent line, as shown in Fig. 6 (b) as far as possible.Analysis based on above-mentioned as shown in Figure 7, proposes the following geometrical constraint boundary condition of determining initial forming parameters:

(a) row roller section porch strip edge end points D _iwith certain 1 P on row's running roller profile _ioverlap;

(b) contact point P on float running roller profile _iwith the tangential direction of shaping pipe EDGE CONTACT end points, be consistent.

Investigation under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant row's roller curved surface equation, by geometrical constraint boundary condition (a), can be obtained:

X _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)＝X _d(θ _i，z _i) (9)

Y _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)＝Y _d(θ _i，z _i) (10)

Wherein: X _zand Y _zon the row's of being running roller profile, the XY of contact point, can be according to row's roller curved surface to coordinate figure

solving Equations obtain; X _dand Y _dcan calculate according to flower type method for designing.

By geometrical constraint boundary condition (b), can be obtained:

T _pi(s _wqs，x _iqs，y _iqs，θ _i，z _i)＝T _di(θ _i，z _i) (11)

Wherein: T _pifor the tangent line direction vector at contact point place on row's running roller profile, can be according to row's roller curved surface

solving Equations obtain; T _difor the tangent line direction vector of strip flower type at the contact terminal place, can try to achieve according to flower type method for designing.

Simultaneous formula (9), (10) and (11), can try to achieve rotation and control parameter S _wqsand initial translation parameters X _iqs0, Y _iqs0.

The 9th step, construct, strip edge, porch end points along width (X) and height (Y) direction to dynamic row's roller curved surface apart from functional ∏, then substitution initial parameter, after the iteration of several times, can calculate all forming parameters S that meet particular requirement apart from functional ∏ _wqs, X _iqs, Y _iqs, Y _oqsand X _oqs.

Try to achieve rotation control parameter S _wqsand initial translation parameters X _iqs0, Y _iqs0basis on, in order further to try to achieve the forming parameters X of final entrance and exit side height and width _iqs, Y _iqs, Y _oqsand X _oqs, structure outlet and strip edge, porch end points D _oand D _ialong width (X) and height (Y) direction to row's roller curved surface apart from functional:

I＝∏(f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)，f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _o，z _o))

＝f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)+f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _o，z _o) (12)

Wherein

$f_i(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs},}{s}_{\mathrm{wqs}},{\mathrm{\&theta;}}_i{z}_i)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-X_{\mathrm{di}})}^2{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-Y_{\mathrm{di}})}^2}$

$f_o(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs},}{s}_{\mathrm{wqs}},{\mathrm{\&theta;}}_o{z}_o)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-X_{\mathrm{do}})}^2{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{aqs}},y_{\mathrm{aqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-Y_{\mathrm{do}})}^2}$

Normally, to different forming parameters, all can obtain the value apart from functional I according to (12) formula, when distance functional I is less than certain value, can think the forming parameters X that it is corresponding _iqs, Y _iqs, X _oqs, Y _oqsand S _wqsfor final design forming parameters out.

The nonlinear equation that to consider apart from functional I be multi-parameter, corresponding forming parameters while utilizing general method to be difficult to obtain apart from functional I minimalization, in order to obtain more quickly and accurately the parameter with practical value, the iterative method proposed according to the control characteristic of each forming parameters as shown in Figure 8.

Initialize the control parameter of outlet side width and short transverse, get x _oqs0=x _iqs0

y _oqs0＝yi _qs0

By X _iqs, Y _iqs, X _oqs, Y _oqsand S _wqssubstitution row roller curved surface

equation (8) formula obtain arranging roller curved surface entrance side contact point coordinate x _zxyi, y _zxyiwith outlet side contact point coordinate x _zxyo, y _zxyo, then according to flower type method for designing, calculate row's roller section entrance side strip marginal end point coordinates X _di, Y _diand outlet side strip marginal end point coordinates X _do, Y _do, then by (12) formula, calculate apart from functional I value and revise step-length d _xi, d _yi, d _xoand d _yo.Whether judging distance functional I value satisfies condition simultaneously, if meet, exports current each forming parameters; If do not meet, according to revising current each forming parameters of step-length correction, and recalculate apart from functional I, until meet stopping criterion for iteration apart from functional I value.

In the iterative process, the corrected Calculation formula of outlet and each forming parameters of porch is as follows:

x _iqs＝x _iqs-dx _i

y _iqs＝y _iqs-dy _i

x _oqs＝x _oqs-dx _o

y _oqs＝y _oqs-dy _o

According to above-mentioned computational methods, the initial forming parameters of substitution φ 244.5mm unit, after the iteration through several times, corresponding each forming parameters X while can be regarded as to such an extent that dynamically arrange the meeting the demands apart from functional ∏ of roller curved surface _iqs, Y _iqs, X _oqs, Y _oqsand S _wqsvalue, as listed as table 1.The forming parameters of welded pipe cage forming technique produced on-site φ 244.5mm welded tube is as listed as table 2.

Row's roller section forming parameters (φ 244.5mm unit) that table 1 is new

	The preform section	Line is shaped and arranges the roller first paragraph	Line is shaped and arranges the roller second segment	Line is shaped and arranges the 3rd section, roller
					X iqs/mm	1372.44	3062.44	2963.93	2877.83
X oqs/mm	1273.55	3016.59	2911.37	2827.36
					Y iqs/mm	273.12	221.53	168.61	153.09
Y oqs/mm	390.00	206.81	223.62	207.19
					S wqs/ degree	-2.95	79.01	62.82	47.53

Table 2 production scene row's roller section forming parameters (φ 244.5mm unit)

	The preform section	Line is shaped and arranges the roller first paragraph	Line is shaped and arranges the roller second segment	Line is shaped and arranges the 3rd section, roller
					X iqs/mm	1304.5	3103.4	2990.3	2914.7
X oqs/mm	1227.0	3038.4	2945.2	2824.7

Y iqs/mm	363.0	206.9	148.4	151.8
					Y oqs/mm	406.9	160.35	200.9	190.9
S wqs/ degree	5.7	87.6	66.0	50.2

The passage place relative curvature integrated value that respectively is shaped under row's roller section forming parameters of new row's roller section forming parameters and production scene distributes more as shown in Figure 9.As shown in Figure 9, with respect to the forming parameters of production scene, under new forming parameters, the crystallized ability of preform section row roller brings up to 0.498 by 0.332, and amplification reaches 50.2%; The roll off the production line crystallized ability of shaped segment row roller of new forming parameters also brings up to 0.712 by 0.505, and amplification reaches 41.1%; As can be seen here, under new forming parameters, the crystallized ability of φ 244.5mm welded tube row roller forming unit is greatly improved.

Under row's roller section forming parameters of production scene and new row's roller section forming parameters, how much of the shapings of preform section and line shaped segment strip are respectively as shown in Figure 10-Figure 13.By contrast, can find, with respect to the forming parameters of production scene, no matter new forming parameters is that the shaping at strip edge is all more stable in preform row's roller section or the online row's of shaping roller section, and its lateral cross section degree of crook is also more abundant.

Claims (10)

1. the technique optimization method of a welded pipe cage forming unit comprises the following steps:

The first step, row's roller roll centre of take is initial point, sets up the first local coordinate system;

Second step, take that to cross the roller beam cross section center of circle arrange roll axis be initial point, sets up the second local coordinate system and construct the initial static row roller curved surface of all row's running roller profiles;

The 3rd step adopts the mode of inclination correction to arrange after the roller curved surface is revised and obtain the relevant row of forming parameters roller curved surface initial static under the second local coordinate system;

The 4th step, the reference point of arranging roller frame of take is initial point, be the cylinder boss axis of entrance side slide block and the intersection point of round hole axial, set up the 3rd local coordinate system, and be transition and conversion to the row's roller curved surface under global coordinate system by the relevant row of forming parameters roller curved surface with the 3rd local coordinate;

The 5th step, be rotated correction by the row's roller curved surface under global coordinate system, obtains the forming parameters correlation surface;

The 6th step, utilize flower type method for designing to calculate the colored type figure of strip under the row differing formed position of roller section, thereby the shape of cross section of the row's of acquisition roller section entry and exit side plate band, the forming parameters correlation surface obtained in conjunction with geometrical constraint boundary condition and the 5th step, can be regarded as and to obtain rotation and control parameter S _wqs, the entrance side width controls parameter X _iqsand the entrance side height is controlled parameter Y _iqsinitial parameter;

The 7th step, construct, strip edge, porch end points along the width X under global coordinate system and height Y-direction to dynamic row's roller curved surface apart from functional ∏, then substitution initial parameter after the iteration of several times, calculate all forming parameters S that meet particular requirement apart from functional ∏ _wqs, X _iqs, Y _iqs, the outlet side height controls parameter Y _oqsand the outlet side width is controlled parameter X _oqs;

The 8th step, according to calculating determined each forming parameters S _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsvalue, be used directly in float roller on production scene adjustment row roller section shaping unit and, at the shaping position in space, carry out production and the manufacture of ERW.

2. method according to claim 1, is characterized in that, described the first local coordinate system, i.e. X ₃y ₃z ₃refer to: row's roll axis is X ₃axle, the Z of the first local coordinate system ₃axle is consistent with the Z-direction under global coordinate system, according to the cross section profile shape of row's roller, sets up corresponding cross section profile parametric equation, establishes P for a bit (x on row's running roller profile ₃, y ₃, z ₃), at the initial point O of the first local coordinate system ₃, arrange under the roller roll centre, according to the contour shape of float roller, the parametric equation of the row's of writing out running roller profile

$\stackrel{\&RightArrow;}{O_{3}P}=\left(\begin{array}{c}{x}_3\\ y_3\\ z_3\end{array}\right)=\left(\begin{array}{c}{R}_p\sin \mathrm{\&theta;}\\ R_p(1-\cos \mathrm{\&theta;})+R\\ 0\end{array}\right)---\left(1\right)$

Wherein: R _pfor the profile radius of float roller, the footpath, the end that R is the float roller.

3. method according to claim 1, is characterized in that, described the second local coordinate system, i.e. X ₂y ₂z ₂in X ₂axle is consistent with the X-direction under global coordinate system, Z ₂axle is consistent with the Z-direction under global coordinate system, and the rule of arranging according to row's roller group in space obtains the direction that longitudinally is shaped and respectively arranges the first primary dip of roll axis in space, works as S _wqs=0 o'clock, and then constructed the initial static row roller curved surface of all row's running roller profiles

:

$\stackrel{\&RightArrow;}{O_{2}P}=\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\end{array}\right)---\left(2\right)$

Wherein: P is at local coordinate system O ₂under coordinate be (x ₂, y ₂, z ₂), the roll centre O of row's roller ₃at local coordinate system X ₂y ₂z ₂under coordinate position be ²o ₃=(x ₃₂, y ₃₂, z ₃₂) ^t, work as S _wqs=0, when roller beam axis is parallel to the shaping direction, ²o ₃position according to row roller group, in the rule of arranging in space, determine:

Write formula (2) as homogeneous form, can be constructed the initial static row roller curved surface of all row's running roller profiles

homogeneous form:

$\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_3^2\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e1,\mathrm{\&alpha;})& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& O_3^2\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_3+x_{32}\\ y_3+y_{32}\\ z_3+z_{32}\\ 1\end{array}\right]---\left(3\right)$

Wherein: α controls parameter S for rotation _wqs=0 o'clock, the first primary dip value of row's roller section, e1=(0,0,1) ^t.

4. method according to claim 1, is characterized in that, described inclination correction refers to: obtaining initial static row roller curved surface

basis on, control parameter S according to rotation _wqsthe correction value θ at the row's of calculating roller inclination angle _z(S _wqs), at the second local coordinate system X ₂y ₂z ₂under, can obtain revised and forming parameters S through a rotation transformation _wqsrelevant row's roller curved surface

homogeneous form:

$\left(\begin{array}{c}{x}_{2z}\\ y_{2z}\\ z_{2z}\\ 1\end{array}\right)=\left[\begin{array}{cc}R(e2,{\mathrm{\&theta;}}_z\left(S_{\mathrm{wqs}}\right))& 0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_2\\ y_2\\ z_2\\ 1\end{array}\right)---\left(4\right)$

Wherein: e2=(0,0,1) ^t.

5. method according to claim 1, is characterized in that, described the 3rd local coordinate system, i.e. X ₁y ₁z ₁middle X ₁axle is consistent with the X-direction under global coordinate system, Z ₁axle is consistent with the Z-direction under global coordinate system, and the axis of roller beam is parallel to strip be shaped longitudinally direction, i.e. X _iqs=X _oqs, Y _iqs=Y _oqs, row's roller curved surface now is only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, first will arrange the roller curved surface convert at local coordinate system O ₁under curved surface

again according to an O ₁and the relative distance relation between O, utilize translation transformation, again by curved surface

convert the curved surface under global coordinate system O to

curved surface

be under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant curved surface.

6. method according to claim 1, is characterized in that, described is that transition and conversion refers to the 3rd local coordinate: the coordinate system X of section sets a trap ₂y ₂z ₂initial point O ₂at local coordinate system X ₁y ₁z ₁under coordinate be (x ₂₁, y ₂₁, z ₂₁) ^t, consider that now the axis of roller beam is parallel to the strip direction that is shaped longitudinally, according to an O ₂with O ₁between the relative distance relation, utilize translation transformation, by local coordinate system X ₂y ₂z ₂under row's roller curved surface convert local coordinate system X to ₁y ₁z ₁under row's roller curved surface

:

$\stackrel{\&RightArrow;}{O_1{P}_z}=\stackrel{\&RightArrow;}{O_1{O}_2}+\stackrel{\&RightArrow;}{O_2{P}_z}=\left(\begin{array}{c}{x}_{1z}\\ y_{1z}\\ z_{1z}\end{array}\right)=\left(\begin{array}{c}{x}_{2z}+x_{21}\\ y_{2z}+y_{21}\\ z_{2z}+z_{21}\end{array}\right)---\left(5\right)$

Wherein: local coordinate system X ₁y ₁z ₁initial point O ₁coordinate under global coordinate system XYZ is (x ₁₀, y ₁₀, z ₁₀) ^t, due to initial point O ₁for the axis of row's reference point of roller frame and roller beam is parallel to strip be shaped longitudinally direction, i.e. X _oqs=X _iqs, Y _oqs=Y _iqsso, initial point O ₁coordinate position only by S _wqs, X _iqsand Y _iqsthree forming parameters are determined, according to an O ₁and the relative distance relation between an O, utilize translation transformation again, by local coordinate system X ₁y ₁z ₁under row's roller curved surface

convert the row's roller curved surface under global coordinate system XYZ to :

$\stackrel{\&RightArrow;}{O{P}_z}=\stackrel{\&RightArrow;}{O{O}_1}+\stackrel{\&RightArrow;}{O_1{P}_z}=\left(\begin{array}{c}{x}_z\\ y_z\\ z_z\end{array}\right)=\left(\begin{array}{c}{x}_{1z}+x_{10}\\ y_{1z}+y_{10}\\ z_{1z}+z_{10}\end{array}\right)---\left(6\right)$

7. method according to claim 1, is characterized in that, described forming parameters correlation surface refers to:

7.1) under global coordinate system O, if y _iqs≠ Y _oqs, X _iqs=X _oqs, mean curved surface

understood the reference point O that arranges roller frame ₁rotate θ around X-axis _x, θ _xcan be by according to Y _iqs, Y _oqsdifference and the spacing of chute calculate, therefore arrange the roller curved surface

the reference point O of the row's of mistake roller frame ₁rotate θ around X-axis _xafter curved surface

can be tried to achieve by the complex transformation of coordinate:

$\stackrel{\&RightArrow;}{{\mathrm{OP}}_{\mathrm{zx}}}=\left(\begin{array}{c}{z}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\end{array}\right),\left(\begin{array}{c}{x}_{\mathrm{zx}}\\ y_{\mathrm{zx}}\\ z_{\mathrm{zx}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e3,{\mathrm{\&theta;}}_x)& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_z\\ y_z\\ z_z\\ 1\end{array}\right)---\left(7\right)$

Wherein: e3=(1,0,0) ^t, curved surface

under global coordinate system, cross row's running roller profile and with 4 forming parameters S _wqs, X _iqs, Y _iqsand Y _oqsrelevant curved surface;

7.2) at the row's of trying to achieve roller curved surface basis on, consider under global coordinate system O Y _iqs≠ Y _oqs, and X _iqs≠ X _oqs, this means curved surface

the further reference point O of the row's of walking around roller frame ₁and direction cosines are (0, cos θ _x, sin θ _x) ^tstraight line rotation, the anglec of rotation is according to Y _iqsand Y _oqsbetween difference, X _iqsand X _oqsbetween difference and chute the distance calculate, finally according to the complex transformation of coordinate, can obtain:

$\stackrel{\&RightArrow;}{{\mathrm{OP}}_{\mathrm{zxy}}}=\left(\begin{array}{c}{z}_{\mathrm{zxy}}\\ y_{\mathrm{zxy}}\\ z_{\mathrm{zxy}}\end{array}\right),\left(\begin{array}{c}{x}_{\mathrm{zxy}}\\ y_{\mathrm{zxy}}\\ z_{\mathrm{zxy}}\\ 1\end{array}\right)=\left[\begin{array}{cc}I& O_1^0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}R(e4,{\mathrm{\&alpha;}}_2)& 0\\ 0^T& 1\end{array}\right]\left[\begin{array}{cc}I& -O_1^0\\ 0^T& 1\end{array}\right]\left(\begin{array}{c}{x}_z\\ y_z\\ z_z\\ 1\end{array}\right)---\left(8\right)$

So far curved surface

be under global coordinate system, cross row's running roller profile and with 5 forming parameters S _wqs, X _iqs, Y _iqs, Y _oqsand X _oqsrelevant dynamic row's roller curved surface.

8. method according to claim 1, is characterized in that, described geometrical constraint boundary condition refers to:

(a) row roller section porch strip edge end points D _iwith certain 1 P on row's running roller profile _ioverlap, and

(b) contact point P on float running roller profile _iwith the tangential direction of shaping pipe EDGE CONTACT end points, be consistent, specific as follows:

Investigation under global coordinate system, cross row's running roller profile and with 3 forming parameters S _wqs, X _iqsand Y _iqsrelevant row's roller curved surface

equation, by geometrical constraint boundary condition (a), can be obtained:

X _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)=X _d(θ _i，z _i) (9)

Y _z(x _iqs，y _iqs，s _wqs，θ _i，z _i)=Y _d(θ _i，z _i) (10)

Wherein: X _zand Y _zon the row's of being running roller profile, the XY of contact point, can be according to row's roller curved surface to coordinate figure

solving Equations obtain; X _dand Y _dcan calculate according to flower type method for designing;

By geometrical constraint boundary condition (b), can be obtained:

T _pi(s _wqs，x _iqs，y _iqs，θ _i，z _i)=T _di(θ _i，z _i) (11)

Wherein: T _pifor the tangent line direction vector at contact point place on row's running roller profile, can be according to row's roller curved surface

solving Equations obtain; T _difor the tangent line direction vector of strip flower type at the contact terminal place, can try to achieve according to flower type method for designing.

9. method according to claim 1, is characterized in that, described the 7th step concrete steps are as follows:

9.1) try to achieve rotation control parameter S _wqsand initial translation parameters x _iqs0, y _iqs0basis on, in order further to try to achieve the forming parameters X of final entrance and exit side height and width _iqs, Y _iqs, Y _oqsand X _oqs, structure outlet and strip edge, porch end points D _pand D _ialong width (X) and height (Y) direction to row's roller curved surface apart from functional:

I=∏(f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)，f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _oz _o))

=f _i(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _i，z _i)+f _o(x _iqs，y _iqs，x _oqs，y _oqs，s _wqs，θ _o，z _o) (12)

Wherein:

$f_i(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-X_{\mathrm{di}})}^2+{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_i,z_i)-Y_{\mathrm{di}})}^2}$

$f_o(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)=\sqrt{{(x_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-X_{\mathrm{do}})}^2+{(y_{\mathrm{zxy}}(x_{\mathrm{iqs}},y_{\mathrm{iqs}},x_{\mathrm{oqs}},y_{\mathrm{oqs}},s_{\mathrm{wqs}},{\mathrm{\&theta;}}_o,z_o)-Y_{\mathrm{do}})}^2}$

9.2) initialize the control parameter of outlet side width and short transverse, get x _pqs0=x _iqs0, y _opqs=y _iqs0; By X _iqs, Y _iqs, X _oqs, Y _oqsand S _wqssubstitution row roller curved surface

equation (8) formula obtain arranging roller curved surface entrance side contact point coordinate x _zxyi, y _zxyiwith outlet side contact point coordinate x _zxyo, y _zxyo, then according to flower type method for designing, calculate row's roller section entrance side strip marginal end point coordinates X _di, Y _diand outlet side strip marginal end point coordinates X _do, Y _do, then by (12) formula, calculate apart from functional I value and revise step-length d _xi, d _yi, d _xoand d _yo; Whether judging distance functional I value satisfies condition simultaneously, if meet, exports current each forming parameters; If do not meet, according to revising current each forming parameters of step-length correction, and recalculate apart from functional I, until meet stopping criterion for iteration apart from functional I value, corresponding each forming parameters X while can be regarded as to such an extent that dynamically arrange the meeting the demands apart from functional ∏ of roller curved surface _iqs, Y _iqs, X _oqs, Y _oqsand S _wqsvalue.

10. method according to claim 9, is characterized in that, in the solution procedure of described iteration, the corrected Calculation formula of outlet and each forming parameters of porch is: x _iqs=x _iqs-dx _i, y _iqs=y _iqs-dy _i, x _pqs=x _oqs-dx _p, y _oqs=y _oqs-dy _o.

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