CN103394561B - Method for determining bending angle of each pass of cold roll forming of plate and strip - Google Patents

Abstract

The invention relates to a method for determining a bending angle of each pass of cold roll forming of a plate and strip. According to the technical scheme of the method for determining the bending angle of each pass of the cold roll forming of the plate and strip, the number n of passes of cold roll forming is set at first, the bending angle of each pass and the working roller diameter of a roller are selected as experimental factors, an average value of all the experimental factors is selected in advance, and a virtual experimental scheme of each experimental factor and each corresponding average value is designed; the strain distribution of the plate and strip of each virtual experimental scheme is calculated, a mathematical model of the maximum value of a positive strain absolute value of the outer edge of each pass of the plate and strip in the tangential direction is built up; based on the constraint condition that the maximum value of the positive strain absolute value of each pass is smaller than or equal to 1% and the constraint conditions of the top and bottom limitation of the average value of each experimental factor, the pursuit target is the minimum of the maximum value of the positive strain absolute value of each pass, and the number of passes of cold roll forming, the bending angle of each pass of the cold roll forming of the plate and strip and the working roller diameter of the roller are optimized and determined. The method for determining the bending angle of each pass of the cold roll forming of the plate and strip has the advantages of giving full play to the capacity of cold roll unit equipment, avoiding warping of the plate and strip, and being capable of overcoming the shape wave of edges of the plate and strip.

Description

A kind of method determining each passage angle of bend of Strip cold roll forming

Technical field

The invention belongs to Strip roll-forming technology field, particularly relate to a kind of method determining each passage angle of bend of Strip cold roll forming.

Background technology

Cold roll forming is the multi-pass molding roller by being arranged in order, and metal plates and strips is constantly carried out transverse curvature, to make the technology of specific section section bar.Cold roll forming is a kind of material-saving, energy-conservation, efficient, advanced and applicable metal forming process, is a key areas of Strip deep processing.

The cold-bending deformation process of Strip has the characteristics such as obvious geometrical non-linearity, physical nonlinearity and boundary nonlinear.Therefore, up to now, clod wash technology is still mainly based on the Heuristics of engineers and technicians, and rely on trial-and-error method and obtain Process Law, cold-bending molding technology is still generally considered a kind of " art do not grasped ".

Determine that the angle of bend of each passage of cold roll forming is the important content of cold-bending molding technology design.In general, the leading portion of cold roll forming and back segment adopt less flexural deformation, and interlude adopts larger distortion, and hypothesis is when Strip stile end horizontal face projected footprint represents with cubic curve, it is best (littlely how expanding that the angle of bend of Strip distributes, Liu Jiying. roll-forming technology [M]. Beijing: Chemical Industry Press's in January, 2008 first edition), can derive accordingly and determine the relational expression that the corresponding each passage angle of bend of different molding mode distributes under total shaping passage number specified criteria.

But, when frame spacing is unequal, use said method directly can not derive the relations of distribution of each passage angle of bend; Moreover this method fails the impact considering that the instrument and supplies parameter such as roller diameter, Strip material, rolled piece/roll contact state is out of shape Strip; In addition, the determination of total shaping passage number still depends on practical experience, if this value obtains comparatively large, then unit capacity can not give full play to, if value is less, then can produce the defect of Strip warpage and edge shape wave.

Summary of the invention

The present invention is intended to overcome prior art defect, object be to provide a kind of be suitable for frame spacing unequal, clod wash unit capacity of equipment can be given full play to, Strip warpage can be avoided and the method for each passage angle of bend of determination Strip cold roll forming of Strip edge shape wave defect can be overcome.

For achieving the above object, the present invention adopts the concrete steps of technical scheme to be:

The design of the first step, virtual test scheme

First according to form factor function or knowhow, the road frequency n of setting cold roll forming, carries out the design of roller floral diagram, then chooses the first angle of bend of each passage of Strip cold roll forming, the second angle of bend and roll working roll footpath as experimental factor; Then the level value of each experimental factor of preliminary election, designs the virtual test scheme of each experimental factor and corresponding level value.

Second step, finite element simulation calculation

First set up respective finite element geometrical model according to the virtual test scheme of each passage of first step design, choose unit, adopt finite element software to carry out network division, then determine the friction model between Strip and roll:

μ＝μ _d+(μ _s-μ _d)e ^-cv（1）

In formula (1): the relative sliding velocity of v-between Strip and roll, m/s;

U _s-confficient of static friction, u _s=0.2;

U _d-the coefficient of kinetic friction, u _d=0.1;

C-damped expoential, c=0.02 ~ 0.08.

Finally respectively finite element simulation calculation is carried out to each virtual test scheme, obtain the Strip Strain Distribution of each virtual test scheme of each passage.

3rd step, model are set up

According to the Strip Strain Distribution of each virtual test scheme of each passage of second step, determine that each virtual test scheme Strip outward flange of each passage is along its tangential direction normal strain value, obtains the maximum of each passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_i=a_{i1}+a_{i2}{\mathrm{\β}}_i+a_{i3}{\mathrm{\γ}}_i+a_{i4}{D}_i+a_{i5}{\mathrm{\β}}_i^2+a_{i6}{\mathrm{\β}}_i{\mathrm{\γ}}_i+a_{i7}{\mathrm{\β}}_i{D}_i+a_{i8}{\mathrm{\γ}}_i^2+a_{i9}{\mathrm{\γ}}_i{D}_i+a_{i10}{D}_i^2$

$+a_{i11}{\mathrm{\β}}_i^3+a_{i12}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i+a_{i13}{\mathrm{\β}}_i^2{D}_i+a_{i14}{\mathrm{\γ}}_i^2{\mathrm{\β}}_i+a_{i15}{\mathrm{\γ}}_i^3+a_{i16}{\mathrm{\γ}}_i^2{D}_i+a_{i17}{D}_i^2{\mathrm{\β}}_i+a_{i18}{D}_i^2{\mathrm{\γ}}_i---\left(2\right)$

$+a_{i19}{D}_i^3+a_{i20}{\mathrm{\β}}_i^4+a_{i21}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i^2+a_{i22}{\mathrm{\β}}_i^2{D}_i^2+a_{i23}{\mathrm{\γ}}_i^2{D}_i^2+a_{i24}{D}_i^2{\mathrm{\β}}_i^2+a_{i25}{D}_i^4$

In formula (2): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _ifor i passage Strip first angle of bend;

γ _ifor i passage Strip second angle of bend;

β _iand γ _iin have at least an angle of bend to be experimental factor;

D _ifor i passage roll working roll footpath;

I is 1,2 ..., n.

Minimum of a value in the maximum of the 4th step, normal strain absolute value

With the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _iminimum is optimization aim, with the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _i≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0.

By the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0the first angle of bend β corresponding in replacement formula (2) _i, the second angle of bend γ _iwith roll working roll footpath D _i, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{i0}=a_{i1}+a_{i2}{\mathrm{\β}}_{i0}+a_{i3}{\mathrm{\γ}}_{i0}+a_{i4}{D}_{i0}+a_{i5}{\mathrm{\β}}_{i0}^2+a_{i6}{\mathrm{\β}}_{i0}{\mathrm{\γ}}_{i0}+a_{i7}{\mathrm{\β}}_{i0}{D}_{i0}+a_{i8}{\mathrm{\γ}}_{i0}^2+a_{i9}{\mathrm{\γ}}_{i0}{D}_{i0}+a_{i10}{D}_{i0}^2$

$+a_{i11}{\mathrm{\β}}_{i0}^3+a_{i12}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}+a_{i13}{\mathrm{\β}}_{i0}^2{D}_{i0}+a_{i14}{\mathrm{\γ}}_{i0}^2{\mathrm{\β}}_{i0}+a_{i15}{\mathrm{\γ}}_{i0}^3+a_{i16}{\mathrm{\γ}}_{i0}^2{D}_{i0}+a_{i17}{D}_{i0}^2{\mathrm{\β}}_{i0}+a_{i18}{D}_{i0}^2{\mathrm{\γ}}_{i0}---\left(3\right)$

$+a_{i19}{D}_{i0}^3+a_{i20}{\mathrm{\β}}_{i0}^4+a_{i21}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}^2+a_{i22}{\mathrm{\β}}_{i0}^2{D}_{i0}^2+a_{i23}{\mathrm{\γ}}_{i0}^2{D}_{i0}^2+a_{i24}{D}_{i0}^2{\mathrm{\β}}_{i0}^2+a_{i25}{D}_{i0}^4$

In formula (3): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _i0for the optimal value of i passage Strip first angle of bend;

γ _i0for the optimal value of i passage Strip second angle of bend;

β _i0and γ _i0in have at least the optimal value of an angle of bend to be experimental factor;

D _i0for the optimal value in i passage roll working roll footpath;

I is 1,2 ..., n.

The determination of the 5th step, clod wash road number of times

If first substep formula (3) determined each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0all in 0.8 ~ 1.0% scope, then the road frequency n of first step setting is determined;

If certain the passage Strip outward flange in second substep formula (3) determined each passage is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0be less than 0.8%, then the road frequency n that the first step sets subtracted 1, then repeat the first step to the 4th step, until meet the 5th step first substep;

If certain the passage Strip outward flange in the 3rd substep formula (3) determined each passage is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0do not exist, then the road frequency n that the first step sets is added 1, then repeat the first step to the 4th step, until meet the 5th step first substep;

The determination in the 6th step, angle of bend and roll working roll footpath

If each passage Strip outward flange of the first substep is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be less than or equal to 10%, then the optimal value β of Strip cold roll forming each passage first angle of bend _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0determined.

If each passage Strip outward flange of the second substep is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange be greater than 10% along the ratio of the mean value of the minimum of a value in the maximum of its tangential direction normal strain absolute value, then to the determined each passage Strip outward flange of the 5th step along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0sort by its size, then the level value of passage experimental factor corresponding to minimum of a value in maximum in sequence and sequence is adjusted, repeat the first step to the 5th step, until meet the 6th step first substep.

Described unit is shell unit or for hexahedral element or for tetrahedron element.

Owing to adopting technique scheme, the present invention compared with prior art has following good effect:

The method of the determination that the present invention relates to each passage Strip angle of bend considers the impact that the factors such as roll working roll footpath, Strip material, rolled piece/roll contact state are determined clod wash each passage Strip angle of bend, be applicable to frame spacing unequal time situation.

The present invention is minimum for optimization aim along the maximum of its tangential direction normal strain absolute value with each passage Strip outward flange, 1% is less than or equal to for constraints along the maximum of its tangential direction normal strain absolute value with Strip outward flange, therefore can not produce warpage and limit wave defect when Strip is shaping, and the productive potentialities of unit equipment can be given full play to.

Therefore, the present invention have be suitable for frame spacing unequal, clod wash unit capacity of equipment can be given full play to, Strip warpage can be avoided and the feature of Strip edge shape wave defect can be overcome.

Accompanying drawing explanation

Fig. 1 is one of the present invention asymmetric Z-shape steel roller flower design diagram;

The result of calculation cloud atlas of the 7th road order 7# experimental program that Fig. 2 is Strip shown in Fig. 1.

Specific implementation method

Below in conjunction with the drawings and specific embodiments, the invention will be further described, the restriction not to its protection domain.

Embodiment 1

A kind of method determining each passage angle of bend of Strip cold roll forming.The concrete steps of the method are:

The design of the first step, virtual test scheme

According to form factor function, the cold roll forming road frequency n setting asymmetric Z-shape steel is 11, completes roller floral diagram design as shown in Figure 1.This step, for the 7th passage, chooses the 7th passage first angle of bend β ₇, the second angle of bend γ ₇with roll working roll footpath D ₇as experimental factor; Each experimental factor respectively gets three level values, i.e. the first angle of bend β ₇value is respectively 16 °, 23 ° and 30 °, the second angle of bend γ ₇value is respectively 6 °, 12 ° and 18 °, roll working roll footpath D ₇value is respectively 320mm, 400mm and 480mm; By orthogonal arrage L ₉(3 ⁴) determine each experimental factor as shown in table 1 and the virtual test scheme of corresponding level value.

The virtual test scheme of table 1. the 7th passage

Tested number	First angle of bend β 7（°）	Second angle of bend γ 7（°）	Roller footpath D 7（mm）
				1	16.0	6.0	320
2	16.0	12.0	400
				3	16.0	18.0	480
4	23.0	6.0	400
				5	23.0	12.0	480
6	23.0	18.0	320
				7	30.0	6.0	480
8	30.0	12.0	320
				9	30.0	18.0	400

Second step, finite element simulation calculation

First set up respective finite element geometrical model according to the virtual test scheme of each passage of first step design, due to Strip thickness compared with its length and width much little, choose hexahedral element, adopt finite element software to carry out network division, then determine the friction model between Strip and roll:

μ＝μ _d+(μ _s-μ _d)e ^-cv（1）

In formula (1): the relative sliding velocity of v-between Strip and roll, m/s;

U _s-confficient of static friction, u _s=0.2;

U _d-the coefficient of kinetic friction, u _d=0.1;

C-damped expoential, in the present embodiment, c=0.02 ~ 0.06.

Finally respectively finite element simulation calculation is carried out to each virtual test scheme, obtain the Strip Strain Distribution of each virtual test scheme of each passage.As: set up finite element geometrical model with the virtual test scheme of the 7th passage of first step table 1 design, obtain the Strain Distribution of the Strip of 9 virtual experimental schemes of the 7th passage, Fig. 2 is the Strain Distribution cloud atlas of the 7# virtual experimental scheme of the 7th passage.

3rd step, model are set up

The Strain Distribution of the Strip corresponding to each virtual test scheme of each passage of second step, determine that each virtual test scheme Strip outward flange of each passage is along its tangential direction normal strain value, obtains the maximum of each passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_i=a_{i1}+a_{i2}{\mathrm{\β}}_i+a_{i3}{\mathrm{\γ}}_i+a_{i4}{D}_i+a_{i5}{\mathrm{\β}}_i^2+a_{i6}{\mathrm{\β}}_i{\mathrm{\γ}}_i+a_{i7}{\mathrm{\β}}_i{D}_i+a_{i8}{\mathrm{\γ}}_i^2+a_{i9}{\mathrm{\γ}}_i{D}_i+a_{i10}{D}_i^2$

$+a_{i11}{\mathrm{\β}}_i^3+a_{i12}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i+a_{i13}{\mathrm{\β}}_i^2{D}_i+a_{i14}{\mathrm{\γ}}_i^2{\mathrm{\β}}_i+a_{i15}{\mathrm{\γ}}_i^3+a_{i16}{\mathrm{\γ}}_i^2{D}_i+a_{i17}{D}_i^2{\mathrm{\β}}_i+a_{i18}{D}_i^2{\mathrm{\γ}}_i---\left(2\right)$

$+a_{i19}{D}_i^3+a_{i20}{\mathrm{\β}}_i^4+a_{i21}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i^2+a_{i22}{\mathrm{\β}}_i^2{D}_i^2+a_{i23}{\mathrm{\γ}}_i^2{D}_i^2+a_{i24}{D}_i^2{\mathrm{\β}}_i^2+a_{i25}{D}_i^4$

In formula (2): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _ifor i passage Strip first angle of bend;

γ _ifor i passage Strip second angle of bend;

D _ifor i passage roll working roll footpath;

I is 1,2 ..., n.

7 are equaled for i, according to the Strip Strain Distribution of each virtual test scheme of second step the 7th passage, determine that each virtual test scheme Strip outward flange of the 7th passage is along its tangential direction normal strain value, obtains the maximum of the 7th passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_7=a_{71}+a_{72}{\mathrm{\β}}_7+a_{73}{\mathrm{\γ}}_7+a_{74}{D}_7+a_{75}{\mathrm{\β}}_7^2+a_{76}{\mathrm{\β}}_7{\mathrm{\γ}}_7+a_{77}{\mathrm{\β}}_7{D}_7+a_{78}{\mathrm{\γ}}_7^2+a_{79}{\mathrm{\γ}}_7{D}_7+a_{710}{D}_7^2$

$+a_{711}{\mathrm{\β}}_7^3+a_{712}{\mathrm{\β}}_7^2{\mathrm{\γ}}_7+a_{713}{\mathrm{\β}}_7^2{D}_7+a_{714}{\mathrm{\γ}}_7^2{\mathrm{\β}}_7+a_{715}{\mathrm{\γ}}_7^3+a_{716}{\mathrm{\γ}}_7^2{D}_7+a_{717}{D}_7^2{\mathrm{\β}}_7+a_{718}{D}_7^2{\mathrm{\γ}}_7---(2-1)$

$+a_{719}{D}_7^3+a_{720}{\mathrm{\β}}_7^4+a_{721}{\mathrm{\β}}_7^2{\mathrm{\γ}}_7^2+a_{722}{\mathrm{\β}}_7^2{D}_7^2+a_{723}{\mathrm{\γ}}_7^2{D}_7^2+a_{724}{D}_7^2{\mathrm{\β}}_7^2+a_{725}{D}_7^4$

In formula (2-1): a ₇₁, a ₇₂..., a ₇₂₅it is the regression coefficient of 7 passages;

β ₇it is the first angle of bend of 7 passage Strips;

γ ₇it is the second angle of bend of 7 passage Strips;

D ₇be 7 passage roll working roll footpaths.

Minimum of a value in the maximum of the 4th step, normal strain absolute value

With the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _iminimum is optimization aim, with the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _i≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0.

By the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0the first angle of bend β corresponding in replacement formula (2) _i, the second angle of bend γ _iwith roll working roll footpath D _i, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{i0}=a_{i1}+a_{i2}{\mathrm{\β}}_{i0}+a_{i3}{\mathrm{\γ}}_{i0}+a_{i4}{D}_{i0}+a_{i5}{\mathrm{\β}}_{i0}^2+a_{i6}{\mathrm{\β}}_{i0}{\mathrm{\γ}}_{i0}+a_{i7}{\mathrm{\β}}_{i0}{D}_{i0}+a_{i8}{\mathrm{\γ}}_{i0}^2+a_{i9}{\mathrm{\γ}}_{i0}{D}_{i0}+a_{i10}{D}_{i0}^2$

$+a_{i11}{\mathrm{\β}}_{i0}^3+a_{i12}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}+a_{i13}{\mathrm{\β}}_{i0}^2{D}_{i0}+a_{i14}{\mathrm{\γ}}_{i0}^2{\mathrm{\β}}_{i0}+a_{i15}{\mathrm{\γ}}_{i0}^3+a_{i16}{\mathrm{\γ}}_{i0}^2{D}_{i0}+a_{i17}{D}_{i0}^2{\mathrm{\β}}_{i0}+a_{i18}{D}_{i0}^2{\mathrm{\γ}}_{i0}---\left(3\right)$

$+a_{i19}{D}_{i0}^3+a_{i20}{\mathrm{\β}}_{i0}^4+a_{i21}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}^2+a_{i22}{\mathrm{\β}}_{i0}^2{D}_{i0}^2+a_{i23}{\mathrm{\γ}}_{i0}^2{D}_{i0}^2+a_{i24}{D}_{i0}^2{\mathrm{\β}}_{i0}^2+a_{i25}{D}_{i0}^4$

In formula (3): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _i0for the optimal value of i passage Strip first angle of bend;

γ _i0for the optimal value of i passage Strip second angle of bend;

D _i0for the optimal value in i passage roll working roll footpath;

I is 1,2 ..., n.

7 are equaled, namely with the maximum ε of the 7th passage Strip outward flange along its tangential direction normal strain absolute value for i ₇minimum is optimization aim, with the maximum ε of the 7th passage Strip outward flange along its tangential direction normal strain absolute value ₇≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of the 7th passage Strip ₇₀be 25.98 °, the optimal value γ of the second angle of bend ₇₀be the optimal value D in 17.93 ° and roll working roll footpath ₇₀for 348.27mm.

By the optimal value β of the first angle of bend ₇₀, the second angle of bend optimal value γ ₇₀with the optimal value D in roll working roll footpath ₇₀the first angle of bend β corresponding in replacement formula (2) ₇, the second angle of bend γ ₇with roll working roll footpath D ₇, obtain the 7th passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{70}=a_{71}+a_{72}{\mathrm{\β}}_{70}+a_{73}{\mathrm{\γ}}_{70}+a_{74}{D}_{70}+a_{75}{\mathrm{\β}}_{70}^2+a_{76}{\mathrm{\β}}_{70}{\mathrm{\γ}}_{70}+a_{77}{\mathrm{\β}}_{70}{D}_{70}+a_{78}{\mathrm{\γ}}_{70}^2+a_{79}{\mathrm{\γ}}_{70}{D}_{70}+a_{710}{D}_{70}^2$

$+a_{711}{\mathrm{\β}}_{70}^3+a_{712}{\mathrm{\β}}_{70}^2{\mathrm{\γ}}_{70}+a_{713}{\mathrm{\β}}_{70}^2{D}_{70}+a_{714}{\mathrm{\γ}}_{70}^2{\mathrm{\β}}_{70}+a_{715}{\mathrm{\γ}}_{70}^3+a_{716}{\mathrm{\γ}}_{70}^2{D}_{70}+a_{717}{D}_{70}^2{\mathrm{\β}}_{70}+a_{718}{D}_{70}^2{\mathrm{\γ}}_{70}---(3-1)$

$+a_{719}{D}_{70}^3+a_{720}{\mathrm{\β}}_{70}^4+a_{721}{\mathrm{\β}}_{70}^2{\mathrm{\γ}}_{70}^2+a_{722}{\mathrm{\β}}_{70}^2{D}_{70}^2+a_{723}{\mathrm{\γ}}_{70}^2{D}_{70}^2+a_{724}{D}_{70}^2{\mathrm{\β}}_{70}^2+a_{725}{D}_{70}^4$

In formula (3-1): a ₇₁, a ₇₂..., a ₇₂₅it is the regression coefficient of 7 passages;

β ₇₀it is the optimal value of 7 passage Strip first angle of bend;

γ ₇₀it is the optimal value of 7 passage Strip second angle of bend;

D ₇₀it is the optimal value in 7 passage roll working roll footpaths.

By the optimal value β of the first angle of bend in the optimum results after consolidation ₇₀=26 °, the optimal value γ of the second angle of bend ₇₀the optimal value D in=18 ° and roll working roll footpath ₇₀=348mm substitutes in formula (3-1), obtains ε ₇₀=0.89%.

In like manner, can be obtained by formula (3): ε ₁₀=0.82%, ε ₂₀=0.83%, ε ₃₀=0.87%, ε ₄₀=0.95%, ε ₅₀=0.92%, ε ₆₀=0.85%, ε ₈₀=0.90%, ε ₇₀=0.89%, ε ₉₀=0.92%, ε ₁₀₀=0.96%, ε ₁₁₀=0.89%.

The determination of the 5th step, clod wash road number of times

Because the determined each passage Strip outward flange of formula (3) is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0all in 0.8 ~ 1.0% scope, then the road number of times 11 of first step setting is determined.

The determination in the 6th step, angle of bend and roll working roll footpath

Because each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange be greater than 10% along the ratio of the mean value of the minimum of a value in the maximum of its tangential direction normal strain absolute value, then to the determined each passage Strip outward flange of the 5th step along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0sort by its size, refer to table 2.

Table 2 ε _i0(%) the size sequence of value

Size sorts	1	2	3	4	5	6	7	8	9	10	11
												Road number of times	10	4	5	9	8	7	11	3	6	2	1
ε i0（%）	0.96	0.95	0.92	0.92	0.90	0.89	0.89	0.87	0.85	0.83	0.82

Known by table 2, three level values that should be corresponding to each experimental factor of the 10th passage and the 1st passage respectively adjust, and repeat the first step to the 5th step.Obtain each passage Strip outward flange shown in table 3 along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0.

ε after table 3 adjusts _i0(%) value

Road number of times	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th	11st
												ε i0（%）	0.86	0.88	0.89	0.96	0.88	0.88	0.90	0.92	0.92	0.89	0.89

Can find out: each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be less than 10%, then the optimal value β of Strip cold roll forming each passage first angle of bend again after suboptimization _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0determined.As the optimal value β of the first angle of bend of the 7th passage after suboptimization again ₇₀be 26.04 °, the optimal value γ of the second angle of bend ₇₀be the optimal value D in 18.03 ° and roll working roll footpath ₇₀for 347.87mm.

Embodiment 2

A kind of method determining each passage angle of bend of Strip cold roll forming.The concrete steps of the method are: the design of the first step, virtual test scheme

According to knowhow, tentatively determine that the cold roll forming road frequency n of asymmetric Z-shape steel is 12, complete the design of roller floral diagram accordingly.This step, for the 6th passage, chooses the 6th passage first angle of bend β ₆, the second angle of bend γ ₆with roll working roll footpath D ₆as experimental factor; Each experimental factor respectively gets three level values, i.e. the first angle of bend β ₆value is respectively 16 °, 21 ° and 26 °, the second angle of bend γ ₆be respectively 6 °, 11 ° and 16 °, roll working roll footpath D ₆be respectively 320mm, 380mm and 440mm; By orthogonal arrage L ₉(3 ⁴) determine each experimental factor as shown in table 1 and the virtual test scheme of corresponding level value.

The virtual test scheme of table 1. the 6th passage

Tested number	First angle of bend β 6(°)	Second angle of bend γ 6(°)	Roller footpath D 6(mm)
				1	16.0	6.0	320
2	16.0	12.0	380
				3	16.0	18.0	440
4	21.0	6.0	380
				5	21.0	12.0	440
6	21.0	18.0	320
				7	26.0	6.0	440
8	26.0	12.0	320
				9	26.0	18.0	380

Second step, finite element simulation calculation

First set up respective finite element geometrical model according to the virtual test scheme of each passage of first step design, due to Strip thickness compared with its length and width much little, choose tetrahedron element, adopt finite element software to carry out network division, then determine the friction model between Strip and roll:

μ＝μ _d+(μ _s-μ _d)e ^-cv（1）

In formula (1): the relative sliding velocity of v-between Strip and roll, m/s;

U _s-confficient of static friction, u _s=0.2;

U _d-the coefficient of kinetic friction, u _d=0.1;

C-damped expoential, in the present embodiment, c=0.03 ~ 0.07.

Finally respectively finite element simulation calculation is carried out to each virtual test scheme, obtain the Strip Strain Distribution of each virtual test scheme of each passage.

3rd step, model are set up

According to the Strip Strain Distribution of each virtual test scheme of each passage of second step, determine that each virtual test scheme Strip outward flange of each passage is along its tangential direction normal strain value, obtains the maximum of each passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_i=a_{i1}+a_{i2}{\mathrm{\β}}_i+a_{i3}{\mathrm{\γ}}_i+a_{i4}{D}_i+a_{i5}{\mathrm{\β}}_i^2+a_{i6}{\mathrm{\β}}_i{\mathrm{\γ}}_i+a_{i7}{\mathrm{\β}}_i{D}_i+a_{i8}{\mathrm{\γ}}_i^2+a_{i9}{\mathrm{\γ}}_i{D}_i+a_{i10}{D}_i^2$

$+a_{i11}{\mathrm{\β}}_i^3+a_{i12}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i+a_{i13}{\mathrm{\β}}_i^2{D}_i+a_{i14}{\mathrm{\γ}}_i^2{\mathrm{\β}}_i+a_{i15}{\mathrm{\γ}}_i^3+a_{i16}{\mathrm{\γ}}_i^2{D}_i+a_{i17}{D}_i^2{\mathrm{\β}}_i+a_{i18}{D}_i^2{\mathrm{\γ}}_i---\left(2\right)$

$+a_{i19}{D}_i^3+a_{i20}{\mathrm{\β}}_i^4+a_{i21}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i^2+a_{i22}{\mathrm{\β}}_i^2{D}_i^2+a_{i23}{\mathrm{\γ}}_i^2{D}_i^2+a_{i24}{D}_i^2{\mathrm{\β}}_i^2+a_{i25}{D}_i^4$

In formula (2): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _ifor i passage Strip first angle of bend;

γ _ifor i passage Strip second angle of bend;

D _ifor i passage roll working roll footpath;

I is 1,2 ..., n.

6 are equaled for i, according to the Strip Strain Distribution of each virtual test scheme of second step the 6th passage, determine that each virtual test scheme Strip outward flange of the 6th passage is along its tangential direction normal strain value, obtains the maximum of the 6th passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_6=a_{61}+a_{62}{\mathrm{\β}}_6+a_{63}{\mathrm{\γ}}_6+a_{64}{D}_6+a_{65}{\mathrm{\β}}_6^2+a_{66}{\mathrm{\β}}_6{\mathrm{\γ}}_6+a_{67}{\mathrm{\β}}_6{D}_6+a_{68}{\mathrm{\γ}}_6^2+a_{69}{\mathrm{\γ}}_6{D}_6+a_{610}{D}_6^2$

$+a_{611}{\mathrm{\β}}_6^3+a_{612}{\mathrm{\β}}_6^2{\mathrm{\γ}}_6+a_{613}{\mathrm{\β}}_6^2{D}_6+a_{614}{\mathrm{\γ}}_6^2{\mathrm{\β}}_6+a_{615}{\mathrm{\γ}}_6^3+a_{616}{\mathrm{\γ}}_6^2{D}_6+a_{616}{D}_6^2{\mathrm{\β}}_6+a_{618}{D}_6^2{\mathrm{\γ}}_6---(2-1)$

$+a_{619}{D}_6^3+a_{620}{\mathrm{\β}}_6^4+a_{621}{\mathrm{\β}}_6^2{\mathrm{\γ}}_6^2+a_{622}{\mathrm{\β}}_6^2{D}_6^2+a_{623}{\mathrm{\γ}}_6^2{D}_6^2+a_{624}{D}_6^2{\mathrm{\β}}_6^2+a_{625}{D}_6^4$

In formula (2-1): a ₆₁, a ₆₂..., a ₆₂₅it is the regression coefficient of 6 passages;

β ₆it is the first angle of bend of 6 passage Strips;

γ ₆it is the second angle of bend of 6 passage Strips;

D ₆be 6 passage roll working roll footpaths.

Minimum of a value in the maximum of the 4th step, normal strain absolute value

With the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _iminimum is optimization aim, with the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _i≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0.

By the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0the first angle of bend β corresponding in replacement formula (2) _i, the second angle of bend γ _iwith roll working roll footpath D _i, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{i0}=a_{i1}+a_{i2}{\mathrm{\β}}_{i0}+a_{i3}{\mathrm{\γ}}_{i0}+a_{i4}{D}_{i0}+a_{i5}{\mathrm{\β}}_{i0}^2+a_{i6}{\mathrm{\β}}_{i0}{\mathrm{\γ}}_{i0}+a_{i7}{\mathrm{\β}}_{i0}{D}_{i0}+a_{i8}{\mathrm{\γ}}_{i0}^2+a_{i9}{\mathrm{\γ}}_{i0}{D}_{i0}+a_{i10}{D}_{i0}^2$

$+a_{i11}{\mathrm{\β}}_{i0}^3+a_{i12}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}+a_{i13}{\mathrm{\β}}_{i0}^2{D}_{i0}+a_{i14}{\mathrm{\γ}}_{i0}^2{\mathrm{\β}}_{i0}+a_{i15}{\mathrm{\γ}}_{i0}^3+a_{i16}{\mathrm{\γ}}_{i0}^2{D}_{i0}+a_{i17}{D}_{i0}^2{\mathrm{\β}}_{i0}+a_{i18}{D}_{i0}^2{\mathrm{\γ}}_{i0}---\left(3\right)$

$+a_{i19}{D}_{i0}^3+a_{i20}{\mathrm{\β}}_{i0}^4+a_{i21}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}^2+a_{i22}{\mathrm{\β}}_{i0}^2{D}_{i0}^2+a_{i23}{\mathrm{\γ}}_{i0}^2{D}_{i0}^2+a_{i24}{D}_{i0}^2{\mathrm{\β}}_{i0}^2+a_{i25}{D}_{i0}^4$

In formula (3): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _i0for the optimal value of i passage Strip first angle of bend;

γ _i0for the optimal value of i passage Strip second angle of bend;

D _i0for the optimal value in i passage roll working roll footpath;

I is 1,2 ..., n.

6 are equaled, namely with the maximum ε of the 6th passage Strip outward flange along its tangential direction normal strain absolute value for i ₆minimum is optimization aim, with the maximum ε of the 6th passage Strip outward flange along its tangential direction normal strain absolute value ₆≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of the 6th passage Strip ₆₀be 18.87 °, the optimal value γ of the second angle of bend ₆₀be the optimal value D in 13.14 ° and roll working roll footpath ₆₀for 327.25mm;

By the optimal value β of the first angle of bend ₆₀, the second angle of bend optimal value γ ₆₀with the optimal value D in roll working roll footpath ₆₀the first angle of bend β corresponding in replacement formula (2) ₆, the second angle of bend γ ₆with roll working roll D ₆, obtain the 6th passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{60}=a_{61}+a_{62}{\mathrm{\β}}_{60}+a_{63}{\mathrm{\γ}}_{60}+a_{64}{D}_{60}+a_{65}{\mathrm{\β}}_{60}^2+a_{66}{\mathrm{\β}}_{60}{\mathrm{\γ}}_{60}+a_{67}{\mathrm{\β}}_{60}{D}_{60}+a_{68}{\mathrm{\γ}}_{60}^2+a_{69}{\mathrm{\γ}}_{60}{D}_{60}+a_{610}{D}_{60}^2$

$+a_{611}{\mathrm{\β}}_{60}^3+a_{612}{\mathrm{\β}}_{60}^2{\mathrm{\γ}}_{60}+a_{613}{\mathrm{\β}}_{60}^2{D}_{60}+a_{614}{\mathrm{\γ}}_{60}^2{\mathrm{\β}}_{60}+a_{615}{\mathrm{\γ}}_{60}^3+a_{616}{\mathrm{\γ}}_{60}^2{D}_{60}+a_{617}{D}_{60}^2{\mathrm{\β}}_{60}+a_{618}{D}_{60}^2{\mathrm{\γ}}_{60}---(3-1)$

$+a_{619}{D}_{60}^3+a_{620}{\mathrm{\β}}_{60}^4+a_{621}{\mathrm{\β}}_{60}^2{\mathrm{\γ}}_{60}^2+a_{622}{\mathrm{\β}}_{60}^2{D}_{60}^2+a_{623}{\mathrm{\γ}}_{60}^2{D}_{60}^2+a_{624}{D}_{60}^2{\mathrm{\β}}_{60}^2+a_{625}{D}_{60}^4$

In formula (3-1): a ₆₁, a ₆₂..., a ₆₂₅it is the regression coefficient of 6 passages;

β ₆₀it is the optimal value of 6 passage Strip first angle of bend;

γ ₆₀it is the optimal value of 6 passage Strip second angle of bend;

D ₆₀it is the optimal value in 6 passage roll working roll footpaths.

By the optimal value β of the first angle of bend in the optimum results after consolidation ₆₀=19 °, the optimal value γ of the second angle of bend ₆₀=13 °, the optimal value D in roll working roll footpath ₆₀=327mm substitutes in formula (3-1), obtains ε ₆₀=0.86%

In like manner, can be obtained by formula (3): ε ₁₀=0.76%, ε ₂₀=0.80%, ε ₃₀=0.86%, ε ₄₀=0.90%, ε ₅₀=0.84%, ε ₇₀=0.89%, ε ₈₀=0.90%, ε ₉₀=0.88%, ε ₁₀₀=0.84%, ε ₁₁₀=0.83%, ε ₁₂₀=0.81%.

The determination of the 5th step, clod wash road number of times

Because certain the passage Strip outward flange in the determined each passage of formula (3) is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0be less than 0.8%, then the road number of times 12 that the first step sets subtracted 1, i.e. the road number of times of second time setting is 11.

Then repeat the first step to the 4th step, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value: ε ₁₀ ^'=0.82%, ε ₂₀ ^'=0.85%, ε ₃₀ ^'=0.86%, ε ₄₀ ^'=0.91%, ε ₅₀ ^'=0.87%, ε ₆₀ ^'=0.85%, ε ₇₀ ^'=0.88%, ε ₈₀ ^'=0.92%, ε ₉₀ ^'=0.94%, ε ₁₀₀ ^'=0.89% and ε ₁₁₀ ^'=0.88%.

Can find out: each passage Strip outward flange again determined is along the minimum of a value in the maximum of its tangential direction normal strain absolute value all in 0.8 ~ 1.0% scope, then the road number of times 11 again set is determined.

The determination in the 6th step, angle of bend and roll working roll footpath

Because each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be greater than 10%, then to the determined each passage Strip outward flange of the 5th step along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0sort by its size, refer to table 2.

Table 2 ε _i0(%) the size sequence of value

Size sorts	1	2	3	4	5	6	7	8	9	10	11
												Road number of times	9	8	4	10	11	7	5	6	3	2	1
ε i0（%）	0.94	0.92	0.91	0.89	0.88	0.88	0.87	0.87	0.86	0.85	0.82

Known by table 2, three level values that should be corresponding to each experimental factor of the 9th passage and the 1st passage respectively adjust, and repeat the first step to the 5th step.Obtain each passage Strip outward flange shown in table 3 along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0.

ε after table 3 adjusts _i0(%) value

Road number of times	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th	11st
												ε i0（%）	0.85	0.87	0.89	0.92	0.87	0.86	0.92	0.90	0.92	0.87	0.88

Can find out: each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be less than 10%, then the optimal value β of Strip cold roll forming each passage first angle of bend again after suboptimization _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0determined.As the optimal value β of the first angle of bend of the 6th passage after suboptimization again ₆₀be 19.24 °, the optimal value γ of the second angle of bend ₆₀be the optimal value D in 13.32 ° and roll working roll footpath ₆₀for 326.87mm.

Embodiment 3

A kind of method determining each passage angle of bend of Strip cold roll forming.The concrete steps of the method are:

The design of the first step, virtual test scheme

According to form factor function, the cold roll forming road frequency n setting asymmetric Z-shape steel is 10, completes the design of roller floral diagram accordingly.Choose the angle of bend of each passage Strip and roll working roll footpath as experimental factor, the level value of each experimental factor of preliminary election, this step, for the 3rd passage, chooses the first angle of bend β ₃with roll working roll footpath D ₃for experimental factor; Each experimental factor respectively gets three level values, i.e. the first angle of bend β ₃be respectively 16 °, 22 ° and 28 °, roll working roll footpath D ₃be respectively 400mm, 450mm and 500mm; By orthogonal arrage L ₉(3 ⁴) determine each experimental factor as shown in table 1 and the virtual test scheme of corresponding level value.

The virtual test scheme of table 1. the 3rd passage

Tested number	First angle of bend β 3（°）	Roller footpath D 3（mm）
			1	16.0	400
2	16.0	450
			3	16.0	500
4	22.0	400
			5	22.0	450
6	22.0	500
			7	28.0	400
8	28.0	450
			9	28.0	500

Second step, finite element simulation calculation

First set up respective finite element geometrical model according to the virtual test scheme of each passage of first step design, due to Strip thickness compared with its length and width much little, choose shell unit, adopt finite element software to carry out network division, then determine the friction model between Strip and roll:

μ＝μ _d+(μ _s-μ _d)e ^-cv（1）

In formula (1): the relative sliding velocity of v-between Strip and roll, m/s;

U _s-confficient of static friction, u _s=0.2;

U _d-the coefficient of kinetic friction, u _d=0.1;

C-damped expoential, in the present embodiment, c=0.04 ~ 0.08.

Finally respectively finite element simulation calculation is carried out to each virtual test scheme, obtain the Strip Strain Distribution of each virtual test scheme of each passage.

3rd step, model are set up

According to each virtual test scheme of each passage of second step Strip Strain Distribution, determine that each virtual test scheme Strip outward flange of each passage is along its tangential direction normal strain value, obtains the maximum of each passage Strip outward flange along its tangential direction normal strain absolute value:

$\begin{array}{c}{\mathrm{\ϵ}}_i=a_{i1}+a_{i2}{\mathrm{\β}}_i+a_{i3}{D}_i+a_{i4}{\mathrm{\β}}_i^2+a_{i5}{\mathrm{\β}}_i{D}_i+a_{i6}{D}_i^2+a_{i7}{\mathrm{\β}}_i^3+a_{i8}{\mathrm{\β}}_i^2{D}_i\\ +a_{i9}{D}_i^2{\mathrm{\β}}_i+a_{i10}{D}_i^3+a_{i11}{\mathrm{\β}}_i^4+a_{i12}{\mathrm{\β}}_i^2{D}_i^2+a_{i13}{D}_i^2{\mathrm{\β}}_i^2+a_{i14}{D}_i^4\end{array}---\left(2\right)$

In formula (2): a _i1, a _i2..., a _i14for the regression coefficient of i passage

β _ifor i passage Strip first angle of bend;

D _ifor i passage roll working roll footpath;

I is 1,2 ..., n.

3 are equaled for i, according to the Strip Strain Distribution of each virtual test scheme of second step the 3rd passage, determine that each virtual test scheme Strip outward flange of the 3rd passage is along its tangential direction normal strain value, obtains the maximum of the 3rd passage Strip outward flange along its tangential direction normal strain absolute value:

$\begin{array}{c}{\mathrm{\ϵ}}_3=a_{31}+a_{32}{\mathrm{\β}}_3+a_{33}{D}_3+a_{34}{\mathrm{\β}}_3^2+a_{35}{\mathrm{\β}}_3{D}_3+a_{36}{D}_3^2+a_{37}{\mathrm{\β}}_3^3+a_{38}{\mathrm{\β}}_3^2{D}_3\\ +a_{39}{D}_3^2{\mathrm{\β}}_3+a_{310}{D}_3^3+a_{311}{\mathrm{\β}}_3^4+a_{312}{\mathrm{\β}}_3^2{D}_3^2+a_{313}{D}_3^2{\mathrm{\β}}_3^2+a_{314}{D}_3^4\end{array}---(2-1)$

In formula (2-1): a ₃₁, a ₃₂..., a ₃₁₄it is the regression coefficient of 3 passages;

β ₃be 3 passage Strip first angle of bend;

D ₃be 3 passage roll working roll footpaths.

Minimum of a value in the maximum of the 4th step, normal strain absolute value

With the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _iminimum is optimization aim, with the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _i≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of each passage Strip _i0with the optimal value D in roll working roll footpath _i0.

By the optimal value β of the first angle of bend of each passage Strip _i0with the optimal value D in roll working roll footpath _i0the first angle of bend β corresponding in replacement formula (2) _iwith roll working roll footpath D _i, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

$\begin{array}{c}{\mathrm{\ϵ}}_{i0}=a_{i1}+a_{i2}{\mathrm{\β}}_{i0}+a_{i3}{D}_{i0}+a_{i4}{\mathrm{\β}}_{i0}^2+a_{i5}{\mathrm{\β}}_{i0}{D}_{i0}+a_{i6}{D}_{i0}^2+a_{i7}{\mathrm{\β}}_{i0}^3+a_{i8}{\mathrm{\β}}_{i0}^2{D}_{i0}\\ +a_{i9}{D}_{i0}^2{\mathrm{\β}}_{i0}+a_{i10}{D}_{i0}^3+a_{i11}{\mathrm{\β}}_{i0}^4+a_{i12}{\mathrm{\β}}_{i0}^2{D}_{i0}^2+a_{i13}{D}_{i0}^2{\mathrm{\β}}_{i0}^2+a_{i14}{D}_{i0}^4\end{array}---\left(3\right)$

In formula (3): a _i1, a _i2..., a _i14for the regression coefficient of i passage;

β _i0for the optimal value of i passage Strip first angle of bend;

D _i0for the optimal value in i passage roll working roll footpath;

I is 1,2 ..., n.

3 are equaled, namely with the maximum ε of the 3rd passage Strip outward flange along its tangential direction normal strain absolute value for i ₃minimum is optimization aim, with the maximum ε of the 3rd passage Strip outward flange along its tangential direction normal strain absolute value ₃≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of the 3rd passage Strip ₃₀be the optimal value D in 21.87 ° and roll working roll footpath ₃₀for 324.15mm.

By the optimal value β of the first angle of bend ₃₀with the optimal value D in roll working roll footpath ₃₀the first angle of bend β corresponding in replacement formula (2) ₃with roll working roll D ₃, obtain this passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

$\begin{array}{c}{\mathrm{\ϵ}}_{30}=a_{31}+a_{32}{\mathrm{\β}}_{30}+a_{33}{D}_{30}+a_{34}{\mathrm{\β}}_{30}^2+a_{35}{\mathrm{\β}}_{30}{D}_{30}+a_{36}{D}_{30}^2+a_{37}{\mathrm{\β}}_{30}^3+a_{38}{\mathrm{\β}}_{30}^2{D}_{30}\\ +a_{39}{D}_{30}^2{\mathrm{\β}}_{30}+a_{310}{D}_{30}^3+a_{311}{\mathrm{\β}}_{30}^4+a_{312}{\mathrm{\β}}_{30}^2{D}_{30}^2+a_{313}{D}_{30}^2{\mathrm{\β}}_{30}^2+a_{314}{D}_{30}^4\end{array}---(3-1)$

In formula (3-1): a ₃₁, a ₃₂..., a ₃₁₄it is the regression coefficient of 3 passages;

β ₃₀it is the optimal value of 3 passage Strip first angle of bend;

D ₃₀it is the optimal value in 3 passage roll working roll footpaths;

By the optimal value β of the first angle of bend in the optimum results after consolidation ₃₀the optimal value D in=22 ° and roll working roll footpath ₃₀=324mm substitutes in formula (3-1), obtains ε ₃₀=0.94%.

In like manner, can be obtained by formula (3): ε ₁₀=0.89%, ε ₂₀=0.92%, ε ₄₀=0.93%, ε ₅₀=0.89%, ε ₆₀=0.96%, ε ₇₀> 1%.

The determination of the 5th step, clod wash road number of times

ε ₇₀> 1% illustrates not existed in restriction range along the minimum of a value in the maximum of its tangential direction normal strain absolute value by the determined 7th passage passage Strip outward flange of formula (3), then the road number of times 10 that the first step sets is added 1, i.e. the road number of times of second time setting is 11.

Then repeat the first step to the 4th step, obtain each passage Strip outward flange after suboptimization again along the minimum of a value in the maximum of its tangential direction normal strain absolute value: ε ₁₀ ^'=0.83%, ε ₂₀ ^'=0.86%, ε ₃₀ ^'=0.87%, ε ₄₀ ^'=0.92%, ε ₅₀ ^'=0.89%, ε ₆₀ ^'=0.86%, ε ₇₀ ^'=0.87%, ε ₈₀ ^'=0.95%, ε ₉₀ ^'=0.89%, ε ₁₀₀ ^'=0.87% and ε ₁₁₀ ^'=0.84%.

Can find out: each passage Strip outward flange again determined is along the minimum of a value in the maximum of its tangential direction normal strain absolute value all in 0.8 ~ 1.0% scope, then the road number of times 11 again set is determined.

The determination in the 6th step, angle of bend and roll working roll footpath

Because each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be greater than 10%, then to the determined each passage Strip outward flange of the 5th step along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0sort by its size, refer to table 2.

Table 2 ε _i0(%) the size sequence of value

Size sorts	1	2	3	4	5	6	7	8	9	10	11
												Road number of times	8	4	5	9	10	3	7	6	2	11	1
ε i0（%）	0.95	0.92	0.89	0.89	0.87	0.87	0.87	0.86	0.86	0.84	0.83

Known by table 2, three level values that should be corresponding to each experimental factor of the 8th passage and the 1st passage respectively adjust, and repeat the first step to the 5th step.Obtain each passage Strip outward flange shown in table 3 along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0.

ε after table 3 adjusts _i0(%) value

Road number of times	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th	11st
												ε i0（%）	0.86	0.86	0.87	0.91	0.90	0.87	0.88	0.92	0.89	0.86	0.89

Can find out: each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be less than 10%, then the optimal value β of Strip cold roll forming each passage first angle of bend again after suboptimization _i0with the optimal value D in roll working roll footpath _i0determined.As the optimal value β of the first angle of bend of the 3rd passage after suboptimization again ₆₀be the optimal value D in 21.75 ° and roll working roll footpath ₆₀for 324.38mm.

This detailed description of the invention compared with prior art has following good effect:

The distribution method of each passage Strip angle of bend that this detailed description of the invention relates to considers the impact that the factors such as roll working roll footpath, Strip material, rolled piece/roll contact state are determined clod wash each passage Strip angle of bend, situation when applicable frame spacing is unequal, and methodological science, too need not rely on practical experience.

This detailed description of the invention is minimum for optimization aim along the maximum of its tangential direction normal strain absolute value with each passage Strip outward flange, 1% is less than or equal to for constraints along the maximum of its tangential direction normal strain absolute value with Strip outward flange, therefore can not produce warpage and limit wave defect when Strip is shaping, and the productive potentialities of unit equipment can be given full play to.

Therefore, this detailed description of the invention have be suitable for frame spacing unequal, clod wash unit capacity of equipment can be given full play to, Strip warpage can be avoided and the feature of Strip edge shape wave defect can be overcome.

Claims (2)

1. determine a method for each passage angle of bend of Strip cold roll forming, it is characterized in that the concrete steps of the method are:

The design of the first step, virtual test scheme

First according to form factor function or knowhow, the road frequency n of setting cold roll forming, carry out the design of roller floral diagram, then choose two angle of bend of each passage of Strip cold roll forming and roll working roll footpath as experimental factor or any one angle of bend chosen again in two angle of bend of each passage of Strip cold roll forming and roll working roll footpath as experimental factor; Then the level value of each experimental factor of preliminary election, designs the virtual test scheme of each experimental factor and corresponding level value;

Second step, finite element simulation calculation

First set up respective finite element geometrical model according to the virtual test scheme of each passage of first step design, then choose unit, adopt finite element software to carry out network division, then determine the friction model between Strip and roll:

μ＝μ _d+(μ _s-μ _d)e ^-cv（1）

In formula (1): the relative sliding velocity of v-between Strip and roll, m/s;

U _s-confficient of static friction, u _s=0.2;

U _d-the coefficient of kinetic friction, u _d=0.1;

C-damped expoential, c=0.02 ~ 0.08;

Finally respectively finite element simulation calculation is carried out to each virtual test scheme, obtain the Strip Strain Distribution of each virtual test scheme of each passage;

3rd step, model are set up

According to the Strip Strain Distribution of each virtual test scheme of each passage of second step, determine that each virtual test scheme Strip outward flange of each passage is along its tangential direction normal strain value, obtains the maximum of each passage Strip outward flange along its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_i=a_{i1}+a_{i2}{\mathrm{\β}}_i+a_{i3}{\mathrm{\γ}}_i+a_{i4}{D}_i+a_{i5}{\mathrm{\β}}_i^2+a_{i6}{\mathrm{\β}}_i{\mathrm{\γ}}_i+a_{i7}{\mathrm{\β}}_i{D}_i+a_{i8}{\mathrm{\γ}}_i^2+a_{i9}{\mathrm{\γ}}_i{D}_i+a_{i10}{D}_i^2$

$+a_{i11}{\mathrm{\β}}_i^3+a_{i12}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i+a_{i13}{\mathrm{\β}}_i^2{D}_i+a_{i14}{\mathrm{\γ}}_i^2{\mathrm{\β}}_i+a_{i15}{\mathrm{\γ}}_i^3+a_{i16}{\mathrm{\γ}}_i^2{D}_i+a_{i17}{D}_i^2{\mathrm{\β}}_i+a_{i18}{D}_i^2{\mathrm{\γ}}_i---\left(2\right)$

$+a_{i19}{D}_i^3+a_{i20}{\mathrm{\β}}_i^4+a_{i21}{\mathrm{\β}}_i^2{\mathrm{\γ}}_i^2+a_{i22}{\mathrm{\β}}_i^2{D}_i^2+a_{i23}{\mathrm{\γ}}_i^2{D}_i^2+a_{i24}{D}_i^2{\mathrm{\β}}_i^2+a_{i25}{D}_i^4$

In formula (2): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _ifor i passage Strip first angle of bend;

γ _ifor i passage Strip second angle of bend;

β _iand γ _iin have at least an angle of bend to be experimental factor;

D _ifor i passage roll working roll footpath;

I is 1,2 ..., n;

Minimum of a value in the maximum of the 4th step, normal strain absolute value

With the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _iminimum is optimization aim, with the maximum ε of each passage Strip outward flange along its tangential direction normal strain absolute value _i≤ 1% and each experimental factor level value be limited to constraints up and down, determine the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0;

By the optimal value β of the first angle of bend of each passage Strip _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0the first angle of bend β corresponding in replacement formula (2) _i, the second angle of bend γ _iwith roll working roll footpath D _i, obtain each passage Strip outward flange along the minimum of a value in the maximum of its tangential direction normal strain absolute value:

${\mathrm{\ϵ}}_{i0}=a_{i1}+a_{i2}{\mathrm{\β}}_{i0}+a_{i3}{\mathrm{\γ}}_{i0}+a_{i4}{D}_{i0}+a_{i5}{\mathrm{\β}}_{i0}^2+a_{i6}{\mathrm{\β}}_{i0}{\mathrm{\γ}}_{i0}+a_{i7}{\mathrm{\β}}_{i0}{D}_{i0}+a_{i8}{\mathrm{\γ}}_{i0}^2+a_{i9}{\mathrm{\γ}}_{i0}{D}_{i0}+a_{i10}{D}_{i0}^2$

$+a_{i11}{\mathrm{\β}}_{i0}^3+a_{i12}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}+a_{i13}{\mathrm{\β}}_{i0}^2{D}_{i0}+a_{i14}{\mathrm{\γ}}_{i0}^2{\mathrm{\β}}_{i0}+a_{i15}{\mathrm{\γ}}_{i0}^3+a_{i16}{\mathrm{\γ}}_{i0}^2{D}_{i0}+a_{i17}{D}_{i0}^2{\mathrm{\β}}_{i0}+a_{i18}{D}_{i0}^2{\mathrm{\γ}}_{i0}---\left(3\right)$

$+a_{i19}{D}_{i0}^3+a_{i20}{\mathrm{\β}}_{i0}^4+a_{i21}{\mathrm{\β}}_{i0}^2{\mathrm{\γ}}_{i0}^2+a_{i22}{\mathrm{\β}}_{i0}^2{D}_{i0}^2+a_{i23}{\mathrm{\γ}}_{i0}^2{D}_{i0}^2+a_{i24}{D}_{i0}^2{\mathrm{\β}}_{i0}^2+a_{i25}{D}_{i0}^4$

In formula (3): a _i1, a _i2..., a _i25for the regression coefficient of i passage;

β _i0for the optimal value of i passage Strip first angle of bend;

γ _i0for the optimal value of i passage Strip second angle of bend;

β _i0and γ _i0in have at least the optimal value of an angle of bend to be experimental factor;

D _i0for the optimal value in i passage roll working roll footpath;

I is 1,2 ..., n;

The determination of the 5th step, clod wash road number of times

If first substep formula (3) determined each passage Strip outward flange is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0all in 0.8 ~ 1.0% scope, then the road frequency n of first step setting is determined;

If certain the passage Strip outward flange in second substep formula (3) determined each passage is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0be less than 0.8%, then the road frequency n that the first step sets subtracted 1, then repeat the first step to the 4th step, until meet the 5th step first substep;

If certain the passage Strip outward flange in the 3rd substep formula (3) determined each passage is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0do not exist, then the road frequency n that the first step sets is added 1, then repeat the first step to the 4th step, until meet the 5th step first substep;

The determination in the 6th step, angle of bend and roll working roll footpath

If each passage Strip outward flange of the first substep is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0the ratio of mean value be less than or equal to 10%, then the optimal value β of Strip cold roll forming each passage first angle of bend _i0, the second angle of bend optimal value γ _i0with the optimal value D in roll working roll footpath _i0determined;

If each passage Strip outward flange of the second substep is along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0differential and each passage Strip outward flange be greater than 10% along the ratio of the mean value of the minimum of a value in the maximum of its tangential direction normal strain absolute value, then to the determined each passage Strip outward flange of the 5th step along the minimum of a value ε in the maximum of its tangential direction normal strain absolute value _i0sort by its size, then the level value of passage experimental factor corresponding to minimum of a value in maximum in sequence and sequence is adjusted, repeat the first step to the 5th step, until meet the 6th step first substep.

2. determine the method for each passage angle of bend of Strip cold roll forming according to claim 1, it is characterized in that described unit is shell unit or for hexahedral element or for tetrahedron element.