CN100333845C - Method for designing roller shape and milling roller for inhibiting higher-order wave shape - Google Patents

Abstract

The present invention provides a design method for roller shapes. Rollers manufactured according to the present invention can separately and continuously adjust the high order wave shapes. The design method of the roller shapes of the present invention has the steps that (1), a coefficient of a function of a basic roller gap is determined according to a predetermined secondary convexity, and the function of the basic roller gap is a second power function; (2), coefficients of corresponding functions of variable roller gaps are respectively determined according to high order convexity of a predetermined roller when the predetermined roller is in a maximum position of the positive shift and in a maximum position of the negative shift, and the function of the variable roller gaps is power functions with the power which is larger than two; (3), the second power functions of the roller gaps are respectively added with the functions of the variable roller gaps when the roller is arranged at the positive shift maximum position and the negative shift maximum position to obtain the roller gap functions when the roller is arranged at the positive shift maximum position and the negative shift maximum position; curves of the roller shapes are determined according to the play travel of the roller, the length of the roller, and the functions of the roller gaps when the roller is arranged at the positive shift maximum position and the negative shift maximum position.

Description

The roll of a kind of roll forming method for designing and inhibition high order shape wave

Technical field

The present invention relates to the metallurgical production technology, the roll of particularly a kind of roll forming method for designing and inhibition high order shape wave.

Background technology

In the process of rolling flat material, make metal generation plastic deformation by the effect between roll pair and the processing metal, thereby reach required shape.Since a variety of causes, strip surface that is rolled and non-planar surface, but be the heaving of the sea shape.This fluctuating is also referred to as glacing flatness, in the variation of rolling front and back convexity direct corresponding relation is arranged with band.So-called convexity, promptly thickness difference or the thickness difference with the steel cross section distributes, and in this manual, unless specialize, the thickness difference that convexity generally refers to band steel cross section distributes, and the position of high point or low spot on the cross section is called the convexity position.Fig. 1 shows a kind of typical band steel cross section, this cross-sectional outling can be represented with power function, that is to say, the cross-sectional outling curve is formed by stacking by constant, once linear function, secondary power function and high order power function, correspondingly, cross sectional thickness difference or its distribution of secondary power function part are called the secondary convexity, and cross sectional thickness difference or its distribution of high order power function part are called the high order convexity.

When rolling flat strip,, need control accurately roll gap in order to guarantee the glacing flatness of finished product.Roll gap control method commonly used comprises means such as roll forming of the roll, roller, roll intersection and roll play.Using at present is HC series rolling mill and CVC series rolling mill more widely, they adopt diverse ways to control roll gap, and wherein, the HC series rolling mill does not generally adopt special roll forming, but change the contact situation of roll, thereby reach the purpose of control roll gap by the long stroke play of roll; Roll and up-down rollers that the CVC series rolling mill adopts roll forming to be " S " or " bottle " shape are inverted, so just can obtain required roll gap shape with cooperating of roll forming by the little stroke play of roll, Fig. 2 shows the shape in roll gap under the different relative position of this roll (zone of representing with black among the figure), wherein the accompanying drawing of the top shows the shape of up-down rollers to punctual roll gap, middle accompanying drawing shows that top roll is done axially-movable to the right and the shape of lower roll roll gap when doing axially-movable left, and the accompanying drawing of below shows that top roll is done axially-movable left and the shape of lower roll roll gap when doing axially-movable to the right.

In the CVC milling train, the roll shape curve of roll generally all is designed to the cube functional form with formula (1) expression:

y＝a ₀+a ₁·x+a ₂·x ²+a ₃·x ³ (1)

Wherein, a ₀～a ₃Be constant, x be roll mandrel to position coordinates, y is the roller diameter at coordinate x place.

Make that the play stroke is b, then the roll shape curve y of top roll and lower roll ₁₁And y ₁₂Be respectively:

y ₁₁＝a ₀+a ₁·(x-b)+a ₂·(x-b) ²+a ₃·(x-b) ³ (2a)

y ₁₂＝a ₀+a ₁·(x+b)+a ₂·(x+b) ²+a ₃·(x+b) ³ (2b)

Therefore the shape (the following roll gap function that is called again) of the roll gap z under the no-load situation can formula (3) be expressed as:

z＝y ₁₁-y ₁₂＝c ₀+c ₁·x+c ₂·x ² (3)

C wherein ₀～c ₂Be constant.

In traditional C VC milling train, generally adopt the means of work roll bending, intermediate calender rolls roller and intermediate calender rolls play to regulate and control for the secondary shape wave.By formula (3) as seen, the no-load roll gap function that traditional C VC roll produces when play is the conic section of standard, therefore it only can have the improvement effect to the secondary shape wave in theory, and work roll bending and intermediate calender rolls roller equally also have only the ability of improving the secondary shape wave, therefore the control method of above-mentioned control methods repeats, and does not give full play to the ability of regulation and control of roll to plate shape.

For the high order shape wave, then often adopt the means of subregion cooling to regulate and control.But because the long response time that heat transfer rate causes slowly, and the roller temperature partial deviations are to heat conducting restriction, and it is very limited that these means are eliminated the effect of high order shape wave.Yet in practical condition, the many problems that run into are last often all can be owing to the control ability to M type and W type high order shape wave, and therefore the control to the high order shape wave is a very important technological factor.

In order to control the high order shape wave, in being the European patent of EP0294544, the patent No. disclosed the roll forming technology of a kind of CVCPLUS of being called, and it is designed to the CVC roll shape five power functions of following form:

y＝a ₀+a ₁·x+a ₂·x ²+a ₃·x ³+a ₄·x ⁴+a ₅·x ⁵ (4)

A wherein ₀～a ₅Be constant, x be roll mandrel to position coordinates, y is the roller diameter at coordinate x place.

Be inverted and little stroke play can be regulated and control the secondary convexity by the roll up-down rollers that will have roll forming shown in the following formula (4), meanwhile, also can carry out to a certain degree adjusting the high order convexity.But owing between secondary convexity and the high order convexity coupled relation is arranged, also be to have specific syntagmatic between them, therefore be difficult to control separately the high order convexity.In addition, the roll gap that utilizes roll forming shown in the following formula (4) to form can't be controlled the maximum value position of high order convexity.

Austrian patent AT410765B discloses another kind ofly has the roll of regulating power to the high order convexity, and its roll forming is designed to the stack of SIN function and linear function.But every roll forming can only overcome specific high order defective in the roll play, can't online dynamic adjustments high order roll gap.

Chinese patent CN2044910U also discloses a kind of roll, and its roll forming vary in diameter rule is the power series of following form:

D(x)＝a ₀+a ₁(x-F ₀)+a ₃(x-F ₀) ³+…+a _n(x-F ₀) ⁿ (5)

F wherein ₀Be initial displacement, a ₀～a _nBe roll forming parameter undetermined.Roll forming parameter undetermined is by the minimum and maximum roller poor Δ D in footpath, the extreme value place e decision of basic roll forming roller footpath, for example for three power series:

D(x)＝a ₀+a ₁(x-F ₀)+a _n(x-F ₀) ⁿ (5a)

Its roll forming parameter is determined by following formula:

$a_0=D_0+\frac{\mathrm{\ΔD}\·F_0}{2(n-1)e^n}(F_0^{n-1}-{\mathrm{ne}}^{n-1})---\left(6a\right)$

$a_1=-\frac{\mathrm{\ΔD}}{2(n-1)e^n}\·{\mathrm{ne}}^{n-1}---\left(6b\right)$

$a_n=\frac{\mathrm{\ΔD}}{2(n-1)e^n}---\left(6c\right)$

Above-mentioned roll can be regulated continuously to the secondary convexity and the high order convexity of roll gap, but its secondary convexity and high order convexity still are coupled, and therefore can't regulate separately secondary convexity or high order convexity.In addition, this roll is before roll forming designs, and maximum and the poor Δ D in pony roll footpath, basic roll forming roller footpath extreme value place e can't determine according to the requirement of technology.

Summary of the invention

The purpose of this invention is to provide a kind of roll forming method for designing, can regulate the high order shape wave independently, continuously according to the roll of its design.

Above-mentioned purpose of the present invention realizes by following technical proposal:

A kind of roll forming method for designing comprises following steps:

(1) determine the coefficient of basic roll gap function according to the preset secondary convexity, described basic roll gap function is the secondary power function;

(2) be in forward according to default roll and move the coefficient that high order convexity when moving maximum position with negative sense is determined corresponding variable roll gap function respectively, described variable roll gap function is a power time greater than 2 power function;

(3) described basic secondary roll gap function being in forward with roll respectively moves described variable roll gap function when moving maximum position with negative sense and is obtained roll mutually and be in forward and move roll gap function when moving maximum position with negative sense;

(4) according to play stroke, the length of roll be in the described roll gap function that forward moves when moving maximum position with negative sense and determine roll shape curve.

Reasonable is that in above-mentioned roll forming method for designing, described basic roll gap function adopts following form: S1 (x)=g ₁₂X ², wherein, x be roll mandrel to position coordinates, g ₁₂Be the coefficient of determining according to the preset secondary convexity.

Reasonablely be that in above-mentioned roll forming method for designing, roll is in forward and moves described variable roll gap function S 2 when moving maximum position with negative sense ₊(x) and S2 _-(x) adopt following form respectively:

S2 ₊(x)＝g ₂₂₊·x ²+g ₂₄₊·x ⁴+g ₂₆₊·x ⁶+g ₂₈₊·x ⁸

S2_(x)＝g _22-·x ²+g _24-·x ⁴+g _26-·x ⁶+g _28-·x ⁸

Wherein, x be roll mandrel to position coordinates, g ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊, g _22-, g _24-, g _26-And g _28-Move the coefficient that the high order convexity when moving maximum position with negative sense is determined for be in forward according to default roll.

Reasonable is that in above-mentioned roll forming method for designing, described roll shape curve adopts following form:

Y=a ₀+ a ₁X+a ₂X ²+ a ₃X ³+ a ₄X ⁴+ a ₅X ⁵+ a ₆X ⁶+ a ₇X ⁷+ a ₈X ⁸+ a ₉X ⁹Wherein, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place, a ₀Be the datum diameter of roll, a ₁Be the coefficient of setting according to the monolateral gradient situation of belt steel surface, a ₂～a ₉Determine according to following equation:

$\frac{\stackrel{\‾}{y}(x+b)+\stackrel{\‾}{y}(L-x+b)}{2}=S1\left(x\right)+{S2}_{+}\left(x\right)$

$\frac{\stackrel{\‾}{y}(x-b)+\stackrel{\‾}{y}(L-x-b)}{2}=S1\left(x\right)+{S2}_{-}\left(x\right)$

Here, b is the play stroke of roll, and L is a roll barrel length, $\stackrel{\‾}{y}\left(x\right)=y\left(x\right)-a_0.$

Another object of the present invention provides a kind of roll, and it can regulate the high order shape wave independently, continuously.

Above-mentioned purpose of the present invention realizes by following technical proposal:

A kind of roll, its roll shape curve is represented with the power function form, power time is more than or equal to 2 the power coefficient play stroke by roll, length and roll are in the roll gap function that forward moves when moving maximum position with negative sense and determine, described roll gap function is that basic secondary roll gap function and roll are in that forward moves or the variable roll gap function sum of negative sense when moving maximum position, wherein, described basic roll gap function is the secondary power function, its coefficient is determined according to the preset secondary convexity, described variable roll gap function is a power time greater than 2 power function, and its coefficient is in the high order convexity that forward moves when moving maximum position with negative sense and determines according to default.

Reasonable is that in above-mentioned roll, described basic roll gap function adopts following form: S1 (x)=g ₁₂X ², wherein, x be roll mandrel to position coordinates, g ₁₂Be the coefficient of determining according to the preset secondary convexity.

Reasonablely be that in above-mentioned roll, roll is in forward and moves described variable roll gap function S 2 when moving maximum position with negative sense ₊(x) and S2 _-(x) adopt following form respectively:

S2 ₊(x)＝g ₂₂₊·x ²+g ₂₄₊·x ⁴+g ₂₆₊·x ⁶+g ₂₈₊·x ⁸

S2_(x)＝g _22-·x ²+g _24-·x ⁴+g _26-·x ⁶+g _28-·x ⁸

Wherein, x be roll mandrel to position coordinates, g ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊, g _22-, g _24-, g _26-And g _28-Move the coefficient that the high order convexity when moving maximum position with negative sense is determined for be in forward according to default roll.

Reasonable is that in above-mentioned roll, described roll shape curve adopts following form:

y＝a ₀+a ₁·x+a ₂·x ²+a ₃·x ³+a ₄·x ⁴+a ₅·x ⁵+a ₆·x ⁶+a ₇·x ⁷+a ₈·x ⁸+a ₉·x ⁹

Wherein, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place, a ₀Be the datum diameter of roll, a ₁Be the coefficient of setting according to the monolateral gradient situation of belt steel surface, a ₂～a ₉Determine according to following equation:

$\frac{\stackrel{\‾}{y}(x+b)+\stackrel{\‾}{y}(L-x+b)}{2}=S1\left(x\right)+{S2}_{+}\left(x\right)$

$\frac{\stackrel{\‾}{y}(x-b)+\stackrel{\‾}{y}(L-x-b)}{2}=S1\left(x\right)+{S2}_{-}\left(x\right)$

Here, b is the play stroke of roll, and L is a roll barrel length, $\stackrel{\‾}{y}\left(x\right)=y\left(x\right)-a_0.$

In the present invention, by designing suitable roll forming according to roll gap shape, secondary shape wave and high order shape wave are controlled respectively by the axial float of roller and roll, therefore given full play to the potentiality of these plate shape control measures of roll play, obviously improved strip shape quality.

Description of drawings

By below in conjunction with the description of accompanying drawing to preferred embodiment of the present invention, can further understand purpose of the present invention, feature and advantage, wherein:

Fig. 1 shows a kind of typical band steel transverse shape.

Fig. 2 shows the shape of top and bottom rolls roll gap under different relative positions.

Fig. 3 is the roll forming method for designing flow chart according to preferred embodiment of the present invention.

The convexity schematic diagram of variable roll gap when Fig. 4 a and 4b show forward and negative sense respectively and move maximum position.

The specific embodiment

As mentioned above, the secondary shape wave of band steel can realize controlling completely by means such as work roll bending and intermediate calender rolls rollers, therefore can consider by the axial float of the roll with suitable roll forming the high order shape wave independently to be controlled.Based on above-mentioned thinking, the present inventor proposes following a kind of new roll forming method for designing and roll shape curve, this method is at first selected one by fixing basic roll gap function and the roll gap function of forming with the different variable roll gap functions that change of play direction, determine corresponding roll shape curve according to this roll gap function then, the axial float of roll can be specifically designed to control thus the high order shape wave.

In said method, basic roll gap function adopts the secondary power functional form, and variable roll gap function comprises that roll is in forward and moves two functions when moving maximum position with negative sense, and it all adopts power time greater than 2 power function form, it will be appreciated that as following power is inferior to the convexity Feature Selection.From mathematics, when the coordinate of the enough points of known power function curve epipodium and/or derivative value, just can determine the shape of whole power function, also be the coefficient of power function.In the present invention, owing to can determine required roll gap shape easily thus according to the secondary convexity of process parameters design sheet materials such as board quality requirement, the condition of production and milling train characteristics, high order convexity and corresponding roll mandrel to position coordinates (also promptly having determined the coordinate and/or the derivative value of specified point on the roll gap shape curve).

In the present invention, the roll forming of up-down rollers also adopts the power function form.Obviously, roll gap shape depends on the roll forming and the relative position of up-down rollers, also be to have certain mathematical relationship between them, roll gap shape when therefore determining to be in forward and negative sense and moving maximum position is equivalent to the enough coordinates of known roll shape curve epipodium, can instead release the roll forming function of up-down rollers like this.

Below by the preferred embodiment of flow chart description shown in Figure 3 method for designing of the present invention.

As shown in Figure 3, in step 1, at first determine basic roll gap function S 1 (x).For the sake of simplicity, present embodiment hypothesis secondary convexity curve is the left-right symmetry shape, and the expression-form of therefore basic roll gap function S 1 (x) is:

S1(x)＝g ₁₂·x ² (7a)

Here, x be roll mandrel to position coordinates, g ₁₂For determining the power coefficient of basic roll gap shape.Because the convexity curve is even function, so convexity position (being the position of peak or minimum point) be positioned at roll gap central authorities, supposes that the secondary convex value is C2, and the half width of roll gap is B2, then:

S1(B ₂)＝C ₂ (7b)

Can calculate coefficient g thus ₁₂Thereby, determine basic roll gap function.

Then, in step 2, determine the variable roll gap function S 2 when roll is in forward and moves maximum position ₊(x).For the sake of simplicity, convexity when present embodiment hypothesis forward moves maximum position is the symmetrical distribution shown in Fig. 4 a, abscissa is the roll axial coordinate among the figure, ordinate is the roll gap convex value, high point is positioned at roll gap half width place and low spot is positioned at roll gap 1/4 width place, and the first derivative of convexity curve in these convexity positions is 0, therefore selects for use 8 power function forms of following form as variable roll gap function S 2 here ₊(x):

S2 ₊(x)＝g ₂₂₊·x ²+g ₂₄₊·x ⁴+g ₂₆₊·x ⁶+g ₂₈₊·x ⁸ (8)

Here, x be roll mandrel to position coordinates, g ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊For determining variable roll gap shape S2 ₊(x) the power coefficient of even item, and the power coefficient of odd item is 0.

Variable roll gap shape when being in forward and moving maximum position for roll, if hypothesis high order convexity (vertical range of high point and low spot among the figure) is C4, the half width of roll gap is B2,1/4 width is B4, then can obtain following 4 equations:

S2 ₊(B ₂)＝0 (9a)

S2 ₊(B ₄)＝C ₄ (9b)

$\frac{d\left[{S2}_{+}\left(B_2\right)\right]}{\mathrm{dx}}=0---\left(9c\right)$

$\frac{d\left[{S2}_{+}\left(B_4\right)\right]}{\mathrm{dx}}=0---\left(9d\right)$

By calculating coefficient g to aforesaid equation (9a)～(9d) simultaneous solution ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊Thereby, determine variable roll gap function S 2 ₊(x).

Then in step 3, determine the variable roll gap function S 2 when roll is in negative sense and moves maximum position _-(x).For the sake of simplicity, convexity when present embodiment hypothesis negative sense moves maximum position is the symmetrical distribution shown in Fig. 4 b, abscissa is the roll axial coordinate among the figure, ordinate is the roll gap convex value, low spot is positioned at roll gap half width place and high point is positioned at roll gap 1/4 width place, and the first derivative of convexity curve in these convexity positions is 0, therefore selects for use 8 power function forms of following form as variable roll gap function S 2 here _-(x):

S2_(x)＝g _22-·x ²+g _24-·x ⁴+g _26-·x ⁶+g _28-·x ⁸ (10)

Here, x be roll mandrel to position coordinates, g ^22-, g ^24-, g ^26-, g ^28-Be the power coefficient of even item, and the power coefficient of odd item is 0.

Equally, the variable roll gap shape when being in negative sense and moving maximum position for roll, if hypothesis high order convexity (vertical range of high point and low spot among the figure) is C4, the half width of roll gap is B2,1/4 width is B4, then can obtain following 4 equations:

S2_(B ₂)＝C ₄ (11a)

S2_(B ₄)＝0 (11b)

$\frac{d\left[{S2}_{-}\left(B_2\right)\right]}{\mathrm{dx}}=0---\left(11c\right)$

$\frac{d\left[{S2}_{-}\left(B_4\right)\right]}{\mathrm{dx}}=0---\left(11d\right)$

By calculating coefficient g to aforesaid equation (11a)～(11d) simultaneous solution _22-, g _24-, g _26-, g _28-Thereby, determine variable roll gap function S 2 _-(x).

Enter step 4 subsequently, basic secondary roll gap function S 1 (x) is in forward with roll respectively moves variable roll gap function S 2 when moving maximum position with negative sense ₊(x) and S2 _-(x) being obtained mutually roll is in forward and moves roll gap function S when moving maximum position with negative sense ₊(x) and S _-(x):

S ₊(x)＝S1(x)+S2 ₊(x)＝g ₂₊·x ²+g ₄₊·x ⁴+g ₆₊·x ⁶+g ₈₊·x ⁸ (12a)

S_(x)＝S1(x)+S2_(x)＝g _2-·x ²+g _4-·x ⁴+g _6-·x ⁶+g _8-·x ⁸ (12b)

Here, g ₂₊, g ₄₊, g ₆₊, g ₈₊Roll gap function S when being in forward and moving maximum position for roll ₊(x) power coefficient, g _2-, g _4-, g _6-, g _8-Roll gap function S when being in negative sense and moving maximum position for roll _-(x) power coefficient is owing to function S 1 (x), S2 ₊(x) and S2 _-(x) power coefficient is determined in step 1～3, so these coefficients also are known.

Then enter step 5, according to the roll gap function S ₊(x) and S _-(x) with the relational expression of roll forming function y (x), by the roll gap function S ₊(x) and S _-(x) solve the power time coefficient of roll forming function.As mentioned above, the roll forming function adopts the power function form, so its general expression formula is:

Y (x)=a ₀+ a ₁X+a ₂X ²+ a ₃X ³+ a ₄X ⁴+ ... .+a _N-1X ^N-1+ a _nX ⁿ(13) here, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place, a ₀For the roll axial coordinate is the roller diameter at 0 place, generally be taken as the datum diameter of roll aborning, it is by the decision of milling train self structure, a ₁Represented the slope of roll forming linear change, generally set according to the big roller footpath of roll and the condition of the poor minimum in pony roll footpath aborning, other power time coefficient is then found the solution according to the relational expression between roll gap function and the roll forming function and is obtained.Below this is further described.

In the present embodiment, because the roll gap function S ₊(x) and S _-(x) total comprises 8 coefficient g ₂₊, g ₄₊, g ₆₊, g ₈₊, g _2-, g _4-, g _6-, g _8-, therefore at coefficient a ₀And a ₁Known situation lower roll shape function y (x) also comprises 8 powers to be determined time coefficient.Again, when roll moves to forward and negative sense maximum position vertically, the roll gap function S ₊(x) and S _-(x) and have following relationship between the roll function y (x):

$\frac{\stackrel{\‾}{y}(x+b)+\stackrel{\‾}{y}(L-x+b)}{2}=S_{+}\left(x\right)=g_{2+}\·x^2+g_{4+}\·x^4+g_{6+}\·x^6+g_{8+}\·x^8---\left(14a\right)$

$\frac{\stackrel{\‾}{y}(x-b)+\stackrel{\‾}{y}(L-x-b)}{2}=S_{-}\left(x\right)=g_{2-}\·x^2+g_{4-}\·x^4+g_{6-}\·x^6+g_{8-}\·x^8---\left(14b\right)$

Here, b is the play stroke of roll, and L is a roll barrel length, $\stackrel{\‾}{y}\left(x\right)=y\left(x\right)-a_0.$ In order to make above-mentioned equation (14a) and left-hand component (14b) only comprise the power coefficient of power function even item, thereby coefficient that can identical power with right-hand component time is corresponding one by one, and present embodiment is set at following form with roll forming function y (x):

Y=a ₀+ a ₁X+a ₂X ²+ a ₃X ³+ a ₄X ⁴+ a ₅X ⁵+ a ₆X ⁶+ a ₇X ⁷+ a ₈X ⁸+ a ₉X ⁹(15) wherein, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place.

When adopting the power function shown in the following formula (15) to represent roll forming function y (x), because the inferior coefficient of the identical power with right-hand component in the left side of equation (14a) and (14b) can be corresponding one by one, obtain 8 equations thus, each all comprises power coefficient a ₂～a ₉In several, therefore by calculating coefficient a to these equational simultaneous solutions ₂～a ₉Thereby, finally determine roll forming function y (x).

By foregoing description as seen, roll gap shape is determined by convexity extreme value and position thereof, particularly, variable roll gap shape is determined by high order convexity extreme value and position thereof, and roll shape curve is obtained by roll gap shape, and therefore the roll that obtains according to the inventive method design can carry out independent control to the high order convexity by play.It is worthy of note, in the above-described embodiments, at as shown in Figs. 4a and 4b fairly simple high order convexity situation, but this just for ease of describe and understand for the purpose of, in fact thinking of the present invention and principle can be applied to more complicated convexity situation fully, only need select more complicated power function for use for the roll gap function this moment, and determine that roll gap function and required simultaneous equations quantity and the amount of calculation of roll forming function will be more also.

Claims (8)

1, a kind of roll forming method for designing is characterized in that, comprises following steps:

(1) determine the coefficient of basic roll gap function according to the preset secondary convexity, described basic roll gap function is the secondary power function:

(2) be in forward according to default roll and move the coefficient that high order convexity when moving maximum position with negative sense is determined corresponding variable roll gap function respectively, described variable roll gap function is a power time greater than 2 power function;

(3) described basic roll gap function being in forward with roll respectively moves described variable roll gap function when moving maximum position with negative sense and is obtained roll mutually and be in forward and move roll gap function when moving maximum position with negative sense;

(4) according to play stroke, the length of roll be in the described roll gap function that forward moves when moving maximum position with negative sense and determine roll shape curve.

2, roll forming method for designing as claimed in claim 1 is characterized in that, described basic roll gap function adopts following form: S1 (x)=g ₁₂X ², wherein, x be roll mandrel to position coordinates, g ₁₂Be the coefficient of determining according to the preset secondary convexity.

3, roll forming method for designing as claimed in claim 2 is characterized in that, roll is in forward and moves described variable roll gap function S 2 when moving maximum position with negative sense ₊(x) and S2 _-(x) adopt following form respectively:

S2 ₊(x)＝g ₂₂₊·x ²+g ₂₄₊·x ⁴+g ₂₆₊·x ⁶+g ₂₈₊·x ⁸

S2 _-(x)＝g _22-·x ²+g _24-·x ⁴+g _26-·x ⁶+g _28-·x ⁸

Wherein, x be roll mandrel to position coordinates, g ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊, g _22-, g _24-, g _26-And g _28-Move the coefficient that the high order convexity when moving maximum position with negative sense is determined for be in forward according to default roll.

4, roll forming method for designing as claimed in claim 3 is characterized in that, described roll shape curve adopts following form:

y＝a ₀+a ₁·x+a ₂·x ²+a ₃·x ³+a ₄·x ⁴+a ₅·x ⁵+a ₆·x ⁶+a ₇·x ⁷+a ₈·x ⁸+a ₉·x ⁹

Wherein, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place, a ₀Be the datum diameter of roll, a ₁Be the coefficient of setting according to the monolateral gradient situation of belt steel surface, a ₂～a ₉Determine according to following equation:

$\frac{\stackrel{\‾}{y}(x+b)+\stackrel{\‾}{y}(L-x+b)}{2}=S1\left(x\right)+{S2}_{+}\left(x\right)$

$\frac{\stackrel{\‾}{y}(x-b)+\stackrel{\‾}{y}(L-x-b)}{2}=S1\left(x\right)+{S2}_{-}\left(x\right)$

Here, b is the play stroke of roll, and L is a roll barrel length, $\stackrel{\‾}{y}\left(x\right)=y\left(x\right)-a_0.$

5, a kind of roll, its roll shape curve is represented with the power function form, it is characterized in that, power time is more than or equal to 2 the power coefficient play stroke by roll, length and roll are in the roll gap function that forward moves when moving maximum position with negative sense and determine, described roll gap function is that basic secondary roll gap function and roll are in that forward moves or the variable roll gap function sum of negative sense when moving maximum position, wherein, described basic secondary roll gap function is the secondary power function, its coefficient is determined according to the preset secondary convexity, described variable roll gap function is a power time greater than 2 power function, and its coefficient is in the high order convexity that forward moves when moving maximum position with negative sense according to default roll and determines.

6, roll as claimed in claim 5 is characterized in that, described basic roll gap function adopts following form: S1 (x)=g ₁₂X ², wherein, x be roll mandrel to position coordinates, g ₁₂Be the coefficient of determining according to the preset secondary convexity.

7, roll as claimed in claim 6 is characterized in that, roll is in forward and moves described variable roll gap function S 2 when moving maximum position with negative sense ₊(x) and S2 _-(x) adopt following form respectively:

S2 ₊(x)＝g ₂₂₊·x ²+g ₂₄₊·x ⁴+g ₂₆₊·x ⁶+g ₂₈₊·x ⁸

S2 _-(x)＝g _22-·x ²+g _24-·x ⁴+g _26-·x ⁶+g _28-·x ⁸

Wherein, x be roll mandrel to position coordinates, g ₂₂₊, g ₂₄₊, g ₂₆₊, g ₂₈₊, g _22-, g _24-, g _26-And g _28-Move the coefficient that the high order convexity when moving maximum position with negative sense is determined for be in forward according to default roll.

8, roll as claimed in claim 7 is characterized in that, described roll shape curve adopts following form:

y＝a ₀+a ₁·x+a ₂·x ²+a ₃·x ³+a ₄·x ⁴+a ₅·x ⁵+a ₆·x ⁶+a ₇·x ⁷+a ₈·x ⁸+a ₉·x ⁹

Wherein, x be roll mandrel to position coordinates, y is the diameter of roll at coordinate x place, a ₀Be the datum diameter of roll, a ₁Be the coefficient of setting according to the monolateral gradient situation of belt steel surface, a ₂～a ₉Determine according to following equation:

$\frac{\stackrel{\‾}{y}(x+b)+\stackrel{\‾}{y}(L-x-b)}{2}=S1\left(x\right)+{S2}_{+}\left(x\right)$

$\frac{\stackrel{\‾}{y}(x-b)+\stackrel{\‾}{y}(L-x-b)}{2}=S1\left(x\right)+{S2}_{-}\left(x\right)$

Here, b is the play stroke of roll, and L is a roll barrel length, $\stackrel{\‾}{y}\left(x\right)=y\left(x\right)-a_0.$

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