EP2379241B1 - Roll stand for rolling a product, in particular made of metal - Google Patents

Description

The invention relates to a roll stand for rolling a metal material, in particular, comprising a pair of first rolls contacted by a pair of second rolls supporting the first rolls, the first rolls and the second rolls having a radius profile (CVC) asymmetric with respect to a center plane -Slip), the radius profile of the first rolls being represented by a polynomial of the third or fifth order.

Such a rolling stand is from the EP 1 307 302 B1 known. There, a polynomial course of the type mentioned is provided as a radius profile to minimize the axial forces of the roller bearings, which can be minimized by appropriate choice of the radius profile in the horizontal direction acting moments without additional effort. Of particular importance is the wedge portion of the CVC work roll contour. The design is such that the wedging of the work roll grinding or the work roll contour is optimized to avoid rotational moments or axial forces. The linear part of the polynomial (a ₁ ) is used as an optimization parameter. This avoids cross-rolling of the rolls and minimizes the axial forces in the roll bearings.

The said solution according to the EP 1 307 302 B1 is based on a profiling of the work rolls, which interact with cylindrical support rollers. This is the optimization of the wedge of the work rolls off. Efforts are underway to extend the CVC system positioning range to further increase the tape profile setting range. In order to avoid high surface pressures between working and support rollers, increasingly CVC backup rollers are used. However, it has turned out that In order to optimize the taper of the CVC contour of the back-up rolls, it is not possible to use the same design as for the work roll, if optimal conditions are desired.

The invention is therefore based on the object, a rolling stand of the type mentioned in such a way that the wedging of a first roller supporting second roller (usually, but not exclusively: the wedging of a support roller, which cooperates with a work roll) is designed so that to set optimal operating conditions.

mit:

R_AW (x):

Radiusverlauf der ersten Walze

x:

Koordinate in Ballen-Längsrichtung mit dem Ursprung (x = 0) in Ballenmitte

a₀:

aktueller Radius der ersten Walze

a₁:

Optimierungsparameter (Keilfaktor)

a₂ ,a₃:

Koeffizienten (Stellbereich des CVC-Systems)

The solution of this problem by the invention according to a first embodiment is characterized in that in a rolling stand of the type mentioned a radius profile of the first rolls is provided, which satisfies the relationship: $${\mathrm{R}}_{\mathrm{AW}}\left(\mathrm{x}\right)={\mathrm{a}}_{\mathrm{0}}+{\mathrm{a}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{a}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{a}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}$$

With:

R _AW (x):

Radius of the first roller

x:

Coordinate in bale longitudinal direction with the origin (x = 0) in the center of the bale

a ₀ :

current radius of the first roller

a ₁ :

Optimization parameter (wedge factor)

a ₂ , a ₃ :

Coefficients (setting range of the CVC system)

mit:

R_SW(x):

Radiusverlauf der zweiten Walze

x:

Koordinate in Ballen-Längsrichtung mit dem Ursprung (x = 0) in Ballenmitte

s₀:

aktueller Radius der zweiten Walze

s₁:

Optimierungsparameter (Keilfaktor)

s₂, s₃:

Koeffizienten (Stellbereich des CVC-Systems)

wobei folgende Beziehung zwischen den genannten Größen besteht: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="imgf0001.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{3}}\right]$$

mit:

b_contAW:

Kontaktlänge der beiden ersten Walzen

b_contSW:

Kontaktlänge zwischen erster und zweiter Walze oder Länge der zweiten Walze

• f₁ =-1/20 bis -6/20

Here, the function is provided for the radius profile of the second rolls: $${\mathrm{R}}_{\mathrm{SW}}\left(\mathrm{x}\right)={\mathrm{s}}_{\mathrm{0}}+{\mathrm{s}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{s}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="imgf0001.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}$$

With:

R _SW (x):

Radius of the second roller

x:

Coordinate in bale longitudinal direction with the origin (x = 0) in the center of the bale

s ₀ :

current radius of the second roller

s ₁ :

Optimization parameter (wedge factor)

s ₂ , s ₃ :

Coefficients (setting range of the CVC system)

the following relationship exists between the mentioned quantities: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="imgf0001.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{3}}\right]$$

With:

b _contAW :

Contact length of the first two rolls

b _contSW :

Contact length between the first and second rolls or length of the second roll

• f ₁ = -1 / 20 to -6/20

mit: f₁ = -1/20 bis -6/20Between the coefficients of the radius profile of the first rolls preferably applies: $${\mathrm{a}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot {\mathrm{a}}_{\mathrm{3}}\cdot {{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contAW}}$$

with: f ₁ = -1/20 to -6/20

mit:

R_AW (x):

Radiusverlauf der ersten Walze

x:

Koordinate in Ballen-Längsrichtung

a₀:

aktueller Radius der ersten Walze

a₁:

Optimierungsparameter (Keilfaktor)

a₂ bis a₅:

Koeffizienten (Stellbereich des CVC-Systems)

An alternative solution provides for a rolling mill of the type mentioned a radius profile of the first rolls, which satisfies the relationship: $${\mathrm{R}}_{\mathrm{AW}}\left(\mathrm{x}\right)={\mathrm{a}}_{\mathrm{0}}+{\mathrm{a}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{a}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{a}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}+{\mathrm{a}}_4\cdot {\mathrm{x}}^4+{\mathrm{a}}_5\cdot {\mathrm{x}}^5$$

With:

R _AW (x):

Radius of the first roller

x:

Coordinate in bale longitudinal direction

a ₀ :

current radius of the first roller

a ₁ :

Optimization parameter (wedge factor)

a ₂ to a ₅ :

Coefficients (setting range of the CVC system)

mit:

R_SW(x):

Radiusverlauf der zweiten Walze

x:

Koordinate in Ballen-Längsrichtung

s₀:

aktueller Radius der zweiten Walze

s₁:

Optimierungsparameter (Keilfaktor)

s₂ bis s₅:

Koeffizienten (Stellbereich des CVC-Systems)

wobei folgende Beziehung zwischen den genannten Größen besteht: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{s}}_{\mathrm{3}}\right]+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contAW}}-{{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_5+{{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contSW}}\cdot {\mathrm{<figure-callout\; id="5"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_5\right]$$

mit:

b_contAW:

Kontaktlänge der beiden ersten Walzen

b_contSW:

Kontaktlänge zwischen erster und zweiter Walze oder Länge der zweiten Walze

• f₁ = -1/20 bis -6/20
• f₂ = 0 bis -9/112

Here, the function is provided for the radius profile of the second rolls: $${\mathrm{R}}_{\mathrm{SW}}\left(\mathrm{x}\right)={\mathrm{s}}_{\mathrm{0}}+{\mathrm{s}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{s}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="imgf0001.png"\; state="\{\{state\}\}">s</figure-callout>}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}+{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="imgf0001.png"\; state="\{\{state\}\}">s</figure-callout>}}_4\cdot {\mathrm{x}}^4+{\mathrm{<figure-callout\; id="5"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_5\cdot {\mathrm{x}}^5$$

With:

R _SW (x):

Radius of the second roller

x:

Coordinate in bale longitudinal direction

s ₀ :

current radius of the second roller

s ₁ :

Optimization parameter (wedge factor)

s ₂ to s ₅ :

Coefficients (setting range of the CVC system)

the following relationship exists between the mentioned quantities: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{s}}_{\mathrm{3}}\right]+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contAW}}-{{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_5+{{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^4}_{\mathrm{contSW}}\cdot {\mathrm{<figure-callout\; id="5"\; label="s"\; filenames="imgf0002.png"\; state="\{\{state\}\}">s</figure-callout>}}_5\right]$$

With:

b _contAW :

Contact length of the first two rolls

b _contSW :

Contact length between the first and second rolls or length of the second roll

• f ₁ = -1/20 to -6/20
• f ₂ = 0 to -9/112

mit:

• f₁ = -1/20 bis -6/20
• f₂ = 0 bis -9/112

In this case, between the coefficients of the radius profile of the first rolls preferably applies: $${\mathrm{a}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot {\mathrm{a}}_{\mathrm{3}}\cdot {{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{2}}}_{\mathrm{contAW}}+{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{2}}\cdot {\mathrm{a}}_{\mathrm{5}}\cdot {{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">b</figure-callout>}}^{\mathrm{4}}}_{\mathrm{contAW}}$$

With:

• f ₁ = -1/20 to -6/20
• f ₂ = 0 to -9/112

The coefficients a ₄ and a _{5 of} the radius profile of the first rolls can be zero. In this case, therefore, the course of the radius of the first rolls is represented as a third order polynomial, while the course of the radius of the second rolls is shown as a fifth order polynomial.

Conversely, it is also possible that the coefficients s ₄ and s _{5 of} the radius profile of the second rolls are zero. Then, the course of the radius of the first rolls is represented as a fifth order polynomial, while the course of the radius of the second rolls is represented as a third order polynomial.

As previously known as such, it is preferably provided that the radius profile of the first rollers is designed such that the tangent, which touch an end diameter and the convex portion of the roller, and the tangent, which touch the other end diameter and the concave portion of the roller, parallel to each other and inclined with respect to the roll axes inclined by a wedge angle. The same applies to the radius profile R _SW (x) of the second roller.

The first rolls are preferably work rolls and the second rolls are preferably back-up rolls.

But it is also possible that the rolling mill is a Sextogerüst and the first rolls are intermediate rolls and the second rolls are backup rolls.

In general, the respective linear component (wedge component), the contact length and the diameter of the corresponding adjacent roller are taken into account.

Fig. 1

schematisch ein Walzgerüst, in dem ein Walzgut von Zwei Arbeitswalzen gewalzt werden, die von zwei Stützwalzen abgestützt werden,

Fig. 2

in perspektivischer Ansicht eine Arbeitswalze, die von einer Stützwalze gestützt wird und

Fig. 3

die Arbeitswalzen samt Walzgut in Walzrichtung betrachtet.

In the drawing, an embodiment of the invention is shown. Show it:

Fig. 1

schematically a rolling mill in which a rolling of two work rolls are rolled, which are supported by two support rollers,

Fig. 2

in perspective view of a work roll, which is supported by a support roller and

Fig. 3

the work rolls including rolling considered in the rolling direction.

In the figures, the conditions are shown, already from the EP 1 307 302 B2 are known, to which extent expressly made reference. In Fig. 1 is a rolling 1 to see in the form of a metal slab, which is rolled by two first rolls 2 in the form of work rolls. The first rollers 2 are supported by second rollers 3, namely back-up rollers.

The work rolls 2 and the support rollers 3 have a so-called. CVC ship, ie with respect to a center plane 4, the profile is not symmetrical. Details on this are in the mentioned EP 1 307 302 B1 described. Accordingly, the rollers 2, 3 over the coordinate x in the bale longitudinal direction have a functional course resulting from nth-order polynomials, with third- or fifth-order polynomials being preferred or, for the most part, sufficient.

If the work rolls 2 are displaced axially relative to one another, the roll gap can be influenced accordingly. The load between the work rolls 2 and the backup rolls 3 is over the contact area b _cont (s. Fig. 2 ) unevenly distributed and changes with the shift position of the work rolls.

The resulting from the roll shapes loads and the local positive or negative relative speed lead - as in Fig. 2 is illustrated - to different circumferential forces Q _i over the contact width b _cont . The distribution of the roller peripheral force Q _i creates a moment M around the center of the rolling stand, which can lead to the "rolling" of the rolls and thus to axial forces in the roll bearings. This can be avoided by giving the rolls a corresponding cut. In the present case this is done with a radius course, which is given as a polynomial of the third or fifth order.

From the EP 1 307 302 B2 It is known to optimize the so-called wedge factor, ie the coefficient before the linear polynomial part, for which corresponding relationships are proposed.

As in Fig. 3 can be seen, it is provided that the radius profile of the work rolls 2 is formed so that the tangent 5, the end diameter 6 and the convex portion of the work roll 2 touch, and the tangent 7, the other end diameter 8 and the concave portion of the Touch roller 2, parallel to each other and inclined relative to the roll axes by a wedge angle α. The same applies to the Radusverlauf the support rollers. 3

Accordingly, the present concept can be summarized again as follows:

The rule for the design of the work roll contour and the definition of the wedge component (linear coefficient of the polynomial function) are obtained according to or very similar to those already known EP 1 307 302 B1 , The coefficients a ₂ , a ₃ , a ₄ and a ₅ (in the case of a fifth-order polynomial) result from the desired setting range or effect in the roll gap. The contact length between the working and support rollers or, alternatively, the working roller length for the design of the CVC work rolls and, in particular, for the wedge component (a ₁ ), is to be used as the contact width, as in US Pat EP 1 307 302 B1 described. If these rules are adhered to, the work roll contours and, in particular, the a ₁ coefficient (wedge component) are optimally designed.

For the wedge component s ₁ of the backup roll contour, which can also be described by a polynomial function, similar relationships apply (which can be calculated iteratively offline). The values for the wedge component s ₁ vary depending on the associated work roll contour and length. The backup roll form must therefore be adapted to the work roll shape. The coefficients s ₂ , s ₃ , s ₄ and s ₅ (in the case of a representation of the back-up roll contour by a fifth-order polynomial) result from the desired adjustment range or adaptation to the work roll S shape. For the linear component, the above-mentioned procedure for the design of the support roller contour applies here.

For the special case that - in a representation of the radius profile as a third-order polynomial - the backup roller has no CVC contour, the coefficient s _{3 is} equal to zero.

The above relationships also apply to contours similar to an S-shaped contour, e.g. B. for a so-called. "SmartCrown" function (sine function) or for contours that are specified by a point sequence and are approximated with one of the above polynomial functions.

For a sexto framework, the procedure can be carried out in the same way. Here, the work roll is designed analogously. The design of the wedging of the intermediate roll is carried out as in the backup roll. After the intermediate roll has been fixed, the design of the support roll of the Sexto is carried out analogously to the design of the quarto support roll. Generally speaking, the respective linear component, the contact length and the diameter of the corresponding adjacent roller are taken into account.

In a special case z. B. the work roll contour by a polynomial function fifth order and the backup roll or intermediate roll by a polynomial function third order or vice versa be executed. Here, the above laws apply to the work rolls. For the support and intermediate roll contours, the wedges are also optimized according to the above procedure.

The above statements apply once to the approximation of the radius profile by a third order polynomial and once to a fifth order polynomial. In principle, however, it is also possible to provide polynomials of even higher order. In most cases, however, higher-order polynomials than five are used.

LIST OF REFERENCE NUMBERS

1

rolling

2

first roller (work roll)

3

second roller (back-up roller)

4

midplane

5

tangent

6

final diameter

7

tangent

8th

final diameter

α

wedge angle

Claims (10)

1. A roll stand for rolling a product (1), particularly a metal product, which comprises a pair of first rolls (2) in contact with a pair of second rolls (3) which support the first rolls, wherein the first rolls (2) and the second rolls (3) are provided with a radius course, a so-termed CVC grind, which is asymmetrical relative to a centre plane (4), wherein the radius course of the first rolls (2) satisfies the equation: $${\mathrm{R}}_{\mathrm{AW}}\left(\mathrm{x}\right)={\mathrm{a}}_{\mathrm{0}}+{\mathrm{a}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{a}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{a}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}$$

   

   
   wherein

   R_SW(x): radius course of the second roll

   x: co-ordinate in the longitudinal direction of the barrel with the origin x = 0 in the barrel centre

   s₀: actual radius of the second roll

   s₁: optimisation parameter, wedge factor

   s₂, s₃: coefficients, adjustment range of the CVC system

   R_AW(x): radius course of the first roll

   x: co-ordinate in longitudinal direction of the barrel with the origin x = 0 in the barrel centre

   a₀: actual radius of the first roll

   a₁: optimisation parameter, wedge factor

   a₂, a₃: coefficients, adjustment range of the CVC system

   characterised in that
   the radius course of the second roll (3) satisfies the equation: $${\mathrm{R}}_{\mathrm{SW}}\left(\mathrm{x}\right)={\mathrm{s}}_{\mathrm{0}}+{\mathrm{s}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{s}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{s}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}$$

   

   
   wherein
   wherein the following relation exists between the said variables: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{s}}_{\mathrm{3}}\right]$$

   

   
   wherein

   b² _contAW: contact length of the two first rolls

   b² _contSW: contact length between the first and second rolls or length of the second roll

   f₁ = -1/20 to -6/20.
2. Roll stand according to claim 1, characterised in that the following relation exists between the coefficients of the radius course of the first rolls (2): $${\mathrm{a}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot {\mathrm{a}}_{\mathrm{3}}\cdot {{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contAW}}$$

   

   
   wherein

   f₁ = -1/20 to -6/20.
3. Roll stand for rolling a product (1), particularly a metal product, which comprises a pair of first rolls (2) in contact with a pair of second rolls (3) which support the first rolls, wherein the first rolls (2) and the second rolls (3) are provided with a radius course, a so-termed CVC cut, which is asymmetrical relative to a centre plane (4), wherein the radius course of the first rolls (2) satisfies the equation: $${\mathrm{R}}_{\mathrm{AW}}\left(\mathrm{x}\right)={\mathrm{a}}_{\mathrm{0}}+{\mathrm{a}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{a}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}+{\mathrm{a}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}={\mathrm{a}}_4\cdot {\mathrm{x}}^4+{\mathrm{a}}_5\cdot {\mathrm{x}}^5$$

   

   
   wherein

   R_AW(x): radius course of the first roll

   x: co-ordinate in the longitudinal direction of the barrel

   a₀: actual radius of the first roll

   a₁: optimisation parameter, wedge factor

   a₂ to a₅: coefficients, adjustment range of the CVC system

   characterised in that
   the radius course of the second rolls (3) satisfies the equation: $${\mathrm{R}}_{\mathrm{SW}}\left(\mathrm{x}\right)={\mathrm{s}}_{\mathrm{0}}+{\mathrm{s}}_{\mathrm{1}}\cdot \mathrm{x}+{\mathrm{s}}_{\mathrm{2}}\cdot {\mathrm{x}}^{\mathrm{2}}={\mathrm{s}}_{\mathrm{3}}\cdot {\mathrm{x}}^{\mathrm{3}}+{\mathrm{s}}_4\cdot {\mathrm{x}}^4+{\mathrm{s}}_5\cdot {\mathrm{x}}^5$$

   

   
   wherein

   R_SW(x): radius course of the second roll

   x: co-ordinate in the longitudinal direction of the barrel

   s₀: actual radius of the second roll

   s₁: optimisation parameter, wedge factor

   s₂ to s₅: coefficients, adjustment range of the CVC system

   wherein the following relation exists between the said variables: $${\mathrm{s}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contAW}}-{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_{\mathrm{3}}+{{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contSW}}\cdot {\mathrm{s}}_{\mathrm{3}}\right]+{\mathrm{f}}_2\cdot \left[{\mathrm{R}}_{\mathrm{SW}}/{\mathrm{R}}_{\mathrm{AW}}\cdot \left({{\mathrm{b}}^4}_{\mathrm{contAW}}-{{\mathrm{b}}^4}_{\mathrm{contSW}}\right)\cdot {\mathrm{a}}_5+{{\mathrm{b}}^4}_{\mathrm{contSW}}\cdot {\mathrm{s}}_5\right]$$

   

   
   wherein

   b_contAW: contract length of the two first rolls

   b_contSW: contact length between first and second rolls or length of the second roll

   f₁ = -1/20 to -6/20

   f₂ = 0 to -9/112.
4. Roll stand according to claim 3, characterised in that the following relation exists between the coefficients of the radius course of the first rolls (2): $${\mathrm{a}}_{\mathrm{1}}={\mathrm{f}}_{\mathrm{1}}\cdot {\mathrm{a}}_{\mathrm{3}}\cdot {{\mathrm{b}}^{\mathrm{2}}}_{\mathrm{contAW}}+{\mathrm{f}}_{\mathrm{2}}\cdot {\mathrm{a}}_{\mathrm{5}}\cdot {{\mathrm{b}}^{\mathrm{4}}}_{\mathrm{contAW}}:$$

   

   
   wherein

   f₁ = -1/20 to -6/20

   f₂ = 0 to -9/112.
5. Roll stand according to claim 3, characterised in that the coefficients a₄ and a₅ of the radius course of the second rolls (2) are zero.
6. Roll stand according to claim 3, characterised in that the coefficients s₄ and s₅ of the radius course of the second rolls (2) are zero.
7. Roll stand according to any one of claims 1 to 6, characterised in that the radius course R_AW(x) of the first rolls (2) and/or the radius course R_SW(x) of the second rolls (3) is so designed that the tangents (5) that touch one end diameter (6) and the convex part of the work roll (2) and the tangents (7) that touch the other end diameter (8) and the concave part of the work roll (2) are parallel to each other and are inclined relative to the roll axes by a wedge angle α.
8. Roll stand according to claim 1 or 3, characterised in that the first rolls are work rolls (2) and the second rolls are backing rolls (3).
9. Roll stand according to claim 1 or 3, characterised in that the roll stand is a six-high stand and the first rolls are intermediate rolls and the second rolls are backing rolls.
10. Roll stand according to claims 1 to 9, consisting of a plurality of rolls, characterised in that in general the respective linear component, the contact length and the diameter of the corresponding adjacent roll are taken into consideration in the determination of the coefficients.

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