EP1209286B1 - Calender and process for treating a web - Google Patents

Abstract

A calender has a bunched array of rollers with two end-rollers and a number of intermediate rollers. In operation two neighbouring rollers, each of which sags slightly, form a nip. The sag of adjacent rollers (i, i + 1) differs. especially the second roller facing the concave surface of the first roller, has less sag than the first. Also claimed is a process to treat a material web passing through several nips where it is subjected to pressure and each nip is formed by a first and second roller. The sag in each roller has a bending amplitude on the convex side of the first roller which is essentially identical to the bending amplitude on the concave side of the second roller. Each roller has a set of support bearings left and right. The distance MbML between the bearings on one roller is 0.1 to 2 per cent different to the distance MbML in the second roller bearing, with reference to the longer of the two dimensions. At least one of the intermediate bearings has a variable bearing distance MbML.

Description

The invention relates to a calender with a roll stack, which has two end rolls and a plurality of intermediate rolls therebetween, wherein in operation two adjacent rolls, each having a deflection, form a nip. Further, the invention relates to a method of treating a web of material passed through and pressurized by a plurality of nips, each nip being formed by a first roll and a second roll adjacent thereto (see, for example, document FR-A-1 326) 392).

Such a calender is used, for example, to satinize a paper web. In this case, one wishes to achieve as uniform a pressure profile as possible over the entire width of the paper web in order to avoid thickness and quality differences transversely to the running direction of the paper web. The paper webs to be calendered currently have widths of the order of magnitude of up to 10 m. The correspondingly long rollers therefore tend to be due to their own weight in the axial center "sagging", so they have a deflection. Even if this deflection is not too great, it makes itself disturbing in the pressure treatment of the paper web or another material web noticeable.

One has tried to counteract this phenomenon. For example, it is known from EP 0 679 204 B1 to select the intermediate rolls so that they all have the same inherent deflection, and the weight of the rolls and the so-called overhanging loads, i. Relieve the weight of the parts connected to the rollers, such as guide rollers or bearing housings.

Another approach, which is described in DE 198 20 089 A1, assumes that the line load profiles are changed by introducing deformation forces on the roll neck of the intermediate roll. In this case, one chooses the deformation forces such that the intermediate rollers for applying loading or unloading pressures receive a substantially same deflection, wherein a degree of deflection is set according to a determinable change in a roll-related line load difference between the upper and lower nip. The deflection controllable rollers at the ends of the roller stack are then adapted to this bend. It can now be observed that despite these same deflections, the calendering results are sometimes unsatisfactory.

The invention has for its object to make uniform the load in the nip.

This object is achieved with a calender of the type mentioned above in that the deflections of adjacent rollers differ from each other, wherein one of the convex side of a first roller adjacent second rollers has a weaker deflection than the first roller.

Although this leaves the hitherto pursued approach to impart the same deflection to all the rolls or to select the rolls so that they inherently have the same deflection. However, one opens up the possibility that the deflection in the nips can be more closely approximated than previously. The consideration plays a role that one has not taken into account in the deflection of a roller the different effects that arise at the concave and on the convex side. If you now choose the deflections differently, then you can consider these effects.

It is particularly preferred that adjacent rollers each have a deflection in which an amplitude of the deflection of the surface line on the convex side of the first roller substantially coincides with an amplitude of deflection of the surface line of the adjacent second roller at its concave side. Thus, you can adjust the deflections of the two rollers that form the nip under consideration, in the nip to each other, so that the pressure curve in the nip over the width of the material web is much more uniform. The adjustment is therefore where it is needed. It can be readily accepted that the deflections of the two rolls per se, ie the deflection on the axes, differ from each other. Such a deviation is even a prerequisite that one the deflections at the two generatrices coincide with each other.

Preferably, at least one of a pair of adjacent rollers has a force introduction device. One is then no longer dependent on selecting rollers that have the required deflections of their own accord. You can also cause such a deflection by the introduction of external forces.

wobei $$f_{{\mathrm{EU}}_{\left(i\right)}}=f_{{\mathrm{EM}}_{\left(i\right)}}-\frac{1}{4}{K}^2·f_{{\mathrm{EM}}_{\left(i\right)}}^2·D_{\left(i\right)}$$

$$K=\frac{16}{\mathrm{AB}}·\frac{1+3\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}{5+12\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}$$

AB =

Arbeitsbreite

MbML =

Lagerabstand

D_(i) =

Durchmesser der ersten Walze

D_(i+1) =

Durchmesser der zweiten Walze

i =

Index der ersten Walze

i+1 =

Index der zweiten Walze.

Preferably, the amplitude f _EM depends _{( i +1)} the deflection of the second roll according to the relationship of the amplitude f _{EM ( i )} the deflection of the first roll $$f_{{\mathrm{EM}}_{\left(i+1\right)}}=\sqrt{{\left(\frac{2}{D_{\left(i+1\right)}{K}^2}\right)}^2+\frac{4}{D_{\left(i+1\right)}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2}·f_{{\mathrm{EU}}_{\left(i\right)}}}-\frac{2}{D_{\left(i+1\right)}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2}$$

in which $$f_{{\mathrm{EU}}_{\left(i\right)}}=f_{{\mathrm{EM}}_{\left(i\right)}}-\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2·f_{{\mathrm{EM}}_{\left(i\right)}}^2·D_{\left(i\right)}$$

$$K=\frac{16}{\mathrm{FROM}}·\frac{1+3\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}}{5+12\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}}$$

AB =

working width

MbML =

bearing distance

D _(i) =

Diameter of the first roller

D _{(i + 1)} =

Diameter of the second roller

i =

Index of the first roll

i + 1 =

Index of the second roll.

Preferably, adjacent rolls have different bearing spacings if they deviate from one another in at least one parameter. With this configuration, one not only reaches a conformity of the deflections, more precisely the amplitudes of the deflections at the two adjacent generatrices of the two nip forming rollers, but one has the possibility to set the same bending lines. The bending lines are not only dependent on the amplitude of the deflection, but also for example on the curve shape of the bending line, which depends on the shear deformation, for example, on the degree of slimming of the rolls. If one now has the possibility of varying the bearing spacings of the intermediate rolls, one obtains the possibility of actually having the curve shape of the bending lines of the surface lines, i. better match the two nip-limiting lines.

Preferably, the difference of the bearing distances in the range of 0.1% to 2% based on the larger bearing distance. Such a deviation is perfectly tolerable. Major changes to the stance are not required because the forces acting on the stool do not receive significantly different force application points. Nevertheless, these small changes can already bring considerable benefits.

It is particularly preferred that the bearing spacing of at least one intermediate roll is variable. After the replacement of the respective roller can then optionally bring the bending line in the desired shape.

It is preferred that the storage of all rolls is symmetrical to the axial center. This also applies to the intermediate roller whose bearing distance is adjusted. Although this means that you must make the adjustment of the bearing at both axial ends. The bending of the generatrix of this roll is then adapted over the entire working width of the bend of the corresponding second roll.

The object is achieved in a method of the type mentioned above by choosing the deflections of the two rolls differently.

As explained above in connection with the calender, it is with different deflections of the rolls, i. their center lines, possible to equalize the deflections at the crucial points, namely at the nip forming generatrix lines to each other. In this way, the calendering result over the working width, i. the width of the web, drastically improved.

Here, it is preferable that the deflection of the first roller is controlled so that the amplitude of the deflection of the generatrix on the convex side of the first roller coincides with the amplitude of the deflection of the generatrix on the concave side of the second roller. Matching the deflections results in improved work across the width of the rolls.

It is also advantageous if, in the case of unequal rollers, the bearing distance of one roller is adjusted differently from the bearing distance of the other roller. As stated above, not only the amplitude of the deflection at the two generatrices is in this way in accordance bring, but also the curve shape of the bending line.

Fig. 1

eine erste Prinzipskizze zur Erläuterung wichtiger Größen,

Fig. 2

eine zweite Prinzipskizze zur Erläuterung weiterer Größen und

Fig. 3

eine schematische Darstellung von Biegelinien.

The invention will be described in more detail below with reference to preferred embodiments in conjunction with the drawings. Herein show:

Fig. 1

a first schematic diagram for explaining important quantities,

Fig. 2

a second schematic diagram for explaining further sizes and

Fig. 3

a schematic representation of bending lines.

Fig. 1 shows a section of a roll stack of a calender. Shown is a first roller i and a second roller i + 1, which form a Nip N between them. During operation, a material web, for example a paper web (not shown in detail), is guided through this nip N, where it is subjected to pressure and optionally also to elevated temperature. It is desired that the treatment. over the entire width of the nip N (that is, the extension in the axial direction of the two rollers i, i + 1) takes place evenly. A prerequisite for this is that the two rollers i, i + 1 can also form the nip N uniformly.

In order to achieve such a uniform formation, the two rollers i, i + 1 have different deflections. The deflections are selected according to a specific procedure, which will be explained below. The goal is to make the deflection the lower surface line of the upper roll i to adapt to the deflection of the upper generatrix of the lower roll i + 1. This is simplified assuming that the deflection is caused solely by gravity and the associated weight forces on the rollers. The considerations apply in principle even if the deflection is caused by external forces or moments.

The starting point for the following consideration is the opened roll stack, i. The center rollers i, i + 1, supported in their bearings, hang freely according to their self-bending lines of gravity and rigidity. This results in the form of a parabola, at least in the first approximation. For the following consideration, however, it is sufficient if one looks at the deflection line as a circular line.

For the closing of the nips, it is to be regarded as ideal if the contact lines of the two nip N forming rollers which are to be moved towards one another have the best possible conforming shape. The two lines of contact are the lower surface line of the upper roller and the upper surface line of the lower roller. Here, one is largely independent of whether in the subsequent operating case, the roll weight are partially or fully compensated.

The requirement that the lower surface line of the roller i in its deflection amplitude f _{EU i} the deflection amplitude f _{EO ( i +1)} corresponds to the upper surface line of the underlying roller i + 1, can be at exactly the same internal deflections f _EM adjacent center rollers i and i + 1 do not meet, as can be deduced from the sketch of FIG.

gleich der Distanz XM der Walzen in der Walzenmitte $$XM=\frac{1}{2}\left(D_i+D_{\left(i+1\right)}\right)+\Delta f$$

d.h. die Walzenspaltdifferenz Δf = XR-XM ergibt sich zu $$\Delta f=\frac{1}{2}\left(D_i+D_{\left(i+1\right)}\right)\left(\frac{1}{\cos \alpha }-1\right)$$

Zwischen der Durchbiegung f_EM und dem Neigungswinkel α der Eigenbiegelinie am Ballenrand besteht nach bekannten Formeln eine feste Beziehung (bei Vernachlässigung der Schubverformung) $$f_{\mathrm{EM}}=\frac{9E·{\mathrm{AB}}^4}{384EJ}\left(5+12·\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}\right)$$

$$\tan \alpha =\frac{9E·{\mathrm{AB}}^3}{24\mathrm{EJ}}\left(1+3·\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}\right)$$

daraus folgt: $$\tan \alpha =\frac{16}{\mathrm{AB}}·\frac{1+3\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}{5+12\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}·f_{\mathrm{EM}}=K·f_{\mathrm{EM}}$$

Due to the same bending lines, the distance XR of the rollers at the ball edges is $$XR=\frac{1}{2\cos \alpha }\left(D_i+D_{\left(i+1\right)}\right)$$

equal to the distance XM of the rolls in the roll center $$XM=\frac{1}{2}\left(D_i+D_{\left(i+1\right)}\right)+\Delta f$$

ie the nip difference Δf = XR-XM results too $$\Delta f=\frac{1}{2}\left(D_i+D_{\left(i+1\right)}\right)\left(\frac{1}{\cos \alpha }-1\right)$$

Between the deflection f _EM and the angle of inclination α of the self-bending line at the edge of the bale, according to known formulas, a fixed relationship exists (neglecting shear deformation) $$f_{\mathrm{EM}}=\frac{9e·{\mathrm{FROM}}^4}{384eJ}\left(5+12·\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}\right)$$

$$\tan \alpha =\frac{9e·{\mathrm{FROM}}^3}{24\mathrm{EJ}}\left(1+3·\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}\right)$$

it follows: $$\tan \alpha =\frac{16}{\mathrm{FROM}}·\frac{1+3\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}}{5+12\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}}·f_{\mathrm{EM}}=K·f_{\mathrm{EM}}$$

Next applies: $$\frac{1}{\cos \alpha }=\sqrt{1+{\tan }^2\alpha }$$

Since tan ² α will always be very small compared to 1, the permissible simplification is: $$\sqrt{1+{\tan }^2\alpha }=1+\frac{1}{2}{\tan }^2\alpha$$

This will be $$\Delta f=\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2·f_{\mathrm{EM}}^2\left(D_i+D_{\left(i+1\right)}\right)$$

In order to obtain the ideal fitting, ie Δf = 0, the deflection f _{EM of} the roll i + 1 must be deliberately smaller than that of the overlying roll i. If the amplitude of the deflection of the lower generatrix of the upper roller i with f _{EU i} and the amplitude of the deflection of the upper generatrix of the lower roll i + 1 with f _{EO ( i +1)} is designated, then should apply $$f_{{\mathrm{EU}}_i}=f_{{\mathrm{EO}}_{\left(i+1\right)}}$$

$$f_{{\mathrm{EO}}_{\left(i+1\right)}}=f_{{\mathrm{EM}}_{\left(i+1\right)}}-\frac{1}{4}{K}^2·f_{{\mathrm{EM}}_{\left(i+1\right)}}^2·D_{\left(i+1\right)}$$

daraus folgt: $$f_{{\mathrm{EM}}_{\left(i+1\right)}}=f_{{\mathrm{EU}}_i}-\frac{1}{4}{K}^2·f_{{\mathrm{EM}}_{\left(i+1\right)}}^2·D_{\left(i+1\right)}$$

The sizes f _{EU i} and f _{EO ( i +1)} can be derived from the following relationships $$f_{{\mathrm{EU}}_i}=f_{{\mathrm{EM}}_i}-\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2·{\mathrm{<figure-callout\; id="2"\; label="f\; EM\; i"\; filenames="imgf0001.png"\; state="\{\{state\}\}">f\; </figure-callout>}}_{{\mathrm{EM}}_i}^{{}_{}}·D_i$$

$$f_{{\mathrm{EO}}_{\left(i+1\right)}}=f_{{\mathrm{EM}}_{\left(i+1\right)}}-\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2·f_{{\mathrm{EM}}_{\left(i+1\right)}}^2·D_{\left(i+1\right)}$$

it follows: $$f_{{\mathrm{EM}}_{\left(i+1\right)}}=f_{{\mathrm{EU}}_i}-\frac{1}{4}{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2·f_{{\mathrm{EM}}_{\left(i+1\right)}}^2·D_{\left(i+1\right)}$$

wobei f _{EU i} oben definiert worden ist.If one this expression after f _{EM ( i +1)} dissolve, you get $$f_{{\mathrm{EM}}_{\left(i+1\right)}}=\sqrt{{\left(\frac{2}{D_{\left(i+1\right)}·K^2}\right)}^2+\frac{4}{D_{\left(i+1\right)}·{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2}·f_{{\mathrm{EU}}_i}}-\frac{2}{D_{\left(i+1\right)}·{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="imgf0001.png"\; state="\{\{state\}\}">K</figure-callout>}}^2}$$

where f _{EU i} has been defined above.

• AB = 10.000 mm
• MbML = 11.700 mm

Walzenposition Nenn-∅ D f_EM/mm f_EU/mm Δf_EM/mm zu Walze 2 2 760 2,37000 2,36987 0 3 825 2,36974 2,36960 0,00026 4 760 2,36948 2,36935 0,00052 5 825 2,36921 2,36908 0,00079 6 825 2,36894 2,36880 0,00106 7 760 2,36868 2,36855 0,00132 8 825 2,36842 2,36828 0,00158 9 760 2,36816 2,36803 0,00184 10 825 2,36789 2,36776 0,00211 11 760 2,36763 ---- 0,00237 Thus, when starting with the top center roll of a calender (i = 2), one can compute the entire stack of rolls in terms of its ideal differential self-deflections. This is stated in the following table, where:

• AB = 10,000 mm
• MbML = 11,700 mm

roll position Nominal ∅ D f _{EM / mm} f _{EU / mm} Δf _{EM / mm} to roll 2 2 760 2.37000 2.36987 0 3 825 2.36974 2.36960 0.00026 4 760 2.36948 2.36935 0.00052 5 825 2.36921 2.36908 0.00079 6 825 2.36894 2.36880 0.00106 7 760 2.36868 2.36855 0.00132 8th 825 2.36842 2.36828 0.00158 9 760 2.36816 2.36803 0.00184 10 825 2.36789 2.36776 0.00211 11 760 2.36763 ---- 0.00237

The roll stack has twelve rolls, i. two deflection-adjustable end rollers and intermediate intermediate rollers at the roller positions 2-11, which are formed in a known manner alternately as hard and soft rollers. The hard rolls are chill rolls with diameters of 760/410 mm (outer diameter, inner diameter). The soft rolls are designed as GG tube rolls with plastic cover and have a diameter of 825/800/428 mm (outside diameter with reference, outside diameter without reference, inside diameter).

It can be seen that a deviation Δf _EM to the roll 2 of 0.00237 mm has already resulted in the 11th roll.

This first approach has already been largely proven. However, only the amplitudes of the deflections are adapted to each other in the first place.

To further improve the homogenization of the load in the nip in that one selects or sets different storage distances in the center rolls. The adjustment may be necessary, for example, after a change of a roller.

In Mehrwalzenkalandern adjacent rolls are usually not equal. This applies not only to the first and last nip, which are usually limited by an intermediate or center roll and a deflection roll, but also to the remaining nips, which are delimited by two intermediate rolls. For example, the elastic rolls, i. the rollers with an elastic surface and the hard rollers, i. the rollers with an unyielding or hard surface, different slenderness grades and roller diameters. The degree of slimming results from the outer diameter Da divided by the working width AB.

Die Schubverformung beeinflußt aber auch die Kurvenform der Biegelinie (Fig. 3) gemäß nachfolgender Gleichung für die Kurvenfaktoren zwischen Walzenmitte (y = 1 bei x = 0) und dem Rand der Arbeitsbreite (y = 0 bei x = ½ AB). $$y=1-4\frac{x^2}{{\mathrm{AB}}^2}·\frac{6-4\frac{x^2}{{\mathrm{AB}}^2}12\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}+f\left(\frac{D{a}^2}{{\mathrm{AB}}^2}\right)}{5+12\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}+f\left(\frac{D{a}^2}{{\mathrm{AB}}^2}\right)}$$

mit MbML als Lagerabstand (Mitte bis Mitte Lager).The shear deformation of a roll is, among other things, a function of the slenderness degree $\frac{Da}{\mathrm{FROM}},$

The shear strain also affects the curve shape of the bendline (Figure 3) according to the following equation for the cam factors between roll center (y = 1 at x = 0) and the edge of the working width (y = 0 at x = ½ AB). $$y=1-4\frac{{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}{{\mathrm{FROM}}^2}·\frac{6-4\frac{{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="imgf0001.png"\; state="\{\{state\}\}">x</figure-callout>}}^2}{{\mathrm{FROM}}^2}12\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}+f\left(\frac{D{a}^2}{{\mathrm{FROM}}^2}\right)}{5+12\frac{\mathrm{MbML}-\mathrm{FROM}}{\mathrm{FROM}}+f\left(\frac{D{a}^2}{{\mathrm{FROM}}^2}\right)}$$

with MbML as bearing distance (middle to middle bearing).

(Definition weiter unten) ergeben sich zwangsläufig abweichende Kurvenformen ihrer Biegelinien, wie dies aus der schematischen Darstellung der Fig. 3 zu erkennen ist.At common bearing distance MbML of medium rolls with uneven $f\left(\frac{{\mathrm{There}}^2}{{\mathrm{FROM}}^2}\right)$

(Definition below) inevitably deviate curve shapes of their bending lines, as can be seen from the schematic representation of FIG.

Even if the deflection amplitudes in the middle of the roll coincide, the dreaded M or W profiles can sometimes result in the line load distribution of the nips. Although these are already mitigated, if one adapts the deflection amplitudes to each other. An improvement results, however, if one chooses the bearing distances MbML accordingly.

oder aufgelöst nach MbML_(i+1) $${\mathrm{MbML}}_i+1=\frac{\mathrm{AB}}{12}\left(\frac{12}{\mathrm{AB}}\left({\mathrm{MbML}}_i-\mathrm{AB}\right)+f\left(\frac{{\mathrm{Da}}_i^2}{{\mathrm{AB}}^2}\right)-f\left(\frac{{\mathrm{Da}}_{\left(i+1\right)}^2}{{\mathrm{AB}}^2}\right)\right)+\mathrm{AB}$$

It is assumed that the working width AB remains the same for all nips N. For two neighboring rollers i and i + 1 then applies $$12\frac{{\mathrm{MbML}}_{\left(i+1\right)}-\mathrm{FROM}}{\mathrm{FROM}}+f\left(\frac{{\mathrm{THERE}}_i+1^2}{{\mathrm{FROM}}^2}\right)=12\frac{{\mathrm{MbML}}_i-\mathrm{FROM}}{\mathrm{FROM}}+f\left(\frac{{\mathrm{There}}_i^2}{{\mathrm{FROM}}^2}\right)$$

or resolved according to MbML _{(i + 1)} $${\mathrm{MbML}}_i+1=\frac{\mathrm{FROM}}{12}\left(\frac{12}{\mathrm{FROM}}\left({\mathrm{MbML}}_i-\mathrm{FROM}\right)+f\left(\frac{{\mathrm{There}}_i^2}{{\mathrm{FROM}}^2}\right)-f\left(\frac{{\mathrm{There}}_{\left(i+1\right)}^2}{{\mathrm{FROM}}^2}\right)\right)+\mathrm{FROM}$$

hängt die Schubverformung noch von der Schubverteilungszahl κ des Walzenquerschnittes, der Querdehnzahl µ des Walzenwerkstoffs und dem Durchmesserverhältnis $\frac{Di}{Da}$

bei Hohlbohrung Di wie folgt ab $$f\left(\frac{{\mathrm{Da}}^2}{{\mathrm{Ab}}^2}\right)=6\left(1+\mu \right)\kappa \left(1+\frac{{\mathrm{Di}}^2}{{\mathrm{Da}}^2}\right)\frac{{\mathrm{Da}}^2}{{\mathrm{AB}}^2}$$

Except from the degree of slimming $\frac{Da}{\mathrm{FROM}}$

the shear strain still depends on the thrust distribution coefficient κ of the roll cross-section, the transverse strain coefficient μ of the roll material and the diameter ratio $\frac{Di}{Da}$

Hollow bore Di as follows $$f\left(\frac{{\mathrm{There}}^2}{{\mathrm{From}}^2}\right)=6\left(1+\mu \right)\kappa \left(1+\frac{{\mathrm{di}}^2}{{\mathrm{There}}^2}\right)\frac{{\mathrm{There}}^2}{{\mathrm{FROM}}^2}$$

These considerations will be explained with reference to the following example example FROM = 6,360 mm MbML _i = 7,500 mm Roller 1: Since _i = 560 mm Material = Di _i = 250 mm chill casting κ _i = 2.01 μ _i = 0.25 Roller 2: Since _{(i + 1)} = 477 mm Material = Di _{(i + 1)} = 327mm stole κ _{(i + 1)} = 2.07 (the elastic relation is disregarded) μ _{(i + 1)} = 0.30 Result MbML _{(i + 1)} = 7,517.4 mm ⇒ ΔL ≈ 17.5 mm.

It can be seen that one gets a distance of the order of 17.4 mm. This is quite a practicable order of magnitude.

Claims (11)

1. Calender having a roll stack which has two end rolls and a plurality of intermediate rolls in between, two mutually adjacent rolls which each exhibit a deflection forming a nip during operation, characterized in that the deflections of adjacent rolls are different from one another, one of the second rolls adjacent to the convex side of a first roll exhibiting a smaller deflection than the first roll.
2. Calender according to Claim 1, characterized in that adjacent rolls in each case exhibit a deflection in which an amplitude of the deflection of the envelope line on the convex side of the first roll substantially coincides with an amplitude of the deflection of the envelope line of the adjacent second roll on its concave side.
3. Calender according to Claim 1 or 2, characterized in that, of mutually adjacent rolls, at least one has a force-introducing device.
4. Calender according to one of Claims 1 to 3, characterized in that the amplitude f _{EM (i+1)} of the deflection of the second roll depends on the amplitude f _{EM (i)} of the deflection of the first roll in accordance with the following relationship: $$f_{{\mathrm{EM}}_{\left(i+1\right)}}=\sqrt{{\left(\frac{2}{D_{\left(i+1\right)}{K}^2}\right)}^2+\frac{4}{D_{\left(i+1\right)}{K}^2}·f_{{\mathrm{EU}}_{\left(i\right)}}}-\frac{2}{D_{\left(i+1\right)}{K}^2}$$

   

   
   where $$f_{{\mathrm{EU}}_{\left(i\right)}}=f_{{\mathrm{EM}}_{\left(i\right)}}-\frac{1}{4}{K}^2·f_{{\mathrm{EM}}_{\left(i\right)}}^2·D_{\left(i\right)}$$

   

   $$K=\frac{16}{\mathrm{AB}}·\frac{1+3\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}{5+12\frac{\mathrm{MbML}-\mathrm{AB}}{\mathrm{AB}}}$$

   

   AB = working width

   MbML = bearing spacing

   D_(i) = diameter of the first roll

   D_(i+1) = diameter of the second roll

   i = index of the first roll

   i+1 = index of the second roll.
5. Calender according to one of Claims 1 to 4, characterized in that adjacent rolls have different bearing spacings if they differ from one another in at least one parameter.
6. Calender according to Claim 5, characterized in that the difference in the bearing spacings lies in the range from 0.1% to 2%, based on the larger bearing spacing.
7. Calender according to Claim 5 or 6, characterized in that the bearing spacing of at least one intermediate roll can be varied.
8. Calender according to one of Claims 1 to 7, characterized in that all the rolls are mounted symmetrically with respect to the axial centre.
9. Process for treating a web, which is led through a plurality of nips and has pressure applied to it there, each nip being formed by a first roll and a second roll adjacent to the first, characterized in that the deflections of the two rolls are chosen to be different.
10. Process according to Claim 9, characterized in that the deflection of the first roll is controlled in such a way that the amplitude of the deflection of the envelope line on the convex side of the first roll coincides with the amplitude of the deflection of the envelope line on the concave side of the second roll.
11. Process according to Claim 9 or 10, characterized in that, in the case of non-identical rolls, the bearing spacing of one roll is set differently from the bearing spacing of the other roll.

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