WO2009074719A1

WO2009074719A1 - Method and arrangement for adjusting a nip force

Info

Publication number: WO2009074719A1
Application number: PCT/FI2008/050727
Authority: WO
Inventors: Jari Tiitta; Marko Tiilikainen; Risto MÄKINEN
Original assignee: Metso Paper Oy
Current assignee: Valmet Technologies Oy
Priority date: 2007-12-12
Filing date: 2008-12-11
Publication date: 2009-06-18
Anticipated expiration: 2010-06-12
Also published as: FI120728B; DE112008003027T5; FI20070965L; AT510667A5; FI20070965A0; AT510667B1

Abstract

The invention relates to a method and arrangement for adjusting a nip force (Fn) between a winding cylinder (203) and a machine roll (204) in a winder unit, wherein the winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the winding cylinder's shaft and diverges from a horizontal direction. The winder unit includes a force generating unit (205) for pressing the winding cylinder in the adjustment direction against the machine roll. The arrangement according to the invention comprises a load cell assembly (206), which is adapted to determine a horizontal component force acting on the winding cylinder, and an adjustment unit (208), which is adapted to regulate the strength of a force produced by the force generating unit on the basis of the determined horizontal component force. The adjustment of nip force is not substantially hampered by gravity, because the nip force is adjusted on the basis of such a component force which is substantially perpendicular to gravity.

Description

Method and arrangement for adjusting a nip force

Field of the invention

The invention relates to a method and arrangement for adjusting a nip force between a machine roll and a winding cylinder. The invention relates also to a winder unit.

Background of the invention

Fig. 1 shows a view in principle of a winder unit, wherein paper or other material 101 subject to winding is reeled around a winding shaft 102. In the context of paper machines, said winding shaft is referred to as a reeling drum and the assembly consisting of a reeling drum, as well as of a material wound around it, is referred to as a machine roll 104. The winding arrangement includes a winding cylinder 103 which is movable in vertical direction. Said vertical direction is the y- direction of a coordinate system 110. The material subject to reeling travels between the winding cylinder and the machine roll 104. The winding cylinder 101 is pressed against the machine roll by means of a force generating unit 105, which typically includes a hydraulic cylinder and piston. The winding cylinder 103 is subjected to a torque M1 and the winding shaft 102 is subjected to a torque M2. The device generating the torque M2 is often referred to as a center drive. The force existing between the winding cylinder 103 and the machine roll 104 has its radial component Fn referred to as a nip force, which is often expressed as a force per machine roll width (Wm). Other forces relevant to winding include a tangentially directed circumferential force acting along the surface of the machine roll 104 and caused by the torque M2, and a tangentially directed force caused by the torque M1 and applied by the winding cylinder to the material 101 subject to winding. Said tangentially directed forces have an impact on the web tension of the winding material 101. An objective of adjusting the nip force Fn is to maintain the resulting machine roll 104 within a desired range in terms of its tightness.

One prior art solution comprises measuring the strength of a vertical component Fy in a force acting on the winding cylinder 103, and the nip force Fn has its strength adjusted by adjusting the strength of said vertical component force Fy. Said vertical component force Fy can be measured for example by load cells, which are connected with the winding cylinder's bearing housings and which can be for example column type or ring type sensors. A vertical component Fny of the nip force is quite modest with respect to gravity acting on the winding cylinder. The nip force is typically in the order of 1-6 kN/m, but the mass of a winding cylinder eight to ten meters in width can be as high as 20000 kg, the winding cylinder being thus subjected to gravity in the order of 200 kN. Hence, the nip force strength is but a fraction of said vertical component force Fy. Said vertical component force is influenced not only by gravity but also by web tension and a circumferential force, as well as by gravity applied to a power transmission shaft coupled with the winding cylinder. Primarily because of the gravity applied to the winding cylinder, the load cells must have their measuring range dimensioned to be so extensive that the component force Fy has an adjustment range which is just a few percent of the load cells' measuring range. This impedes adjustment of the nip force Fn especially at low nip force values, because a major relative change in the nip force only represents a very small relative change in the vertical component force Fy.

One prior art solution comprises measuring a compression load directly from the nip, i.e. from the compression zone between a winding cylinder and a machine roll. However, the solution requires a special-purpose winding cylinder with integrated pressure sensors.

Summary of the invention

The invention relates to a novel type of method for adjusting a nip force between a winding cylinder and a machine roll in a winder unit, wherein said winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity, and which includes a force generating unit for pressing said winding cylinder against said machine roll in said adjustment direction. The method according to the invention comprises:

-determining a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and has its direction diverging from said adjustment direction, and

-regulating the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx₁ wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity. The invention relates also to a novel type of arrangement for adjusting a nip force between a winding cylinder and a machine roll in a winder unit, wherein said winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity, and which includes a force generating unit for pressing said winding cylinder against said machine roll in said adjustment direction. The arrangement according to the invention comprises:

-a load cell assembly, which is adapted to determine a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and which has its direction diverging from said adjustment direction, and

-an adjustment unit, which is adapted to regulate the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx, wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity.

Said load cell assembly may contain a load cell, which has its force measuring direction substantially perpendicular to gravity. Alternatively, said load cell assembly may contain a multi-directional load cell, which is adapted to measure forces acting in at least two directions divergent from each other. Any one of the force measuring directions of said multi-directional load cell can be selected to be perpendicular to gravity, or a component force perpendicular to gravity can be established by calculation on the basis of forces measured in directions divergent from each other.

The invention relates also to a novel type of winder unit, which comprises:

-a winding cylinder, which is adapted to be movable in an adjustment direction that is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity,

-a force generating unit, which is adapted to press said winding cylinder against a machine roll in said adjustment direction,

- a load cell assembly, which is adapted to determine a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and which has its direction diverging from said adjustment direction, and -an adjustment unit, which is adapted to regulate the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx₁ wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of a nip force between the winding cylinder and the machine roll, which component is substantially perpendicular to gravity.

The method, arrangement, and winder unit according to the invention all make use of the condition that the gravity applied to a winding cylinder, to a power transmission shaft or a motor coupled therewith has no effect on a component force which is perpendicular to gravity. In the method, arrangement, and winder unit of the invention, the adjustment of a nip force is not substantially hampered by gravity, the nip force being adjusted on the basis of the value of such a component force which is substantially perpendicular to gravity.

The horizontal component force, which is acting on a winding cylinder and which is substantially perpendicular to gravity, can also be used for the determination of a nip force value. The estimated nip force value can be established by calculation on the basis of the value of said horizontal component force, because the angle between the nip force and said horizontal component force is known on the basis of the winder unit's geometry.

Various embodiments of the invention are characterized by what is presented in the dependent claims.

Brief description of the figures

Embodiments of the invention and benefits gained thereby will now be described in more detail with reference to the accompanying drawings, in which:

fig. 1 shows a winder unit of the prior art in a side view, fig. 2 shows a side view of a winder unit, which is provided with an arrangement according to one embodiment of the invention for adjusting a nip force between a machine roll and a winding cylinder,

fig. 3 shows a side view of a winder unit, which is provided with an arrangement according to one embodiment of the invention for adjusting a nip force between a machine roll and a winding cylinder, fig. 4 shows a winder unit according to one embodiment of the invention, and fig. 5 is a flow chart, showing a method according to one embodiment of the invention for adjusting a nip force between a machine roll and a winding cylinder.

Fig. 1 has been discussed earlier in this document as part of the prior art description.

Detailed description relating to embodiments of the invention

Fig. 2 shows a side view of a winder unit, which is provided with an arrangement according to one embodiment of the invention for adjusting a nip force Fn between a machine roll 204 and a winding cylinder 203. The winding cylinder 203 is adapted to be movable in an adjustment direction, which is perpendicular to the winding cylinder's shaft and diverges from a horizontal direction perpendicular to gravity. In the winder unit shown in fig. 2, said adjustment direction is substantially vertical, i.e. parallel (= co-directional or counter-directional) to gravity. In the device shown in fig. 2, said horizontal direction is parallel to the x-axis of a coordinate system 210, and gravity is counter-directional with respect to the y-axis of said coordinate system. The winder unit includes a force generating unit 205 for pressing the winding cylinder 203 against the machine roll 204 in said adjustment direction. The force generating unit 205 is coupled with a bearing housing 221 of the winding cylinder. A corresponding force generating unit is also coupled with a bearing housing present at an opposite end of the winding cylinder 203. The force generating unit may comprise for example an actuator established by a hydraulic cylinder and piston. The arrangement for adjusting the nip force Fn comprises a load cell assembly 206, which is adapted to determine a horizontal component force Fx, which is acting on the winding cylinder 203 and which is substantially perpendicular to gravity. A corresponding load cell assembly is preferably mounted also on an opposite end of the winding cylinder 203. The arrangement includes also an adjustment unit 208, which is adapted to regulate the strength of a force produced by the force generating unit 205 on the basis of a value of the determined horizontal component force Fx. The adjustment unit 208 is preferably adapted to control the force generating units present at various ends of the winding cylinder on the basis of horizontal component forces determined by the load cell assemblies present at various ends of the winding cylinder.

In an arrangement according to one embodiment of the invention, the load cell assembly 206 is a force sensor, which has its force measuring direction substantially perpendicular to gravity. In an arrangement according to one embodiment of the invention, the load cell assembly 206 is a load cell, which is adapted to measure component forces Fx and Fy acting in two directions divergent from each other, and which has one of its force measuring directions substantially perpendicular to gravity. Said load cell can be for example a Vishay-Nobel HTU sensor (Vishay Nobel AB). A measurement of the vertical force Fy can be utilized in such winder arrangements, in which a winding shaft (reeling drum) 202 is carried at the early stage of winding in the direction of the x-axis over the winding cylinder 203.

In an arrangement according to one embodiment of the invention, the adjustment unit 208 is adapted to regulate the strength of a force produced by the force generating unit 205 on the basis of a differential quantity e = Fnx_ref - Fx (1 ), wherein Fnx_ref is a target value for a horizontal component Fnx of the nip force Fn, which component is substantially perpendicular to gravity. The target value Fnx_ref for the horizontal component of a nip force can be determined on the basis of a target nip force value Fn_ref and an angle γ as follows: Fnx_ref = Fn_ref * cosγ.

An arrangement according to one embodiment of the invention comprises a calculation unit, which is adapted to work out a current value estimate Fn_est for the nip force Fn on the basis of an equation Fn_est = Fx / cosγ.

In an arrangement according to one embodiment of the invention, the adjustment unit 208 is adapted to regulate the strength of a force produced by the force generating unit 205 on the basis of a differential quantity e = Fnx_ref - (Fx + Frx) (2),

wherein Fnx_ref is a target value for a horizontal component Fnx of the nip force Fn and Frx is an estimate for a horizontal component force applied to the winding cylinder 203, which component is caused by a web tension of the material 201 subject to winding and by a circumferential force existing the machine roll's 204 surface. In the calculation of a differential quantity e, it is necessary to regard Frx as a singed quantity. Said circumferential force depends on a torgue M2 applied to the winding shaft 202 and on a radius of the machine roll 204. The component force Frx can be determined on the basis of said circumferential force, a web tension estimate, an overlap angle α and the angle γ . The ratio of the horizontal component Frx of a force, which is caused by web tension and a circumferential force and applied to the winding cylinder, to the vertical component of said force depends on a circumferential force, web tension, as well as on the angles γ ja α. The horizontal component is often so insignificant that a sufficiently high-grade adjustment of the nip force Fn is attainable, even if the web tension value would involve a considerable proportional uncertainty. It is often possible to achieve a sufficiently high-grade adjustment of the nip force Fn, even if the component force Frx were totally ignored.

An arrangement according to one embodiment of the invention comprises a calculation unit, which is adapted to work out a current value estimate Fn_est for the nip force Fn on the basis of an equation Fn_est = (Fx + Frx) / cosγ , wherein Frx must be regarded as a signed quantity.

In an arrangement according to one embodiment of the invention, the adjustment unit 208 is adapted to regulate the strength of a force produced by the force generating unit 205 with a PID control on the basis of a differential quantity e as set forth in the equation (1 ) or (2) or calculated in some other way. The force being produced by the force generating unit 205 can be expressed for example as F = F₀ + P * e + | ^χ J edt + D ^χ de/dt, wherein P, I ja D are parameters of the PID control, F₀ is a constant component of the produced force, and the derivation and integration of a differential quantity e is conducted with regard to time t.

Fig. 3 illustrates a side view of a winder unit, which is provided with an arrangement according to one embodiment of the invention for adjusting a nip force Fn between a machine roll 304 and a winding cylinder 303. The winding cylinder 303 is adapted to be movable in an adjustment direction, which is the direction of the y-axis of a coordinate system 310. The winder unit includes a force generating unit 305 for pressing the winding cylinder 303 against the machine roll 304 in said adjustment direction. The arrangement for adjusting the nip force Fn comprises a load cell assembly 306, 307, which is adapted to determine a horizontal component force Fx acting on the winding cylinder 303. The arrangement comprises also an adjustment unit 308, which is adapted to regulate the strength of a force produced by the force generating unit 305 on the basis of a value of the determined horizontal component force Fx. The load cell assembly includes a first load cell 306, which has its force measuring direction substantially perpendicular to gravity and which is adapted to measure said horizontal component force Fx. The load cell assembly includes a second load cell 307, which has its force measuring direction substantially co-directional with gravity and which is adapted to measure a vertical component force Fy. The load cell 307 can be a column type sensor, which is fitted in the link of a hydraulic piston and which can be for example a Vishay-Nobel KISD6 sensor (Vishay Nobel AB). The load cell 307 may also be a ring type sensor fitted in the link of a hydraulic piston. Likewise, the load cell 306 can be a ring type sensor. A measurement of the vertical force Fy can be utilized in such winder configurations, in which a winding shaft (reeling drum) 302 is carried at the early stage of winding in the direction of the x-axis of the coordinate system 310 over the winding cylinder 303. The use of separate load cells 306 and 307 for measuring the divergent component forces Fx and Fy serves to provide such an advantage that the measuring ranges of the load cells 306 and 307 can be selected independently of each other. The load cell 307 has a measuring range preferably more extensive than that of the load cell 306, because the gravity applied to the winding cylinder and its drive shaft is included in the vertical component force Fy.

Fig. 4 illustrates a side view of winder unit according to one embodiment of the invention, which is provided with an arrangement for adjusting a nip force Fn between a machine roll 404 and a winding cylinder 403. The winding cylinder 403 is adapted to be movable in an adjustment direction, which is perpendicular to the winding cylinder's shaft and which diverges from a horizontal direction perpendicular to gravity. Said adjustment direction is co-directional with a straight line 411 and said horizontal direction is the x-direction of a coordinate system 410. The winder unit includes a force generating unit 405 for pressing the winding cylinder 403 against the machine roll 404 in said adjustment direction 411. The winder unit is provided with a load cell assembly, which is adapted to determine a horizontal component force Fx, which is acting on the winding cylinder 403 and which is substantially perpendicular to gravity. Said load cell assembly comprises a load cell 406, which is adapted to measure component forces F1 and F2 acting in two directions divergent from each other, and a calculation unit 409, which is adapted to work out said horizontal component force Fx on the basis of the measured component forces F1 and F2. The horizontal component force Fx can be calculated, because the strength and direction of a resultant F of the measured component forces F1 and F2 are known on the basis of the strengths and directions of the measured component forces F1 and F2. The winder unit includes an adjustment unit 408, which is adapted to regulate the strength of a force produced by the force generating unit 405 on the basis of a value of the determined horizontal component force Fx. Fig. 5 shows in a flow chart a method according to one embodiment of the invention for adjusting a nip force Fn between a winding cylinder and a machine roll in a winder unit, wherein said winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the shaft of said winding cylinder and which diverges from a horizontal direction perpendicular to gravity, and which is provided with a force generating unit for pressing said winding cylinder against said machine roll in said adjustment direction. A step 501 comprises determining a horizontal component force Fx₁ which is acting on said winding cylinder and which is substantially perpendicular to gravity and which has its direction diverging from said adjustment direction. A step 502 comprises regulating the strength of a force produced by said force generating unit on the basis of a value of said horizontal component force Fx.

In a method according to one embodiment of the invention, said adjustment direction is substantially vertical, i.e. parallel to gravity.

In a method according to one embodiment of the invention, said horizontal component force Fx is determined by measuring said horizontal component force Fx with a load cell, which has its force measuring direction substantially perpendicular to gravity.

In a method according to one embodiment of the invention, said horizontal component force Fx is determined by measuring said horizontal component force Fx with a load cell assembly, which is adapted to measure component forces acting in two directions divergent from each other and which has one of its force measuring directions substantially perpendicular to gravity.

In a method according to one embodiment of the invention, said horizontal component force Fx is determined by calculation on the basis of values of two component forces, said two component forces having been measured with a load cell assembly, which is adapted to measure component forces acting in two directions divergent from each other.

In a method according to one embodiment of the invention, the strength of a force produced by said force generating unit is regulated on the basis of a differential quantity e = Fnx_ref - Fx, wherein Fnx_ref is a target value for the horizontal component of said nip force, which component is substantially perpendicular to gravity. A method according to one embodiment of the invention comprises calculating a current value estimate Fn_est for the nip force Fn on the basis of an equation Fn_est = Fx / cosγ . The angle γ is shown in fig. 2.

In a method according to one embodiment of the invention, the strength of a force produced by said force generating unit is regulated on the basis of a differential quantity e = Fnx_ref - (Fx + Frx), wherein Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity, and Frx is an estimate for a horizontal component force, which is applied to said winding cylinder and which is caused by the web tension of a material subject to winding and by a circumferential force existing on the surface of said machine roll and which is substantially perpendicular to gravity.

A method according to one embodiment of the invention comprises calculating a current value estimate Fn_est for the nip force Fn on the basis of an equation Fn_est = (Fx + Frx) / cosγ .

As obvious for a person skilled in the art, the invention and its embodiments are not limited to the above-described exemplary embodiments, but the invention and its embodiments can be modified within the scope of the independent claim. Expressions like for example "the arrangement is provided with a load cell assembly", which are included in the claims and used in reference to the existence of characterizing features, are open in the way that the presentation of characterizing features does not exclude the existence of other such characterizing features which have not been presented in the independent or dependent claims.

Claims

1. A method for adjusting a nip force between a winding cylinder and a machine roll in a winder unit, wherein said winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity, and which includes a force generating unit for pressing said winding cylinder against said machine roll in said adjustment direction, characterized in that the method comprises:

-determining (501 ) a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and has its direction diverging from said adjustment direction, and

-regulating (502) the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx, wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity.

2. A method as set forth in claim 1 , characterized in that said adjustment direction is substantially parallel to gravity.

3. A method as set forth in claim 1 , characterized in that said horizontal component force is determined by measuring said horizontal component force with a load cell, which has its force measuring direction substantially perpendicular to gravity.

4. A method as set forth in claim 1 , characterized in that said horizontal component force is determined by measuring said horizontal component force with a load cell assembly, which is adapted to measure component forces acting in two directions divergent from each other and which has one of its force measuring directions substantially perpendicular to gravity.

5. A method as set forth in claim 1 , characterized in that said horizontal component force is determined by calculation on the basis of values of two component forces, said two component forces having been measured with a load cell assembly, which is adapted to measure component forces acting in two directions divergent from each other.

6. A method as set forth in claim 1 , characterized in that the strength of a force produced by said force generating unit is regulated on the basis of a quantity e - Frx = Fnx_ref - (Fx + Frx), wherein Fx is a value of said horizontal component force, Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity, and Frx is an estimate for a horizontal component force, which is applied to said winding cylinder and which is caused by the web tension of a material subject to winding and by a circumferential force existing on the surface of said machine roll and which is substantially perpendicular to gravity.

7. An arrangement for adjusting a nip force between a winding cylinder (203, 303, 403) and a machine roll (204, 304, 404) in a winder unit, wherein said winding cylinder is adapted to be movable in an adjustment direction, which is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity, and which includes a force generating unit (205, 305, 405) for pressing said winding cylinder against said machine roll in said adjustment direction, characterized in that the arrangement comprises:

-a load cell assembly (206, 306, 307, 406), which is adapted to determine a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and which has its direction diverging from said adjustment direction, and

-an adjustment unit (208, 308, 408), which is adapted to regulate the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx, wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity.

8. An arrangement as set forth in claim 7, characterized in that said adjustment direction is substantially parallel to gravity.

9. An arrangement as set forth in claim 7, characterized in that said load cell assembly is a load cell (206, 306), which has its force measuring direction substantially perpendicular to gravity.

10. An arrangement as set forth in claim 7, characterized in that said load cell assembly includes a first load cell (306), which has its force measuring direction substantially perpendicular to gravity and which is adapted to measure said horizontal component force, and a second load cell (307), which has its force measuring direction substantially co-directional with gravity.

11. An arrangement as set forth in claim 7, characterized in that said load cell assembly is a load cell (206), which is adapted to measure component forces acting in two directions divergent from each other and which has one of its force measuring directions substantially perpendicular to gravity.

12. An arrangement as set forth in claim 7, characterized in that said load cell assembly includes a load cell (406), which is adapted to measure component forces acting in two directions divergent from each other, and a calculation unit (409), which is adapted to work out said component force on the basis of values of the component forces measured by said load cell.

13. An arrangement as set forth in claim 7, characterized in that said adjustment unit is adapted to regulate the strength of a force produced by said force generating unit on the basis of a quantity e - Frx = Fnx_ref - (Fx + Frx), wherein Fx is a value of said horizontal component force, Fnx ref is a target value for a horizontal component of said nip force, which component is substantially perpendicular to gravity, and Frx is an estimate for a horizontal component force, which is applied to said winding cylinder and which is caused by the web tension of a material subject to winding and by a circumferential force existing on the surface of said machine roll and which is substantially perpendicular to gravity.

14. A winder unit, which comprises:

-a winding cylinder (203, 303, 403), which is adapted to be movable in an adjustment direction that is perpendicular to the shaft of said winding cylinder and diverges from a horizontal direction perpendicular to gravity, and

-a force generating unit (205, 305, 405), which is adapted to press said winding cylinder against a machine roll (204, 304, 404) in said adjustment direction,

characterized in that said winder unit further comprises:

- a load cell assembly (206, 306, 307, 406), which is adapted to determine a horizontal component force acting on said winding cylinder, which component is substantially perpendicular to gravity and which has its direction diverging from said adjustment direction, and -an adjustment unit (208, 308, 408), which is adapted to regulate the strength of a force produced by said force generating unit on the basis of a differential quantity e = Fnx_ref - Fx, wherein Fx is a value of said horizontal component force and Fnx_ref is a target value for a horizontal component of a nip force between the winding cylinder and the machine roll, which component is substantially perpendicular to gravity.