JP7193257B2 - Method for manufacturing roll supporting device - Google Patents

Description

The present invention relates to a method for manufacturing a roll supporting device.

Conventionally, when a roll for conveying a web is rotatably supported, a rotating shaft projecting from both left and right ends of the roll is supported by a pair of left and right ball bearings.

JP 2010-1437212 A

However, in the structure where the rotating shaft of the roll is supported by the ball bearings as described above, the ball bearings generate rotational resistance, requiring maintenance and hindering rotation when used at high temperatures. Therefore, instead of ball bearings, a structure in which the rotating shaft is supported by bearings made of permanent magnets is conceivable. there were.

SUMMARY OF THE INVENTION Accordingly, it is an object of the present invention to provide a method of manufacturing a roll supporting device capable of absorbing fluctuations in tension of a web in a radial bearing made of permanent magnets.

The present invention comprises a roll that holds a running web and is horizontally supported and rotates passively, a pair of left and right rotating shafts projecting from both left and right ends of the roll, and a radial load of the pair of left and right rotating shafts. and a pair of left and right thrust bearings for receiving the axial load of the pair of left and right rotating shafts. The radial bearings include an inner ring made of a permanent magnet attached to the rotating shaft. and an outer ring made of permanent magnets having the same thickness as the inner ring, the outer ring being spaced apart from the outer circumference of the inner ring, wherein the mass of the roll is m, the thickness of the web is The tension T, the angle 2θ of the web, the magnetic flux density B of the inner ring and the outer ring, and the axial length L of the inner ring and the outer ring are inputted. The load FK applied to the two radial bearings is obtained, and the dimension t of the gap between the outer ring and the inner ring when the natural frequency fr of the roll is within a predetermined range of the tension fluctuation frequency ft of the web is Obtained from the tension fluctuation frequency ft, the amount of movement Δy of the center of the rotating shaft is obtained from the dimension t, the length L, the inner diameter r4 of the inner ring, the amount of movement Δy, the outer diameter r1 of the outer ring, and the magnetic flux density. The supporting magnetic force FP between the inner ring and the outer ring in one radial bearing is calculated from B, and the outer diameter r1 of the outer ring is increased in order until the supporting magnetic force FP and the load FK become equal. and repeating the calculation of the supporting magnetic force FP, and setting the outer diameter r1 of the outer ring when the supporting magnetic force FP and the load FK become equal to the optimum outer diameter r1.

According to the present invention, when the natural frequency fr of the roll is within a predetermined range of the tension fluctuation frequency ft of the web, the dimension t of the gap between the outer ring and the inner ring is defined by the tension fluctuation frequency ft The thickness of the inner ring and the thickness of the outer ring are the same, and the mass m, the tension T, the embrace angle 2θ, the magnetic flux density B, the length L, the inner diameter r4, the obtained gap dimension Using t and the outer diameter r1 of the outer ring as parameters, the supporting magnetic force between the inner ring and the outer ring in one of the radial bearings is obtained, and the supporting magnetic force is equal to the load applied to the radial bearing. The outer diameter r1 of the outer ring is determined, and this outer diameter r1 can absorb the fluctuations in the tension of the web.

1 is an explanatory diagram of a roll supporting device showing an embodiment of the present invention; FIG. FIG. 4 is an explanatory diagram of a radial bearing and a thrust bearing of a portion that receives a rotating shaft; FIG. 5 is an explanatory diagram of a state in which the roll embraces the web and rotates; (a) is a front view of a radial bearing, and (b) is an axial longitudinal sectional view of the radial bearing. 4 is a perspective view of virtual inner magnets ac and virtual outer magnets bd of the radial bearing; FIG. FIG. 4 is an explanatory diagram of a virtual inner magnet ac and a virtual outer magnet bd; 4 is a flow chart for obtaining the minimum outer diameter r1 of the outer ring.

A supporting device 10 for a roll 1 according to an embodiment of the present invention will be described below with reference to FIGS. 1 to 7. FIG. The roll 1 holds a long web W and is passively rotated by the conveying force of the web W. Examples of the web W include film, metal foil, mesh-like metal, cloth, and paper.

(1) Configuration of Support Device 10 The configuration of the support device 10 will be described with reference to FIG.

The support device 10 has a pair of left and right support legs 14 , 14 erected on the upper surface of a base 12 . A roll 1 is rotatably supported horizontally between a pair of left and right support legs 14 , 14 . Examples of the roll 1 include a metal roll made of metal and a rubber roll whose surface is made of rubber. A pair of left and right rotating shafts 16 , 16 protrude from both left and right ends of the roll 1 .

The roll 1 and the support leg 14 are provided with a radial bearing 18 that receives the load in the radial direction of the rotating shaft 16 and a thrust bearing 20 that receives the load in the axial direction of the rotating shaft 16 .

(2) Radial bearing 18
Next, the radial bearing 18 will be described with reference to FIG. The radial bearing 18 is composed of an inner ring 22 and an outer ring 24 . The inner ring 22 is provided on the outer circumference of the end portion of the rotating shaft 16 and is made of a ring-shaped neodymium magnet. The outer ring 24 is fixed to the support leg 14, is made of a ring-shaped neodymium magnet, and is arranged around the outer circumference of the inner ring 22 at regular intervals.

The outer peripheral surface of the neodymium magnet of the inner ring 22 and the inner peripheral surface of the neodymium magnet of the outer ring 24 have the same poles at the same positions as shown in FIG. S poles are arranged to correspond to the poles. As a result, the outer ring 24 is in a floating state with respect to the inner ring 22 at its center, and can be rotatably supported in the radial direction of the rotating shaft 16 .

A "neodymium magnet" is one of rare earth magnets containing neodymium, iron, and boron as main components, and is also called a neodymium magnet.

(3) Thrust bearing 20
Next, the thrust bearing 20 will be described with reference to FIG. The thrust bearing 20 is composed of a shaft end portion 26 and a receiving plate 30 .

The shaft end portion 26 is cylindrical and protrudes from the end portion of the rotating shaft 16 . The tip of the shaft end portion 26 is hemispherical, and a ruby 28 of a spherical first jewel is partly embedded at the highest position.

The receiving plate 30 is provided on a fixed portion 32 inside the support leg 14 corresponding to the position of the ruby 28 on the shaft end portion 26 . The receiving plate 30 is disc-shaped with the axial direction of the rotating shaft 16 as its normal direction, and is made of sapphire, which is the second jewel. A bearing plate 30 made of ruby 28 and sapphire at the shaft end 26 receives the axial load of the rotating shaft 16 .

The size of the backing plate 30 is larger than the range of motion in which the inner ring 22 moves inside the outer ring 24 . As a result, the axial end portion 26 of the roll 1 can be prevented from falling off the receiving plate 30 made of sapphire.

The first gem and the second gem mean not only natural gem but also artificial gem, including natural gem, treated gem, synthetic gem, and artificial gem.

(4) Operating State of Support Device 10 The operating state of the support device 10 will be described with reference to FIGS. 1 to 3. FIG. As shown in FIG. 3, the roll 1 is passively rotated by the force that the web W conveys. At this time, the radial direction of the rotation shaft 16 of the roll 1 is rotatably supported by the radial bearing 18 . In the radial bearing 18, the inner ring 22 and the outer ring 24 made of neodymium magnets, which are permanent magnets, are provided with a certain gap therebetween. Rotate in the The embrace angle 2 θ of the web W by the roll 1 is determined by the magnetic force of the neodymium magnet in the radial bearing 18 . That is, as the embrace angle 2θ increases, the radial load on the radial bearing 18 increases, and the stronger the magnetic force, the better.

Due to the repulsive force of the neodymium magnets of the radial bearings 18, the rotary shaft 16 causes the rolls 1 to vibrate in the axial direction. However, on the left and right sides of the roll 1, the spherical rubies 28 of the shaft ends 26 of the thrust bearings 20 abut on the receiving plates 30 made of sapphire and do not vibrate in the axial direction.

(5) Load FK applied to radial bearing 18
First, the load FK applied to the radial bearing 18 will be described with reference to FIG.

As shown in FIG. 3, the force FT on the roll 1 due to the tension T of the web W is

FT=2T*sin(θ) (1)

becomes. However, T is the tension, and θ is the half value of the embrace angle of the web W.

Also, as shown in FIG. 3, the magnitude of FG due to the mass m of the roll 1 is

FG=m*g (2)

becomes. However, m is the mass of the roll 1 and g is the gravitational acceleration.

The resultant force FO applied to the rotating shaft 16 of the roll 1 is

FO=FG+FT (3)

becomes. Since a pair of left and right radial bearings 18, 18 are attached to the left and right ends of the roll 1, the load FK applied to each radial bearing 18 is

FK=FO/2 (4)

becomes. Since it is necessary to form the supporting magnetic force FP of one radial bearing 18 as a reaction force of the load FK due to the mass m of the roll 1 and the tension T, from the relationship of dynamic equilibrium,

FK-FP=0 (5)

becomes.

(6) Dimensions of Inner Ring 22 and Outer Ring 24 Dimensions of the inner ring 22 and outer ring 24 are defined with reference to FIGS. As shown in FIG. 4A, the outer diameter of the outer ring 24 is r1, and the inner diameter is r2. The outer diameter of the inner ring 22 is r3, and the inner diameter is r4. Note that r4 is the radius of the rotating shaft 16 .

First, the thickness of the outer ring 24 and the thickness of the inner ring 22 are made the same. i.e.

r1-r2=r3-r4 (6)

becomes. As shown in FIG. 4(a), the distance t of the gap 23 between the outer ring 24 and the inner ring 22 is

r2-r3=t (7)

and For example, t=1-10 mm. Then, as shown in FIG. 4A, the movement amount Δy is the distance that the center O of the rotating shaft 16 moves to the center O′ by the resultant force FO. In FIG. 4A, the y-axis is shown in the vertical direction, but when compared with FIG. 3, the direction of the FO and the y-axis are set to match (xy axis reference). The allowable range of the movement amount Δy of the center of the rotation shaft 16 of the inner ring 22 when the roll 1 rotates is

Δy<=0.5*t (8)

and

As shown in FIG. 4B, let L be the axial length of the inner ring 22 and the outer ring 24 .

(7) Region setting for inner ring 22 and outer ring 24 In order to explain the supporting magnetic force FP between the inner ring 22 and the outer ring 24 made of permanent magnets, each region is set. b) for explanation.

As shown in FIG. 4A, the inner ring 22 made of a cylindrical permanent magnet is divided into a plurality of fine N-pole fan-shaped regions ai in the radial direction. However , 0°<i<=360°.

As shown in FIG. 4(a), a plurality of sectoral regions ci of minute S poles are set by dividing in the radial direction. However , 0°<i<=360°. The fan-shaped region ai and the fan-shaped region ci have the same physical position, but since they are N poles and S poles, the positive and negative forces are opposite. is. A virtual permanent magnet composed of a fan-shaped region ai and a fan-shaped region ci which are virtually divided is assumed to be a virtual inner magnet ac.

As shown in FIG. 4A, the outer ring 24 made of a cylindrical permanent magnet is radially divided into a plurality of fine fan-shaped regions bj having N poles. However , 0°<i<=360°.

As shown in FIG. 4( a ), a plurality of minute S-pole fan-shaped regions dj are set by dividing in the radial direction. However , 0°<i<=360°. The fan-shaped region bj and the fan-shaped region dj have the same physical position, but since they are N poles and S poles, the positive and negative forces are opposite. is. A permanent magnet composed of the fan-shaped region bj and the fan-shaped region dj that are virtually divided is assumed to be a virtual outer magnet bd.

(8) Support magnetic force FP between inner ring 22 and outer ring 24
Next, the supporting magnetic force FP between the inner ring 22 and the outer ring 24 will be described. In the following description, all capital letters 'F', 'E' and 'M' denote vectors even if there is a subscript. The divided magnetic force Fij between the virtual inner magnet ac and the virtual outer magnet bd obtained by dividing the supporting magnetic force FP is

Fij=Faibj+Fcidj+Faidj+Fbjci (9)

becomes. Faibj is the individual magnetic force between fan-shaped region ai and fan-shaped region bj, Fcidj is the individual magnetic force between fan-shaped region ci and fan-shaped region dj, and Faidj is the individual magnetic force between fan-shaped region ai and fan-shaped region dj. , Fbjci are the individual magnetic forces between sector bj and sector cj. How to obtain the individual magnetic forces Faibj, Fcidj, Faidj, and Fbjci between the respective fan-shaped regions will be described below. From Coulomb's law of magnetic force,

Faibj=Φai*Φbj/(4πμ0*γ ² aibj)Eaibj
(10)

Φai=B*Sai, Φbj=B*Sbj (11)

γ ² aibj
={0.5*(r1+r2)*sin(π/2−α−β)−0.5*(r3+r4)*sin(π/2−β)} ² +{0.5*(r1+r2)*cos (π/2−α−β)−0.5*(r3+r4)*cos(π/2−β)+Δy} ² +(ΔL) ²
(12)

is. However, Φai is the number of magnetic fluxes in the fan-shaped area ai, Φbi is the number of magnetic fluxes in the fan-shaped area bi, μ0 is the vacuum permeability, γ is the distance between the magnetic pole points, B is the magnetic flux density, and Sai is the number of magnetic fluxes in one fan-shaped area ai. Area value, Sbj is the area value of one fan-shaped region bj, Eaibj is the unit vector of the magnetic force from the fan-shaped region ai to the fan-shaped region bj, α is the distance between the center of the fan-shaped region ai and the center of the fan-shaped region bj The phase angle (see FIG. 4(a)), β is the included angle between the center of the fan-shaped area ai and the Y axis (see FIG. 4(a)), and ΔL is the inner ring 22 and the outer ring 24 in the axial direction (thrust direction). (see FIG. 4(b)). Note that the amount of positional deviation of the roll 1 in the axial direction (thrust direction) is approximated to ΔL=0 because of the presence of the pair of left and right thrust bearings 20 , 20 .

Fbjci=Φbj*Φci/(4πμ0* ^γ2cibj )Ecibj
(13)

Φbj=B*Sbj, Φci=-B*Sai (14)

γ ² cibj
={0.5*(r1+r2)*sin(π/2−α−β)−0.5*(r3+r4)*sin(π/2−β)} ² +{0.5*(r1+r2)*cos (π/2−α−β)−0.5*(r3+r4)*cos(π/2−β)+Δy} ² +(L−ΔL) ²
(15)

is. However, Ecibj is the unit vector of the magnetic force from the fan-shaped region ci to the fan-shaped region bj.

Faidj=Φai*Φdj/(4πμ0*γ ² aidj)Eaidj
(16)

Φai=B*Sai, Φdj=−B*Sbj (17)

is. Φdi is the number of magnetic fluxes in the fan-shaped region dj.

γ ² aidj
={0.5*(r1+r2)*sin(π/2−α−β)−0.5*(r3+r4)*sin(π/2−β)} ² +{0.5*(r1+r2)*cos (π/2−α−β)−0.5*(r3+r4)*cos(π/2−β)+Δy} ² +(L+ΔL) ²
(18)

is. Since the magnitude of the individual magnetic force Faibj and the individual magnetic force Fcidj are the same from the geometrically symmetrical relationship between the virtual inner magnet ac and the virtual outer magnet bd,

|Faibj|=|Fcidj| (19)

becomes. The direction of the individual magnetic force Fcidj is represented by the unit vector Ecidj.

The split magnetic force Fij is, as shown in the equation (9), the individual magnetic force Faibj determined by the equation (10), the individual magnetic force Fbjci determined by the equation (13), the individual magnetic force Faidj determined by the equation (16), (19) by summing the individual magnetic force Fcidj obtained by the formula.

The support magnetic force FP between the inner ring 22 and the outer ring 24 can be obtained by totaling all the divided magnetic forces Fij obtained as described above in the radial direction with respect to the inner ring 22 and the outer ring 24 . i.e.

formula 1

becomes. This equation (20) integrates the divided magnetic force Fij due to magnetism with respect to the fan-shaped region ai with the total cross-sectional area of the inner ring 22, with respect to the fan-shaped region bi with the total cross-sectional area of the outer ring 24, and with respect to the fan-shaped region ci, the inner ring 22 and the total cross-sectional area of the outer ring 24 with respect to the fan-shaped region di to obtain the overall supporting magnetic force FP.

(9) Absorption of variation in tension T As a precondition, the supporting magnetic force FP between the inner ring 22 and the outer ring 24 is larger than the load FK. It is necessary to bring the tension fluctuation frequency ft of the web W close to the number fr. i.e.

fr=h*ft (21)

must have a relationship of However, 0.7<=h<=1.3. This unique value of h is predetermined from the range of 0.7 to 1.3.

First, the tension fluctuation frequency ft of the web W can be obtained by frequency analysis of the tension of the web W measured by the tension pickup. Therefore, the natural frequency fr of the roll 1 can be obtained from the equation (21).

On the other hand, the natural frequency fr of the roll 1 is

fr=1/2π*(k/M) ^1/2 (22)

is. However, k is the spring coefficient of the radial bearing 18, and M is the combined mass of the radial bearing 18. This synthetic mass M is

M=0.5*FO/g (23)

is. However, FO is the resultant force obtained by the above equation (3), and g is the gravitational acceleration.

Therefore, transforming equation (22) for k and substituting M in equation (23) yields

k=(2π*fr) ² *M=2*FO/g*(π*fr) ² (24)

becomes. Further, from the resultant force FO and the spring coefficient k of the radial bearing 18, the movement amount Δy of the center of the inner ring 22 is

Δy=0.5*FO/k (25)

becomes. The permissible range of the movement amount Δy of the center of the rotation shaft 16 of the inner ring 22 when the roll 1 rotates is Δy<=0.5*t as shown in the above equation (8). Transforming for t,

t=2*Δy (8′)

becomes. By substituting the formula (25) into the formula (8′) and further substituting k in the formula (24), from the relationship of the formula (21),

t=2*Δy=2*(0.5*FO/k)=FO/k

=FO/{2*FO/g*(π*fr) ² }

=1/{2/g*(π*fr) ² }

=g/{2*(π*h*ft) ² } (26)

becomes. As described above, the dimension t of the gap 23 for absorbing the variation of the tension T of the web W can be obtained from the tension variation frequency ft of the web W and the equation (26).

Then, in this embodiment, in order to satisfy the supporting magnetic force FP=>load FK, r1 is increased as a variable by substituting it into the equation (20). However, t is obtained from the formula (26), and r1, r2 and r3 are made to satisfy the formulas (6) and (7). As a result, it is possible to obtain the optimum outer diameter r1 that satisfies the supporting magnetic force FP=>load FK while absorbing the variation in the tension T of the web W. The processing will be described below with reference to a flowchart.

In step S1, the tension T, the embrace angle 2θ, and the mass m of the roll 1 are input, and the process proceeds to step S2.

In step S2, the magnetic flux densities B of the inner ring 22 and the outer ring 24 made of permanent magnets are input. Assuming that the magnetic flux densities B of the inner ring 22 and the outer ring 24 are the same, the process proceeds to step S3.

In step S3, the axial length L of the radial bearing 18 and the inner diameter of the inner ring 22 (that is, the outer diameter of the rotary shaft 16) r4 are input, and the process proceeds to step S4.

In step S4, the tension fluctuation frequency ft is obtained from the tension T of the web W measured by the tension pickup, and the process proceeds to step S5.

In step S5, the dimension t of the gap 23 is obtained from the tension fluctuation frequency ft and the equation (26), and the process proceeds to step S6.

At step S6, Δy is obtained from t and equation (8), and the process proceeds to step S7.

At step S7, the minimum r1 is assumed and the process proceeds to step S8.

At step S8, r2 and r3 are obtained from the equations (6) and (7), and the process proceeds to step S9.

In step S9, the supporting magnetic force FP is obtained based on the formulas (9) to (20), and the process proceeds to step S10.

In step S10, if the obtained supporting magnetic force FP is greater than or equal to the load FK, proceed to step S12 (Y), otherwise proceed to step S11 (N).

In step S11, r1=r1+Δr1 and the process returns to step S8.

In step S12, the outer diameter r1 at this time is set as the outer diameter of the thrust bearing 20, and the thrust bearing 20 is manufactured with this size. and finish.

(10) Effect According to this embodiment, the optimum outer diameter r1 of the outer diameter 24 of the radial bearing 18 that makes the supporting magnetic force FP larger than the load FK of the roll 1 while absorbing the variation in the tension T of the web W is obtained. be able to. As a result, tension fluctuations in the running web W can be alleviated.

(11) Modification In the above-described embodiment, the thrust bearing 20 uses a jewel, but instead of the jewel 28 such as ruby, this portion may be made of metal or the like and supported by the receiving plate 30 .

Also, in the above embodiment, the first gem was the ruby 28, but other gems may be used. Also, although the second jewel forming the receiving plate 30 was sapphire, other jewels may be used.

In the above embodiment, the disk-shaped receiving plate 30 made of sapphire has a flat surface, but instead of this, a slightly hemispherical concave portion may be provided so that the spherical ruby 28 can be fitted therein. .

While one embodiment of the invention has been described above, this embodiment is provided by way of example and is not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and modifications can be made without departing from the spirit of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the scope of the invention described in the claims and equivalents thereof.

DESCRIPTION OF SYMBOLS 1... Roll, 10... Support apparatus, 14... Support leg, 16... Rotating shaft, 18... Radial bearing, 20... Thrust bearing, 22... Inner ring, 23...・Gap 24... Outer ring 26... Shaft end 28... Ruby 30... Receiving plate

Claims (8)

A roll that holds the running web and is horizontally supported and rotates passively,
A pair of left and right rotating shafts projecting from both left and right ends of the roll;
a pair of left and right radial bearings for receiving a load in the radial direction of the pair of left and right rotating shafts;
a pair of left and right thrust bearings for receiving an axial load of the pair of left and right rotating shafts;
has
The radial bearing is
an inner ring made of a permanent magnet attached to the rotating shaft;
an outer ring made of a permanent magnet having the same thickness as the inner ring and arranged with a gap on the outer circumference of the inner ring;
A method for manufacturing a roll supporting device comprising:
inputting the mass m of the roll, the tension T of the web, the web embrace angle 2θ, the magnetic flux density B of the inner ring and the outer ring, and the axial length L of the inner ring and the outer ring;
Obtaining the load FK applied to one of the radial bearings from the mass m, the tension T, and the embrace angle 2θ;
When the natural frequency fr of the roll is within a predetermined range of the tension fluctuation frequency ft of the web, the dimension t of the gap between the outer ring and the inner ring is obtained from the tension fluctuation frequency ft,
Obtaining a movement amount Δy of the center of the rotation axis from the dimension t,
A supporting magnetic force FP between the inner ring and the outer ring in one radial bearing is calculated from the length L, the inner ring inner diameter r4, the displacement Δy, the outer ring outer diameter r1, and the magnetic flux density B. The calculation of the support magnetic force FP is repeated by increasing the outer diameter r1 of the outer ring until the support magnetic force FP and the load FK become equal, and when the support magnetic force FP and the load FK become equal The outer diameter r1 of the outer ring of is the optimum outer diameter r1,
A method for manufacturing a roll supporting device. The dimension t of the gap when g is the acceleration of gravity and h is a unique numerical value within the predetermined range,

t=g/{2*(π*h*ft) ² }

is
The method for manufacturing the roll support device according to claim 1 . 0.7<=h<=1.3,
3. The method for manufacturing the roll supporting device according to claim 2. The permanent magnet is a neodymium magnet,
The method for manufacturing the roll support device according to claim 1 . The thrust bearing is a jewel bearing,
a shaft end provided at the tip end of the rotating shaft;
a spherical first jewel attached to the shaft end;
a backing plate formed from a second gem;
The method for manufacturing a roll supporting device according to claim 1, comprising: The embrace angle 2θ of the web is 0°<θ<=30°.
The method for manufacturing the roll support device according to claim 1 . dividing the inner ring into virtual inner magnets with fan-shaped cross sections, and dividing the outer ring into virtual outer magnets with fan-shaped cross sections;
Finding the divided magnetic force between the virtual inner magnet and the virtual outer magnet,
The supporting magnetic force FP is obtained by summing the divided magnetic forces in the radial direction,
The method for manufacturing the roll support device according to claim 1 . With respect to the virtual inner magnet, an N-pole fan-shaped region ai and an S-pole fan-shaped region ci are set (where 0°<i, j<=360°),
setting an N-pole fan-shaped region bj and an S-pole fan-shaped region dj for the virtual outer magnet;
obtaining an individual magnetic force Faibj between the fan-shaped region ai and the fan-shaped region bj;
obtaining an individual magnetic force Fcidj between the fan-shaped region ci and the fan-shaped region dj;
Obtaining an individual magnetic force Faidj between the fan-shaped region ai and the fan-shaped region dj,
obtaining an individual magnetic force Fbjci between the fan-shaped region bj and the fan-shaped region ci;
The divided magnetic force Fij is obtained by summing the individual magnetic force Faibj, the individual magnetic force Fbjci, the individual magnetic force Faidj, and the individual magnetic force Fcidj,
The method for manufacturing the roll supporting device according to claim 7 .

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