JP6798865B2 - Tension cut roll device - Google Patents

Description

The present invention relates to a tension cut roll device.

Conventionally, when processing a long web while transporting it, it is necessary to adjust the tension of the web carried out from, for example, a heating device. Therefore, a tension cut roll is provided on the outlet side of the drying device or the like.

This tension cut roll is a tension cut (adjusts the tension difference) by rotating the web while holding it at a predetermined holding angle in order to change the tension of the web in front of the tension cut roll and the tension in the rear. It is carried out.

Japanese Unexamined Patent Publication No. 2000-211784

In the tension cut roll as described above, the tension cut (tension difference) ability changes depending on the transport conditions of the web. Therefore, there is a problem that slip occurs between the web and the tension cut roll when the tension difference before and after the tension cut roll exceeds the tension cut ability.

Therefore, in view of the above problems, an object of the present invention is to provide a tension cut roll device capable of calculating a condition in which slip does not occur between the tension cut roll and the web.

In the first embodiment of the present invention, the control unit, the web conveyed at a speed V adjustable by the control unit, and the web guided by the preset front tension T1 are held at a preset holding angle θ. A tension cut roll having a radius R, which is held and rotated to perform tension cut, and then conveyed with a preset tension T2 (however, T1 and T2 are not equal), and a cross-sectional area S on the surface of the tension cut roll. It has a groove spirally carved at a pitch interval a and a motor that rotates the tension cut roll at the speed V, and the control unit has the front tension T1, the radius R, the air viscosity η, and the said. The velocity V is calculated using the thickness h0 of the air layer between the tension cut roll and the web, and the web is conveyed at the calculated velocity V.
With respect to the speed V

V = {h0 / (0.589 * R)} ^3/2 * T1 / 12η ・ ・ ・ (A)

Calculated from
The thickness h0 of the air layer is a tension cut roll device calculated from h0 = S / a .

In the second embodiment of the present invention, the control unit, the web conveyed at a preset speed V, and the web guided by the preset pretension T1 are held and rotated at a preset holding angle θ. A tension cut roll having a radius R and a tension cut roll having a radius R and a cross-sectional area S on the surface of the tension cut roll, which are tension-cut and conveyed by a post-tension T2 (however, T1 and T2 are not equal) that can be adjusted by the control unit . It has a groove spirally carved at a pitch interval a and a motor that rotates the tension cut roll at the speed V, and the control unit has the speed V, the front tension T1, and the holding angle θ. The post-tension T2 is calculated using the above, and the web is conveyed by the calculated post-tension T2 .
With respect to the post-tension T2

When T2> T1, T2 = T1 + T1 * ε * {exp (μ * θ) -1} ... (B),
When T1> T2, T2 = T1-T2 * ε * {exp (μ * θ) -1} ... (C)
Calculated from, where μ is the effective coefficient of friction and ε is the known contact area ratio between the web and the tension cut roll.
Regarding the effective friction coefficient μ

μ = μ0 (where h0 <= S / a) ・ ・ ・ (D)
μ = 0 (where h0> S / a) ・ ・ ・ (E)

Calculated from, at this time, μ0 is the coefficient of static friction between the tension cut roll and the web, and h0 is the thickness of the air layer between the tension cut roll and the web. Is.

In the third embodiment of the present invention, the control unit, the web conveyed at a preset speed V, and the web guided by the pre-tension T1 adjustable by the control unit are held at a preset holding angle θ. A tension cut roll having a radius R, which is held and rotated to perform tension cut, and then conveyed with a preset tension T2 (however, T1 and T2 are not equal), and a cross-sectional area S on the surface of the tension cut roll. It has a groove spirally carved at a pitch interval a and a motor that rotates the tension cut roll at the speed V, and the control unit has the speed V, the rear tension T2, and the holding angle θ. The pre-tension T1 is calculated using the above, and the calculated pre-tension T1 guides the web .
With respect to the pretension T1

When T2> T1, T1 = T2-T1 * ε * {exp (μ * θ) -1}
... (G),
When T1> T2, T1 = T2 + T2 * ε * {exp (μ * θ) -1}
... (G')

Calculated from, where μ is the effective coefficient of friction and ε is the known contact area ratio between the web and the tension cut roll.
Regarding the effective friction coefficient μ

μ = μ0 (However, h0 <= S / a) ... (H)
μ = 0 (where h0> S / a) ・ ・ ・ (I)

Calculated from, at this time, μ0 is the coefficient of static friction between the tension cut roll and the web, and h0 is the thickness of the air layer between the tension cut roll and the web. Is.

According to the present invention, no slip occurs between the tension cut roll and the web.

It is explanatory drawing of the tension cut roll apparatus of one Embodiment of this invention. It is a front view of a cut roll. It is an enlarged view of the groove part of a cut roll. It is a flowchart of the first pattern. It is a flowchart of the 2nd pattern. It is a flowchart of the 3rd pattern.

Hereinafter, the tension cut roll device (hereinafter, simply referred to as “the device”) 10 according to the embodiment of the present invention will be described with reference to FIGS. 1 to 6. The long web W conveyed in the apparatus 10 is, for example, a film, a metal foil, a cloth, a paper, or the like.

(1) Configuration of the Device 10 The device 10 will be described with reference to FIG. The apparatus 10 coats the outlet side of the heat treatment device that heat-treats and heats the web W, the inlet side of the heat treatment device, the inlet side of the web W winding device, the inlet side of the web W unwinding device, and the web W. It is provided on the inlet side of the coating device for applying the liquid or on the outlet side of the coating device.

The apparatus 10 includes a tension cut roll (hereinafter, simply referred to as “cut roll”) 12, a front guide roll 14 arranged in front of the cut roll 12, a rear guide roll 16 arranged behind the cut roll 12, and a front guide. It has a pair of upper and lower front transfer rolls 18 and 20 arranged in front of the roll 14, and a pair of upper and lower rear transfer rolls 22 and 23 arranged behind the rear guide roll 16.

As shown in FIG. 2, a spiral groove 32 is engraved on the surface of the cut roll 12. As shown in the enlarged view of FIG. 3, the groove 32 has a triangular cross-sectional shape. The cross-sectional area S of the groove 32 is obtained from b * c / 2 from the width b and the depth c of the groove 32. Further, the pitch interval of the adjacent grooves 32, 32 is a, and this pitch interval a is known. The cut roll 12 is rotated by a motor 24 capable of torque control and rotation speed control.

The control unit 26 of the present device 10 has an input unit 28 including a keyboard, a mouse, and a display unit 30 including a display, controls the motor 24, and has a tension in front of the cut roll 12 (hereinafter, “pre-tension””. T1 or the tension behind the cut roll 12 (hereinafter referred to as "post-tension") T2 is controlled.

In this device 10, as shown in FIG. 1, the web W passes between a pair of upper and lower front transport rolls 18 and 20, and the lower surface of the rear guide roll 16 passes from below the front guide roll 14 through the upper surface of the cut roll 12. And pass between the pair of upper and lower rear transport rolls 22 and 24. At this time, the cut roll 12 holds the web W at a holding angle θ and rotates to perform tension cut (adjustment of the tension difference). In the present embodiment, the hugging angle θ is a known value.

(2) Explanation of the theoretical formula of the present device 10 Next, the theoretical formula under the condition that slip does not occur when the web W is conveyed by the cut roll 12 of the present device 10 to perform tension cut will be described.

First, determine the base tension. The "base tension" is referred to as the smaller tension when the front tension T1 and the rear tension T2 are compared. Further, the "tension" means a force per unit width of the web W, and is obtained by dividing the tension applied to the entire web W by the width L of the web W.

If T1 <T2 and T1 is the base tension, the tension difference ΔT at both ends of the cut roll 12 has the relationship of Eq. (1) according to Euler's belt formula.

ΔT = T2-T1 = T1 * {exp (μ * θ) -1} * ε ・ ・ ・ (1)

On the other hand, when T1> T2 and T2 is the base tension, the tension difference ΔT at both ends of the cut roll 12 has the relation of the equation (1') from Euler's belt formula.

ΔT = T1-T2 = T2 * {exp (μ * θ) -1} * ε ・ ・ ・ (1')

However, μ indicates the effective friction coefficient between the cut roll 12 and the web W, ε indicates the contact area ratio between the web W and the cut roll 12, and ε is known. Further, θ is known as described above.

As shown in FIG. 3, assuming that the thickness of the air existing between the surface of the cut roll 12 and the web W is the thickness h0 of the air layer, the thickness h0 of the air layer is

h0 = 0.589 * R (6η * (VR + V) / T1) ^2/3 ... (2)

Can be expressed as. However, R is the radius of the cut roll 12, VR is the rotation speed of the cut roll 12, V is the transport speed of the web W, and η is the air viscosity. R and η are known. Then, under the condition that the web W does not slip, since VR = V, the equation (2) becomes the equation (3).

h0 = 0.589 * R (6η * 2V / T1) ^2/3
= 0.589 * R (12 * η * V / T1) ^2/3 ... (3)

There is a relationship of the following equation (4) between the thickness h0 of the air layer and the effective friction coefficient μ. However, μ0 is the coefficient of static friction between the web W and the cut roll 12, and is determined in advance by an experiment or the like.

If h0 * a <= S, μ = μ0 ... (4)

If h0 * a> S, μ = 0 ... (5)

In the present embodiment, the transport speed V, the back tension T2, or the front tension T1 under the condition that the web W does not slip is calculated based on the above equations (1) to (5). The calculation will be described by dividing it into the following three patterns.

(3) First pattern In the first pattern, when the front tension T1 and the back tension T2 are set in advance and only the transport speed V can be adjusted, the transport speed V at which the web W does not slip on the cut roll 12 To calculate. This calculation method will be described with reference to the flowchart of FIG.

In step S1, the input unit 28 is used to input a plurality of known parameters such as the radius R of the cut roll 12 and the holding angle θ to the control unit 26, and the process proceeds to step S2.

In step S2, the input unit 28 is used to input the width b and the depth c of the groove 12 carved on the surface of the cut roll 12 to the control unit 26. As a result, the control unit 26 calculates the cross-sectional area S = b * c / 2 . Further, the pitch interval a is also input to the control unit 26. Then, the process proceeds to step S3.

In step S3, the width L of the web W and the coefficient of static friction μ0 between the web W and the cut roll 12 are input. The width L is used to calculate the tension per unit width of the web W, but when the tension per unit width is input from the beginning, it is not necessary to input the width L. Then, the process proceeds to step S4.

In step S4, the base tension is selected. That is, it is selected whether the base tension is the front tension T1 or the rear tension T2. This is to select either the equation (1) or the equation (1') described above. Here, the description continues assuming that T1 <T2 and T1 is the base tension. Then, the process proceeds to step S5.

In step S5, the set front tension T1 and rear tension T2 are input to the control unit 26 using the input unit 28. Then, the process proceeds to step S6.

In step S6, the control unit 26 calculates the transport speed V using a plurality of input parameters such as T1, T2, known R, and ε. The calculation method will be described.

First, the effective friction coefficient μ is not 0 because the condition is that the web W is not slipping. Therefore, when the equation (4) is modified, the equation (6) below is obtained, which is stored in the control unit 26.

h0 = S / a ... (6)

Since the cross-sectional area S and the pitch interval a are known, the control unit 26 calculates h0 from the equation (6).

Secondly, when the equation (3) is modified, the following equation (7) is obtained, which is stored in the control unit 26.

V = {h0 / (0.589 * R)} ^3/2 * T1 / 12η ・ ・ ・ (7)

Since h0, T1, R, and θ are known to the control unit 26, V is calculated from the equation (7).

From the above, the transport speed V at which slip does not occur in the web W can be calculated. Even when the base tension is T2, it can be calculated in the same manner by using the equation (1') instead of the equation (1).

(4) Second pattern In the second pattern, when the front tension T1 and the transport speed V are preset and only the back tension T2 can be adjusted, the back tension T2 that does not cause slip on the web W on the cut roll 12 The calculation method of the above will be described with reference to the flowchart of FIG. Since steps S1 to S4 are the same as the first pattern, the description thereof will be omitted.

In step S5, the set front tension T1 and the transfer speed V are input to the control unit 26 by using the input unit 28. Then, the process proceeds to step S6.

In step S6, the control unit 26 calculates the post-tension T2 using a plurality of input parameters such as T1, T2, known R, and ε. The calculation method will be described.

First, since the base tension is T1, the equation (1) is modified to obtain the equation (8), which is stored in the control unit 26.

T2 = T1 + T1 * ε * {exp (μ * θ) -1} ・ ・ ・ (8)

Secondly, the control unit 26 calculates the effective friction coefficient μ from the equations (4) and (5). However, the effective friction coefficient μ is not 0 because the condition is that the web W is not slipping. Therefore, μ = μ0 in Eq. (4).

Third, the control unit 26 calculates h0 by substituting the known R, ε, and the input T1 and V into the equation (3).

Fourth, the control unit 26 calculates the post-tension T2 by substituting the calculated h0, μ, and the input T1 into the equation (8).

From the above, the post-tension T2 at which slip does not occur in the web W can be calculated. Even when the base tension is T2, it can be calculated in the same manner by using the equation (1') instead of the equation (1).

(5) Third pattern In the third pattern, when the rear tension T2 and the transport speed V are preset and only the front tension T1 can be adjusted, the front tension T1 that does not cause slip on the web W on the cut roll 12 The calculation method will be described with reference to the flowchart of FIG. Since steps S1 to S4 are the same as the first pattern, the description thereof will be omitted.

In step S5, the set rear tension T2 and the transfer speed V are input to the control unit 26 by using the input unit 28. Then, the process proceeds to step S6.

In step S6, the control unit 26 calculates the pretension T1 using a plurality of input parameters such as T2, V, known R, and ε. The calculation method will be described.

When calculating h0 from the equation (2), since T1 is required as a parameter, h0 cannot be calculated directly. Therefore, instead of T1 in the equation (2), the post-tension T2 is substituted although there is a tension difference, the following calculations are performed a plurality of times, and the finally obtained value is set as the pre-tension T1.

First, the control unit 26 substitutes T2 in Eq. (2) for T2 as shown in Eq. (9) below.

h0'= 0.589 * R {6η * 2V / T2} ^2/3 ... (9)

To calculate.

Secondly, the control unit 26 calculates μ'from h0'using the equations (4) and (5). However, since the web W is not slipping, the effective friction coefficient μ is not 0, and μ ′ = μ0 from the equation (4).

Thirdly, the equation (1) is modified to obtain the equation (10) as described below and stored in the control unit 26.

T1 = T2- T1 * ε * {exp (μ * θ) -1} ・ ・ ・ (10)

Fourth, the control unit 26 calculates T1'by substituting μ'for μ in equation (10).

Fifth, the control unit 26 calculates h0 ″ by substituting the calculated T1 ′ as T1 into the equation (2).

Sixth, the control unit 26 recalculates μ ″ from h0 ″ using the equation (2). However, since the web W is not slipping, the effective friction coefficient μ is not 0, so μ ″ = μ0 from Eq. (4).

Seventh, the control unit 26 resubstitutes μ ″ into equation (10) and finally calculates T1.

From the above, the pretension T1 at which slip does not occur in the web W can be calculated. Even when the base tension is T2, the same calculation can be performed by using the following equation (10') instead of the equation (10). Equation (10') is a modification of equation (1').

T1 = T2 + T2 * ε * {exp (μ * θ) -1} ・ ・ ・ (10')

(6) Effect Based on the above, the apparatus 10 can calculate the optimum values of the front tension T1, the rear tension T2, and the transport speed V to prevent the occurrence of slip between the cut roll 12 and the web W.

(7) Modified Example Although one embodiment of the present invention has been described above, this embodiment is presented as an example and is not intended to limit the scope of the invention. These novel embodiments can be implemented in various other embodiments, and various omissions, replacements, and changes can be made without departing from the gist 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 the equivalent scope thereof.

10 ... This device, 12 ... Cut roll, 14 ... Front guide roll, 16 ... Rear guide roll, 24 ... Motor, 26 ... Control unit, 32 ... Groove

Claims (5)

Control unit and
A web that is conveyed at a speed V that can be adjusted by the control unit ,
The web guided by the preset pre-tension T1 is held by the preset hugging angle θ and rotated to perform tension cut, and the preset post-tension T2 (however, T1 and T2 are not equal). Tension cut roll with radius R to be transported by
A groove spirally engraved on the surface of the tension cut roll with a cross-sectional area S and a pitch interval a,
A motor that rotates the tension cut roll at the speed V,
Have,
The control unit
The velocity V is calculated using the front tension T1, the radius R, the air viscosity η, and the thickness h0 of the air layer between the tension cut roll and the web, and the web is conveyed at the calculated velocity V. To do
With respect to the speed V

V = {h0 / (0.589 * R)} ^3/2 * T1 / 12η ・ ・ ・ (A)

Calculated from
The thickness h0 of the air layer is calculated from h0 = S / a.
Tension cut roll device. Control unit and
A web that is transported at a preset speed V and
The web guided by the preset front tension T1 is held by the preset holding angle θ and rotated to perform tension cut, and the rear tension T2 (however, T1 and T2 are adjustable) adjusted by the control unit. Tension cut roll with radius R to be transported with (not equal)
A groove spirally engraved on the surface of the tension cut roll with a cross-sectional area S and a pitch interval a,
A motor that rotates the tension cut roll at the speed V,
Have,
The control unit
The back tension T2 is calculated using the velocity V, the front tension T1, and the holding angle θ, and the web is conveyed by the calculated back tension T2.
With respect to the post-tension T2

When T2> T1, T2 = T1 + T1 * ε * {exp (μ * θ) -1} ... (B),
When T1> T2, T2 = T1-T2 * ε * {exp (μ * θ) -1} ... (C)
Calculated from, where μ is the effective coefficient of friction and ε is the known contact area ratio between the web and the tension cut roll.
Regarding the effective friction coefficient μ

μ = μ0 (where h0 <= S / a) ・ ・ ・ (D)
μ = 0 (where h0> S / a) ・ ・ ・ (E)

Calculated from, μ0 is the coefficient of static friction between the tension cut roll and the web, and h0 is the thickness of the air layer between the tension cut roll and the web.
Tension cut roll device. The control unit sets η as the air viscosity with respect to the thickness h0 of the air layer.

h0 = 0.589 * R {6η * 2V / T1} ^2/3 ... (F)

The tension cut roll device according to claim 2, which is calculated from. Control unit and
A web that is transported at a preset speed V and
The web guided by the pre-tension T1 adjustable by the control unit is held by a preset hugging angle θ and rotated to perform tension cut, and the preset post-tension T2 (however, T1 and T2 are Tension cut roll with radius R to be transported with (not equal)
A groove spirally engraved on the surface of the tension cut roll with a cross-sectional area S and a pitch interval a,
A motor that rotates the tension cut roll at the speed V,
Control unit and
Have,
The control unit
The front tension T1 is calculated using the velocity V, the rear tension T2, and the holding angle θ , and the calculated front tension T1 guides the web.
With respect to the pretension T1

When T2> T1, T1 = T2-T1 * ε * {exp (μ * θ) -1}
... (G),
When T1> T2, T1 = T2 + T2 * ε * {exp (μ * θ) -1}
... (G')

Calculated from, where μ is the effective coefficient of friction and ε is the known contact area ratio between the web and the tension cut roll.
Regarding the effective friction coefficient μ

μ = μ0 (However, h0 <= S / a) ... (H)
μ = 0 (where h0> S / a) ・ ・ ・ (I)

Calculated from, μ0 is the coefficient of static friction between the tension cut roll and the web, and h0 is the thickness of the air layer between the tension cut roll and the web.
Tension cut roll device. The control unit uses η as the air viscosity with respect to the front tension T1.
First, h0'= 0.589 * R {6η * 2V / T2} ^2/3 is calculated.
Next, μ'is calculated from h0'using equation (H), and
Next, T1'is calculated from μ'using the formula (G) or the formula (G').
Next, h0'' = 0.589 * R {6η * 2V / T1'} ^2/3 is calculated, and
Next, μ'' is calculated from h0'' using equation (H), and
Next, T1 is calculated from μ ″ using Eq. (G) or Eq. (G').
The tension cut roll device according to claim 4 .

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