JP2013004060A - Simulation device and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation device and a program capable of suitably simulating the behavior of a flexible medium.SOLUTION: A simulation device comprises: a route creation part 11 that creates a conveyance path in an arrangement space on the basis of a position information storage table 21 stored in a RAM 20; a model creation part 12 that creates a model of flexible media on the basis of a model information storage table 22 stored in the RAM 20; a motion calculation part 14 that, when the model of flexible media is conveyed by a plurality of conveyance elements according to a conveyance parameter, calculates a temporal change of a motion of the model of flexible media; and a parameter calculation part 13 that calculates the conveyance parameter used by a conveyance device.

Description

  The present invention relates to a simulation apparatus and a program for simulating a behavior of a flexible medium conveyed along a conveyance path according to a conveyance parameter by a model.

  2. Description of the Related Art Conventionally, a technology for simulating the conveyance behavior of a flexible medium conveyed by a web conveyance device (for example, a continuous sheet extending in one direction and a fixed size sheet with standardized vertical and horizontal sizes) has been known. (For example, Patent Document 1).

  In the technique of Patent Document 1, the flexible medium is divided into a plurality of rigid bodies having a mass and a plurality of spring elements, and two adjacent ones of the plurality of rigid bodies are connected by corresponding spring elements. Yes. Then, by analyzing the behavior of each rigid body moved by the corresponding spring element, the behavior of the flexible medium is simulated.

  It has also been conventionally known that when a flexible medium is conveyed by a rotating roller, the friction coefficient of the conveyance medium with respect to the roller changes due to air being caught between the flexible medium and the roller (for example, Non-patent document 1).

JP 2010-282650 A

Hashimoto, “Basic Theory and Application of Web Handling” Processing Technology Study Group, April 1, 2008, p. 46-47, p. 78-81

  However, neither of Patent Document 1 and Non-Patent Document 1 can simulate the behavior of the flexible medium conveyed by the web conveying device based on the change in the friction coefficient. As a result, there has been a problem that the conveyance state of the flexible medium is different between the simulation and the web apparatus.

  Therefore, an object of the present invention is to provide a simulation apparatus and a program that can favorably simulate the behavior of a flexible medium.

  In order to solve the above problems, the invention of claim 1 is a simulation device that simulates the behavior of a flexible medium conveyed along a conveyance path according to a conveyance parameter using a model, and the conveyance path includes a conveyance roller. The model includes a plurality of mass points, and a plurality of springs each connecting between two adjacent mass points of the plurality of mass points. Each of the transport elements is arranged in accordance with corresponding position information, a route creating unit that creates the transport route, a model creating unit that creates the model based on model information, and the transport parameters, A parameter calculator for calculating a coefficient of friction between each mass point of the model and the surface of the transport roller, and the model according to the transport parameter, In the case of being transported by a plurality of transport elements, a motion computation unit that computes temporal changes in the motion of the model is provided, and the parameter computation unit computes the friction coefficient for each time according to the flying height The flying height is calculated for each time as a distance between each mass point of the model and the surface of the transport roller.

  The invention according to claim 2 is the simulation apparatus according to claim 1, further comprising: a display unit that displays a temporal change in the motion of the model calculated by the motion calculation unit as a behavior of the flexible medium. It is characterized by providing.

  According to a third aspect of the present invention, there is provided a computer-readable program for simulating a behavior of a flexible medium conveyed along a conveyance path according to a conveyance parameter by a model, wherein the conveyance path includes a plurality of conveyance rollers. The model includes a plurality of mass points and a plurality of springs each connecting two adjacent mass points of the plurality of mass points, and the program by the computer The execution of (a) a function of creating each of the plurality of transport elements according to the corresponding position information by creating each of the plurality of transport elements, and (b) the model based on the model information. A model creating unit to create, and (c) calculating a friction coefficient between each mass point of the model and the surface of the transport roller among the transport parameters. A parameter calculator, and (d) when the model is transported by the plurality of transport elements according to the transport parameter, realizing a function of calculating a temporal change in motion of the model, and the function (c) The friction coefficient is calculated at each time according to the flying height, and the flying height is calculated at each time as a distance between each mass point of the model and the surface of the transport roller. To do.

  According to the first to third aspects of the present invention, the friction coefficient at each time is calculated according to the flying height between each mass point of the model and the surface of the conveying roller. Thereby, the behavior of the flexible medium in the vicinity of the conveyance roller can be grasped according to the change in the flying height and the friction coefficient. Therefore, the behavior of the flexible medium can be simulated more accurately.

  In particular, according to the second aspect of the invention, the behavior of the flexible medium can be displayed on the display unit. Therefore, the user can visually observe the behavior of the flexible medium, and can easily grasp the behavior of the flexible medium.

It is a block diagram which shows an example of a structure of the simulation apparatus in embodiment of this invention. It is a front view which shows an example of a conveyance path | route. It is a graph which shows the relationship between the conveyance speed of the flexible medium calculated by the motion calculating part, and the time t. FIG. 6 is a front view illustrating an example of a configuration near a conveyance roller. It is a graph which shows the relationship between the average value of the flying height calculated by the parameter calculating part, the effective friction coefficient, and the time t. It is a graph which shows the relationship between the conveyance speed of the flexible medium calculated by the motion calculating part, and the time t. It is a figure for demonstrating the example of an analysis, and the test conditions of a real machine test. It is a graph which shows the example of an analysis and the test result of a real machine test.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<1. Configuration of simulation apparatus>
FIG. 1 is a block diagram showing an example of the configuration of a simulation apparatus 1 according to the embodiment of the present invention. The simulation apparatus 1 simulates the behavior of the flexible medium conveyed by the web conveyance apparatus using a model.

  As illustrated in FIG. 1, the simulation apparatus 1 mainly includes a CPU 10, a RAM 20, a ROM 30, a large capacity storage unit 40, a display processing unit 50, and an input / output unit 60. Further, the CPU 10, the RAM 20, the ROM 30, the large-capacity storage unit 40, the display processing unit 50, and the input / output unit 60 are electrically connected via the bus 8.

  A RAM (Random Access Memory) 20 is a volatile storage unit, and stores, for example, data used in the calculation of the CPU 10. As shown in FIG. 1, the RAM 20 stores a position information storage table 21 and a model information storage table 22.

  The position information storage table 21 stores each conveyance element (for example, a conveyance roller, a linear guide, or an arc guide) used for conveyance of the flexible medium in association with the corresponding position information. Here, the conveyance element includes, for example, the above-described conveyance roller, linear guide, or arc guide, and forms a conveyance path through which the flexible medium is conveyed.

  The model information storage table 22 stores information about a model for imitating a flexible medium. Here, the model of the flexible medium mainly has a plurality of mass points and a plurality of springs each connecting two adjacent mass points among the plurality of mass points.

  A ROM (Read Only Memory) 30 is a so-called nonvolatile storage unit, and stores, for example, a program 31. As the ROM 30, a flash memory that is a readable / writable nonvolatile memory may be used.

  The large-capacity storage unit 40 is a storage unit configured by an element having a larger storage capacity than the RAM 20 such as a silicon disk drive or a hard disk drive, and exchanges data with the RAM 20 as necessary. .

  A CPU (Central Processing Unit) 10 executes operation control and data processing according to a program 31 in the ROM 30. In addition, the CPU 10 realizes arithmetic functions corresponding to blocks (indicated by reference numerals 11 to 14 respectively) described in the CPU 10 in FIG. In addition, the calculation function corresponding to each block 11-14 is mentioned later.

  The display processing unit 50 is configured by a so-called video controller, and is electrically connected to the display unit 51 through a signal line 50a. The display processing unit 50 displays characters, graphics, and the like on the screen of the display unit 51 by executing a drawing process.

  The input / output unit 60 is configured by a so-called I / O port (Input / Output Port), and an input / output device of the simulation apparatus 1 (for example, an operation unit 61 having a keyboard and a touch pad) via a signal line 60a. Electrically connected. Therefore, the input / output unit 60 exchanges data between the CPU 10 and the input / output device.

<2. Arithmetic functions realized by CPU>
FIG. 2 is a front view for explaining an example of the transport path 70b. FIG. 3 is a graph showing the relationship between the conveyance speed of the flexible medium 80 calculated by the motion calculation unit 14 and time t. Here, functions corresponding to the route creation unit 11, the model creation unit 12, the parameter computation unit 13, and the motion computation unit 14 will be described with reference to FIGS.

  In FIG. 2 and subsequent figures, an XYZ orthogonal coordinate system in which the Z-axis direction is the vertical direction and the XY plane is the horizontal plane is appropriately attached as necessary to clarify the directional relationship.

  The route creation unit 11 creates a transport route 70b in the arrangement space 70a based on the position information storage table 21 stored in the RAM 20. For example, as shown in FIG. 2, each of the plurality of transport elements (the driven rollers 71 to 73, the tension roller 74, the transport roller 75, etc.) is disposed in the placement space 70a according to the corresponding position information. Thereby, the conveyance path 70b along the driven rollers 71 to 73, the tension roller 74, and the conveyance roller 75 is formed.

  The model creation unit 12 creates a model of the flexible medium 80 based on the model information storage table 22 stored in the RAM 20. For example, the flexible medium 80 of FIG. 2 is imitated by a plurality of mass points and a plurality of springs as described above.

  Here, the position information storage table 21 used in the route creation unit 11 and the model information storage table 22 used in the model creation unit 12 are instructed by the user of the simulation device 1 via the operation unit 61 in the simulation device 1. May be created according to Further, the position information storage table 21 and the model information storage table 22 are information processing apparatuses different from the simulation apparatus 1 and may be created by a user of the information processing apparatus. Furthermore, the position information storage table 21 and the model information storage table 22 may be created by simulation.

The parameter calculation unit 13 calculates a conveyance parameter used in the conveyance device. For example, the parameter calculation unit 13 calculates an effective friction coefficient μ _eff between each mass point of the model of the flexible medium 80 and the surface of the conveyance roller 75 among the conveyance parameters. Details of the calculation executed by the parameter calculation unit 13 will be described later.

When the model of the flexible medium 80 is transported by a plurality of transport elements according to the transport parameters, the motion calculation unit 14 calculates a temporal change in the motion of the model of the flexible medium 80. For example, in FIG. 3, the flexible when not considering the temporal change in the transport speed of the model of the flexible medium 80 in the case of considering the temporal change in the effective friction coefficient mu _eff, the temporal change in the effective friction coefficient mu _eff The time variation of the transport speed of the model of the medium 80 is shown.

  The display unit 51 displays the behavior of the flexible medium based on the temporal change in the movement of the flexible medium model calculated by the movement calculation unit 14. For example, as illustrated in FIG. 3, the motion calculation unit 14 can cause the display unit 51 to display the speed of the flexible medium at each time t. That is, the display unit 51 can display the temporal change of the model motion calculated by the motion calculation unit 14 as the behavior of the flexible medium. Therefore, the user of the simulation apparatus 1 can visually observe the behavior of the flexible medium, and can easily grasp the behavior of the flexible medium.

<3. Calculation by parameter calculation unit>
FIG. 4 is a front view illustrating an example of the configuration in the vicinity of the conveyance roller 75. Here, a method for calculating the effective friction coefficient μ _eff (t) will be described with reference to FIG.

Here, as shown in FIG. 4, when the flexible medium 80 is transported in the direction of the arrow AR1 (hereinafter also referred to as “transport direction”) by rotating the transport roller 75 in the direction of the arrow R1, the transport roller 75 some peripheral velocity U _r, air caught in between the conveying roller 75 and the flexible medium 80. As a result, the flexible medium 80 floats with respect to the transport roller 75.

  In this case, as the flying height h of the flexible medium 80 with respect to the conveyance roller 75 increases, the coefficient of friction between the flexible medium 80 and the surface of the conveyance roller 75 decreases. When the flying height h is equal to or greater than a certain value, the friction coefficient becomes “0”, and the conveyance roller 75 rotates idly with respect to the flexible medium 80.

  Further, the flying height h is a distance between each mass point of the model of the flexible medium 80 and the surface of the conveying roller 75 and can be expressed as Expression (1).

However, in Formula (1),
a) R is the radius of the transport roller 75,
b) Θ is the winding angle,
c) σ is the composite surface roughness between the flexible medium 80 and the transport roller 75,
d) η is the air viscosity,
e) U _r is the peripheral speed of the transport roller 75,
f) U _w represents the conveyance speed of the flexible medium 80 along the conveyance path 70b.
g) T ₁ is the tension applied to the flexible medium 80,
h) k is the air permeability of the flexible medium 80,
i) _tw is the thickness of the flexible medium 80,
i) x is the position on the transport path 70b,
Each is shown.

  The value of the position x in the formula (1) is a negative number on the downstream side in the transport direction (winding start position P1 side) from the origin P0, and a positive number on the upstream side in the transport direction (winding end position P2 side) from the origin P0. It is set to be.

Further, the conveying speed U _w of the circumferential velocity U _r and flexible medium 80 of the transfer roller 75 can be viewed as a function of time t. Therefore, Expression (1) can be transformed as Expression (2), and the flying height h can be calculated at each position x at each time t.

  However, a, b, c, p (t), and q (t) in the formula (2) are respectively the formula (3), the formula (4), the formula (5), the formula (6), and the formula (7). ).

Therefore, the average value h _ave (t) of the flying height h from the winding start position P1 to the winding end position P2 is expressed as in Expression (8).

However, in Formula (8),
j) μ _s is the initial coefficient of friction,
It is shown.

Further, the friction coefficient μ ₁ of the flexible medium 80 with respect to the conveying roller 75 can be expressed as in Expression (9).

Therefore, when the equation (8) is substituted into the equation (9), the effective friction coefficient μ _eff (t) can be expressed as the equation (10).

As can be seen from equation (10), the parameter calculation unit 13 calculates an effective friction coefficient μ _eff (t) from a predetermined initial friction coefficient μ _s and an average value h _ave (t) of the flying height h. can do. That is, the parameter calculation unit 13 can calculate the effective friction coefficient μ _eff (t) at every time t according to the average value h _ave (t) of the flying height h.

Thereby, the conveyance speed U _w of the flexible medium 80 considering that the effective friction coefficient μ _eff (t) changes due to air levitation can be easily calculated. Therefore, the behavior of the flexible medium 80 can be accurately simulated without increasing the calculation cost.

  Note that “air floating” means that air is trapped between the conveyance roller 75 and the flexible medium 80, and the flexible medium 80 floats with respect to the conveyance roller 75.

<4. Simulation results>
FIG. 5 is a graph showing the relationship between the average value h _ave (t) and effective friction coefficient μ _eff (t) of the flying height h calculated by the parameter calculation unit 13 and time t. FIG. 6 is a graph showing the relationship between the conveyance speed U _w of the flexible medium 80 calculated by the motion calculation unit 14 and the time t.

In FIG. 5, the horizontal axis indicates time t. In FIG. 5, the left vertical axis represents the effective friction coefficient μ _eff (t), and the dotted line corresponds to it. On the other hand, the vertical axis on the right side shows the average value h _ave (t) of the flying height h, and the solid line corresponds to it.

3 and 6, the horizontal axis represents time t, and the vertical axis represents the conveyance speed U _w of the flexible medium 80. The dotted lines in FIGS. 3 and 6 indicate the conveyance speed U _w of the flexible medium 80 in consideration of the change in the effective coefficient of friction μ _eff (t) due to air levitation. On the other hand, the solid line in FIG. 3 and FIG. 6 indicates the conveyance speed U _w of the flexible medium 80 when air levitation is not considered.

  Note that “air floating” means that air is trapped between the conveyance roller 75 and the flexible medium 80, and the flexible medium 80 floats with respect to the conveyance roller 75. In this simulation, the value of the synthetic surface roughness σ is set to “0.583” (μm).

As shown in FIGS. 5 and 6, the flexible medium 80 starts to rise with respect to the conveyance roller 75 at time t1. However, since the average value h _ave (t1) of the flying height h is smaller than the combined surface roughness σ at time t1, the effective friction coefficient μ _eff (t1) becomes the initial friction coefficient μ _s . In this case, the circumferential velocity U _r of the conveying roller 75, the peripheral velocity U _r of the flexible medium 80 are the same value.

Next, at time t2, the average value h _ave (t2) of the flying height h becomes equal to or greater than the combined surface roughness σ, and the effective friction coefficient μ _eff starts to decrease. Further, as shown in FIG. 6, during the period from time t2 to time t3, and the circumferential velocity U _r of the conveying roller 75, the peripheral velocity U _r of the flexible medium 80, is the same value.

Subsequently, at time t <b> 3, the flexible medium 80 starts to slide with respect to the conveyance roller 75. As a result, as shown in FIG. 6, the conveyance speed U _w of the flexible medium 80 becomes equal to or less than the peripheral speed U _r of the conveyance roller 75.

Subsequently, at time t4, the average value h _ave (t4) of the flying height h is three times the combined surface roughness σ, and the effective friction coefficient μ _eff is “0”. That is, at time t5, the conveyance speed U _w of the flexible medium 80 becomes a constant value. That is, at time t7 at least time t5, even if the circumferential velocity U _r of the transfer roller 75 increases, the conveying speed U _w of the flexible medium 80 does not change.

Then, (see Fig. 3) peripheral the speed U _r is a constant conveying rollers 75 at time t6, the average value h _ave (t7) of the flying height h at time t7 after becomes a constant value.

<5. Advantages of Simulation Device of Embodiment>
As described above, in the simulation apparatus 1 of the present embodiment, the effective friction coefficient μ _{eff at} each time is the average value h of the flying height h between each mass point of the model of the flexible medium 80 and the surface of the conveying roller 75. Calculated according to _ave (t).

Thereby, the behavior of the flexible medium 80 in the vicinity of the conveyance roller 75 can be grasped according to the change in the average value h _ave (t) of the flying height h and the effective friction coefficient μ _eff . For example, the conveyance speed of the flexible medium 80 taking into account the effective friction coefficient μ _eff can be obtained. Therefore, the behavior of the flexible medium 80 can be simulated more accurately.

<6. Modification>
Although the embodiments of the present invention have been described above, the present invention is not limited to the above embodiments, and various modifications can be made.

  (1) In the simulation of the present embodiment, continuous paper (see FIG. 2) extending in one direction is used as the flexible medium 80, but the invention is not limited to this. For example, a fixed-size sheet with standardized vertical and horizontal sizes may be used as the flexible medium 80.

  (2) In the present embodiment, the functions realized by the route creation unit 11, the model creation unit 12, the parameter calculation unit 13, and the motion calculation unit 14 are all realized by the CPU 10 as software. Although described, the present invention is not limited to this. For example, these functions may be realized by hardware such as an electronic circuit.

  EXAMPLES Hereinafter, although an Example demonstrates this invention further in detail, this invention is not limited to these examples at all.

<Example 1>
FIG. 2 is a front view showing an example of the configuration of the experimental apparatus 70 that has executed an “actual machine test” for confirming the effectiveness of the present embodiment, as well as an example of the transport path 70b. FIG. 7 is a diagram for explaining an analysis example and test conditions of an actual machine test. FIG. 8 is a graph showing analysis examples and test results of actual machine tests.

Here, in FIG. 8, the speed U _r Analysis examples and physical testing of the drive roller is expressed by the same broken lines. A solid line and a dotted line indicate the web speed U _w of the analysis example and the actual machine test, respectively. As shown in FIG. 7, continuous paper formed of PTME (Poly Tetramethylene Ether) is used as the flexible medium 80 in the analysis example and the actual machine test.

The analysis example simulates the conveyance speed U _w of the flexible medium 80 in consideration of the change in the effective friction coefficient μ _eff (t) due to air levitation, and plots the calculation result in a graph. . Further, the actual machine test is a plot of the conveyance speed U _w of the flexible medium 80 measured by the experimental apparatus 70.

As shown in FIG. 8, the test result of the actual machine test coincided with the test result of the analysis example. Thus, by considering that the effective friction coefficient μ _eff (t) changes due to air levitation, the behavior of the flexible medium 80 can be simulated more accurately.

1 Simulation device 10 CPU
11 path creation unit 12 model creation unit 13 parameter computation unit 14 motion computation unit 20 RAM
21 Position information storage table 22 Model information storage table 30 ROM
31 Program 50 Display Processing Unit 51 Display Unit 60 Input / Output Unit 61 Operation Unit 70 Experimental Device 70b Transport Path 75 Transport Roller 80 Flexible Medium

Claims (3)

A simulation device for simulating, with a model, the behavior of a flexible medium conveyed along a conveyance path according to a conveyance parameter,
The transport path is formed by a plurality of transport elements including transport rollers,
The model is
Multiple mass points,
A plurality of springs each connecting between two adjacent mass points of the plurality of mass points;
Have
(a) a path creation unit that creates the transport path by arranging each of the plurality of transport elements according to corresponding position information;
(b) a model creation unit that creates the model based on model information;
(c) Among the transport parameters, a parameter calculation unit that calculates a friction coefficient between each mass point of the model and the surface of the transport roller;
(d) When the model is transported by the plurality of transport elements according to the transport parameters, a motion calculation unit that calculates a temporal change in motion of the model;
With
The parameter calculation unit calculates the friction coefficient for each time according to the flying height,
The flying height is calculated for each time as a distance between each mass point of the model and the surface of the transport roller. The simulation apparatus according to claim 1,
(e) a display unit for displaying a temporal change in the motion of the model calculated by the motion calculation unit as the behavior of the flexible medium;
A simulation apparatus further comprising: A computer-readable program for simulating, with a model, the behavior of a flexible medium transported along a transport path according to transport parameters,
The transport path is formed by a plurality of transport elements including transport rollers,
The model is
Multiple mass points,
A plurality of springs each connecting between two adjacent mass points of the plurality of mass points;
Have
The computer executes the program on the computer.
(a) a function of creating the transport path by arranging each of the plurality of transport elements according to corresponding position information;
(b) a model creation unit that creates the model based on model information;
(c) Among the transport parameters, a parameter calculation unit that calculates a friction coefficient between each mass point of the model and the surface of the transport roller;
(d) When the model is transported by the plurality of transport elements according to the transport parameters, a function of calculating a temporal change in the movement of the model;
Realized,
The function (c) calculates the friction coefficient for each time according to the flying height,
The flying height is calculated for each time as a distance between each mass point of the model and the surface of the transport roller.

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