JPH1123390A - Motion analysis method of yarn of twisted woven fabric - Google Patents

Abstract

(57) [Summary] [Problem] To propose a yarn model of twisted woven fabric that is easy to analyze, and to easily analyze the movement state of each yarn such as movement, deformation, breakage, orientation, or stress. A yarn of a twisted woven fabric is approximated by an aggregate of spheres, a total force and a total torque acting on each sphere at a certain time are obtained, and a translational motion of each sphere is calculated from the total force and the total torque.
Formulate a motion equation for the rotational motion, numerically analyze the motion equation to determine the position and rotation angle of each sphere, and using those values, the total force acting on each sphere at the next time,
Analyzing the movement state of the yarn movement, deformation, breakage, orientation, or stress by repeating the sequential calculation of finding the total torque and finding the position and rotation angle of each sphere at the next time by the same analysis I do.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing a movement state such as movement, deformation, breakage, orientation, or stress of a yarn constituting a twisted woven fabric.

[0002]

2. Description of the Related Art As a test and analysis method for designing a twisted woven fabric that requires strength and durability, a woven fabric test apparatus (Japanese Patent Application Laid-Open No. 3-502366 and Japanese Patent Application Laid-Open No. 3-502367) has been proposed.
Also, a method for testing a yarn (Japanese Patent Application Laid-Open No. 62-255847) is known. In order to analyze the stress of the yarn, a finite element analysis method using a model obtained by dividing the yarn by finite elements can be considered.

[0003]

However, in the case where the twisted woven fabric is deformed with time, it is necessary to perform element division again in accordance with the deformation, which requires enormous calculations.
In addition, the design of twisted woven fabric is not only the force acting on the whole woven fabric,
It is important to know at most how much force is acting on a single thread, from which the strength of the thread must be determined. In the conventional method, it is possible to estimate the force acting on the entire woven fabric or the average value of the force acting on the yarn therefrom. However, it is not known how much force acts on the yarns constituting the woven fabric at the maximum.

Accordingly, an object of the present invention is to propose a model of a yarn of a twisted woven fabric, which is easy to analyze, and to easily analyze the movement state of each yarn such as movement, deformation, breakage, orientation, or stress. That is.

[0005]

Means for Solving the Problems According to a structure of the invention for solving the problems, a yarn of a twisted woven fabric is approximated by an aggregate of spheres, and a total force and a total torque acting on each sphere at a certain time are obtained. From the total force and total torque, the translational motion of each sphere,
Formulate a motion equation for the rotational motion, numerically analyze the motion equation to determine the position and rotation angle of each sphere, and using those values, the total force acting on each sphere at the next time,
Analyzing the movement state of the yarn movement, deformation, breakage, orientation, or stress by repeating the sequential calculation of finding the total torque and finding the position and rotation angle of each sphere at the next time by the same analysis It is characterized by doing.

[0006]

According to the present invention, since the yarn is approximated by an aggregate of spheres, it is not necessary to redivide the yarn every time the yarn is deformed, so that the analysis time is shortened. Also, since the yarn is approximated by the aggregate of spherical bodies, arbitrarily twisted yarn can be handled. The motion equations for translational motion and rotational motion are established in consideration of the total force and total torque acting on each sphere, so the interaction between the spheres due to contact between the spheres and the It becomes possible to analyze the motion state taking into account the interaction.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described based on specific embodiments. The yarns constituting the twisted woven fabric are approximated by an aggregate of spheres. For example, as shown in FIG.
Is approximated by an aggregate of spheres A1 to A5 arranged on a straight line. Also, as shown in FIG. 2, the twisted yarn 20 is a single yarn 1
It is constituted by a plurality of 0 being twisted. Then, as shown in FIGS. 3 and 4, the woven fabric 30 is woven using the twisted yarn 20. Thus, the twisted yarn 20 is
And a model based on the yarns 10 constituting the twisted yarns 20, and each yarn 10 is approximated by spheres A1 to A5 as shown in FIG.

FIG. 3 shows a state in which the twisted woven fabric 30 is wound around the tube as a reinforcing material for the tube 40. FIG. 4 shows the deformed shape of the twisted woven fabric 30 and the force acting on the yarn 10 when the tube 40 is twisted.

The present invention analyzes the motion state such as the force acting on each yarn 10 and the displacement of each yarn in such a case.

FIG. 5 shows a configuration of an analyzer for executing the method of the embodiment. This analyzer is configured by a computer system. That is, a CPU 60 that executes various calculations, a RAM 62 that stores an analysis program and various coefficients for analysis, an initial position of the yarn, and the like, a storage medium 66 that stores the analysis program and these data, and data stored in the storage medium 66. A reading device 67 for loading the data into the RAM 62 is provided. In addition, a ROM 63 that stores predetermined programs and data, a printer 61 that outputs an analysis result, a CRT 64 that displays the state of the deformation and stress of the yarn over time as the analysis result, and a keyboard 65 for inputting data are provided. Is provided. RAM 62
Is formed with an initial value area 621 for storing an initial position of each sphere constituting the thread and an initial rotation angle of each sphere, and a basic information area 622 for storing basic information. The basic information includes material information, sphere information, initial information, and environmental information. The material information is information that determines the physical properties of the yarn, such as the elastic modulus and friction coefficient of the yarn. The sphere information is information such as the configuration of an aggregate of spheres that model the yarn, the degree of freedom of the coupling length and the degree of coupling angle between the spheres, the size of each sphere, and the like. The initial information is information that gives the initial position and orientation of the yarn according to the twisted form of the yarn. The environmental information is information that determines the physical properties of the environmental medium such as the viscosity of the environmental medium on which the yarn is placed, and information about the external force distribution on the yarn.

Next, an analysis procedure by the CPU 60 will be described with reference to a flowchart of FIG. In step 100, modeling of the woven fabric 30 with the twisted yarn 20 as shown in FIG. 3, modeling of the twisted yarn 20 with the yarn 10 as shown in FIG. 2, and aggregation of spheres A1 to A5 of the yarn 10 as shown in FIG. Modeling is performed. Then, based on the position and orientation of the thread 10 given as the initial information, the initial center positions O1 to O5 of the spheres constituting the thread 10 and the initial rotation angle θ1
Are calculated, and these values are stored in the initial value area 621.

Next, at step 102, the time t for calculating the velocity and angular velocity of each sphere is updated by a minute time Δt. In step 104, each sphere i at time t-Δt
Force F _i (vector) and total torque T acting on
_i (vector) is calculated by the following equation.

[0013]

F _i = Σ _j F ^S _ij + Σ _j F _ij + F ^h _i + Σ _j F ^p _ij (1) where the F ^s _ij vector is the coupling force that the sphere i receives from the sphere j and is the distance between the spheres. It is given as an elastic force proportional to the displacement. That is, each sphere is connected by a spring having a spring constant corresponding to the distance between the spheres when there is no displacement, and the coupling force is obtained as a value proportional to the displacement of the distance between the spheres. Since the initial distance between the spheres is given, the displacement for the initial processing of the distance between the spheres is calculated, and F ^S _ij is calculated from the displacement. The F _ij vector is a frictional force at a connection point where the sphere i receives from the sphere j.

The F ^h _i vector is the viscous force that the sphere receives from the environmental medium (air, liquid if the woven cloth is in liquid), and is given by the following equation.

F ^h _i = −6πηaΔE (2) where η is the viscosity of the environmental medium, a is the radius of the sphere, and ΔE vector is the relative velocity of the sphere i with respect to the environmental medium. That is, the velocity vector of the sphere i at time t-Δt is represented by V _i
(T−Δt),

ΔE = V _i (t−Δt) −W (U, t−Δt) (3)

Further, the sphere i in contact with the tube 40 receives an external force due to the deformation of the tube 40, so that the F ^h _i vector becomes the external force on the sphere i. This external force can be given as a time-varying field as an external force distribution. In response to the external force distribution, the stress on each yarn 10 changes and each yarn 10 is displaced.

The F ^p _ij vector is a rigid repulsive force acting between the yarn and another yarn and is given by the following equation.

F ^p _ij = −Dexp [G (1− | r _ij | / 2a)] n _ij (4) where r _ij is the displacement vector of the sphere j of the other thread with respect to the sphere i, and V _i is The velocity vector of the sphere i, V _j is the velocity vector of the sphere j of the other thread, n _ij is a unit vector of the r _ij vector, and D and G are constants determined by the material of the thread 10. In this way, the total force F _i acting on the sphere _i is calculated.

Next, total torque T _i acting on each sphere i at time t-Delta] t is calculated by the following equation.

T _i = Σ _j T ^b _ij + Σ _j T ^t _ij + Σ _j (F _ij × an _ij ) + T ^h _i (5) where T ^b _ij is the coupling torque that sphere i receives from sphere j , The rotational torque about an axis perpendicular to the axis connecting the centers of the two spheres. It is given as an elastic force proportional to the angular displacement between the spheres. That is, the spheres are connected by a spring having a certain spring constant with respect to rotation, and the connection torque is determined as a value proportional to the rotational angular displacement between the spheres. Since the initial rotation angle of each sphere is given, the rotation angle displacement between the spheres is calculated from the deviation of the rotation angle of each sphere from the initial rotation angle, and T ^b _ij is calculated from the displacement.

T ^t _ij is the torsional torque that sphere i receives from sphere j and is the torque about the axis connecting the two spheres. This torsion torque can be calculated in the same manner as the coupling torque.

F _ij × an _ij is the torque due to the frictional force at the connection point that sphere i receives from sphere j. T ^h _i is the torque received from the substrate.

Next, at step 106, the velocity V _i and the angular velocity ω _i of each sphere i at time t are calculated by the following difference equation.

V _i (t) −V _i (t−Δt) = F _i (t−Δt) Δt / m (6)

Ω _i (t) −ω _i (t−Δt) = 5T _i (t−Δt) Δt / ( ² ma ² ) (7)

Here, m is the mass of the sphere. The condition that does not slip at the connection point of the sphere is given by the following equation.

V _i (t) + aω _i (t) × n _ij = V _j (t) + aω _j (t) × n _ji (8) Therefore, taking into account the constraint condition of equation (8), 6),
According to equation (7), the velocity V of each sphere i at time t
_i (t) and each speed ω _i (t) are obtained. Note that V
_i (t−Δt) and ω _i (t−Δt) are the previous time t−Δ
t is obtained by the calculation of t or t if there is no previous calculation.
= 0 is the value given under the initial condition.

Next, at step 108, the speed V
with _i (t) and the speed ω _i (t), the position of the spherical bodies i at _{t + Δt O i (t +} Δt) and the rotation angle theta _i (t +
Δt) is calculated by the following equation.

O _i (t + Δt) −O _i (t) = V _i (t) Δt (9)

Θ _i (t + Δt) −θ _i (t) = ω _i (t) Δt (10) where O _i (t) and θ _i (t) are obtained by the previous calculation of time t−Δt. Or the value given under the initial condition of t = 0 if there is no previous calculation. The obtained position O _i (t + Δt) and rotation angle θ _i (t + Δt) of each sphere i are used to calculate the speed at time t + 2Δt, the total force when obtaining the angular speed, and the total torque.

Thus, in step 110, it is determined whether or not the position fluctuation of each sphere is equal to or less than a predetermined value. If this value is equal to or less than the predetermined value, it is determined that the displacement of the yarn 10 has stopped in response to the external force, that is, the shape is determined to be stable, and the calculation is terminated. On the other hand, if the displacement of the thread 10 has not yet stopped, the process returns to step 102, where the time t is updated by Δt, and the position O _i , rotation The angle θ _i is determined.

By displaying the position and orientation of each sphere i in accordance with the position and rotation angle of each sphere i at each time obtained in this manner, how the yarn is deformed with the passage of time. You can get an image of what to go. Also, by displaying the magnitude of the total force F _i and the total torque T _i acting on each sphere i in color, it is possible to see what kind of stress and torque change is applied to each part of the yarn 10 over time. be able to. FIG. 4 shows the result of calculating the stress of each part of each yarn 10 constituting the woven fabric 30 when the deformation is stabilized by applying a twist to the tube 40 around which the woven fabric 30 shown in FIG. 3 is wound. It was done. The magnitude of the stress is indicated by lightness. In the torsion direction shown in FIG. 4, it can be seen that a tensile stress acts on the twisted yarn 20 in the X-axis direction and a compressive stress acts on the twisted yarn 20 in the Y direction. In addition, it can be determined that the strength of the stress is different in each part of the yarn 10. By comparing the strength of the stress of each part with the strength of the yarn, the breakage of the yarn can be predicted. In this manner, the maximum stress of the yarn 10 with respect to the predetermined torsional force and the portion to which the stress is applied are known, and the strength design of the twisted woven fabric is facilitated.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram showing a method of approximating a yarn constituting a twisted woven fabric by a set of spheres.

FIG. 2 is an explanatory view showing a yarn constituting a twisted yarn.

FIG. 3 is an explanatory diagram showing a state in which the woven fabric is constituted by twisted yarns and a state in which the woven fabric is wound around a tube.

FIG. 4 is an explanatory diagram showing a result of calculating a stress applied to each portion of the yarn of the twisted woven fabric when a torsional force is applied to the tube shown in FIG. 3;

FIG. 5 is a block diagram showing an apparatus for implementing the method of the present invention.

FIG. 6 shows a CP used in an apparatus for implementing the method of the present invention.
9 is a flowchart showing a processing procedure of U.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 ... Yarn A1-A5 ... sphere O1-O5 ... center position of a sphere 20 ... twisted yarn 30 ... twisted yarn woven fabric 40 ... tube

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Satoshi Yamamoto 41-cho, Yokomichi, Nagakute-machi, Aichi-gun, Aichi Prefecture Inside Toyota Central R & D Laboratories Co., Ltd. No. 1, Nagahata, Toyoda Gosei Co., Ltd. (72) Inventor, Fumio Ikeda

Claims (1)

[Claims] 1. A yarn of a twisted woven fabric is approximated by an aggregate of spheres,
The total force and total torque acting on each sphere at a certain time are obtained, the translational and rotational motion equations of each sphere are established from the total force and total torque, and the motion equation is numerically analyzed to determine the position and position of each sphere. The rotation angle is determined, the total force acting on each sphere at the next time is calculated using the values thereof, the total torque is determined, and the position and rotation angle of each sphere at the next time are determined by the same analysis. By repeating the sequential calculation, the movement, deformation,
A motion analysis method for a yarn of a twisted woven fabric, characterized by analyzing a motion state such as breakage, orientation, or stress.