SU1406612A1 - Method of simulating the process of generating a pattern-cutting chart for sheet materials - Google Patents

Abstract

The invention relates to methods for modeling the process of mapping cutting materials (metal, fabrics, leather, wood, etc.) and can be used in engineering, the textile industry, leather industry, the woodworking industry, as well as in other sectors of the national economy. ytsva. The aim of the invention is to maximize the filling of the area of a sheet of cuts. The goal is achieved by flat dielectric templates at the boundaries of which electric charges of the same name are fixed on the sheet model cutting and fixing the positions of stable equilibrium, the distance between the circuits that completed the dissipative movement of the templates until they reach the maximum of the area of the sheet model. 3 il. with (L

Description

U

about

Od

The invention relates to methods for modeling the process of mapping cutting materials (metal, fabrics, leather, wood) and can be used in mechanical engineering, textile industry, leather processing, woodworking industry, as well as in other sectors of the national economy.

The aim of the invention is to maximize the filling of the area of a sheet of cuts.

FIG. 1 shows a scheme for implementing the method; in fig. 2 and 3 are a graphic representation of the relative position of the templates.

The method is carried out as follows.

For example, it is necessary to map a model of a cutting sheet of a fixed width L for parts of complex shape with a total number of patterns N (some may be the same) so that the minimum length of the sheet is cut. This corresponds to the task of rational use of the material area.

The plane dissipative motion of templates that are spread on a sheet pattern, as solid dielectric bodies of arbitrary configuration, under the action of forces arising from the arrangement of elements charged with the same size and the same size as electric charges rigidly fixed at points equidistant from each other along the perimeters patterns and models of the sheet are cut, described by the following system of equations (i 1, N):

d

 m

(m1).

) (ij-yue) l (ij-u). ABOUT)

Kio

 M

 () (yij-yu) (y.j-yu). (2)

 M

(n + t

.C r M, r, j

k: 0

j, “iO

((xi ...) - (yi | -y o) (x, .j-x,) j.

X. and y

Yu

- Cartesian coordinates of Nata (y-axis along the sheet cutting the center of mass of the i-ro pattern;

45

Cartesian coordinates to (J 1, М) along the perimeter of the i-ro pattern, in which elements with electric charges are fixed;

(m1).

(n + t)

(3)

about

five

year

0

five

 M

and 0

j

K and Kj

- the coordinates of these points in the polar coordinate system with the center in the center of mass of the template and the template orientation line defined by the angle o (io and passing through this center of mass;

-coefficients that ensure that the predominant role of rotation when moving patterns (K (f):

PC O, f is the distance between electrically 14066

charges on the perimeters of the patterns and on the borders of the sheet model);

n - coefficient

matched empirically (for the considered IQ example);

M - the number of points in. elements of which are electrically charged with J5 charges (M M. for the ith template, M M for the edge of the tape). |

Equations (1-3) model the removal of points (xj, y.yi) and (x 1,) as j O, K according to the law

20

(x .. (y.j-y,

those. the action of the forces is inversely proportional to the square of the distance between the corresponding points of the patterns. Equations (1.2) describe the motion of the centers of mass of the patterns, and equation (3) the rotation of the patterns relative to the centers of mass. Moreover, a viscous movement takes place - only the first arbitrary in time are included in the equations.

With the discrete nature of modeling the motion of the templates, the values of the process parameters in the next step (, y V, e (V) are determined by the values of these parameters in the previous step (x, y, o / A) as follows:

35

R 0,, r - (, - x,). ,, s .- (. u,),

.,., A - (- ..,. (6,

Achievement of the position of a stable equilibrium is fixed by stopping the translational motion of the centers of mass of all the patterns and their relative to these centers:

1C

 "C

I in Y

g)

x {1x („-

 -; J l-r, | .E. (7)

Q

five

0

five

g

five

12

where E is a valid deviation value of the parameters x. , y , o / | p from the position of stable equilibrium.

The value of E is determined in specific technological processes, based on a compromise between material savings and the duration of the modeling process. The smaller the E, the longer the time spent on the simulation.

After reaching the position of stable equilibrium (Z E), the mixing of the sheet border is cut as with the initial length Y of this value:

E rain (Y - y ,.). J

The value of E corresponds to the mixing of the border of the sheet before contact with the contour of the nearest template.

Then, the motion of the patterns is simulated in accordance with equations (1-6) until a new position of stable equilibrium is reached, defined by condition (7).

The set of operations for simulating the displacement of the border of the tape (8), the movement of the templates (1-3), and fixing the position of the stable equilibrium (7) are repeated successively until the established density of placement of the templates is achieved:

g ...,; - x,). (y ,, - y ,,)

(.)

(9)

45

55

The required value of the density of the patterns is limited from above by the parameters of the technological process of cutting the material, as the minimum value is acceptable, and also below by the condition E c /, i.e. The achievable density of placement of the templates cannot be less than the distance between the electric charges (this is a method error).

Based on equation (1-9), the proposed method is constructed.

The input of the sheet model 1 is cut and the model of the control device 2 is supplied with the input signal Zj, which determines the initial placement of the patterns on the cut sheet for model 1 and the source data for creating the system of equations (1-6) in model 2. From model 2 to model 1 admin51

the second signal U., which is used to change the position of the patterns, i.e. maps are cut according to equations (3-6). From the output of model 1 to the input of model 2, a signal Z is received, which determines the new placement of tabs, which is used in model 2 to calculate the values of Zj and Z in accordance with expressions (7) and (9). For the time being, ZQ, (, 7E1, the control signal is sequentially input to the input of model 1. And. With Z 7 E, and Z, - & E, a stable equilibrium position occurs.

The position of a stable equilibrium of patterns will be reached when the interaction energy, depending on the distance between the patterns, is minimal, i.e. distance between facing each other; the borders of the nearest patterns change smoothly, which means that the sleeves tend to concavities. Thus, the position of the patterns 1 and 2 in FIG. 2 will move to the position shown in FIG. 3, with fixed centers of mass 3 and 4,

marked with asterisks.

i

Then, instead of the signal U, a signal J is fed to the input of model 1, which is used to model the offset of the sheet border by cutting by the value E, j, defined by (8). Next, the process is repeated until the conditions and Z are satisfied simultaneously (o -K, i.e., until the required density of the patterns is reached in the presence of a stable equilibrium state. Then a control signal U} is fed to the input of model 1, with which

06612, 6

The output of model 1 is given a signal that determines the resulting placement of the patterns on the cutting sheet model.

Claims (1)

Invention Formula A method for simulating the process of mapping the cutting of Q-sheet materials based on the placement of flat patterns of parts to be cut within the boundaries of the sheet model is cut, characterized in that, in order to maximize the area of the cut sheet, the patterns placed within the cut sheet borders made of dielectric material, fastened around the perimeters of the patterns The 20 moving boundaries of the sheet model, the cutting elements charged by the same electric charges, place the fabricated templates on the fixed surface of the sheet model 25, fix the positions of stable equilibrium and the distance between the contours of the templates after the completion or free dissipative movement on the sheet model electric charges displace the edges of the sheet before contacting them with the contour of the nearest template and after the templates have reached a stable equilibrium use repeat process are offset sheet borders is disclosed and fixing position of stable equilibrium distances between the contours completed dissipation tivioe movement patterns to achieve maximum filling of 35 40 square sheet model is open. Phi. one .2 FIG.