On a local coordinate system on a smooth surface, used in computer simulation of the manufacturing process of composite structures

Аuthors

Bityukov Y. I.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: yib72@mail.ru

Abstract

In the design of complex equipment we observe a replacement of the traditional processing means of geometric-graphical information by the paperless technologies. Thanks to that new opportunities appear to use of automated design systems. New technologies arise which associate with the use of electronic models of design object. The main advantage of using the electronic model of the product is possibility of its use in the different modules of the systems of continuous design of the class CAD/CAM/CAE. In the modern CAD/CAM/CAE-systems geometric modeling of objects, computer solution of geometrical and engineering-graphics tasks occupy the central place.
This article is devoted to working out of mathematical model of packing of a tape under the set scheme of reinforcing on the technological surface, considering changing width of the tape. Besides, some characteristics of the scheme of reinforcing are entered in article, and the trajectory of movement of the stacker of the tape on the set picture of packing of a tape is calculated. Modeling of packing of a tape of variable width by means of smooth display is developed for the first time. Existing geometrical models do not consider width of a tape absolutely or they are intended for a tape of constant width.
The paper considers a problem to find the optimal trajectory and a law of motion of the spreading mechanism of a numerical control winding machine for making complex-shaped constructions of fibrous composite. The problem is solved taking into account a real structure of tape of fibrous composite, restrictions on an allowable position of the spreading mechanism, a thread tension and a broaching speed of tape.

Keywords:

winding; the geodetic; semigeodetic system of co-ordinates; the reinforcing scheme

References

1. Zav’yalov Yu. S, Kvasov B.I., Miroshnichenko V.P. Metody splain—funktsii (Methods of spline functions), Moscow, Nauka, 1980, 352 p.
2. Bityukov Yu.I., Kalinin V.A., Deniskin Yu.I., Miroshnichenko P.V. Omsk Scientific Vestnik, 2012, no.2(110), pp. 14-18.
3. Anderson James A. Diskretnaya matematika i kombinatorika (Discrete mathematics and combinatorics), Moscow, Williams, 2004, 960 p.

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