Calculation of the Geometry of Articles Produced by Free Thermoforming through Elliptical Apertures

Abstract

The determination of the geometry of articles produced by free thermoforming through elliptical apertures is examined. The surface of the article is determined using Coons' method.

Calculating the Geometric Parameters of Articles Produced by Free Thermoforming in Apertures of Arbitrary Shape

“…Methods proposed to date [3] have ruled out the possibility of calculation if the contour of the aperture has no point at which a tangent drawn at this point does not coincide with a straight line passing through this point and the centre of a coordinate system positioned inside the contour of the aperture ( Figure 2). This shortcoming can be eliminated by dividing the contour of the aperture into several fragments satisfying the constraint set out above.…”

“…As in Gusev et al [3], it is possible to describe the fragments of the material in the form of two ellipses with central axes of x 1 , y 1 and x, y respectively.…”

“…From the description of an aperture of complex configuration, we will move on to an examination of the surface of material being formed in this aperture. For this, we will present the surface of a quarter of the material being processed, confined by the contour of a rectangle ( Figure 6), using the Coons surface description method [3]. According to this method, the surface of each of the fragments can be presented in parametric form:…”