Approximation of the contour of the side surface of the semimanufactures with the upsetting using deforming flat plates
DOI:
https://doi.org/10.37142/2076-2151/2019-2(49)35Keywords:
upsetting; contour; barreling; superellipse; approximation; formulas.Abstract
Anishchenko A. S., Kukhar V. V., Prysiazhnyi A. H. Approximation of the contour of the side surface of the semimanufactures with the upsetting using deforming flat plates // Material working by pressure. – 2019. – № 2 (49). - Р. 35-40.
The article proposes approximating the Läme superellipse with the contour of the lateral surface of the semimanufactures, which is deformed by the upsetting using flat deforming plates. The contour of the semimanufactures has the shape of a barrel and is determined by the values of the diameters of the barrel, the end face and the height of the semimanufactures. The superellipse has approximation coefficients. The values of these coefficients allow us to determine the shape of the contour of the side surface of the semimanufactures. A contour is: a parabola if the coefficient is slightly less than 2, a circle if the coefficient is 2, and an ellipse if the coefficient is slightly more than 2. The article proposes a new formula for determining the approximation coefficients in the superellipse. The formula is based on the equality of the volumes of the original billet and semimanufactures after deformation. The volume of the semimanufactures is determined by the method of integrating the Lamé superellipse, which was previously laid out in a Fourier series. The formula does not require a large number of measurements of the contour points of the side surface and includes the height and diameter of the original billet, the height and diameters of the end and barrel of the deformed semimanufactures. The article contains information about the approximation of the lateral contours of lead deformed semimanufactures by a superellipse. The first series of semimanufactures obtained from blanks that have the same initial height and diameter, are upset with a degree of deformation equal to 0.4, using different lubricants and without lubricants. The coefficient of friction between the workpiece and the deforming flat plates, determined by the method of Gubkin, was 0.29-0.41. The second series of semimanufactures was deformed without lubrication between the workpieces and plates with degrees of deformation equal to 0.1-0.5 (the step of changing the degree of deformation was 0.1). The height of the original blanks 2 times their diameter.
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