Numerical Study on Single Point Incremental Sheet Metal Forming Process
-Single Point Incremental Sheet Forming (SPIF) is an innovative forming approach for sheet materials. In this process, the forming tool is moved along a predefined tool path which is a series of contour constructed a final shape of product by using numerical controlled technology. This paper investigated finite element analysis simulation to predict the mechanical failures in single point incremental sheet metal forming (SPIF). In the present paper, some of these aspects, namely, the phenomenon of the wall thickness overstretch along depth and the effect of the tool path on the distribution of the wall thickness using finite element simulations etc. are investigated. It is observed from the analysis that the single point incremental sheet metal forming is very much time consuming and also the depth of stretch with different step size and tool diameters have been implemented.
Tool Path and Sheet Thickness Distribution of Axisymmetric Cup in Single Point Incremental Forming
This study involved planning different tool paths for an axisymmetric cup to explore the forming characteristics of the single point incremental forming (SPIF) process. In addition, this study developed a gradient theory to compute the inclined angle between the tangential and horizontal directions of the cup formed using single point incremental forming. The sheet thickness distribution of the cup was also calculated. To verify the theory, circle arc cups were formed by CNC machining using different tool paths. It was found that the cup formed using the spiral evolutional snail-line tool path produced a better surface than that formed using the equal height evolutional tool path. The sheet thicknesses of circle arc cups obtained by the experiment and using the cosine law were compared. A larger deviation was noted in the initial portion of the cup, whereas a smaller deviation was found in the other portion. This study also adopted a dual-conical cup to investigate the relationship between thickness and the initial inclined angle at the initial portion. It was found that a larger initial inclined angle led to good coincidence between the experimental and theoretical sheet thicknesses.
On the analytic complexity of discriminants
The paper deals with the notion of analytic complexity introduced by V.K. Beloshapka. We give an algorithm which allows one to check whether a bivariate analytic function belongs to the second class of analytic complexity. We also provide estimates for the analytic complexity of classical discriminants and introduce the notion of analytic complexity of a knot.