Improvement of the Method for Fixing a Punch in the Punch Holder

The punching process allows large quantities of parts to be produced at very low cost. This paper studies how the technique used for fixing a punch can be improved in order to increase productivity before punch fracture, which results in large numbers of parts failing to be produced, thus creating a significant shortfall. In this context, the study deals with an industrial case, specifically the manufacturing (metal sheeting and metal forming) of a connector made of stainless steel. A broken tool is first analyzed in order to identify the source of the premature breakage. Then, the tool and the process are modeled using finite element analysis (FEA) to act as a reference. Then, the improvements in the geometry and fixing method, intended to increase the tool lifespan, are assessed and modeled using FEA. Finally, the modified profile with only one central hole proves to be very efficient.

The Geometric Kernel of Integral Circulant Graphs

By a suitable representation in the Euclidean plane, each circulant graph $G$, i.e. a graph with a circulant adjacency matrix ${\mathcal A}(G)$, reveals its rotational symmetry and, as the drawing's most notable feature, a central hole, the so-called \emph{geometric kernel} of $G$. Every integral circulant graph $G$ on $n$ vertices, i.e. satisfying the additional property that all of the eigenvalues of ${\mathcal A}(G)$ are integral, is isomorphic to some graph $\mathrm{ICG}(n,\mathcal{D})$ having vertex set $\mathbb{Z}/n\mathbb{Z}$ and edge set $\{\{a,b\}:\, a,b\in\mathbb{Z}/n\mathbb{Z} ,\, \gcd(a-b,n)\in \mathcal{D}\}$ for a uniquely determined set $\mathcal{D}$ of positive divisors of $n$. A lot of recent research has revolved around the interrelation between graph-theoretical, algebraic and arithmetic properties of such graphs. In this article we examine arithmetic implications imposed on $n$ by a geometric feature, namely the size of the geometric kernel of $\mathrm{ICG}(n,\mathcal{D})$.