Analytical form of the Probability Density Function of travel times in rectangular zone with Tchebyshev’s metric

Geometrical dependencies are being researched for analytical representation of the probability density function (pdf) for the travel time between a random, and a known or another random point in Tchebyshev’s metric. In the most popular case - a rectangular area of service - the pdf of this random variable depends directly on the position of the server. Two approaches have been introduced for the exact analytical calculation of the pdf: Ad-hoc approach – useful for a ‘manual’ solving of a specific case; by superposition – an algorithmic approach for the general case. The main concept of each approach is explained, and a short comparison is done to prove the faithfulness.

Surface quality of profile extrusion dies manufactured by Selective Laser Melting

The design of plastics profile extrusion dies becomes increasingly more complex so that conventional manufacture processes reach their limit in the die manufacture. A feasible manufacture of arbitrarily designed dies is only possible by additive manufacturing. An especially promising process is hereby the Selective Laser Melting with which metal parts with series identical mechanical properties can be produced without the need for part specific tooling or downstream sintering processes. Disadvantegeous is, however, the relatively rough surface of additively manufactured parts. Against this background, the manufacturing of an profile extrusion die by Selective Laser Melting and the plastics profile surface quality, that can be achieved with such dies, is investigated. For this purpose, profiles are extruded both with an additively manufactured die and a conventionally milled sample of the same die geometry. In case of the additively manufactured die a concept for the surface finishing of the flow channel is required, which can be applied to arbitrarily shaped geometries. Therefore, two different reworking processes are applied only to the die land of the flow channel. The comparison of the surface roughnesses shows that the additively manufactured die with a polished die land delivers the same surface quality as the conventional die.