FE analysis of multi-cycle micro-forming through using closed-die upsetting models and forward extrusion models

Research in micro-forming leads to the investigation of the effects of heat generation in the workpiece and temperature changes in the tools during the forming. The results reported in this paper relate to the study of cold micro-forming processes which are usually ignored on its thermal characteristics. Two closed-die upsetting models were used for the simulation of the forming of micro-parts in single forming trial and in mass production (multi-cycle loading), respectively. An elastic-plastic finite element simulation was performed for a single forming trial. The heat transferred to the die, computed from the simulation, was then used as an input for the multi-cycle heat loading analysis in the die. Two materials: silver and low carbon steel, were used as the work material. The results show that the die saturation temperature could still go up to 100 °C for small size dies, which is significant for the forming of micro-parts. Forming errors due to the die-temperature changes were further computed, which forms a basis for developing considerations on the forming-error compensation. Using the same methods and procedures, forming of a micro-pin via forward extrusion was analysed

A congruence involving products of qq-binomial coefficients

In this paper we establish a $q$-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.Comment: 9 page

Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy

We theoretically study the width of the s-wave confinement-induced resonance (CIR) in quasi-one-dimensional atomic gases under tunable transversely anisotropic confinement. We find that the width of the CIR can be tuned by varying the transverse anisotropy. The change in the width of the CIR can manifest itself in the position of the discontinuity in the interaction energy density, which can be probed experimentally.Comment: 6 pages, 3 figures, update references, published versio