Two closed forms for the Bernoulli polynomials

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 page

PIM moulding of post consumer mixed plastics

Post consumer plastics from household are highly mixed and contaminated and are thus particularly difficult to recycle. Although advances in sorting and cleaning technologies for waste plastics have enable the relatively pure and clean streams such as bottles to be recycled, there is a increasing need for processing technologies that can utilise the low grade and mixed plastic residues from the plastics recovery facilities (PRF). In this work, potentials of utilisation of such feedstock in Powder Impression Moulding (PIM), a process capable of fabricating lightweight sandwich structures, are investigated in terms effects of loading and size of flakes from PE-rich mixed plastics in the formulations of the core on flexural properties of the sandwich panels. It was demonstrated that sandwich panels can be made by incorporating about 75 wt% of coarse flakes of a low-grade mixed plastics material directly obtained from a PRF

Influences of impurities in recycled plastics on properties of PIM sandwich panels

Powder impression moulding (PIM) is a novel technology for manufacturing lightweight sandwich panels from plastics in powder form. The process is featured by its high tolerant to impurities or contaminants in the feedstock and thus requires much less materials segregation and cleaning operations when use recycled plastics. This paper investigate the influences of polymer impurities and soil contamination on structure and properties of PIM sandwich panels using compositions that simulate a PE-rich recycled plastic feedstock. It is demonstrated that the PIM process can accommodate considerable impurities (rPET residues or soil contamination) in a core dominated by LDPE/HDPE blendes. The variation of flexural properties can be predicted or controlled through monitoring of impurities. There exist significant scopes for reduction of the degree of sorting and cleaning in recycling systems by using lower grades of recyclates and for reduction of the associated costs and energy consumption

Rotor-to-stator rub vibration in centrifugal compressor

One example of excessive vibration encountered during loading of a centrifugal compressor train (H type compressor with HP casing) is discussed. An investigation was made of the effects of the dynamic load on the bearing stiffness and the rotor-bearing system critical speed. The high vibration occurred at a "threshold load," but the machine didn't run smoothly due to rubs even when it had passed through the threshold load. The acquisition and discussion of the data taken in the field as well as a description of the case history which utilizes background information to identify the malfunction conditions is presented. The analysis shows that the failures, including full reverse precession rub and exact one half subharmonic vibration, were caused by the oversize bearings and displacement of the rotor center due to foundation deformation and misalignment between gear shafts, etc. The corrective actions taken to alleviate excessive vibration and the problems which remain to be solved are also presented