Theoretical and experimental analysis of the compaction process in a tapered screw press

PhD ThesisEarlier research reported in the literature of plastic extrusion pointed out the surperiority of a tapered screw for developing high pressure in a short barrel. But the conveying process in the tapered screw and how pressure was generated were not explained. This work is intended to provide a thorough understanding of the conveying and compaction processes by a tapered screw. A complete theory of the performance of a tapered screw conveyor was developed, based on the conventional approach which assumes 'plug flow' , but with the following two modifications: the compressibility of the material was taken into account by using a pressure /density relationship which makes it possible to simulate the density change with pressure during compaction. ii. the effect of the slip of material along the screw channel wall was taken into account in the analysis by using a slip factor Po, which modifies the down channel velocity. Slip, by reducing the down channel velocity, leads to a reduction in the axial velocity and the mass flow rate of the extruder at any speed of rotation. The resulting equations express the relationship between the performances of the tapered screw (mass flow rate and pressure build up) and the screw geometries and frictional conditions. A one dimensional differential equation obtained for the pressure build up indicates that low friction between the material and the screw, and high friction between the material and the barrel can help the pressure generation process. A method measuring accurately the coefficients of friction between the material to be compacted and both the screw and the barrel is proposed. An experimental rig was designed and developed to measure the pressure in a tapered screw conveyor for different mass flow rates at four speeds of revolution in order to confirm the theory. A proposal is made for a better design of inlet to a screw conveyor. Comparisons were made between tapered and standard screw extruders with the same length, which show that the tapered screw is capable of generating a much higher pressure than the standard screw under the same operationing conditions. The experimental results indicate that the predicted pressures agree well with the measured ones.Chinese government, and British Government; ORS Award (1988-1990

Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping

In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate point and the usual approaches to bound the dimension of the entirety of attractors do not work directly. Instead, we develop a new process concerning the dimension near the degenerate point individually and show the finite dimensionality of the attractor.Comment: 33 page

Hybrid Topological Superconductivity and Hinge Majorana Flat Band in Type-II Dirac Semimetals

Type-II Dirac semimetals (DSMs) have a distinct Fermi surface topology, which allows them to host novel topological superconductivity (TSC) different from type-I DSMs. Depending on the relationship between intra- and inter-orbital electron-electron interactions, the phase diagram of superconductivity is obtained in type-II DSMs. We find that when the inter-orbital attraction is dominant, an unconventional inter-orbital intra-spin superconducting (SC) state ($B_{1u}$ and $B_{2u}$ pairing channels of $D_{4h}$ point group) is realized, yielding hybrid TSC, i.e., first- and second-order TSC exists at the same time. Further analysis reveals the Majorana flat bands on the $z$-directed hinges, which penetrate through the whole hinge Brillouin zone and link the projections of the surface helical Majorana cones at time-reversal-invariant momenta. These higher-order hinge modes are symmetry-protected and can even host strong stability against finite $C_{4z}$ rotation symmetry-breaking order. We suggest that experimental realization of these findings can be explored in transition metal dichalcogenides