Stereographic Projections of Symmetry Elements and Single Forms on Quasicrystals

In total, there are 12 systems, 60 point groups and 89 single forms in crystals and quasicrystals. Among them, 5 new systems, 28 new point groups and 42 new single forms belong to quasicrystals, while the other 7 systems, 32 point groups and 47 single forms belong to crystals. In this paper, the point groups and single forms of quasicrystals are deduced and drawn as stereographic projections by the rules of crystallographic point groups. These stereographic projections integrate the crystal and quasicrystal symmetry theories.

Point Groups and Single Forms of Quasicrystals with Eightfold and Twelvefold Symmetry

This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.

A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Microstructure and M echanical Properties of Magnesium Alloy Sheet by Friction Heating Single Point Incremental Forming

By friction heating single point incremental forming,truncated square pyramid parts with different draw angles of a magnesium alloy AZ31 B were formed at room temperature.Metallurgical,tensile and micro-hardness tests were carried out to obtain the effects of wall angle on microstructure and mechanical properties. The results show that grain in side wall of the formed parts becomes refined significantly. Furthermore,with the increase of draw angle,grain size increases,but strength,hardness and plasticity decrease. In addition, surface roughness tests were performed on the formed surface to determine the influence of speed of forming tool. The results show that surface roughness has a little increase with the increase of tool rotational speed.

Mechanical properties and microstructure evolution in incremental forming of AA5754 and AA6061 aluminum alloys

This study performs single point incremental forming(SPIF)on two aluminum alloys(i.e.AA5754 and AA6061),and analyzes their post forming mechanical properties and microstructure evolution.The forming parameters namely wall angle(35°-55°),feed rate(1-4 m/min),spindle rotational speed(50-1000 r/min),and lubricant(grease and hydraulic oil)are varied to probe detailed processing effects.The pre-and post-SPIF mechanical properties and microstructures are characterized by conducting tensile tests and optical microscopy,respectively.It is shown that an increase in the wall angle,feed rate and rotational speed causes microscopic variations in the alloys such that the grains of AA5754 and the second phase particles of AA6061 elongate.As a result,the ultimate tensile strength of the formed parts is increased by 10%for AA5754 and by 8%for AA6061.And,the ductility of AA5754 is decreased from 22.9%to 12%and that of AA6061 is decreased from 16%to 10.7%.Regarding the lubricant effect,it is shown that the mechanical properties remain insensitive to the type of lubricant employed.These results indicate that SPIF processing modifies the microstructure of Al alloys in a way to enhance the strength at the cost of ductility.

Finite element and experimental analyses of cylindrical hole flanging in incremental forming

The influence of the size of pre-cut hole of blank on the formability of cylindrical hole flanging in single point incremental forming（SPIF） was studied. The flange is produced in four stages starting from 45° to 90° and employing aluminum as the test material. It is shown that the hole size has significant effects on the stress/strain distribution on the cylindrical flange. The magnitude of hoop strains increases and the flange thickness increases as the hole size increases. Likewise, the von Mises stress reduces with the increasing of hole size. Further, there is a threshold value of hole size（i.e., 80 mm） below which severe stresses occur, which lead to sheet fracturing thus failing the successful forming of cylindrical flange. Moreover, the formability reduces as the hole size is increased above the threshold size. Finally, it is concluded that 80 mm is the threshold size of hole for maximizing the formability of aluminum sheet in incremental hole flanging.

Single point and asymmetric incremental forming

This paper presents an update on single point incremental forming （SPIF） of sheet metal since 2005. It includes a description of the process with new information on the maximum forming angle, Фmax, for 5052-H32. An indepth example of the successful design and production of parts is given for industry. This includes discussion on production times and surface roughness with details that will help designers. A general design guide for users of SPIF is provided. It is based upon experience gained in the last decade. In general, materials show a trend of decreasing formability with increasing initial thickness. It is shown that for thicker sheet metal, it is recommended using large spherical tools （12.7 mm or larger）, or a large fiat-ended tool. The fiat-ended tool provides the best combination of good formability and very low surface roughness. For aluminum, galvanized steel and stainless steel, it is recommended using a fiat-ended tool. Advances in multi-pass techniques and information on successful and useful numerical models which predict forming behaviour are included. Finally, there is a discussion on future work needed in SPIF.

Time Modulated Array Antennas: A Review

Time-modulated array(TMA)antennas,introduce the dimension of time into antenna design to control the radiation patterns and frequency spectral characteristics,thus improve the reconfigurability of array antennas and provide multiple functional-ities.They have great application potential in military and civilian fields,such as precision guidance and mobile communication,and are currently a hot spot of academic research.This article provides a review on the fundamentals and applications of TMAs.First,the basic theory and mathematical formulations of TMAs are introduced.Second,the most important applications of TMAs,namely time-modulated phased arrays(TMPA),are discussed from the perspectives of harmonic suppression and harmonic utiliza-tion,which are used for single-beam and multibeam radiation.Then,we survey the combination of TMA with various types of novel antenna arrays,such as single-channel digital beamforming(DBF)arrays,frequency diverse arrays(FDAs),and retrodirective arrays,to create new hardware implementation methods and enhance their performance.Next,recent advances in dedicated integrated chips for TMA,which have played a significant role in driving the progress of TMAs from academic research to practical applications,are presented.Finally,the challenges and prospects for TMAs are discussed,including new research directions and emerging applica-tion scenarios.