Discussion on the problems related to NC machining of toroid-shaped taper cutter with constant angle between cutting edge and the cutter axis

Defining the helical angle as the angle between the cutting edge and revolving axis of the cutter presents the designing models of the cutting edge and helical groove of a toroid shaped taper cutter. Under the condition of a certain revolving speed, the relative radial and axial feeding speeds of the grinding wheel in two-axis NC machining of the cutter are deduced. The models for calculating the actual obtained groove and the simulation-method of computer are also provided.The surface near to the top of the end cutter has no helical cutting edges and infinite feeding speeds of NC machine. It is necessary to adopt a supplementary cutting edge. A supplementary cutting edge is designed as a cutting edge with a constant pitch. This paper provides valuable reference for the design and NC machining of this kind of toroid shaped taper cutter.     

Dynamic asymmetrical instability of elastic–plastic beams

Dynamic instability of elastic–plastic beam is investigated by employing a three-degree-of-freedom (3-DoF) beam model. Especially, asymmetrical instability induced by symmetrical load is discussed. The asymmetrical instability is considered as a second-order buckling mode. Four types of perturbations, i.e., geometrical misalignment, material property mismatch, unsymmetry of applied load and disturbance of boundary conditions, are introduced to activate the asymmetrical responses. The asymmetrical response is characterized by a modal participation factor α₂ which corresponds to an asymmetrical mode shape. Phase plane trajectories and Poincaré map are used to illustrate the chaotic characteristics of the beam response. Results show that if the perturbations are small enough, the perturbation type has negligible influence on the critical load for the occurrence of the asymmetrical instability, which implies that the asymmetrical instability is an intrinsic feature of the beam system. However, with the increase of the magnitude of the perturbations, the influence of the asymmetrical vibration is expanded to a large extension of loading parameter.     

Mesh generation and geometrical modelling of 3D woven composites with variable tow cross-sections

The modelling of 3D woven composites represents a key part in both material and component design. Current modelling techniques can struggle to mesh correctly accurate unit cell models and apply the complex but necessary periodic boundary conditions required, often with sacrifices made in idealisation of the weave architecture. An automated voxel meshing technique suitable for modelling failure in 3D woven composite unit cells has been developed, which is generic in nature and allows incorporation of architectural deformities within weaves, including tow rotations and misalignments. The model requires node points with only five independent variables to define the unit cell geometry. Application of a smoothing algorithm to the tow/matrix interface voxels produces a suitable surface for modelling tow/matrix debonding, leading to a more accurate representation of the stress field.     

A practical method to calibrate the slant angle of central X-ray for laminography scanning system

Computed laminography (CL) has a particular function in plate-type structure tomography. For CL reconstruction, slant angle of the central X-ray is an important parameter and must be calibrated accurately. A practical feasible calibration method to determine the slant angle is proposed. According to this method, a spherical phantom is fixed on the rotary table and turns a full 360° rotation. Then, image processing and the least-square fitting are performed to figure out the locus of the projection. Consequently, the slant angle is achieved in accordance with the property of the fitted ellipse. The experimental results prove that this method is easy to implement and meet the inspection requirements.     

Freeform texture representation and characterisation based on triangular mesh projection techniques

Texture characterisation for freeform non-Euclidean surfaces is becoming increasingly important due to the widespread of the use of such surfaces in different applications, e.g. the additive manufacturing. Four main steps are required to analyse and characterise those surfaces which include new surface representation, surface filtration and decomposition, texture representation methods and finally the calculation of the surface parameters. Recently, the representation, as well as the filtration and decomposition, of freeform surfaces have been investigated and some algorithms have been proposed. This paper, however, shed the light on how to represent the texture of freeform non-Euclidean surfaces before calculating the parameters. A novel model for freeform surface parameterisation is introduced; this new model proposes the use of a projection algorithm before the actual calculation of the parameters. Different projection algorithms have been adopted from the mesh projection techniques found in the field of computer graphics. The results of applying those algorithms to represent the texture of both simulated and bio-engineering surfaces are shown, also a comparison between those algorithms has been carried out. Furthermore, examples of calculating some of the surface parameters for freeform surfaces are given.     

A three-dimensional soil–water coupled FE analysis of hollow cylinder test concerning non-uniform deformation

The hollow cylinder shear test is somewhat controversial due to its non-uniform stresses and strains, and has been analyzed by simple theoretical methods and two-dimensional FE calculations. In this paper, the hollow cylinder test under strain control was carried out numerically by treating the specimen as a three-dimensional initial-boundary value problem considering the inertial forces. At first, besides the known nonuniform strain, the non-uniformities of excess pore water pressure and overconsolidation ratio have been shown to benefit from a soil–water coupled analysis that employs the SYS Cam-clay model. Then, the influence of the specimen geometries, including wall thicknesses, heights and outer diameters on the non-uniformity was investigated sequentially. A new method for evaluating non-uniformity was proposed, which is suitable for the three-dimensional analysis. The response under a uniform deformation field, which is indicated by “the perfect path”, was presented to draw a comparison with the apparent behaviors, with non-uniformities taken into consideration. It should be noted that there is a critical height to prevent failure at the specimen ends according to the apparent behavior. Finally, the torque-controlled experiment indicated that 4 ribs could not transfer the torque reliably while 6 or 8 ribs were feasible.     

One-pot synthesis of stable phosphonium ylides using 2-mercaptopyrimidine derivatives

The reaction of dialkyl acetylenedicarboxylates with 2-mercaptopyrimidine and 2-mercapto-4,6-dimethylpyrimidine in the presence of triphenylphosphine leads to stable phosphorus ylides in excellent yields. These stable ylides exist in solution as a mixture of two geometrical isomers as a result of restricted rotation around the carbon-carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbon group.     

CAD tools for aesthetic engineering

The role of computers and of computer-aided design tools for the creation of geometrical shapes that will be judged primarily by aesthetic considerations is reviewed. Examples are the procedural generation of abstract geometrical sculpture or the shape optimization of constrained curves and surfaces with some global ‘cost’ functional. Different possibilities for such ‘beauty functionals’ are discussed. Moreover, rapid prototyping tools based on layered manufacturing now add a new dimension to the visualization of emerging designs. Finally, true interactivity of the CAD tools allows a more effective exploration of larger parts of the design space and can thereby result in an actual amplification of the creative process.     

略论计算机辅助中学生数学空间想象能力培养

从中学数学教学时于空间想象能力的要求和在实际操作过程中的难点出发，结合当前多媒体计算机的特点，主要阐述了多媒体计算机辅助中学空间想象能力培养的五项基本原则：尽可能多地给学生展示各种几何图像和图形；给学生展示几何图形的抽象过程；为学生呈现比较图形；允许学生有比较多的机会参与几何图形操作；逐渐淡化。