Mesoscopic particulate system assembled from three-dimensional irregular particles

Particles around us are generally in the form of irregular characteristics in shape and size. Establishing rational mesoscale models that are suitable for different types of particles is of great significance to comprehensively evaluate the mechanical properties of particulate systems assembled from irregular particles. The preponderances of previous works are mainly focused on particle simulations using regular-shaped geometries or simple polyhedrons, and little is known about quantitative characterization for the particles with complex shape characteristics. In this paper, a series of novel and efficient algorithms are presented to generate three-dimensional particulate systems assembled from particles with irregular characteristics in shape and size. According to the developed particle generation algorithm and vector-growth algorithm, the convex- and concave particles with different shape- and size configurations are obtained. Parametric analysis of corresponding algorithm parameters on the shape- and size configurations of particles are quantitatively investigated in terms of different indexes, such as sphericity, angularity and size, which provides an important guidance for the shape- and size control of irregular particles. Based on the generated irregular particles, a series of algorithms are proposed to generate the particulate systems with random spatial characteristics as well. Employing the developed compaction algorithm, mesoscopic particulate systems with different particle gradations and compactness are generated precisely. To sum up, the present particle model provides insights into capturing and studying the meso-structure characteristics and macroscopic mechanical properties of particulate systems.     

RV减速器摆线轮齿廓曲线的曲率影响因素研究

以工业机器人为例,对RV减速器摆线轮齿廓曲线的曲率的影响因素进行了研究。根据微分几何理论,建立摆线轮齿廓的数学模型,采用坐标变换方法推导出摆线齿廓方程,分析了摆线轮齿廓曲线的凹凸特性,求出拐点的数学解析式。根据摆线齿廓方程计算出曲率和曲率半径的参数表达式,最后推导出可以概括摆线针轮传动的诱导法曲率公式。以RV-20E减速器为例,求解出凹凸区间曲率最大值和最小值,并利用Matlab编制程序进行仿真,详细分析了机构的偏心距、针齿半径、针齿分布圆半径、针齿数对拐点所在位置、曲率变化快慢的影响规律。通过对摆线齿廓的曲率的仿真分析,偏心距和针齿分布圆半径对摆线齿廓的曲率影响显著,同时也会影响拐点位置的变化,针齿半径对其有一定的影响,但影响较小,并且不会影响拐点所在的位置。研究结果为科学地选择摆线轮最佳参数和摆线针轮传动的设计提供了一种理论依据,具有一定的实用价值。     

Optimizing convexity defect in a tile industry using fuzzy goal programming

In most designed experiments, the main focus is to find the factor settings that optimize a quality response regardless of engineer’s preferences about factor settings. Further, in tiles industry convexity defects result in huge quality costs as well as production losses. This research, therefore, aims at optimizing convexity defect while considering process engineers’ preferences using fuzzy goal programming (FGP). Three two-level key process factors are considered, including below-rollers temperature, above-rollers temperature, direct blow air. Experiments are conducted with two repetitions; in each the convexity is measured on four tiles. Two optimization techniques are employed to determine the combination of optimal factor settings, including the Taguchi method and latter technique. The Taguchi approach and FGP approach provide relative improvements of 61.2% and 41.2%, respectively. Although the former technique reduces convexity larger than latter approach, it failed to satisfy the preferences on the settings of process factors. In contrast, the optimal factor settings obtained using FGP completely satisfy engineers’ preferences. In conclusion, FGP successfully optimizes process performance and completely satisfies process engineers’ preferences in tiles industry.     

热轧带钢板形测量技术

介绍了热轧带钢凸度、平直度的测量技术和国内各钢铁厂凸度仪、平直度仪的设置情况,以及凸度仪和平直度仪国外生产厂商的情况.     

An energetic approach to the analysis of anisotropic hyperelastic materials

We demonstrate that for the class of anisotropic hyperelastic materials with stiffening behaviour (i.e., the stiffness increases for increasing strain), it is possible to find an approximation by means of the linear superposition of an anisotropic quadratic potential, generated by the true linear elasticity tensor of the target material, and a suitable correction potential that is isotropic and hyperelastic. The proposed method can be implemented into commercially available Finite Element software by use of featured options only. This approach is intended to provide the solution to a stress-strain problem, based entirely on energetic considerations, which ensures the convexity of the potentials, and provides a simple material characterisation procedure.     

Computing distance transformations in convex and non-convex domains

It is shown that the well known two-pass sequential local transformation algorithm for computing a distance transformation in rectangular domains may fail in some convex integer domains, but that a four-pass algorithm is sufficient in all two-dimensional convex domains. For non-convex domains the number of passes necessary is shown to be generally greater. Two propagation algorithms for computing the distance transformation are described and shown theoretically and experimentally to be computationally more efficient than the sequential local transformation algorithm in non-convex domains of complex shape. The relationship of the distance transformation in non-convex domains to some more general transformations is explored.     

Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

Gravity optimised particle filter for hand tracking

This paper presents a gravity optimised particle filter (GOPF) where the magnitude of the gravitational force for every particle is proportional to its weight. GOPF attracts nearby particles and replicates new particles as if moving the particles towards the peak of the likelihood distribution, improving the sampling efficiency. GOPF is incorporated into a technique for hand features tracking. A fast approach to hand features detection and labelling using convexity defects is also presented. Experimental results show that GOPF outperforms the standard particle filter and its variants, as well as state-of-the-art CamShift guided particle filter using a significantly reduced number of particles.     

CXFTV2: A Fortran subroutine for the discrete least squares convex approximation

A Fortan subroutine calculates the least squares approximation to n data values containing random errors subject to non-negative second divided differences (convexity). The method employs a dual active set quadratic programming technique that allows several concavities of an iterate to be corrected simultaneously, which is a distinctive feature of this calculation. A B-spline representation of the iterates reduces each active set calculation to an unconstrained minimization with fewer variables that requires only O(n) computer operations. Details in these techniques including the data structure that establishes the implementation of the method are specified. Numerical testing on a variety of data sets indicates that the subroutine is particularly efficient, terminating after a small number of active set changes, the subroutine being suitable for large numbers of data. A numerical example and its output is provided to help the use of the software.     

Some results on fuzzy (digital) convexity

The definition of fuzzy convexity is reviewed and some results on projections of convex and fuzzy convex sets are established. Digital fuzzy convexity is defined and relationships among alternative definitions are investigated.