Stereology of isolated objects with the invariator

The invariator is a new stereological design to generate motion invariant test lines in three dimensions on an isotropic plane through a fixed point. The theory has been published recently. The purpose of this paper is to illustrate the application of the invariator on a group of rat brains to estimate brain volume and external surface area. Each brain was first split into its two hemispheres and then embedded into a ball filled with agar following a configuration named the antithetic isector, with the idea of reducing the error variance. After rolling the ball at random it was scanned by magnetic resonance imaging into a stack of parallel systematic sections: this is the isotropic Cavalieri design which, combined with the antithetic isector idea, proves to be very accurate. The invariator used only an equatorial section of the ball, and in the present case the coefficient of error of the volume and surface area estimators of an individual brain was about 30%. As it is design unbiased, the invariator may prove its strength mainly to estimate population means.     

Elastic contact of rough surfaces: A simple criterion to make 2D isotropic roughness equivalent to 1D one

We analyze the periodic contact between an elastic half-space and two types of rough substrates: (i) a perfect isotropically rough rigid substrate (2D isotropic roughness), and (ii) a perfect anisotropically rough rigid substrate, i.e. a substrate with roughness in only one direction (1D roughness). The analysis is carried out with the aid of proprietary codes, that we have developed (both in real and Fourier space) to deal with this type of contacts. Of course, 1D contacts differ from 2D isotropic contacts. However, our results and theoretical arguments suggest a possible criterion to make 2D contacts equivalent to 1D ones from the point of view of contact area and separation calculations. The rule consists in replacing the 2D power spectral density (PSD) of the isotropic surface into an equivalent 1D PSD. Interestingly the transformation rule does not depend on the statistical properties of the surface roughness, hence seems to have a universal character for isotropic surfaces.     

Flowers and wedges for the stereology of particles

Recently, a new decomposition has been found for the motion invariant density of straight lines in, with applications in stereology. The new principle, called the invariator, leads to new rotational formulae which express the surface area and the volume of a bounded subset (called a 'particle') in terms of an observable functional defined in an isotropically oriented section (called a pivotal section) through a fixed point (called the pivotal point). The results have been extended to intrinsic volumes of manifolds in general space forms. The purpose of this paper is to present new results and computational formulae for three-dimensional particles. Explicit estimators are obtained for a convex polyhedral particle with a pivotal point in its interior, in terms of the coordinates of the vertices of the pivotal section. The results are applied to a population of polyhedral grains from a cemented carbide which was studied earlier by alternative methods.     

Studies on depth-of-field effects in microscopy supported by numerical simulations

Micrographs are two-dimensional (2D) representations of three-dimensional (3D) objects. When the depth-of-field of a micrograph is comparable with or larger than the characteristic dimension of objects within the micrograph, measured 2D parameters (e.g. particle number density, surface area of particles, fraction of open space) require stereological correction to determine the correct 3D values. Here, we develop a stereological theory using a differential approach to relate the 3D volume fraction and specific surface area to the 2D projected area and perimeter fractions, accounting for the influence of depth-of-field. The stereological theory is appropriate for random isotropic arrangements of non-interpenetrating particles and is valid for convex geometries (e.g. spheres, spheroids, cylinders). These geometrical assumptions allow the stereological formulae to be expressed as a set of algebraic equations incorporating a single parameter to describe particle shape that is tightly bounded between 1.5π and 2π. The stereological theory may also be applied to arrangements of interpenetrating convex particles, and for this case, the resulting stereological formulae become identical to the formulae previously presented by Miles. To test the accuracy of the stereological theory, random computational arrangements of non-interpenetrating and interpenetrating spheres or cylinders are analysed, and the projected area and perimeter fractions are numerically determined as a function of depth-of-field. The computational results show very good agreement with the theoretical predictions over a broad range of depth-of-field, volume fraction and particle geometry for both non-interpenetrating and interpenetrating particles, demonstrating the overall accuracy of the stereological theory. Applications of the stereological theory towards analysis of biological tissues and extracellular matrix are discussed.     

齿轮渐开线齿面及其三维实体建模

根据渐开线齿轮的原理和渐开线的基本性质，介绍渐开线齿轮齿廓的形成。运用计算机绘图技术按照渐开线原理建立齿轮三维模型，对较直观地认识渐开线原理和齿轮制造过程中的原理性误差有指导意义。     

Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections

Existing design-based direct length estimators require random rotation around at least one axis of the tissue specimen prior to sectioning to ensure isotropy of test probes. In some tissue it is, however, difficult or even impossible to define the region of interest, unless the tissue is sectioned in a specific, nonrandom orientation. Spatial uniform sampling with isotropic virtual planes circumvents the use of physically isotropic or vertical sections. The structure that is contained in a thick physical section is investigated with software-randomized isotropic virtual planes in volume probes in systematically sampled microscope fields using computer-assisted stereological analysis. A fixed volume of 3D space in each uniformly sampled field is probed with systematic random, isotropic virtual planes by a line that moves across the computer screen showing live video images of the microscope field when the test volume is scanned with a focal plane. The intersections between the linear structure and the virtual probes are counted with columns of two dimensional disectors.
Global spatial sampling with sets of isotropic uniform random virtual planes provides a basis for length density estimates from a set of parallel physical sections of any orientation preferred by the investigator, i.e. the simplest sampling scheme in stereology. Additional virtues include optimal conditions for reducing the estimator variance, the possibility to estimate total length directly using a fractionator design and the potential to estimate efficiently the distribution of directions from a set of parallel physical sections with arbitrary orientation.
Other implementations of the basic idea, systematic uniform sampling using probes that have total 3D × 4π freedom inside the section, and therefore independent of the position and the orientation of the physical section, are briefly discussed.     

Estimation of individual feature surface area with the vertical spatial grid

The area of an individual bounded surface (e.g. the boundary of a properly sampled cell) can be estimated from an isotropic uniform random stack of parallel sections, or of non-invasive planar scans, using the well-known spatial grid. A standing problem was to estimate the area of an individual bounded surface with an arbitrary degree of accuracy from a vertical (i.e. not isotropic) stack of sections or scans. A new tool to do this, called the ‘vertical spatial grid’, is presented.     

基于特征线的复杂曲面反求工程中的CAD建模技术

三维轮廓测量技术是实现反求工程的重要手段 ,复杂曲面建模技术是反求工程研究的重点内容。研究了激光线扫描测量原理以及“点云”数据类型。针对栅格点数据 ,提出了一种快速有效的复杂曲面建模技术 ,并以实例说明“点云”数据平滑处理、特征线提取、曲面分块及曲面构造过程     

自由曲面工件多点连续成形方法

为了实现自由曲面工件的高效率、低成本制造,分析与比较常用的柔性成形方法;从成形过程的连续性考虑,将柔性成形分为分段成形与连续成形;从变形区大小考虑,又划分为点成形、面成形与线成形等不同类型。比较不同成形方式的优点与缺点,指出自由曲面工件的高质量、高效率成形是亟待解决的技术难题。提出基于连续线成形方法的自由曲面工件高效、柔性成形思路;并提出采用多点调整式柔性辊的多点连续成形技术方案;探讨多点连续成形技术的基本原理、关键技术及主要特点。运用具有多个控制点的挠性轴设计出可弯曲、可调整的柔性辊,开发出多点卷板成形试验装置。多种三维曲面板类件的连续成形试验结果表明,多点连续成形技术能够解决自由曲面工件的高效加工难题。     

Three-dimensional topography of the matt surface in aluminium pack rolling

A model has been presented in a companion paper (Utsunomiya et al., Int. J. Mech. Sci., in press) to predict the generation of roughness on the matt surface in pack rolling of aluminium foil. This model was based on a two-dimensional (2D) finite element analysis using an isotropic plasticity model for the material. The spread of crystallographic grain orientations was simulated by ascribing different material properties to each grain. The predictions showed good qualitative agreement with experiments. It was found that the formation of shear bands causes roughening of the matt surface. The effect of material properties was further explored in Utsunomiya et al. (Int. J. Mech. Sci., in press).In the current study the model for evolution of the matt surface roughness is extended to a three-dimensional (3D) analysis and compared with predictions using a 2D analysis, a full crystallographic 3D model and experiments. The amplitude of the predicted roughness for the 3D model is lower than for the corresponding 2D analysis. In the 3D model, grains deform more uniformly due to the homogeneous constraint from adjacent grains. The predicted roughness shows good quantitative agreement with experiments, as well as with the predictions of the crystal plasticity model. The influences of grain shape and deformation mode are investigated. It is found that peaks or valleys running perpendicular to the first principal axis of strain are generated at the matt surface, regardless of initial grain shape.     

表面视觉传感器模型参数的简易标定方法

建立了基于多线结构光的表面视觉传感器的数学模型,提出了一种基于自由移动平面标定参照物的表面视觉传感器模型参数的简易标定方法。在自由移动的平面参照物上建立局部世界坐标系,将通过交比不变方法获得的各个光平面上特征点的局部世界坐标,变换到摄像机坐标系,从而获得已知三维的标定特征点。利用构建的位于不同光平面上标定特征点,可以实现工作状态的表面视觉传感器模型参数的优化估计。该标定方法降低了标定设备的成本,简化了标定过程,为表面视觉传感器的工程化应用奠定了基础。试验结果表明,该方法切实可行。     

CATIA斜齿轮全参数化曲面法三维数字建模及精度研究

依据斜齿轮机械原理基本理论,运用CATIAV5实体和高级曲面复合建模(Hybrid modeling)先进技术,提出了一种斜齿轮全参数化曲面法三维数字建模方法,构建了三维斜齿轮理论原型的参数化数字模型,并阐述了该数模的定量几何精度检验方法.为齿轮传动系统的快速三维CAD建模、运动学和动力学分析、强度有限元分析,提供了高精度的斜齿轮全参数化数字模板.     

水下双目立体视觉对应点匹配与三维重建方法研究

针对水下双目立体视觉成像稠密立体匹配因不满足空气中极线约束问题,提出一种水下对应点匹配与三维测量方法, 可将水下双目相机采集的立体图像校正为符合共面行对齐原则的图像对,再套用空气中成熟的立体匹配方法得到水下左右相 机图像视差图,从而实现水下目标的三维重建。 首先,将进入相机的所有光线总和看成光场,采用四维光场参数表达对每一条 光线建模,据此建立相机的折射成像模型和双目立体视觉模型并计算光线的方向向量;根据光线的光场表达将光线转化为点矢 量的形式,计算方向图像上任意像点对应原图像的像素坐标并确定位置映射关系。 通过插值即可快速得到符合行对齐原则的 左、右方向图像,并最终获得每条光线对应的视差图。 仿真结果表明,方向图像的行对齐误差小于 0. 8 pixel。 水池实验采用事 先标定的靶球作为目标物,利用随机散点主动投射以增加目标物表面的纹理信息,对靶球多次测量的均方根误差为 2. 8 mm,具 有较高的测量精度。     

A critical examination of nesting, bounding and memory surface/s plasticity theories under non-proportional loading conditions

This paper assesses the capabilities of Mroz's nesting surfaces plasticity model, the bounding surface model and the memory surface model under conditions of non-proportional loading path that involves a sharp bend. Simple kinematic and isotropic hardening models are also examined. Comparisons with independent test results of a bench mark problem on 304 stainless steel at room temperature show that both the nesting surfaces model and memory surface model are equally capable of adequately predicting experimental data. The next best model is the simple isotropic hardening, equipped with properly chosen yield stress and associated plastic modulus.On the other hand, the bounding surface model which employs the same material constants as the memory surface model, and the simple kinematic hardening model which employs the same constants as the isotropic hardening model, fail to predict the test results. This result indicates the importance of an isotropic hardening component in any successful constitutive plasticity theory. Furthermore, isotropic hardening characteristics should be clearly related to basic material behaviour. These features are provided by the memory surface model, which appears to be supported by experimental observations.It is observed that exact contact between yield and bounding surface cannot be ensured, owing to problems of numerical instability in the near contact position. The origins of this behaviour are briefly discussed.     

线接触滑——滚条件下微凹坑表面摩擦特性

线接触副在工程中广泛存在,且大多工作在弹性流体动压润滑状态下。为研究微凹坑对线接触摩擦副摩擦学性能的影响及表面三维表征参数与摩擦学特性之间的联系,采用激光微造型技术通过控制微凹坑面积占有率、凹坑深度、间距等参数加工制造4个表面粗糙度相同,且表面微凹坑面积占有率分别为7%、14%、21%、28%的圆柱形试件;然后使用Talysurf CCI Lite非接触式三维光学轮廓仪对试样进行三维表面测量,且采用ISO25178定义的参数对三维表面形貌进行表征;并在电气化改造后的JPM-1型双盘摩擦磨损试验机上,针对不同滑滚比、不同载荷、不同转速等工况,完成一系列线接触弹流摩擦试验。结果表明,表面形貌的微观结构特性对线接触摩擦副的摩擦特性具有明显的影响,并给出表面体积参数以及特征参数与摩擦的关系;同时,在不同的工况条件及不同的滑滚比下表面结构特性对摩擦的影响效果也不同。     

Three-dimensional finite element modelling of the scratch test for a TiN coated titanium alloy substrate

A three-dimensional (3D) finite element (FE) simulation of a rigid Rockwell C indenter scratching a TiN/Ti-6Al-4V coating/substrate system is presented. Coulomb friction between the indenter and the surface of the coating/substrate system was considered. The material properties of the coating and substrate were assumed to be elastic–plastic following a bilinear law with isotropic strain hardening. The von Mises yield criteria was used to determine the onset of plastic deformations. The scratch depth profiles at different moving distances were studied. The distributions of the stress field at the contact surface, in the coating, and at the interface of the coating/substrate system were investigated. The finite element results can be used to explain the failure modes of coated materials at the scratch test.     

常规螺杆泵定子有限元求解策略

螺杆泵定子橡胶不仅是易损构件,而且它与转子的配合状况对螺杆泵的工作性能影响显著,为此需要围绕上述问题开展相关的研究工作。目前,还没有能够直接对实际工况下的定子橡胶的变形和受力状态进行测试的有效手段,因此对螺杆泵定子进行有限元分析自然是有益的尝试。利用有限元分析软件ABAQUS,对螺杆泵定子进行研究,得出了螺杆泵定子在不同工况下的受力状态和变形规律。针对常规螺杆泵受均匀和非均匀内压情况,对空间模型与平面应变模型所求出的定子的应力、应变和内轮廓节点位移进行了比较。通过对比分析论证了三维模型和平面应变模型所求出的定子橡胶衬垫在内压作用下其内轮廓线位移是一致的。因此,在这种情况下可以用平面模型来代替三维模型,从而大幅度提高了求解效率。     

Recognition of diamond grains on surface of fine diamond grinding wheel

The accurate evaluation of grinding wheel surface topography, which is necessary for the investigation of the grinding principle, optimism, modeling, and simulation of a grinding process, significantly depends on the accurate recognition of abrasive grains from the measured wheel surface. A detailed analysis of the grain size distribution characteristics and grain profile wavelength of the fine diamond grinding wheel used for ultra-precision grinding is presented. The requirements of the spatial sampling interval and sampling area for instruments to measure the surface topography of a diamond grinding wheel are discussed. To recognize diamond grains, digital filtering is used to eliminate the high frequency disturbance from the measured 3D digital surface of the grinding wheel, the geometric features of diamond grains are then extracted from the filtered 3D digital surface, and a method based on the grain profile frequency characteristics, diamond grain curvature, and distance between two adjacent diamond grains is proposed. A 3D surface profiler based on scanning white light interferometry is used to measure the 3D surface topography of a #3000 mesh resin bonded diamond grinding wheel, and the diamond grains are then recognized from the 3D digital surface. The experimental result shows that the proposed method is reasonable and effective.     

里氏硬度全自动在线测试分选系统的研制

采用里氏硬度测试原理和机电一体化设计方法,综合应用气动技术、微机测试和通讯技术,国内首次研制成功里氏硬度全自动在线测试分选系统,实现了金属表面硬度全自动在线测试。     

Estimation of surface area and length with the orientator

The orientator is a new technique for the estimation of length and surface density and other stereological parameters using isotropic sections. It is an unbiased, design-based approach to the quantitative study of anisotropic structures such as muscle, myocardium, bone and cartilage. A simple method for the practical generation of such isotropic planes in biological specimens is described. No special technical equipment is necessary. Knowledge of an axis of anisotropy can be exploited to optimize the efficiency. To randomize directions in space, points are selected with uniform probability in a square using various combinations of simple random, stratified random, and systematic random sampling. The point patterns thus produced are mapped onto the surface of a hemisphere. The mapped points define directions of sectional planes in space. The mapping algorithm ensures that these planes arc isotropic, hence unbiased estimates of surface and length density can be obtained via the classical stereological formulae. Various implementations of the orientator are outlined: the prototype version, the orientator-gencrated ortrip, two systematic versions, and the smooth version. Orientator sections can be generated without difficulty in large specimens; we investigated human skeletal muscle, myocardium, placenta, and gut tissue. Slight practical modifications extend the applicability of the method to smaller organs like rat hearts. At the ultrastructural level, a correction procedure for the loss of anisotropic mitochondrial membranes due to oblique orientation relative to the electron beam is suggested. Other potential applications of the orientator in anisotropic structures include the estimation of individual particle surface area with isotropic nucleators, the determination of the connectivity of branching networks with isotropic disectors, and generation of isotropic sections for second-order stereology (three-dimensional pattern analysis).