回转曲面的可展切曲面

论文系统地提出了构造回转曲面的可展切曲面及它们间映射分析的理论与方法,建立了回转曲面可展切柱面和可展切锥面的数学模型以及曲面间的映射关系。根据回转曲面及其可展切曲面间微分长度比的理论分析,推出了映射中极值映射曲线和等距映射曲线的微分方程,通过整体和局部的变形分析,可以准确地掌握回转曲面与其可展切曲面间映射中的变形情况。     

曲面片的可展性能及其应用

通过对曲面片可展性能及其应用的研究，在文献[1]的基础上更准确地给出了可展度定量度量曲面片可展性能的概念和方法，同时给出了可展角在不可展曲面近似展开中的应用，一方面可以在曲面展开之前估计近似展开的误差，从而合理选择展开范围，另一方面，基于最佳展开基点均匀分割曲面片可展度的假设，实现了近似展开中最佳展开基点的选取。     

曲面片的可展度及其最佳展开基点

本文通过对不可展曲面近似展开误差机理的分析研究，提出了曲面片最佳展开基点和曲面片可展度的概念和实现方法。     

不可展回转曲面近似展开的精度分析

本文通过对不可展曲面近似展开的整体及局部的误差分析，准确地掌握曲面近似展开的变形规律。为提高展开样板的精度提供了理论依据，本文提出的分析方法对一般规则的曲面近似展开的精度分析也是适用的。     

斜等距曲面及其性质

详细介绍了斜等距曲面的概念及相关公式，证明了锥面和切线曲面的斜等距曲面具有有一些主要性质。     

可展面的实现方法与应用

为解决工程实际中按照已知条件构造可展面的问题，以微分几何学中单参数平面族包络理论为基础，提出了实现可展面的包络方法，即利用单参数平面族的包络来获得可展面，据此发展出按照已知可展面上一条曲线及可展面在该曲线上的法线构造可展面的方法。研究表明，该方法在按照已知条件设计可展的工程曲面方面具有创新性，操作简便，易于被工程所接受，将该方法应用于工程实际，解决了螺旋输送器的核心部件——铰龙的设计问题，使其在平面上的展开成为可能。     

基于映射理论的曲面雕塑技术

本文描述了一种建立在映射基础上的曲面雕塑技术，给出了相应的理论推导和实验图形。任意曲面的雕塑造型一直是图形学中的一个难，久，这里提出的映射方法易于实现，且保持曲面原有的几何属性及其数学上的严密性，这种数据场的映射造型技术可以实现许多复杂的形体造型，如古董、艺术、人体模型等等，更重要的是通过这种数据场变化对形体的作用及其运动过程的控制或显示起到很好的效果。     

考虑弹性变形的可展杆系结构展开分析

为了保证空间可展结构可靠运行,在展开过程分析中需同时考虑机构运动和弹性变形。首先建立可展杆系结构展开分析的基础方程式,然后基于广义逆矩阵的理论提出了空间可展杆系结构机构运动与弹性变形的混合分析新方法,解决了机构运动与弹性变形的耦合问题,取得了较好的展开分析精度。与传统的柔性多体动力学方法相比,其优点是建模简单,能够有效地跟踪大型可展杆系结构的复杂运动。编制了仿真程序进行了算例分析,验证了分析方法的有效性。     

复杂曲面铣削加工变形误差分析及切痕测量仪器开发

随着航空航天、国防等领域的装备制造要求不断提高,一大批具有复杂曲面且制造精度要求高的零件逐渐涌现.复杂曲面的加工能力已经成为检验五轴数控机床加工性能的重要指标.S形检验试件作为一种具有复杂曲面的典型试件,在其加工过程中,试件表面往往存在一定量的弹性变形误差.文章基于S试件,提出一种结合机床综合刚度的复杂曲面铣削受力变形...     

Laser surface mapping of a canister closure weld

Laser surface mapping of a canister closure weld provided data that was used to generate three-dimensional images of the weld failure. These images were invaluable in that they allowed people who did not have access to the canister to see the anomaly in great detail. This aided in the scientific examination while reducing exposure to the radiologically contaminated canister. Precise measurements from the surface maps provided useful information about the location of weld features that were used in the examination of the weld failure. Laser surface mapping proved to be a powerful addition to the nondestructive examination tools available for surface phenomena.     

A noniterative method for robustly computing the intersections between a line and a curve or surface

The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a noniterative method for computing intersections by solving a matrix singular value decomposition and an eigenvalue problem. That is, all intersection points and their parametric coordinates are determined in one-shot using only standard linear algebra techniques available in most software libraries. As a result, the introduced technique is far more robust than the widely used Newton-Raphson iteration or its variants. The maximum size of the considered matrices depends on the polynomial degree q of the shape functions and is 2q × 3q for curves and 6q² × 8q² for surfaces. The method has its origin in algebraic geometry and has here been considerably simplified with a view to widely used high-order finite elements. In addition, the method is derived from a purely linear algebra perspective without resorting to algebraic geometry terminology. A complete implementation is available from http://bitbucket.org/nitro-project/ .     

Mapping road surface features using single-camera images acquired by a mobile mapping system

Mapping road surface features, such as manholes, traffic markings, and cracks, is an essential task for transportation facility management. Although, these features can be rapidly surveyed using the latest mobile mapping techniques, a sophisticated sensor system with a complicated post-processing procedure is usually required. In this study, an efficient framework for modeling road surface features is proposed using a single camera system installed on a moving platform. First, the road surface images along a route of interest are acquired and potential objects are identified based on their shapes and recorded spectra in the images. Then, the contour pixels of the identified objects are extracted by the Canny edge detection technique. Finally, the 3D coordinates of the detected features in object space are obtained by integrating the profile-image technique and the instantaneous exterior orientation parameters of the platform. Based on the numerical results from a case study, it has been demonstrated that a fully automatic and reliable extraction of road surface features can be easily achieved by implementing the proposed approach. Consequently, the modeling of road surface features, which essentially contributes to the management of transportation facilities, can be executed in a cost-efficient manner.     

Nonlocal static analysis of a functionally graded material curved nanobeam

This article is concerned with the analytical solution for a curved nanobeam based on nonlocal elasticity. The structure is made of functionally graded (FG) material, and its property varies in accordance with a power law function through the thickness. To obtain the displacement function, the static differential equations for a curved FG beam are combined with the nonlocal Eringen stress equations. By using the direct method for solving the nonlocal force–strain and moment–curvature relations covering the distributed loads, the explicit expressions of nonlocal strains are achieved. The strain-displacement relations are also employed to find displacement field. Numerical examples with different types of boundary conditions are carried out in order to investigate the effects of nonlocal parameters, the nonhomogeneity index, and geometric characteristics.     

基于HHT变换的超光滑加工表面谱分析

Hilbert-Huang变换是最新发展起来的处理非线性非平稳信号的时频分析方法。其基本的实现分为两步,多分辨经验模态分解和瞬时频率的求解,随后可以获得信号的时—频谱。这种方法的关键部分是多分辨经验模态分解,任何复杂的信号都可以分解为有限数目并且具有一定物理意义的固有模态函数。本文针对表面粗糙度用HHT进行了分析,得出相应结论,对加工有一定的指导意义。     

The generalized Weierstrass system and an application to the study of deformations of surfaces by means of integrable hierarchies

Generalized Weierstrass representations can be used to investigate deformations of surfaces under the action of integrable hierarchies. It will be shown that the generalized Weierstrass representation of Konopelchenko leads to a linear system in a single independent space variable in the case of surfaces of revolution. This result is combined with a second linear problem with an unknown second matrix in terms of a parameter. It is then shown how an integrable hierarchy can be obtained. Solutions to this hierarchy generate deformations which preserve the surface-inducing means of generalized Weierstrass representation.     

Elasticity solution for vibration of 2‐D curved beams with variable curvatures using a spectral‐sampling surface method

An accurate spectral‐sampling surface method for the vibration analysis of 2‐D curved beams with variable curvatures and general boundary conditions is presented. The method combines the advantages of the sampling surface method and spectral method. The formulation is based on the 2‐D elasticity theory, which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced. Specifically, a set of non‐equally spaced sampling surfaces parallel to the beam's middle surface are primarily collocated along the thickness direction, and the displacements of these surfaces are chosen as fundamental beam unknowns. This fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces. Each of the fundamental beam unknowns is then invariantly expanded as Chebyshev polynomials of the first kind, and the problems are stated in variational form with the aid of the penalty technique and Lagrange multipliers, which provide complete flexibility to describe any arbitrary boundary conditions. Finally, the desired solutions are obtained by the variational operation. Copyright © 2016 John Wiley & Sons, Ltd.     

An assumed strain triangular curved solid shell element formulation for analysis of plates and shells undergoing finite rotations

A formulation for 36‐DOF assumed strain triangular solid shell element is developed for efficient analysis of plates and shells undergoing finite rotations. Higher order deformation modes described by the bubble function displacements are added to the assumed displacement field. The assumed strain field is carefully selected to alleviate locking effect. The resulting element shows little effect of membrane locking as well as shear locking, hence, it allows modelling of curved shell structures with curved elements. The kinematics of the present formulation is purely vectorial with only three translational degrees of freedom per node. Accordingly, the present element is free of small angle assumptions, and thus it allows large load increments in the geometrically non‐linear analysis. Various numerical examples demonstrate the validity and effectiveness of the present formulation. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of a stereometric structural analysis for an evaluation of surface and for a forecast of the wear of endoprothesis acetabular cups

To improve the resistance to wear and permanent deformation of polyethylene operating in a polymer/metal friction couple, initial plastic deformation of the polyethylene and its electron irradiation was applied. This contributed to a change of the polymer structure, visible already while machining when the sample surfaces were being prepared for a tribological test. The study shows that the interactions that shape the structure of polyethylene, at the same time cause adequate changes to the stereometric structure of its surface. The parameters of surface microgeometry characterize the future tribological behavior of polyethylene during its operation in a friction couple. It has been shown that an analysis of stereometric parameters may constitute the first projection of polymer wear resistance.     

Numerical analysis and experimental validation of surface roughness and morphology in honing of Inconel 718 nickel-based superalloy

Honing is an important technology for machining onboard system parts. The parts are usually made of difficult-to-machining materials, e.g., Inconel 718 superalloy. Honing can improve the finishing accuracy and surface quality. However, the selection of the honing parameters was primarily based on the results of a large number of experiments. Therefore, the establishment of a reliable model is needed to predict the honed surface roughness and morphology, and offers a theoretical direction for the choice of parameters. In the present study, a numerical simulation model was constructed for analysis of the honing process by Python. The oilstone, workpiece surface morphology and motion trajectory were discretized by Python, and the machined surface was obtained by trajectory interference. Firstly, based on the statistical analysis of the surface topography of oilstone, the shape of grains was simplified and the surface topography of oilstone was built accordingly. Then, the initial surface morphology of the workpiece was constructed and the trajectory of grains on the workpiece surface was analyzed, which showed the distribution of the removed material. Meanwhile, the plastic deformation of material was analyzed in the simulation model. The critical depth of three stages of contact between grains and workpiece was calculated by the theoretical formula: scratching, ploughing and cutting. By analyzing the distribution of bulge, the plastic deformation in ploughing and cutting stage was studied. Further, the simulated results of honed surface roughness and morphology were validated and agreed reasonably well with the honing experiment. Finally, the effects of honing process parameters, including grain size, tangential speed, axial speed, radial speed and abrasive volume percentage, on the surface roughness of the workpiece were analyzed by the simulation model. The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00422-0