Research status and prospects of the fractal analysis of metal material surfaces and interfaces

As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.

Reconstructing DEM using TLS point cloud data and NURBS surface

Underground coal mining inevitably results in land surface subsidence.Acquiring information on land surface subsidence is important in the detection of surface change.However,conventional data acquisition techniques cannot always retrieve information on whole subsidence area.This study focuses on the reconstruction of a digital elevation model（DEM） with terrestrial laser scanning（TLS） point cloud data.Firstly,the methodology of the DEM with terrestrial 3-dimensional laser scanning is introduced.Then,a DEM modeling approach that involves the application of curved non-uniform rational B-splines（NURBS） surface is put forward.Finally,the performance of the DEM modeling approach with different surface inverse methods is demonstrated.The results indicate that the DEM based on the point cloud data and curved NURBS surface can achieve satisfactory accuracy.In addition,the performance of the hyperbolic paraboloid appears to be better than that of the elliptic paraboloid.The reconstructed DEM is continuous and can easily be integrated into other programs.Such features are of great importance in monitoring dynamic ground surface subsidence.

基于NURBS曲面的小麦叶片三维重建

针对小麦叶片三维可视化不易实现的问题,通过NURBS曲面算法对小麦叶片进行三维重建。实测小麦叶片长度、叶片宽度、茎叶夹角、叶鞘长度、叶鞘直径等具体数据,通过主脉控制点算法计算叶片和叶鞘的主脉控制点信息,根据叶片宽度、叶鞘直径等信息计算出全部控制点信息,在visual studio中使用OpenGL构建小麦叶片三维模型。本研究算法得出的小麦叶片模型与真实小麦叶片有较高的相似度,较好地体现了叶片的弯曲度,真实地反映了作物叶片的形态信息。基于NURBS曲面的三维重建控制灵活、使用方便、计算简单,在作物的三维建模方面有较好的应用和参考价值。

NON-CONTACT MEASUREMENT SYSTEM OF FREEFORM SURFACE AND NURBS RECONSTRUCTION OF MEASUREMENT POINTS

Based on the development of the non-contact measurement system of free-formsurface, NURBS reconstruction of measurement points of freeform surface is effectively realized bymodifying the objective function and recursive procedure and calculating the optimum number ofcontrol points. The reconstruction precision is evaluated through Ja-cobi's transformation method.The feasibility of the measurement system and effectiveness of the reconstruction algorithm aboveare proved by experiment.

A Real-time NURBS Surface Interpolator for 5-axis Surface Machining

A real-time non-uniform rational B-spline （NURBS） surface interpolator is proposed and 5-axis machining method with a flat-end cutter is discussed. With the Taylor expansion and the coordinate transformation, the algorithms of NURBS interpolation, cutter effective machining radius, cutter offsetting and.inverse kinematics are deduced and implemented, respectively. Different from the conventional free-form surface machining, the proposed interpolator can real-time generate the motion commands of computer numerical control （CNC） machines with CC feedrate, rather than that of CL. An example part surface is demonstrated and the results of simulation show that the proposed method can be applied in actual 5-axis surface machining.

RESEARCH ON NURBS SKINNING SURFACE VIA COMPLEX CURVES

In order to design the production with complex external shapes, a newmethod is put forward using non-uniform rational B-spline(NURBS)curves to unifythe description of complex curves composed of several segments with different degrees,and then these complex curves are used to construct NURBS skinning surface. Somekinds of skills are used to dispose the knot of NURBS curves and surfaces for practicalproblems. Finally, the method is verified by several complex examples.

DIAGONAL POINT BY POINT SURFACE DEVELOPMENT METHOD BASED ON NURBS SURFACE FOR BLANK SHAPE ESTIMATION OFCOVER PANEL

According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.

运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补

为满足工业机器人高精度复杂曲线运动的需求,本文提出运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补算法.首先,根据轨迹最大轮廓误差和机器人动力学特性对曲线分段.随后,提出优化回溯算法,使各子曲线段均可用S曲线加减速规划.之后,为保证机器人在进给速度极小值处不超速,将各加减速阶段运行时间调整为插补周期的整数倍,并对子曲线段衔接处速度平滑处理.最后,提出模型迭代寻优曲线插补,大大降低了速度波动率.仿真试验表明,该方法插补轨迹的各项指标均满足要求且最大速度波动率仅为0.000099%.真机试验也验证了该方法可有效减小轨迹误差.

基于双NURBS曲线的叶轮叶片工业机器人GMAW增材制造

以双NURBS曲线获得的直纹面广泛存在于各行业复杂零件中,如何实现复杂直纹面的增材制造一直是增材制造领域中极为关心的问题。以双NURBS曲线描述叶片模型,进一步获得直纹面,采用优化工艺参数,以GMAW方法实现了叶轮叶片的增材制造,增材获得的叶片完整,成形良好,表明以GMAW工艺实现双NURBS曲线叶片增材制造是可行的。为叶片模型构建、复杂形状叶片的电弧增材制造提供了新方法,对复杂形状零件增材制造过程控制具有借鉴意义。

NURBS Parameterization for Medical Surface Reconstruction

InVesalius is an open-source software for reconstruction of computed tomography and magnetic resonance images, which allows the user to make analysis and segmentation of virtual anatomical models. Physical models can be printed with the aid of rapid prototyping, giving the medical community a reliable instrument to help planning surgeries. To offer the user more control over the model, this work describes a methodology and tool developed for NURBS parameterization that provides mechanisms for adjusting the shape or even selecting a particular region of interest of the surface. Furthermore, the tool gives the option to export the final results of the process to a STEP file, which allows further edition in any well-known CAD software.

NURBS体参数化模型的无支撑打印算法

处理大角度悬垂结构的打印问题是无支撑打印的主要挑战。针对NURBS(non-uniform rational B-spline)体参数化模型的多自由度无支撑三维打印技术,提出一种锥形切片算法。通过对模型的三维文件进行几何映射,利用水平切片算法对其进行切片,得到模型变形后的连续打印路径G-code;然后对得到的G-code进行逆映射,生成适用于六轴机械臂的多自由度连续打印路径。利用锥形切片算法规划打印路径,可以在无须支撑的情况下,依靠自支撑结构实现对悬空结构部分的打印。最后,通过仿真实验和对比实验,验证了锥形切片算法的准确性、可行性和有效性。锥形切片算法的引入为NURBS体参数化模型的无支撑三维打印提供了一种更加高效、经济和环保的解决方案。

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.

Symmetric alteration of four knots of B-spline and NURBS surfaces

Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

IMPROVED DELAUNAY TRIANGULATION FOR TRIMMED NURBS SURFACE

An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.

Reconstructing NURBS Surface with Features

The method of reconstructing NURBS surface with features is proposed in this paper. Features including boundary curves and feature points are recognized from the scanned data. An initial surface is constructed with boundary curves. The desired NURBS is determined by modifying the initial surface to pass through feature points. Lagrange multiplier is used to find the solution. The error analysis is then done. Examples are given to verify the algorithm at last. The method can keep some features fixed and be widely used in CAD modeling.

Numerical Aspects of Isogeometric Boundary Element Methods:(Nearly)Singular Quadrature,Trimmed NURBS and Surface Crack Modeling

This work presents some numerical aspects of isogeometric boundary element methods(IGABEM).The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface.Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis.Then a numerical implementation of IGABEM on the trimmed NURBS is detailed.Based on this idea,the surface crack problem is modeled incorporation with the phantom element method.The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.

基于改进NURBS和Delta并联机器人的食品分拣轨迹优化

[目的]降低Delta机器人在食品分拣轨迹中的运行时间和冲击,提高Delta机器人运行效率和稳定性。[方法]在分析食品分拣系统(应用Delta机器人)的基础上,提出了一种结合NURBS算法、麻雀搜索算法和蝴蝶优化算法的Delta机器人食品分拣轨迹优化方法。以运行时间和冲击最小化为目标对NURBS曲线规划的Delta机器人运行轨迹进行优化,结合麻雀搜索算法和蝴蝶优化算法求解模型,实现Delta机器人分拣轨迹优化。通过试验对Delta机器人分拣轨迹的运行时间和冲击进行分析。[结果]所提Delta机器人分拣轨迹优化方法可以兼顾运行时间和冲击,运行时间降低6.00%以上,运行冲击降低80.00%以上,系统的动态抓取成功率在99.00%以上,可满足食品分选要求。[结论]通过运行时间和冲击综合最优对NURBS曲线进行优化,可以有效提高Delta机器人食品分拣性能。

基于NURBS曲线拟合的渐开线圆柱齿轮齿形偏差计算

为了提高现有齿轮齿廓曲线的拟合精度,针对现有的齿形偏差计算方法,提出了一种基于非均匀有理B样条(NURBS)曲线拟合的渐开线圆柱齿轮齿形偏差计算方法。首先,建立渐开线圆柱齿轮齿形误差的理论数学模型,然后根据NURBS曲线拟合原理和三坐标测量机测量的齿廓坐标点,用Matlab编程实现了NURBS曲线对实际齿廓曲线的拟合,结合渐开线等效拟合法,计算出了齿轮的齿形偏差。拟合结果表明,与最小二乘法(LS)的拟合结果对比,NURBS曲线拟合齿廓曲线精度更高,误差小,具有良好的拟合效果。齿形偏差计算结果表明,采用的基于NURBS曲线拟合的齿形偏差与实测值一致,表明该方法准确、有效。

Triboelectric‘electrostatic tweezers'for manipulating droplets on lubricated slippery surfaces prepared by femtosecond laser processing

The use of‘Electrostatic tweezers'is a promising tool for droplet manipulation,but it faces many limitations in manipulating droplets on superhydrophobic surfaces.Here,we achieve noncontact and multifunctional droplet manipulation on Nepenthes-inspired lubricated slippery surfaces via triboelectric electrostatic tweezers(TETs).The TET manipulation of droplets on a slippery surface has many advantages over electrostatic droplet manipulation on a superhydrophobic surface.The electrostatic field induces the redistribution of the charges inside the neutral droplet,which causes the triboelectric charged rod to drive the droplet to move forward under the electrostatic force.Positively or negatively charged droplets can also be driven by TET based on electrostatic attraction and repulsion.TET enables us to manipulate droplets under diverse conditions,including anti-gravity climb,suspended droplets,corrosive liquids,low-surface-tension liquids(e.g.ethanol with a surface tension of 22.3 mN·m^(-1)),different droplet volumes(from 100 nl to 0.5 ml),passing through narrow slits,sliding over damaged areas,on various solid substrates,and even droplets in an enclosed system.Various droplet-related applications,such as motion guidance,motion switching,droplet-based microreactions,surface cleaning,surface defogging,liquid sorting,and cell labeling,can be easily achieved with TETs.

A facile strategy for tuning the density of surface-grafted biomolecules for melt extrusion-based additive manufacturing applications

Melt extrusion-based additive manufacturing(ME-AM)is a promising technique to fabricate porous scaffolds for tissue engi-neering applications.However,most synthetic semicrystalline polymers do not possess the intrinsic biological activity required to control cell fate.Grafting of biomolecules on polymeric surfaces of AM scaffolds enhances the bioactivity of a construct;however,there are limited strategies available to control the surface density.Here,we report a strategy to tune the surface density of bioactive groups by blending a low molecular weight poly(ε-caprolactone)5k(PCL5k)containing orthogonally reactive azide groups with an unfunctionalized high molecular weight PCL75k at different ratios.Stable porous three-dimensional(3D)scaf-folds were then fabricated using a high weight percentage(75 wt.%)of the low molecular weight PCL 5k.As a proof-of-concept test,we prepared films of three different mass ratios of low and high molecular weight polymers with a thermopress and reacted with an alkynated fluorescent model compound on the surface,yielding a density of 201-561 pmol/cm^(2).Subsequently,a bone morphogenetic protein 2(BMP-2)-derived peptide was grafted onto the films comprising different blend compositions,and the effect of peptide surface density on the osteogenic differentiation of human mesenchymal stromal cells(hMSCs)was assessed.After two weeks of culturing in a basic medium,cells expressed higher levels of BMP receptor II(BMPRII)on films with the conjugated peptide.In addition,we found that alkaline phosphatase activity was only significantly enhanced on films contain-ing the highest peptide density(i.e.,561 pmol/cm^(2)),indicating the importance of the surface density.Taken together,these results emphasize that the density of surface peptides on cell differentiation must be considered at the cell-material interface.Moreover,we have presented a viable strategy for ME-AM community that desires to tune the bulk and surface functionality via blending of(modified)polymers.Furthermore,the use of alkyne-azide“click”chemistry enables spatial control over bioconjugation of many tissue-specific moieties,making this approach a versatile strategy for tissue engineering applications.