基于区域法的表面形貌滤波

表面形貌的区域法评定与其二维轮廓评定相比,更能体现表面的真实情况。表面形貌的区域法滤波是对其进行区域法评定的基础。文中对最小二乘平面滤波、多项式曲面拟合滤波和三维高斯滤波3种典型的区域法表面滤波技术进行了算法实现,实测结果表明了所开发算法的准确性。     

W-M函数模型下表面轮廓形貌的变化规律

通过将分形理论引入摩擦学,利用分形理论对表面形貌的分形特点即表面形貌的自相似性进行研究。在运用Matlab软件建立W-M函数模型的前提下对表面轮廓形貌进行二维及三维的模拟仿真分析,借此以二维以及三维模型中轮廓曲线随维数D、系数G及特征粗糙度Ra*的变化规律进行探究。最终证明了对分形维数D造成影响的主要因素为表面轮廓的复杂程度且系数G与表面轮廓高度呈正比关系,对于三维模型存在着随着分形维数D的增大则所获得的表面轮廓形貌越来越趋于复杂的规律。     

基于小波的零件表面微观形貌多尺度重构

采用激光测量仪对车削机加工零件表面进行测量,获得零件亚纳米级的微观形貌数据,利用小波分析分时分频精细表达以及多分辨率分析的特点,建立粗糙表面多尺度重构模型,对基于真实测量数据的微观表面进行宏微观重构,并提出在不同尺度上提取粗糙表面的微凸体以精简数据的方法,从而实现在MATLAB和Pro/E中的微观表面建模仿真。提取的低频成分为零件表面二维和三维评定提供了基准,不同尺度上微观粗糙表面的重构为在不同精密等级上分析机加工工艺对零件表面粗糙度的影响提供了方法,Pro/E中重构的表面为有限元分析零件宏微观几何形貌与摩擦、润滑和密封的关联机制提供了几何模型。     

过盈配合单向分形界面微观接触面积研究

通过对模拟压缩机叶轮和轴过盈配合的试件表面轮廓进行分析,发现切削加工的粗糙配合表面具有单向粗糙度特征,同时垂直加工纹理方向的表面轮廓具有明显分形特性。基于M-B分形接触的修正模型,建立了具有单向粗糙度分形特征表面的理论接触模型,推导出接触面积与法向载荷的函数关系式。结合真实粗糙表面,建立了具有分形特性的单向粗糙度实体模型,利用有限元分析软件对实体模型进行了仿真分析,验证了接触面积与法向载荷函数关系的正确性。     

高斯滤波技术提取表面粗糙度信息

在传统高斯滤波理论的基础上,提出稳健高斯滤波算法,引入M估计中的权函数对高斯滤波进行稳健处理,并结合高斯滤波逼近理论,在高斯滤波稳健算法基础上,构建高斯滤波的算法模型和零件表面形貌特征模型。利用MALTAB软件编程和仿真模拟系统,模拟出零件表面原始轮廓信号,并采用simulink系统仿真设计出FIR型数字高斯滤波器。将原始轮廓信号通过高斯滤波器,通过一次有效滤波分离提取出零件表面的粗糙度信号和滤波中线,实现高斯滤波的过程,提取粗糙度信息来评定零件表面质量。     

齿轮齿面的分形模拟

任何加工精度下的齿轮齿面都不会是绝对光滑的,而是有粗糙度的,对于磨削加工的齿轮齿面而言,表面粗糙度在加工纹理的方向和垂直于加工纹理的方向是异性的。而目前基于W-M函数分形模拟的二维粗糙表面轮廓曲线和三维粗糙表面都是针对于各向同性的表面,因此提出利用两个WM函数叠加来分形模拟各向异性齿轮齿面的方法。模拟结果表明,此方法可以很好地模拟两个方向具有不同分形维数和特征尺度系数的粗糙表面,通过改变分形维数和特征尺度系数可以有效控制齿轮齿面的纹理。     

粗糙表面几何形貌特征的分形参数描述

采用分形参数研究表面粗糙度对粗糙表面轮廓几何形貌的影响规律。结合表面粗糙度加工参数和随机抽样方法,模拟得到服从正态分布和预设粗糙度的表面轮廓曲线,根据统计得到的模拟轮廓曲线几何形态共性特征,建立基于平均峰角和平均峰高的等腰三角形轮廓曲线分形模型。采用剖面位形法通过轮廓曲线总长及其相应分形标度获得不同轮廓算术平均偏差下的分形维数,通过幂律拟合得到分形维数与表面粗糙度间的函数关系。在同一表面粗糙度下用数学软件回归得到分形标度与平均峰角的数学表达式,同时建立数学表达式中相关参数与分形维数间的函数关系,最终得到表面粗糙度在0.1-1.6 μm范围内的粗糙表面轮廓几何形貌特征值（平均峰角和平均峰高）的分形参数（分形维数和分形标度）描述公式。     

三维表面粗糙度的均方根斜率评定

基于分形几何理论,通过分析随机表面的轮廓谱矩和表面谱矩的特性,提出了三维粗糙表面的均方根斜率评定方法,并用平磨样块试验证实了该法的正确性。     

表面形貌评定方法对比分析

表面形貌特征直接影响了零件的使用功能和技术性能,为了能合理地对表面形貌特征参数进行评估,分析了传统的最小二乘拟合法和经典的高斯滤波法对表面轮廓参数的评估,讨论了最小二乘拟合和高斯滤波法在评估中所存在的不足。根据表面形貌的综合成分,建立表面形貌的数学模型,首次运用B样条小波分析实现了表面形貌数学模型的小波构建。通过小波的分解与重构原理,分离出表面形貌评定基准线。通过工程实例对比分析,验证了B样条小波对表面形貌多尺度分析的合理性,其结果与实际值的误差最小。     

滚动轴承零件表面的小波模拟与表征

建立了模拟粗糙表面的小波模型,该模型可生成各向同性高斯表面、各向异性高斯表面;分析了模拟表面的统计参数和自相关函数;验证了该模型的正确性和有效性。小波模型与Johnson转换系统结合,模拟了给定偏态、峰态的非高斯表面,结果显示目标值和模拟值吻合。另外,将支承面曲线从二维推广到三维,研究表明三维支承面曲线能够更加准确反映表面真实信息;定义的粗糙峰曲线和空穴曲线为未来研究粗糙表面微润滑、微摩擦、微磨损提供基础。     

An Analysis of the Multiscale Structure of Surfaces with Various Finishes

Even with the various surface finishing techniques, all surfaces are rough with different structures and geometric characteristics over multiple scales. In this work, a profilometer is utilized to measure the profiles of different rough surfaces, and the profiles are characterized using a variety of statistical, spectral, and fractal methodologies. Three different methods are implemented in calculating the fractal dimension, D, and these three methods are then compared. The relationship between the fractal dimension and the fractal scaling constant, G, is investigated as well. The measured rough profiles are also compared with Weierstrass-Mandelbrot (W-M) function–generated rough profiles using the characterization results of the measured profiles. After comparing a series of statistical and fractal parameters, which are calculated based on the surface profile data of the original and regenerated profiles, it can be found that the W-M function does not always appear to be very suitable for representing measured rough profiles. Another important conclusion is that many measured profiles are not always consistent with the quality of self-affinity that many of the popular fractal models assume. Therefore, a discrepancy exists between idealized fractal equations and real profiles. However, these findings are limited to the measurement resolution and specific surfaces considered in this work.     

表面形貌的研究现状及发展趋势

对国内外表面形貌测量仪器、表征方法研究情况进行了阐述,并指出了其发展趋势。随着纳米技术、激光测量等相关技术的发展和新的先进数学方法,如分形理论、小波分析等应用于表面表征中,表面测量仪器、表征方法也越来越多;二维参数表征已不能满足工程界的要求,三维表征参数将取代原来的二维参数;粗糙表面的分形特性研究主要集中在机加工表面与磨损表面,开展密封表面的分形特性研究将大大促进密封技术的发展。     

粗糙表面分形特征的模拟及其表征

为了研究工程表面具有分形的特性,即在不同尺度下具有统计自相似性,探讨粗糙表面的分形特征,用随机中点位移和Weierstrass-Mandelbrot函数两种方法对轮廓和表面进行模拟,并对表面轮廓进行幂率谱分析,建立分形维数和幂率谱的关系,检验计算表明模拟表面的分形维数和指定值吻合良好。讨论分形参数的尺寸独立性和分形表面的统计特征,从幂率谱图可以看出,单分形的幂率谱图为一个区段,而双分形表面的幂率谱呈现明显的两个区段,不同尺度下的分形维数体现在其幂率谱图形上。与传统的统计参数相比,分形维数和特征尺度具有一定程度尺寸独立性。统计检验表明两种方法模拟的表面均符合近似的高斯分布。指出粗糙表面完整的描述和表征应兼顾分形和统计特征两个方面。     

Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled composite hole wall

In this paper, an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall. This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors. Hole profiles in 24 directions are measured. Fractal parameters are calculated to evaluate the measured surface profiles. The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07, whereas the maximum and minimum fractal roughness are 4.05 × 10 ⁻⁵ and 4.36 × 10 ⁻¹⁰ m, respectively. Based on the two-dimensional evaluation results, three-dimensional surface topographies in five typical angles (0°, 45°, 90°, 135°, and 165°) are reconstructed using the improved model. Fractal parameter D _s and statistical parameters Sa, Sq, and Sz are used to evaluate the reconstructed surfaces. Average error of D _s, Sa, Sq, and Sz between the measured surfaces and the reconstructed surfaces are 1.53%, 3.60%, 5.60%, and 9.47%, respectively. Compared with the model in published literature, the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface. Comparative results prove that the proposed model for calculating contraction factors is more reasonable.     

Fractal prediction model of thermal contact conductance of rough surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces,which has been widely studied since last few decades,and for predicting which many theoretical models have been established.However,the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity.In this paper,a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes:elastic,elastoplastic and fully plastic.Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model.The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area.The larger the fractal dimension,or the smaller the fractal roughness,the larger the thermal contact conductance is.The thermal contact conductance increases with decreasing the ratio of Young’s elastic modulus to the microhardness.The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface,which provide certain reference to the further study on the issue of heat transfer between contact surfaces.     

An Elastic-plastic Adhesion Model for Contacting Fractal Rough Surface and Perfectly Wetted Plane with Meniscus

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a micro-sized interface.Today, more and more research works are devoted to understand the adhesion mechanism. This paper concerns the elastic-plastic adhesion of a fractal rough surface contacting with a perfectly wetted rigid plane. The topography of rough surface is modeled with a two-variable Weierstrass-Mandelbrot fractal function. The Laplace pressure is dealt with the Dugdale approximation. Then the adhesion model of the plastically deformed asperities with meniscus can be established with the fractal microcontact model. According to the plastic flow criterion, the elastic-plastic adhesion model of the contacting rough surfaces with meniscus can be solved by combining the Maugis-Dugdale (MD) model and its extension with the Morrow method. The necessity for considering the asperities' plastic deformation has been validated by comparing the simulation result of the presented model with that of the elastic adhesion model. The stiction mechanism of rough surfaces with meniscus is also discussed.     

粗糙表面轮廓分形维数的计算方法

通过对表面轮廓分形和分形曲线的基本概念阐述,针对目前常用于表面轮廓分形维数的五种计算方法进行比较、分析和评价,认为结构函数法计算的分形维数偏差较小,是目前进行表面轮廓分形维数计算的一种可行方法,并为粗糙表面分形维数计算提供了方法和思路。     

分形粗糙表面的计算机模拟

借助MATLAB软件强大的数值计算功能、UG软件强大的几何建模功能以及ANSYS软件的网格划分功能,采用将三者结合的分析方法,对分形粗糙表面进行模拟,快速建立了具有分形特征粗糙表面的三维有限元模型。应用该方法,可有效地为具有分形特征的粗糙表面间接触的有限元分析提供依据。