基于分形、小波理论的碳纤维复合材料加工表面形貌研究
摘要
碳纤维复合材料(CFRP)具有轻质、高强、耐高温、抗腐蚀、热力学性能优良等特点,广泛应用于航空航天领域。由于CFRP具有非均质性和各向异性等特点,其切削加工表面容易出现纤维拔出、纤维破碎、纤维撕裂、表面凹坑等独有的表面形貌特征,采用传统的二维评定标准不能真实反映CFRP的加工表面形貌特征。三维表面形貌测量是当今研究的热点,但国际上尚未建立相应的三维评定标准。而且,目前用于表征加工表面形貌特征的粗糙度参数是与尺度相关的参数,其测量值的大小随测量仪器的分辨率,采样长度的改变而改变,其测量结果不能反映加工表面形貌的固有特征。
研究发现,机械加工表面具有随机、无序、自相似和自仿射等分形特性,而且分形维数是一种与尺度无关的参数,因此,使用分形理论来研究加工表面形貌成为可能。本文从CFRP加工表面的三维形貌出发,应用分形、小波理论,以加工表面SEM灰度图像为研究对象,对CFRP加工表面形貌特征进行研究,主要工作如下:
(1)将分数布朗运动引入到表面形貌的研究中,分析分数布朗运动的特性和分数布朗运动模型参数H的物理意义,利用分数布朗运动模型模拟不同H值的分形曲线和分形曲面,研究了基于SEM图像的离散分数布朗随机场模型。
(2)采用差分盒计数法(DBC)计算了CFRP加工表面图像的分形维数,结果表明,分形维数D与加工表面三维形貌密切相关,加工表面越粗糙,D越大,分形维数D能综合反映加工表面形貌的整体变化特性;引入多重分形对加工表面局部形貌特征进行分析,并利用计算的多重分形谱参数分析加工表面局部形貌的变化特性。
(3)基于离散分数布朗随机场模型对CFRP加工表面图像纹理特征进行了研究,将图像中各点像素的灰度值变为相应的分形参数值H和b,对H进行归类,对同一类的H设定为相同的灰度值,利用设定的不同灰度值对表面图像进行纹理分割,从而提取出加工表面的局部形貌特征。
(4)基于小波变换对CFRP加工表面粗糙度纹理特征的变化规律进行了分析,加工表面的粗糙度纹理变化主要反映在表面图像的高频信息部分,对表面灰度图像进行小波分解,计算分解的各细节子图像所占的能量比例,以此作为加工表面粗糙度纹理在不同方向上变化的依据。
Carbon fiber reinforced plastic composite (CFRP) has many excellent properties, such as light weight, high specific strength, high temperature resistance, corrosion resistance and so on, which is widely used in aeronautics & astronautics. Because of the inhomogeneous structure and anisotropy performance for CFRP, it appeared easily with the unique surface topography characteristics such as fiber pull-out, fiber crushing, fiber tearing, et al. The traditional 2-D evaluation standard is not suitable for CFRP anymore. At present, 3-D topography roughness is the research focus, but the corresponding 3-D evaluation standard has't been established internationally until now, and roughness parameters are relevant to scales, the measured values change with the change of the instruments's resolution and the sampling length, so that it can't reflect the intrinsic characteristic of the surface topogryphy.
Research indicates that machined surfaces have fractal characteristics of randomness, irregularity, self-similiarity and self-affinity, and fractal dimension is a kind of parameter irrelevant to scale, so it is possible to apply fractal theory for surface topography. The author of this paper goes at the 3-D surface topography of CFRP, applies the fractal & wavelet theory, takes the SEM image of the cutting surface as the research object, studies the surface topography characteristic of CFRP, the main studies are as follows:
(1) The fractal Brownian motion (FBM) is introduced to the research of surface topography, the characteristic of FBM and the physical meaning of fractal parameter H are analyzed, and fractal curves and fractal surfaces are simulated with different H. And the Discrete Fractal Brownian Random Field (DFBRF) model which based on SEM image is studied.
(2) The surface fractal dimensions are calculated with the differential box-counting (DBC) method. The results show that the fractal dimension D are closely related 3-D topography of the machined surfaces of CFRP, the rougher the surfaces, the bigger the D, fractal dimension can synthetically evaluated the whole surface topography characteristic. In order to analyze the local topogryphy characteristic of CFRP cutting surfaces, multi-fractal is introduced, the multi-fractal spectrums of the images are calculated, and the multi-fractal spectrum parameters are used to analyze the partial topography change characteristic of the cutting surfaces.
(3) The study on the surface texture feature of CFRP is based on DFBRF, the gray values of the SEM images are changed into the fractal parameters H & b, and then fractal parameters H are classified, the same gray value is endowed with when H is in one class, the image surface texture is segmented into different blocks by the new different gray value, so that the local topography characteristics of CFRP cutting surfaces are extracted.
(4) The study on the change of the surface roughness texture for CFRP is based on wavelet transform. The SEM image is decomposed by using Daubechies wavelet, the energy proportions of the decomposed subimages are calculated, and the energy proportions of the decomposed high frequency subimages are regarded as the change basis of the surface roughness texture in defferent directions.
研究发现,机械加工表面具有随机、无序、自相似和自仿射等分形特性,而且分形维数是一种与尺度无关的参数,因此,使用分形理论来研究加工表面形貌成为可能。本文从CFRP加工表面的三维形貌出发,应用分形、小波理论,以加工表面SEM灰度图像为研究对象,对CFRP加工表面形貌特征进行研究,主要工作如下:
(1)将分数布朗运动引入到表面形貌的研究中,分析分数布朗运动的特性和分数布朗运动模型参数H的物理意义,利用分数布朗运动模型模拟不同H值的分形曲线和分形曲面,研究了基于SEM图像的离散分数布朗随机场模型。
(2)采用差分盒计数法(DBC)计算了CFRP加工表面图像的分形维数,结果表明,分形维数D与加工表面三维形貌密切相关,加工表面越粗糙,D越大,分形维数D能综合反映加工表面形貌的整体变化特性;引入多重分形对加工表面局部形貌特征进行分析,并利用计算的多重分形谱参数分析加工表面局部形貌的变化特性。
(3)基于离散分数布朗随机场模型对CFRP加工表面图像纹理特征进行了研究,将图像中各点像素的灰度值变为相应的分形参数值H和b,对H进行归类,对同一类的H设定为相同的灰度值,利用设定的不同灰度值对表面图像进行纹理分割,从而提取出加工表面的局部形貌特征。
(4)基于小波变换对CFRP加工表面粗糙度纹理特征的变化规律进行了分析,加工表面的粗糙度纹理变化主要反映在表面图像的高频信息部分,对表面灰度图像进行小波分解,计算分解的各细节子图像所占的能量比例,以此作为加工表面粗糙度纹理在不同方向上变化的依据。
Carbon fiber reinforced plastic composite (CFRP) has many excellent properties, such as light weight, high specific strength, high temperature resistance, corrosion resistance and so on, which is widely used in aeronautics & astronautics. Because of the inhomogeneous structure and anisotropy performance for CFRP, it appeared easily with the unique surface topography characteristics such as fiber pull-out, fiber crushing, fiber tearing, et al. The traditional 2-D evaluation standard is not suitable for CFRP anymore. At present, 3-D topography roughness is the research focus, but the corresponding 3-D evaluation standard has't been established internationally until now, and roughness parameters are relevant to scales, the measured values change with the change of the instruments's resolution and the sampling length, so that it can't reflect the intrinsic characteristic of the surface topogryphy.
Research indicates that machined surfaces have fractal characteristics of randomness, irregularity, self-similiarity and self-affinity, and fractal dimension is a kind of parameter irrelevant to scale, so it is possible to apply fractal theory for surface topography. The author of this paper goes at the 3-D surface topography of CFRP, applies the fractal & wavelet theory, takes the SEM image of the cutting surface as the research object, studies the surface topography characteristic of CFRP, the main studies are as follows:
(1) The fractal Brownian motion (FBM) is introduced to the research of surface topography, the characteristic of FBM and the physical meaning of fractal parameter H are analyzed, and fractal curves and fractal surfaces are simulated with different H. And the Discrete Fractal Brownian Random Field (DFBRF) model which based on SEM image is studied.
(2) The surface fractal dimensions are calculated with the differential box-counting (DBC) method. The results show that the fractal dimension D are closely related 3-D topography of the machined surfaces of CFRP, the rougher the surfaces, the bigger the D, fractal dimension can synthetically evaluated the whole surface topography characteristic. In order to analyze the local topogryphy characteristic of CFRP cutting surfaces, multi-fractal is introduced, the multi-fractal spectrums of the images are calculated, and the multi-fractal spectrum parameters are used to analyze the partial topography change characteristic of the cutting surfaces.
(3) The study on the surface texture feature of CFRP is based on DFBRF, the gray values of the SEM images are changed into the fractal parameters H & b, and then fractal parameters H are classified, the same gray value is endowed with when H is in one class, the image surface texture is segmented into different blocks by the new different gray value, so that the local topography characteristics of CFRP cutting surfaces are extracted.
(4) The study on the change of the surface roughness texture for CFRP is based on wavelet transform. The SEM image is decomposed by using Daubechies wavelet, the energy proportions of the decomposed subimages are calculated, and the energy proportions of the decomposed high frequency subimages are regarded as the change basis of the surface roughness texture in defferent directions.
引文
[1]黄凤萍,李缨.碳纤维及其复合材料的发展.陶瓷.2005,(10):11-16.
[2]Sreejith,P S,Krishnamurthy,R,Malhotra,S K,et al.Evaluation of PCD tool performance during machining of carbon/phenolic ablative composites.Journal of Materials Processing Technology.2000,104(1-2):53-58.
[3]Sherrington,I,Smith,E H.Modern measurement techniques in surface metrology:part Ⅰ;stylus instruments,electron microscopy and non-optical comparators.Wear.1988,125(3):271-288.
[4]Mandelbrot,B B.The Fractal Geometry of Nature.NewYork:W.H.Freeman and Company,1982.
[5]林夏水.分形的哲学漫步.北京:首都师范大学出版社,1999.
[6]Majumdar,A,Tien,C L.Fractal characterization and simulation of rough surfaces.Wear.1990,136(2):313-327.
[7]Stupak,P R,Kang,J H,Donovan,J A.Fractal characteristics of rubber wear surfaces as a function of load and velocity.Wear.1990,141(1):73-84.
[8]Brown,C A,Savary,G.Describing ground surface texture using contact profilometry and fractal analysis.Wear.1991,141(2):211-226.
[9]费斌,王海容,蒋庄德.机械加工表面分形特性的研究.西安交通大学学报.1998,32(5):83-86.
[10]陈国安,葛世荣,王军祥.分形理论在摩擦学研究中的应用.摩擦学学报.1998,18(2):179-184.
[11]孙洪军,赵丽红.分形理论的产生及其应用.辽宁工学院学报.2005,25(2):113-117.
[12]全燕鸣,叶邦彦.复合材料的切削加工表面结构与表面粗糙度.复合材料学报.2001,18(4):128-132.
[13]全燕鸣,周泽华.硬脆颗粒增强铝基复合材料的已切削加工表面形貌及影响因素.中国机械工程.1998,9(7):9-11.
[14]于思荣,何镇明,陈凯.ZA22/Al_2O_3复合材料切削加工表面质量的研究.复合材料学报.1996,13(3):60-64.
[15]Sahina,Y,Kokb,M,Celikc,H.Tool wear and surface roughness of Al_2O_3particle-reinforced aluminium alloy composites.Journal of Materials Processing Technology.2002,(128):280-291.
[16]Ciftci,I,Turker,M,Seker,U.Evaluation of tool wear when machining SiCp-reinforced Al-2014 alloy matrix composites.Materials and Design.2004,25(3):251-255.
[17]An,S-O,Lee,E-S,Noh,S-L.A study on the cutting characteristics of glass fiber reinforced plastics with respect to tool materials and geometries.Journal of Materials Processing Technology.1997,68(1):60-67.
[18]杨文堂,杨明勇,王林丰.炭/炭复合材料机轮刹车盘磨削加工方案分析.湖南冶金.2006,34(2):3-7.
[19]蒋建纯,熊翔,杨文堂等.炭/炭复合材料切削加工试验研究.粉末冶金材料科学与工程.2000,5(3):210-214.
[20]张厚江,陈五一,陈鼎昌.碳纤维复合材料的钻削加工.新技术新工艺.1998,(5):16-18.
[21]赵福令,艾传智,杨东军等.碳/碳复合材料切削表面粗糙度的评定方法及评定参数研究.计量学报.2006,27(3):206-211.
[22]艾传智,杨东军,赵福令等.C/C复合材料切削表面粗糙度的测量评定与影响因素研究.航空精密制造技术.2005,41(6):31-34.
[23]杨东军,艾传智,赵福令等.复合材料车削表面2D分析和3D分析的对比研究.机械设计与制造.2006,(1):133-134.
[24]Sreejith,P S,Krishnamurthy,R,Narayanasamy,K,et al.Studies on the machining of carbon/phenolic ablative composites.Journal of Materials Processing Technology.1999,88(1-3):43-50.
[25]Wang,X M,Zhang,L C.An experimental investigation into the orthogonal cutting of unidirectional fibre reinforced plastics.International Journal of Machine Tools and Manufacture.2003,43(10):1015-1022.
[26]Davim,J P,Reis,P.Damage and dimensional precision on milling carbon fiber-reinforced plastics using design experiments.Journal of Materials Processing Technology.2005,160(2):160-167.
[27]Ferreira,J R,Coppini,N L,Levy Nero,F.Characteristics of carbon-carbon composite turning.Journal of Materials Processing Technology.2001,109(1-2):65-71.
[28]李成贵,董申.表面粗糙度的现状及发展.航空精密制造技术.1999,35(5):1-4.
[29]毛起广.表面粗糙度的评定和测量.北京:机械工业出版社,1991.
[30]俞汉清.表面粗糙度标准及其应用.北京:中国计量出版社,1997.
[31]Huang,Y Y,Wu,S M.Grinding surface characterization by CEST.International Journal of Machine Tool Design and Research.1986,26(4):431-444.
[32]黄逸云.三维随机表面形貌的识别.浙江大学学报.1984,18(2):138-148.
[33]Lin,T Y,Blunt,L,Stout,K J.Determination of proper frequency bandwidth for 3D topography measurement using spectral analysis.Part Ⅰ:isotropic surfaces.Wear.1993,166(2):221-232.
[34]T.Klimczak.Three-dimensional characteristic of surface texture,proc 8th Int.conf.of Chemnitz Tech,University Chemnitz.1988.
[35]W P Dong.The development of anintergrated approach to 3D surface finish assessment.Int.conf.of Chemnitz Tech,University Chemnitz.1991.
[36]SAYLES,R S,THOMAS,T R.Surface topography as a nonstationary random process,nature.1978,271(2):431-434.
[37]蒋向前,L.Blunt.三维表面测量的发展.工程设计.2000:98-100.
[38]Stout,K,Blunt,L,Dong,W,et al.Development of Methods for the Characterisation of Roughness in Three Dimensions.Penton press,2000.
[39]Brown,C A,Charles,P D,Johnsen,W A,et al.Fractal analysis of topographic data by the patchwork method.Wear.1993,161(1-2):61-67.
[40]Vandenberg,S,Osborne,C F.Digital image processing techniques,fractal dimensionality and scale-space applied to surface roughness.Wear.1992,159(1):17-30.
[41]Zhou,G Y,Leu,M C,Blackmore,D.Fractal geometry model for wear prediction.Wear.1993,170(1):1-14.
[42]Wu,Y L,Dacre,B,Babus'Haq,R F.Measurements of real surface area by the conical method and fractal approach.Wear.1993,160(2):265-268.
[43]葛世荣,索双富.表面轮廓分形维数计算方法的研究.摩擦学学报.1997,17(4):354-362.
[44]葛世荣,陈国安.磨合表面形貌变化的特征粗糙度参数表征.中国矿业大学学报.1999,28(3):204-207.
[45]陈国安,葛世荣.粗糙表面测量轮廓的分形插值模拟.摩擦学学报.1998,18(4):346-350.
[46]王海容,蒋庄德,尹燕玲.切削加工表面分形机理的研究.机械科学与技术.2002,21(1):13-15.
[47]李成贵,董申.三维表面粗糙度参数的矩表征.计量学报.2001,22(3):168-173.
[48]李成贵.粗糙表面轮廓相关性的倒谱分析.机械工程学报.2004,40(5):87-91.
[49]贺林,朱均.粗糙表面接触分形模型的提出与发展.摩擦学学报.1996,16(4):375-384.
[50]齐东旭.分形及其计算机生成.科学出版社,1994.
[51]陈文超,高静怀,汪文秉.小波变换用于提供过井地震资料分辨率的方法研究.西安交通大学学报.1998,32(12).
[52]徐科,杨德斌,徐金梧.小波变换在齿轮局部缺陷诊断中的应用.机械工程学报.1999,35(3).
[53]郭百巍,陈大融.结合小波分析和分水岭分割法的微观表面形貌分析方法.中国机械工程.2007,18(17):2043-2046.
[54]陈庆虎,李柱.表面粗糙度评定的小波基准线.计量学报.1998,19(4):254-257.
[55]陈庆虎,李柱.表面粗糙度提取的小波频谱法.机械工程学报.1999,35(03).
[56]陈庆虎,周轶尘.表面奇异特征的小波提取。武汉交通科技大学学报。1999,(04).
[57]艾传智.C/C复合材料切削表面粗糙度的评定方法研究:(硕士学位论文).大连:大连理工大学,2005.
[58]杨东军.FRRMC切削表面三维微观形貌测量的研究:(硕士学位论文).大连:大连理工大学,2005.
[59]Ling,F F.Fractals,engineering surfaces and tribology.Wear.1990,136(1):141-156.
[60]孙霞,吴自勤,黄昀.分形原理及其应用.合肥:中国科学技术大学出版社,2003.
[61]李后强.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[62]Stewart,C V,Moghaddam,B,Hintz,K J,et al.Fractional Brownian motion models for synthetic aperture radarimagery scene segmentation.Proceedings of the IEEE.1993,81(10):1511-1522.
[63]全书海.基于表面灰度图像的加工表面形貌分形特征研究:(博士学位论文).武汉:武汉理工大学,2002。
[64]汪慰军,吴昭同,陈历喜等.基于分形的表面形貌特征描述与评定参数的研究.计量学报.1998,19(2).
[65]王安良,杨春信.机械加工表面形貌分形特征的计算方法.中国机械工程.2002,13(8):714-719.
[66]蒋书文,姜斌,李燕等.磨损表面形貌的三维分形维数计算.摩擦学学报.2003,23(6):533-536
[67]Gagnepain,J J,Roques-Carmes,C.Fractal approach to two-dimensional and three-dimensional surface roughness.Wear.1986,109(1-4):119-126.
[68]Sarkar,N,Chaudhuri,B B.An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image.IEEE TRANSACTIONS ON SYSTEMS.1994,24(1):115-120.
[69]Sarkar,N,Chaudhuri,B B.An efficient approach to estimate fractal dimension of textural images.Pattern Recognition.1992,25(9):1035-1041.
[70]Bisoi,A K,Mishra,J.On calculation of fractal dimension of images.Pattern Recognition Letters.2001,22(6-7):631-637.
[71]周承新.基于加工表面图像的刀具磨损检测方法研究:(硕士学位论文).西安:西安理工大学,2006.
[72]Pentland,A P.Fractal-based description of natural scenes.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE.1984,6:661-674.
[73]章毓晋.图像工程.北京:清华大学出版社,2005.
[74]杨福生.小波变换的工程分析与应用.北京:科学出版社,2003.
[75]胡伏原,张艳宁,薛笑荣等.基于树型小波何灰度共生矩阵的SAR图像分类.系统工程与电子应用.2003,25(10):1286-1288.
[76]靳华,王晓丹,赵荣椿.树型小波变换在纹理分析中的应用.计算机应用研究.2001:91-93.
[77]飞思科技产品研发中心.MATLAB 6.5辅助小波分析与应用.北京:电子工业出版社,2003.
[2]Sreejith,P S,Krishnamurthy,R,Malhotra,S K,et al.Evaluation of PCD tool performance during machining of carbon/phenolic ablative composites.Journal of Materials Processing Technology.2000,104(1-2):53-58.
[3]Sherrington,I,Smith,E H.Modern measurement techniques in surface metrology:part Ⅰ;stylus instruments,electron microscopy and non-optical comparators.Wear.1988,125(3):271-288.
[4]Mandelbrot,B B.The Fractal Geometry of Nature.NewYork:W.H.Freeman and Company,1982.
[5]林夏水.分形的哲学漫步.北京:首都师范大学出版社,1999.
[6]Majumdar,A,Tien,C L.Fractal characterization and simulation of rough surfaces.Wear.1990,136(2):313-327.
[7]Stupak,P R,Kang,J H,Donovan,J A.Fractal characteristics of rubber wear surfaces as a function of load and velocity.Wear.1990,141(1):73-84.
[8]Brown,C A,Savary,G.Describing ground surface texture using contact profilometry and fractal analysis.Wear.1991,141(2):211-226.
[9]费斌,王海容,蒋庄德.机械加工表面分形特性的研究.西安交通大学学报.1998,32(5):83-86.
[10]陈国安,葛世荣,王军祥.分形理论在摩擦学研究中的应用.摩擦学学报.1998,18(2):179-184.
[11]孙洪军,赵丽红.分形理论的产生及其应用.辽宁工学院学报.2005,25(2):113-117.
[12]全燕鸣,叶邦彦.复合材料的切削加工表面结构与表面粗糙度.复合材料学报.2001,18(4):128-132.
[13]全燕鸣,周泽华.硬脆颗粒增强铝基复合材料的已切削加工表面形貌及影响因素.中国机械工程.1998,9(7):9-11.
[14]于思荣,何镇明,陈凯.ZA22/Al_2O_3复合材料切削加工表面质量的研究.复合材料学报.1996,13(3):60-64.
[15]Sahina,Y,Kokb,M,Celikc,H.Tool wear and surface roughness of Al_2O_3particle-reinforced aluminium alloy composites.Journal of Materials Processing Technology.2002,(128):280-291.
[16]Ciftci,I,Turker,M,Seker,U.Evaluation of tool wear when machining SiCp-reinforced Al-2014 alloy matrix composites.Materials and Design.2004,25(3):251-255.
[17]An,S-O,Lee,E-S,Noh,S-L.A study on the cutting characteristics of glass fiber reinforced plastics with respect to tool materials and geometries.Journal of Materials Processing Technology.1997,68(1):60-67.
[18]杨文堂,杨明勇,王林丰.炭/炭复合材料机轮刹车盘磨削加工方案分析.湖南冶金.2006,34(2):3-7.
[19]蒋建纯,熊翔,杨文堂等.炭/炭复合材料切削加工试验研究.粉末冶金材料科学与工程.2000,5(3):210-214.
[20]张厚江,陈五一,陈鼎昌.碳纤维复合材料的钻削加工.新技术新工艺.1998,(5):16-18.
[21]赵福令,艾传智,杨东军等.碳/碳复合材料切削表面粗糙度的评定方法及评定参数研究.计量学报.2006,27(3):206-211.
[22]艾传智,杨东军,赵福令等.C/C复合材料切削表面粗糙度的测量评定与影响因素研究.航空精密制造技术.2005,41(6):31-34.
[23]杨东军,艾传智,赵福令等.复合材料车削表面2D分析和3D分析的对比研究.机械设计与制造.2006,(1):133-134.
[24]Sreejith,P S,Krishnamurthy,R,Narayanasamy,K,et al.Studies on the machining of carbon/phenolic ablative composites.Journal of Materials Processing Technology.1999,88(1-3):43-50.
[25]Wang,X M,Zhang,L C.An experimental investigation into the orthogonal cutting of unidirectional fibre reinforced plastics.International Journal of Machine Tools and Manufacture.2003,43(10):1015-1022.
[26]Davim,J P,Reis,P.Damage and dimensional precision on milling carbon fiber-reinforced plastics using design experiments.Journal of Materials Processing Technology.2005,160(2):160-167.
[27]Ferreira,J R,Coppini,N L,Levy Nero,F.Characteristics of carbon-carbon composite turning.Journal of Materials Processing Technology.2001,109(1-2):65-71.
[28]李成贵,董申.表面粗糙度的现状及发展.航空精密制造技术.1999,35(5):1-4.
[29]毛起广.表面粗糙度的评定和测量.北京:机械工业出版社,1991.
[30]俞汉清.表面粗糙度标准及其应用.北京:中国计量出版社,1997.
[31]Huang,Y Y,Wu,S M.Grinding surface characterization by CEST.International Journal of Machine Tool Design and Research.1986,26(4):431-444.
[32]黄逸云.三维随机表面形貌的识别.浙江大学学报.1984,18(2):138-148.
[33]Lin,T Y,Blunt,L,Stout,K J.Determination of proper frequency bandwidth for 3D topography measurement using spectral analysis.Part Ⅰ:isotropic surfaces.Wear.1993,166(2):221-232.
[34]T.Klimczak.Three-dimensional characteristic of surface texture,proc 8th Int.conf.of Chemnitz Tech,University Chemnitz.1988.
[35]W P Dong.The development of anintergrated approach to 3D surface finish assessment.Int.conf.of Chemnitz Tech,University Chemnitz.1991.
[36]SAYLES,R S,THOMAS,T R.Surface topography as a nonstationary random process,nature.1978,271(2):431-434.
[37]蒋向前,L.Blunt.三维表面测量的发展.工程设计.2000:98-100.
[38]Stout,K,Blunt,L,Dong,W,et al.Development of Methods for the Characterisation of Roughness in Three Dimensions.Penton press,2000.
[39]Brown,C A,Charles,P D,Johnsen,W A,et al.Fractal analysis of topographic data by the patchwork method.Wear.1993,161(1-2):61-67.
[40]Vandenberg,S,Osborne,C F.Digital image processing techniques,fractal dimensionality and scale-space applied to surface roughness.Wear.1992,159(1):17-30.
[41]Zhou,G Y,Leu,M C,Blackmore,D.Fractal geometry model for wear prediction.Wear.1993,170(1):1-14.
[42]Wu,Y L,Dacre,B,Babus'Haq,R F.Measurements of real surface area by the conical method and fractal approach.Wear.1993,160(2):265-268.
[43]葛世荣,索双富.表面轮廓分形维数计算方法的研究.摩擦学学报.1997,17(4):354-362.
[44]葛世荣,陈国安.磨合表面形貌变化的特征粗糙度参数表征.中国矿业大学学报.1999,28(3):204-207.
[45]陈国安,葛世荣.粗糙表面测量轮廓的分形插值模拟.摩擦学学报.1998,18(4):346-350.
[46]王海容,蒋庄德,尹燕玲.切削加工表面分形机理的研究.机械科学与技术.2002,21(1):13-15.
[47]李成贵,董申.三维表面粗糙度参数的矩表征.计量学报.2001,22(3):168-173.
[48]李成贵.粗糙表面轮廓相关性的倒谱分析.机械工程学报.2004,40(5):87-91.
[49]贺林,朱均.粗糙表面接触分形模型的提出与发展.摩擦学学报.1996,16(4):375-384.
[50]齐东旭.分形及其计算机生成.科学出版社,1994.
[51]陈文超,高静怀,汪文秉.小波变换用于提供过井地震资料分辨率的方法研究.西安交通大学学报.1998,32(12).
[52]徐科,杨德斌,徐金梧.小波变换在齿轮局部缺陷诊断中的应用.机械工程学报.1999,35(3).
[53]郭百巍,陈大融.结合小波分析和分水岭分割法的微观表面形貌分析方法.中国机械工程.2007,18(17):2043-2046.
[54]陈庆虎,李柱.表面粗糙度评定的小波基准线.计量学报.1998,19(4):254-257.
[55]陈庆虎,李柱.表面粗糙度提取的小波频谱法.机械工程学报.1999,35(03).
[56]陈庆虎,周轶尘.表面奇异特征的小波提取。武汉交通科技大学学报。1999,(04).
[57]艾传智.C/C复合材料切削表面粗糙度的评定方法研究:(硕士学位论文).大连:大连理工大学,2005.
[58]杨东军.FRRMC切削表面三维微观形貌测量的研究:(硕士学位论文).大连:大连理工大学,2005.
[59]Ling,F F.Fractals,engineering surfaces and tribology.Wear.1990,136(1):141-156.
[60]孙霞,吴自勤,黄昀.分形原理及其应用.合肥:中国科学技术大学出版社,2003.
[61]李后强.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[62]Stewart,C V,Moghaddam,B,Hintz,K J,et al.Fractional Brownian motion models for synthetic aperture radarimagery scene segmentation.Proceedings of the IEEE.1993,81(10):1511-1522.
[63]全书海.基于表面灰度图像的加工表面形貌分形特征研究:(博士学位论文).武汉:武汉理工大学,2002。
[64]汪慰军,吴昭同,陈历喜等.基于分形的表面形貌特征描述与评定参数的研究.计量学报.1998,19(2).
[65]王安良,杨春信.机械加工表面形貌分形特征的计算方法.中国机械工程.2002,13(8):714-719.
[66]蒋书文,姜斌,李燕等.磨损表面形貌的三维分形维数计算.摩擦学学报.2003,23(6):533-536
[67]Gagnepain,J J,Roques-Carmes,C.Fractal approach to two-dimensional and three-dimensional surface roughness.Wear.1986,109(1-4):119-126.
[68]Sarkar,N,Chaudhuri,B B.An Efficient Differential Box-Counting Approach to Compute Fractal Dimension of Image.IEEE TRANSACTIONS ON SYSTEMS.1994,24(1):115-120.
[69]Sarkar,N,Chaudhuri,B B.An efficient approach to estimate fractal dimension of textural images.Pattern Recognition.1992,25(9):1035-1041.
[70]Bisoi,A K,Mishra,J.On calculation of fractal dimension of images.Pattern Recognition Letters.2001,22(6-7):631-637.
[71]周承新.基于加工表面图像的刀具磨损检测方法研究:(硕士学位论文).西安:西安理工大学,2006.
[72]Pentland,A P.Fractal-based description of natural scenes.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE.1984,6:661-674.
[73]章毓晋.图像工程.北京:清华大学出版社,2005.
[74]杨福生.小波变换的工程分析与应用.北京:科学出版社,2003.
[75]胡伏原,张艳宁,薛笑荣等.基于树型小波何灰度共生矩阵的SAR图像分类.系统工程与电子应用.2003,25(10):1286-1288.
[76]靳华,王晓丹,赵荣椿.树型小波变换在纹理分析中的应用.计算机应用研究.2001:91-93.
[77]飞思科技产品研发中心.MATLAB 6.5辅助小波分析与应用.北京:电子工业出版社,2003.