摘要
微细电火花线切割加工以其非接触且容易加工高深宽比和复杂形状的微小型构件,决定了其在具有极小尺度和极高精度的微纳制造族群中不可替代的优势地位。然而,到目前为止,对其表面质量的评定还是以二维粗糙度的幅度参数为主,辅以混合参数。由于微细电火花线切割加工表面属于各向同性类型,二维粗糙度对这类表面的评定精度很低,微细电火花线切割表面结构的空间分布特性,决定了只有在三维范围内才能精确表征表面粗糙度。目前国内外学者对微细电火花线切割表面质量的研究主要集中在表面物理性能及与放电参数的关系上,对三维粗糙度研究的很少,对评定三维粗糙度的基础——表面微观形貌的构造和整体几何形态还没有做过深入系统的研究。为此,本文通过扫描探针显微镜测量微细电火花线切割表面微观三维形貌,对其统计特征、表面结构成分的频谱分布和表面三维粗糙度评定进行研究。
首先,采用数学形态学分解表面结构,提取表面凸峰,研究凸峰几何形态及变化规律;通过随机理论建立微细电火花线切割表面高度和轮廓高度的累积概率分布直方图,表明微细电火花线切割表面近似服从高斯分布;采用功率谱密度函数研究微细电火花线切割表面频谱特征,结果显示,微细电火花线切割加工表面属于各向同性表面,并用表面谱矩定量描述了表面的等方向、高度均一性和斜率均一性,与外圆磨削表面相比,微细电火花线切割表面具有较好的高度均一性和斜率均一性。
用小波分析方法提取微细电火花线切割表面三维粗糙度评定基准面。由于正交小波能量守恒的特点,选用正交小波作为基准面提取的小波滤波器。通过对测量表面三维形貌的小波重构误差确定sym5小波为微细电火花线切割表面基准面提取的最优小波基;通过小波分解各层信号能量呈指数变化的规律,确定基准面提取的小波分解次数。并把小波评定基准与传统滤波确定基准做了对比分析,得出小波评定基准面从表面结构的形成原因分离粗糙度信号,没有逼近误差,且不依赖于评定面积的大小。
从表面结构特征与功能特性共5个方面研究微细电火花线切割表面三维粗糙度评定参数。通过数值模拟微细电火花线切割表面磨损过程中形貌变化,分析幅度统计参数随磨损过程的变化规律,确定了磨合期表面的高度区间;赋予高度分布形状参数在微细电火花线切割表面评定中新的表征意义。改进了三维粗糙度空间参数的算法,直接通过二维自相关函数表征表面纹理特征,用微细电火花线切割表面二维自相关谱主截面的圆度表征表面纹理的复杂程度,以主截面最大半径方向计算表面纹理主方向。基于微分几何学的曲面论的思想,改进了混合参数中曲率的算法,并结合微细电火花线切割表面粗糙度结构特征,提出一个新的表征参数:表面凸峰的高斯曲率Sgc。通过研究不同加工能量的微细电火花线切割表面支撑率曲线,结合数值模拟表面磨损过程的结果,确定以支撑率的10%和80%所对应的支撑高度作为表面功能区域的两个分界值,与支撑率曲线一起把表面分为四个功能区域,以体积参数为主建立了9个三维粗糙度的功能参数。用分水岭分割法确定表面峰的数目,再此基础上建立了4个三维粗糙度的特征参数。最终提出22个三维粗糙度参数完成对微细电火花线切割表面的综合评定。
规范了微细电火花线切割表面三维粗糙度评定的10个术语及其定义、4个几何要素、4个典型算法、11个图形表征。探索性研究了微细电火花线切割加工表面三维粗糙度评定的取样面积和评定面积,建议对微细电火花线切割加工表面三维粗糙度用圆形取样面积和方形评定面积,每个取样面积内至少包含3个峰或坑特征,根据所测量表面的粗糙程度,每个评定面积中在其边长或对角线范围内至少包含5个取样面积。
Micro Wire Electrical Discharge Machining, with its non-contact and easy processing ofhigh aspect ratio micro and small components of complex shapes, determines its dominantposition which can not be replaced in the micro-nano manufacturing population with verysmall scale and very high precision. However, up to now, according to the magnitude of thetwo-dimensional roughness Height parameters combined with the Hybrid parameters,theassessment of surface quality is made. Micro-WEDM surface is isotropic type, andtwo-dimensional roughness made a lower precision assessment of the surface of such type.Spatial distribution characteristics of the micro-WEDM surface structure determine that it ispossible to get accurate characterization of surface roughness only in the three-dimensionalrange. Domestic and foreign scholars focus on the relationship between surface physicalproperties and the discharge parameters, while there has fewer research of three-dimensionalroughness, what’s more, there is no in-depth study on surface morphology structure andoverall geometry which is the basis of three-dimensional roughness. Therefore, this paperstudies about statistical characteristics of the spectral distribution of the surface of structuralcomponents and the surface of three-dimensional roughness assessment by scanning probemicroscopy of micro-WEDM surface of microscopic three-dimensional morphology.
Firstly, Mathematical morphology decomposition of surface structure is adopted and thesurface of convex peak is Extracted and Convex peak geometry and the variation is studied aswell. Micro-WEDM surface height and the cumulative probability of the profile heightdistribution histogram are found with stochastic theory, which indicates that Micro-WEDMsurface approximately obeys Gaussian distribution. Power spectral density function is used tostudy of Micro-WEDM surface spectral characteristics with such the result thatMicro-WEDM surface belong to the isotropic surface. And direction of the surface such as ahigh degree of homogeneity and slope homogeneity is described quantitatively with surfacespectral moments. Compared with the cylindrical grinding surface, Micro-WEDM surface hasgood high degree of homogeneity and slope homogeneity.
Wavelet analysis method is used to extract the Micro-WEDM three-dimensional surfaceroughness assessment datum. The orthogonal wavelet as the datum extracted wavelet filter is chosen, because of orthogonal wavelet energy conservation features. By waveletreconstruction error of measurement of three-dimensional morphology of the surface, in orderto determine sym5wavelet for the Micro-WEDM surface datum to extract the optimalwavelet basis; by way of wavelet decomposition layers of signal energy to the law ofexponential change to determine the datum extracted the number of wavelet decomposition.Comparative analysis is made of Wavelet assessment of baseline and Traditional filter todetermine the baseline and we have the result that Wavelet assessment of cause’s separation ofroughness from the surface structure of the signal, there is no approximation error, and doesnot depend on the size of the assessment area.
Micro-WEDM surface of three-dimensional roughness assessment parameters is availabefrom the surface structural characteristics and features a total of five aspects. Morphologychanges in the surface of the wear process by numerical simulation of Micro-WEDM,statistical parameters of the analysis of amplitude with the variation of the wear process, thesurface of the run-in period interval; given height distribution shape parameter inMicro-WEDM surface assessment new characterization significance. Three-dimensionalroughness spatial parameters of the algorithm is Improved, directly through thetwo-dimensional autocorrelation function characterization of surface texture characteristics ofMicro-WEDM the complexity of the surface two-dimensional correlation spectroscopy crosssection roundness characterization of surface texture, the main cross-sectionradius direction tocalculate the main direction of the surface texture. Based on the idea of differential geometryof surfaces, algorithm of curvature in the Hybrid parameters is improved, and micro-WEDMsurface roughness of structural features is combined and consequently a new characterizationparameters is proposed which is the Gaussian curvature of the surface peak Sgc. Surfacesupport rate curve through different processing energy of Micro-WEDM, combined with theresults of numerical simulation of surface wear process, determine the height of the supportrate of10%and80%of the corresponding support as the two cut-off value of the surfacefunctional areas, surface together with the support rate curve is divided into four functionalareas, the main volume parameters9function of the three-dimensional roughness Functionalparameters. Watershed segmentation method to determine the number of surface peaks, andthen established on the basis of four characteristics of the three-dimensional roughnessFeature parameters.22three-dimensional roughness parameters is finally proposed to complete a comprehensive assessment of micro WEDM surface.
Standardized the micro WEDM surface three-dimensional roughness assessment system,including10terms and definitions,4geometrical features,4typical algorithms of parameters,11graphic representations. Exploratory study is made about the micro WEDM processingthree-dimensional surface roughness assessment sampling area and assessment area, it isrecommended that the three-dimensional micro WEDM surface roughness using a circularsampling area within each sampling area contains at least three peaksor pit features, anassessment area within a diameter range contains at least five sampling area.
引文
[1] Masuzawa T,Okajima K,Taguchi T,Fujino.EDM-Lathe for Micromachining.CIRPAnnals.2002,51(1):355-358P
[2] Klocke F,Lung D,T Nothe.Micro contouring by EDM with fine wires.Proceedingsof the13th International Symposium for Electromachining.Aachen Techn Univ.2001,(ISEM XIII):767-779P
[3]褚旭阳.微细电火花集成加工技术的研究.哈尔滨工业大学博士学位论文.2010:7-9页
[4] Shun-Tong Chen,Hong-Ye Yang,Chih-Wei Du.Study of an Ultrafine WEDMTechnique.Journal of MicroMechanics and MicroEngineering.2009,19(11):5033-5041P
[5] G.L.Benavides,L.F.Bieg,M.P.Saavedra.High Aspect Ratio Meso-ScalePartsEnabled by Wire Micro-EDM.Microsystem Techologies.2002,8(9):395-401P
[6] Koch,W.Whrfeld,F.Michel,H.P.Gruber.Recent progress in Micro-ElectroDischarge Machining-Part1:Technology.The13th Int.Symp.on Electro Machining,Spanish.2001:154-163P
[7]于滨.微细电火花线切割加工控制系统及工艺规律研究.哈尔滨工业大学博士论文.2003:7-9页
[8] Nihat Tosun,Can Cogun.An Investigation on Wire Wear in WEDM.Journal ofMaterials Processing Technology.2003,8(9):273-278P
[9]任海滨.微细电火花线切割加工工艺规律研究.哈尔滨工业大学硕士学位论文.2006:2-3页
[10]冯嫦杰,刘小君.表面相互作用下表面形貌表征研究.润滑与密封.2008,33(6):42-45页
[11]程卫民,陈岭丽.工件表面的形貌分析.测控技术.2005,24(5):37-39页
[12]吴松.三维表面形貌的评价技术及其应用基础研究.南京航天航空大学硕士学位论文.2000,19(4):597-601页
[13]吴立群,杨将新,吴昭同.AR(1)的分形特性及在粗糙度表征中的应用.机械科学与技术.2000(2):597-610页
[14] M.Sedla ek,B.Podgornik,J.Vi intin.Influence of surface preparation on roughnessparameters, friction and wear.Wear.2009,266(3-4):482-487P
[15] Pradeep L.Menezes,Kishore,Satish V.Kailas,et al.Friction and transfer layerformation in polymer-steel tribo-system:Role of surface texture and roughnessparameters.Wear.2011,271(9-10):2213-2221P
[16] H.P.Schulze,R.Hermsa,H.Juhr,et al.Comparison of measured and simulatedcrater morphology for EDM.Journal of Materials Processing Technology.2004,149(1-3):316-322P
[17] Segon Heo,Young Hun Jeong,Byung-Kwon Min,et al.Virtual EDM simulator:Three-dimensional geometric simulation of micro-EDM millingprocesses.International Journal of Machine Tools&Manufacture.2009,49(12-13):1029-1034P
[18] M.P.S.Krishna Kiran,Suhas S.Joshi.Modeling of surface roughness and the roleof debris in micro-EDM.Journal of Manufacturing Science and Engineering.2007,129(2):265-273P
[19] S.Sarkar,S.Mitra,B.Bhattacharyya.Parametric analysis and optimization of wireelectrical discharge machining of γ-titanium aluminide alloy.Journal of MaterialsProcessing Technology.2005,159(3):286-294P
[20] T.A.Spedding,Z.Q.Wang.Parametric optimization and surface characterizationof wire electrical discharge machining process.Precision Engineering.1997,20(1):5-15P
[21] M.Kiyak,Q.Cakir.Examination of machining parameters on surface roughness inEDM of tool steel.Journal of M Materials Processing Technology.2007,191(1-3):141-144P
[22] J.C.Rebelo,A.Morao Dias,D.Kremer,et al.Influence of EDM pulse energyon the surface integrity of martensitic steels. Journal of Materials ProcessingTechnology.1998,84(1-3):90-96P
[23] P.Pecas,E.Henriques.Electrical discharge machining using simple and powder-mixeddielectric: The effect of the electrode area in the surface roughness andtopography.Journal of Materials Processing Technology.2008,200(1-3):250-258P
[24] H.Ramasawmy,L.Blunt.3D surface topography assessment of the effect of differentelectrolytes during electrochemical polishing of EDM surfaces.International Journal ofMachine Tools&Manufacture.2002,42(5):567-574P
[25] H.Ramasawmy,L.Blunt.Effect of EDM process parameters on3D surfacetopography.Journal of Materials Processing Technology.2004,148(2):155-164P
[26] K.Kanlayasiri,S.Boonmung.Effects of wire-EDM machining variables on surfaceroughness of newly developed DC53die steel: Design of experiments and regressionmodel.Journal of Materials Processing Technology.2007,192-193(10):459-464P
[27] K.Kanlayasiri,S.Boonmung.An investigation on effects of wire-EDM machiningparameters on surface roughness of newly developed DC53die steel.Journal ofMaterials Processing Technology.2007,187-188(6):26-29P
[28] R.E.Williams,K.P.Rajurkar.Study of wire electrical discharge machined surfacecharacteristics.Journal of Materials Processing Technology.1991,28(1-2):127-138P
[29] S.S.Mahapatra,Amar Patnaik.Optimization of wire electrical discharge machining(WEDM) process parameters using Taguchi method.International Journal of AdvancedManufacturing Technology.2007,34(9-10):911-925P
[30] Y.S.Wong,M.Rahman,H.S.Lim,et al.Investigation of micro-EDM materialremoval characteristics using single RC-pulse discharge. Journal of MaterialsProcessing Technology.2003,140(1-3):303-307P
[31] T.A.Spedding,Z.Q.Wang.Parametric optimization and surface characterizationof wire electrical discharge machining process.Precision Engineering.1997,20(1):5-15P
[32]郭黎滨,田敏茹,张铭钧,等.电火花加工工件表面粗糙度的评定与测试.计量技术.1991,(12):5-6页
[33]郭黎滨,田敏茹,张铭钧,等.电火花加工表面三维粗糙度的评定基准与评定参数.哈尔滨船舶工程学院学报.1991,12(12):444-448页
[34] Fuzhu Han,Jun Jiang,Dingwen Yu.Influence of machining parameters on surfaceroughness in finish cut of WEDM.International Journal of Advanced ManufacturingTechnology.2007,34(5-6):538-546P
[35]耿雷,刘春生,钟华燕,等.电火花线切割加工表面形貌分形特征.黑龙江科技学院学报.2008,18(2):114-117页
[36]陈历喜,黎永前.用随机分析方法研究电加工表面形貌.航空工艺技术.1995,(2):15-19页
[37]陈历喜,黎永前.用统计函数方法评估电加工表面形貌.西安工业学院学报.1994,14(2):140-145页
[38]陈历喜,王萍.用数理统计方法评估特种加工表面形貌.机械科学与技术.1994,(2):83-88页
[39]王瑾.氧化铝颗粒增强铜基复合材料线切割加工研究.重庆工学院学报.2006,20(8):63-65页
[40] Mu-Tian Yan,Yi-Peng Lai.Surface quality improvement of wire-EDM using afine-finish power supply. International Journal of Machine Tools&Manufacture.2007,47(11):1686-1694P
[41] Y.H.Guu,Max Ti-Kuang Hou.Effect of machining parameters on surface texturesin EDM of Fe-Mn-Al alloy.Materials Science and Engineering A.2007,466(1-2):61-67P
[42]刘志东,汪炜,邱明波,等.单晶硅高速走丝电火花线切割试验研究.南京航空航天大学学报.2008,40(6):758-762页
[43]余承业.特种加工新技术.北京:国防工业出版社,1995:113-120页
[44]李成贵,李行善,强锡富.三维表面微观形貌的测量方法.宇航计测技术.2000,20(4):2-10页
[45]李伯奎,刘远伟.表面粗糙度理论发展研究.工具技术.2004,38(1):63-67页
[46] E.S.Gadelmawla,M.M.Koura,et al.Roughness parameters.Journel of MaterialsProcessing Technology.2002(123):133-145P
[47]程卫民,陈岭丽.工件表面的形貌分析.测控技术.2005,24(5):37-39页
[48] Iosif D,Rosca,S V.Highly conductive multiwall carbon nanotube and epoxycomposites produced by threeroll milling.Carbon.2009,47(8):1958-1968P
[49]蒋向前,L.Blunt.三维表面测量的发展.工程设计.2000,(3):98-100P
[50]陈建超.超精密加工表面粗糙度测量方法对比及功率谱密度评价.哈尔滨工业大学硕士学位论文.2009:7-9页
[51]曾文涵.双树复小波表面分析模型及加工过程形貌辨识方法研究.华中科技大学博士学位论文.2005:2-3页
[52]曾文涵,谢铁邦,蒋向前,等.表面粗糙度的稳健提取方法研究.中国机械工程.2004,15(2):127-130页
[53] S.Brinkmann,H.Bodschwinna,H.W.Lemke.Accessing roughness in threedimensions using Gaussian regression filtering.International Journal of Machine Toolsand Manufacture.2001,41(13):2153-2161P
[54]曾文涵,高咏生,谢铁邦,等.三维表面粗糙度高斯滤波快速算法.计量学报.2003,24(1):10-13页
[55] ISO/DTS16610-31:Geometrical Product Specifications(GPS)-Filtration–Part31:Robust profile filters:Gaussian regression filter.2002
[56] J. Raja, V. Radhakrishnan. Filtering of surface profiles using fast Fouriertransform.Int.J.Mach.Tool.1979,19:133-141P
[57] S.Hara,T.Tsukada.The conditions to apply the phase corrected filter to tracedprofilesfor roughness profiles–Application of the Gaussian high-pass digital filter.JJapanSoc.Prec.Eng.1996,62(4):594-598P
[58] M.Krystek.Afast Gauss filtering algorithm for roughness measurements.PrecisionEngineering.1996,19:198-200P
[59] Y.B.Yuan,X.F.Qiang,F.Song, eta.A fast algorithm for determining the Gaussianfiltered means line in surface metrology.Precision Engineering.2000,24:62-69P
[60] S.Brinkmann,H.Bodschwinna,H.W.Lemke.Accessing roughness in threedimensions using Gaussian regression filtering.International Journal of Machine Toolsand Manufacture.2001,41(13):2153-2161P
[61]陈庆虎.表面计量的小波频谱理论与方法的研究.博士学位论文.1998:3-5页
[62]陈庆虎.表面综合形貌的小波分离法.华中理工大学学报.1997,25(5):25-27页
[63]陈庆虎,周轶尘.表面奇异特征的小波提取.武汉交通科技大学报.1999,23(4):343-347页
[64]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页
[65] X.Q.Jiang,L.Blunt,K.J.Stout.Three-dimensional surface characterization fororthopaedic joint prostheses.Journal of Inst.Mech.Eng.,1999:49-68P
[66] X.Q.Jiang,L.Blunt,K.J.Stout.Development of a lifting wavelet representationfor characterization of surface topography.Proc.R.Soc.Lond.A,2000,456:2283-2313P
[67]王安良,杨春信.评价机械加工表面形貌的小波变换方法.机械工程学报.2001,37(8):65-74页
[68] S.H.Lee,H.Zahouani,R.Caterini,T.G.mathia.Morphological characterizationsof engineered surfaces by wavelet transform.Tools Manu fact.1998,38(5):581-589P
[69] Shengyu Fu,B.Muralikrishnan,J.Raja.Engineering surface analysis with differentwavelet bases.Journal of Manufacturing Science and engineering.2003,125:844-852P
[70] Simona E.Rombo.Optimal extraction of motif patterns in2D.Information ProcessingLetters.2009,109(17):1015-1020P
[71] ISO12085:Geometrical Product Specification(GPS)surface texture:Profile method-Motif parameters.1996
[72] J.Lopez,G.Hansali,et al.3D fractal-based characterization for engineered surfacetopography.Int.J.Mach.Tools Manufac.1995,35(2):5211-218P
[73] P.J.Scout.Scale-space techniques.Proceeding of the6th Int. Colloquium onSurfaces.Chemintz.2000:153-161P
[74] F.Barré,J.Lopez.Watershed Lines and Catchment Basins:a New3D-MOTIFMethod.Int.J.Mach.Tools Manufact.2000,40(8):1171-1184P
[75] S.Mezghani,H.Zahouani.Characterisation of the3D waviness and roughnessmotifs.Wear.2004,257(12):1250-1256P
[76]李成贵,董申.三维表面微观形貌的表征参数和方法.宇航计测技术.1999,19(6):33-43页
[77] Bakucz P,Kruger S R.A new wavelet filtering for analysis of fractal engineeringsurfaces.Wear.2009,266(5):539-542P
[78]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页
[79]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页
[80]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页
[81] J C Russ.Fractal dimensional measurement of engineering surfaces.Int.J.Mach.ToolsManufact.1998,38(5):567-571P
[82]李成贵.分形理论在表面粗糙度表征和评定中的应用研究.天津大学博士学位论文.1997:50-53页
[83]杨培中,宋平.分形插值曲面与表面粗糙度三维评定.机械工艺师.2000,10(7):37-38页
[84] Xiaohu Liang,Bin Lin,Xuesong Han,Shangong Chen.Fractal analysis of engineeringceramics ground surface.Applied Surface Science.2012,258(17):6406-6415
[85] Mainsah E, Stout E J. Report on the Second International workshop on thedevelopment of method for characterization of roughness in3D. Brussels:LEB.Official report circulated by BCR,May1993
[86] Stout K J,Blunt L,Dong W,et al.Development of Methods for the Characterisationof Roughness in Three Dimensions.London:Penton press.2000:221-241P
[87] F Sacerdotti, B.J Griffiths, F Benati, et al. Hardware variability in thethree-dimensional measurement of autobody steel panel surfaces.International Journalof Machine Tools and Manufacture.2001,41(13–14):2051-2060P
[88] Liam Blunt,Xiangqian Jiang,Paul J. Scott.13-Future Developments in SurfaceMetrology. Advanced Techniques for Assessment Surface Topography.2003:339-347P
[89] ISO25178-2:Geometrical product specification(GPS)-Surface texture:Areal-Part2:Terms,definitions and surface texture parameters.2006
[90]温秀兰,赵义兵.三维表面粗糙度的研究.计测技术.2001,(6):13-14页
[91]李成贵,董申,张锡富.三维表面粗糙度的均方根斜率评定.仪器仪表学报.1999,20(6):644-647页
[92]李成贵,李行善.三维表面粗糙度的均方根波长评定.北京航空航天大学学报.2002,28(2):190-193页
[93]杨培中,蒋寿伟.表面粗糙度三维评定的研究.机械设计与研究.2002,18(2):64-66页
[94] K.H Ho,S.T Newman,S Rahimifard,et al.State of the art in wire electrical dischargemachining(WEDM).International Journal of Machine Tools and Manufacture.2007,47(11):1744-1751P
[95]张志航.微细电火花线切割表面三维形貌及功能评定研究.哈尔滨工程大学硕士学位论文.2009:18-24页
[96]胡学钢,于海涛.均匀设计在数据挖掘中的应用.合肥工业大学学报.2006,29(3):292-295页
[97]刘永才.均匀设计及其应用.战术导弹技术.2002,(1):58-61页
[98]赵若红,傅继阳,吴玖荣,等.Matlab内建psd函数在工程随机振动谱分析中的修正方法.暨南大学学报(自然科学版).2007,28(5):435-439页
[99]傅广操,樊明捷.Matlab在现代功率谱估计中的应用.电脑学习.2003(6):6-7页
[100]黄志宇,刘保华,陈高平,等.随机信号的功率谱估计及Matlab的实现.现代电子技术.2002(3):21-23页
[101]程晓锋,郑万国,蒋晓东,等.用功率谱密度坍陷评价光学元件波前中频误差特性.强激光与粒子束.2005,17(10):279-282页
[102] Y.H.Liu,L.Teng,et al.Application of power spectral density to specify opticalsuper-smooth surface.Proc.SPIE.2006,6150:311-315P
[103]杨智,戴一帆,王贵林.小波在基于功率谱密度特征曲线评价中的应用.激光技术.2007,31(6):627-629页
[104]李成贵.三维表面微观形貌的二维功率谱表征.计量学报.2004,25(1):11-15页
[105]李成贵,石朝耀.三维粗糙度表面的谱矩特征.北京工业大学学报.2003,29(4):406-410页
[106]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页
[107]葛世荣,朱华著.摩擦学的分形.北京:机械工业出版社,2005:26-27,155-180页
[108]叶菲,俞志富.基于多重和高阶分形特性的雷达信号调制方式识别.船舶电子工程.2010,(4):116-118页
[109] Ding haijuan,Guo libin,Zhang zhihang,et al.Study on fractal characteristic of surfacemicro-topography of micro-WEDM.Applied Mechanics and Materials.2009,16-19:1273-1277P
[110]王炳成,景畅,任朝晖.剪切痕迹表面分形维数的结构函数法计算及其应用.中国人民公安大学学报(自然科学版).2004,(1):4-6页
[111]李成贵,张国雄,袁长良.三维粗表面糙度的均一性研究.计量学报.1999,20(1):32-36页
[112]李成贵,张国雄,袁长良.三维表面粗糙度的等方性评定.机械工程学报.1999,35(1):15-19页
[113]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页
[114] Wen-Ruey Chang,Mikko Hirvonen,Raoul Gr nqvist.The effects of cut-off length onsurface roughness parameters and their correlation with transition friction.SafetyScience.2004,42(8):755-769P
[115]汪恺.表面结构.北京:中国计划出版社,2004:1-2页
[116]潘泉,张磊,孟晋丽,等.小波滤波方法及应用.北京:清华大学出版社,2005:1-3页
[117]程正兴.小波分析算法与应用.西安:西安交通大学出版社,1998:4-5页
[118] Albert B,Franeis J N.A First course inWavelets with Fourier Analysis.电子工业出版社,2002:27-35页
[119]葛哲学,沙威.小波分析理论与MATLAB2007实现.北京:电子工业出版社,2007:33-35页
[120]李建平,唐远炎.小波分析方法的应用.重庆大学出版社,2003:32-34页
[121]孙延奎.小波分析及其应用.北京:机械工业出版社,2005:16-40页
[122]李国华,周涛.基于MATLAB7.x的系统分析与设计:小波分析.西安:西安电子科技大学出版社,2008:7-13页
[123]赵瑞珍,宋国乡,王卫卫.基于紧框架的规范正交小波基.西安电子科技大学学报.2000,27(1):51-54页
[124]陈志杰.微细电火花加工表面粗糙度评定研究.哈尔滨工程大学博士学位论文,2011:48-49页
[125]张志航,崔海,丁海娟,等.MWEDM表面三维粗糙度的小波评定基准面.哈尔滨工程大学学报.2011,32(9):1185-1189页
[126]李翔.基于小波分析的测量信号处理技术研究.哈尔滨工业大学博士学位论文,2009:28-33页
[127] Unser M,Therenaz P,Aldroubi A.Shift-orthogonal wavelet bases using splines.IEEESignal Processing Lett.1996,3(3):85-88P
[128] O. Rioul.Regular Wavelets:A Discrete-Time Approach.IEEE Transactions on SignalProcessing.1993,41(2):3572-3579P
[129] Frédéric Payan,Marc Antonini.Temporal wavelet-based compression for3D animatedmodels.Computers&Graphics.2007,31(1):77-88P
[130] Vetterli M,Herley C.Wavelets and Filter Banks:Theory and Design.IEEE Trans.OnSP.1992,40(9):2207-2232P
[131] Damir Baki. Semi-orthogonal Parseval frame wavelets and generalizedmultiresolution analyses.Applied and Computational Harmonic Analysis.2006,21(3):281-304P
[132] H. Führ, M. Wild. Characterizing wavelet coefficient decay of discrete-timesignals.Applied and Computational Harmonic Analysis.2006,20(2):184-201P
[133]陈国强,张维强,周梓荣.面向功能的表面形貌Areal表征与评定.湖南工程学院学报.2008,18(2):14-17页
[134] Mike Zecchino.Characterizing Surface Quality:Why Average Roughness is NotEnough.Advances Materials&Processes.2003:1-4P
[135] Marko Sedla ek,Bojan Podgornik,et al.Correlation between standard roughnessparameters skewness and kurtosis and tribological behaviour of contactsurfaces.Tribology International.2012,48:102-112P
[136] N. Balakrishnan, Bruno Scarpa. Multivariate measures of skewness for theskew-normal distribution.Journal of Multivariate Analysis.2012,104(1):73-87P
[137] Jér me Antoni.The spectral kurtosis:a useful tool for characterising non-stationarysignals.Mechanical Systems and Signal Processing.2006,20(2):282-307P
[138] Zhang Zhihang,, Guo Libin, Cui Hai, et al. Surface texture evaluation ofmicro-WEDM.Applied Mechanics and Materials.2012,(138-189):1251-1257
[139] Ruth Rosenholtz,Jitendra Malik.Surface Orientation from Texture:Isotropy orHomogeneity (or Both).1997,37(16):2283-2293P
[140] Francois Blatevron. New3D Parameters and Filtration Techniques for SurfaceMetrology.2006:1-7P
[141] Larson,Vincent.E,Golaz,et al.Using probability density functions to deriveconsistent closure relationships among higher-order moments.2005,133(4):1023-1042P
[142] Meijer,Erik.Matrix algebra for higher order moments.Linear Algebra and itsApplications.2005,410(1-3):112-134P
[143]李惠芬,蒋向前,李柱.三维表面功能评定技术发展综述.工具技术.2002,36(2):8-11页
[144] Stanley J.Dapkunas.Surface Engineering Measurement Standards for InorganicMaterials.Materials Science and Engineering Laboratory.2005:136-141P
[145] K Váradi,B Palásti-Kovács,á Czifra,et al.3D Characterization of EngineerineSurfaces.Proceedings of Polytechnic Jubilee Conference,Budapest.2004:4-5P
[146] Lang,Serge.Fundamentals of differential geometry.北京:世界图书出版公司,2010:35-48P
[147]彭家贵,陈卿著,微分几何.北京:高等教育出版社,2002:47-52页
[148]赵颖.具有限定高斯曲率的圆纹曲面.大连理工大学硕士学位论文,2009:4-9页
[149] Ding Haijuan, Guo Libin, Cui Hai. Statistical characteristic and parametercharacterization of3D surface micro-topography on micro-EDM.IEEE InternationalConference on Automation and Logistics.2009:1094-1098P
[150] J.Schm hling,F.A.Hamprecht,D.M.P.Hoffmann.A three-dimensional measureof surface roughness based on mathematical morphology.International Journal ofMachine Tools and Manufacture.2006,46(14):1764-1769P
[151] Paul J.Scott.Feature parameters.Wear.2009,266(5-6):548-551P