机械加工表面形貌分形维数的1/f过程小波识别法
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摘要
结合小波所具有的多尺度分析能力,提出了表征机械加工表面形貌的1/f过程小波识别法,基于MB函数模拟下的分形表面轮廓,计算出不同的小波基函数与不同分解尺度下的分形维数,通过对比挑选出了较为合适的小波基函数与分解尺度;将1/f过程小波识别法的计算结果与计盒维数法、差方法、R/S分析法、功率谱密度法(PSD)、均方根法(RMS)、结构函数法、方程组法等方法进行了对比,得出了1/f过程小波识别法计算结果的准确性与计算上的简便性,进一步说明了该方法能很好地应用到分形表面的多尺度分析上;最后将1/f过程小波识别法应用到了3种实际加工表面上,验证了其实用性。
Combined with multi-scale analysis ability of wavelet, the wavelet identification of 1/f process is proposed for the characterization of machined surface topography, based on the fractal surface profile obtained by MB function, the fractal dimensions of different wavelet functions and different decomposition scales are calculated,by comparison, the more appropriate wavelet basis function and decomposition scale are selected. The calculation results of the wavelet identification of 1/f process are compared with the box counting method, variance method, R/S analysis method, power spectral density method(PSD), root mean square method(RMS), structure function method and the method of equations, and the results show that the wavelet identification of 1/f process is more accurate and more convenient than other algorithms, further shows that the wavelet analysis method can be well applied to the multi-scale fractal analysis on the surface. Finally, the wavelet identification of 1/f process is applied to 3 actual machining surfaces, verified the practicality.
Combined with multi-scale analysis ability of wavelet, the wavelet identification of 1/f process is proposed for the characterization of machined surface topography, based on the fractal surface profile obtained by MB function, the fractal dimensions of different wavelet functions and different decomposition scales are calculated,by comparison, the more appropriate wavelet basis function and decomposition scale are selected. The calculation results of the wavelet identification of 1/f process are compared with the box counting method, variance method, R/S analysis method, power spectral density method(PSD), root mean square method(RMS), structure function method and the method of equations, and the results show that the wavelet identification of 1/f process is more accurate and more convenient than other algorithms, further shows that the wavelet analysis method can be well applied to the multi-scale fractal analysis on the surface. Finally, the wavelet identification of 1/f process is applied to 3 actual machining surfaces, verified the practicality.
引文
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[14] 温淑花,张宗阳,张学良,等.固定结合面刚度分形模型[J].农业机械学报,2013,44(2):255-260.WEN ShuHua,ZHANG ZongYang,ZHANG XueLiang,et al.Stiffness fractal model for fixed joint interfaces[J].Transactions of the Chinese Society for Agricultural Machinery,2013,44(2):255-260(In Chinese).
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[16] 王安良,杨春信.小波变换方法评价曲线的分形特征[J].机械工程学报,2002,38(5):80-85.WANG AnLiang,YANG ChunXin.Wavelet transform method evaluate the fractal characterization of profiles[J].Journal of Mechanical Engineering,2002,38(5):80-85(In Chinese).
[17] 杨红平,傅卫平,王雯,等.小波系数表征机械加工表面分形特征的计算方法[J].仪器仪表学报,2010,31(7):1454-1459.YANG HongPing,FU WeiPing,WANG Wen,et al.Calculation method for fractal characteristics of machining topography surface based on wavelet coefficients[J].Chinese Journal of Scientific Instrument,2010,31(7):1454-1459(In Chinese).
[18] Wornell GW,Wavelet-based representations for the 1/ f family of fractal processes[J].Proceedings of the IEEE,1993,81(10):1428-1450.
[19] 杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:40-50.YANG FuSheng.Engineering analysis and application of wavelet transform[M].Beijing:Science Press,1999:40-50(In Chinese).
[20] Robert L.Jackson.,Jeffrey L.Streator.A Multi-scale Model for contact between rough surfaces[J].Wear,2006,261:1337-1347.
[21] 樊计昌,刘明军,王夫运,等.浅析小波最大分解层[J].科技导报(北京),2008,26(10):40-42.FAN JiChang,LIU MingJun,WANG FuYun,et al.Analysis on maximum wavelet decomposition level from theory and application[J].Science & Technology Review(Bei Jing),2008,26(10):40-42(In Chinese).
[21] 郜峰利,郭树旭,张振国,等.1/f类分形信号的最小二乘法参数估计[J].电子与信息学报.2009,31(7):1746-1748.SHAO FengLi,GUO ShuXu,ZHANG ZhenGuo,et al.Parameter estimation of 1/ f-type fractal signal using least square method[J].Journal of Electronics & Information Technology.2009,31(7):1746-1748(In Chinese).
[2] Majumdar A,Bhushan B.Role of fractal geometry in roughness characterization and contact mechanics of surfaces[J].1990,112(2):205-216.
[3] Majumdar A,Bhushan B.Fractal model of elastic-plastic contact between rough surfaces[J].Journal of Tribology,1991,113(1):1-11.
[4] 葛世荣.粗糙表面的分形特征与分形表达研究[J].摩擦学学报,1997,17(1):73-80.Tonder K.Fractal characteristics and fractal representation of rough surfaces[J].Tribology Journal,1991,113(1):1-11.
[5] Gagnepain JJ,Roques-Carmes C,Fractal approach to two-dimensional and three-dimensional surface roughness[J].Wear,1986,109(1-4):119-126.
[6] Zhou GY,Leu MC,D Blackmore,Fractal geometry model for wear prediction[J].Wear,1993,170(1):1-14.
[7] 葛世荣,索双富.表面轮廓分形维数计算方法的研究[J].摩擦学学报,1997,17(4):354-362.GE ShiRong,SUO ShuangFu.The Computation methods for the fractal dimension of surface profiles[J].Tribology Journal,1997,17(4):354-362(In Chinese).
[8] 李业学,刘建锋.基于R/S分析法与分形理论的围岩变形特征研究[J].四川大学学报(工程科学版),2010,42(3):43-48.LI YeXue,LIU JianFeng.Study on deformation characteristic of surrounding rock by R/S Method and fractal theory[J].Journal of Sichuan University (Engineering Science Edition),2010,42(3):43-48(In Chinese).
[9] Majumdar A,Tien CL.Fractal characterization and simulation of rough surfaces[J].Wear,1990,136(2):313-327.
[10] 朱华,葛世荣.结构函数与均方根分形表征效果的比较[J].中国矿业大学学报,2004,33(4):396-399.ZHU Hua,GE ShiRong.Comparison of fractal characterization effects of structure function and mean square root[J].Journal of China University of Mining & Technology,2004,33(4):396-399(In Chinese).
[11] 李小兵,刘莹.表面形貌分形表征方法的比较[J].南昌大学学报(理科版),2006,30(1):84-86.LI XiaoBin,LIU Ying.The Computation Methods of the fractal Dimension of Surface Profiles[J].Journal of Nanchang University,2006,30(1):84-86.
[12] 刘小君.表面形貌的分形特征研究[J].合肥工业大学学报自然科学版,2000,23(2):236-239.LIU XiaoJun.Investigation on fractal characterization of surfaceTopography[J].Journal of Hefei University of Technology (Natural Science),2000,23(2):236-239(In Chinese).
[13] Mandelbrot BB,Wallis JR,Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence.Water Resources Research,1969,5(5):967-988.
[14] 温淑花,张宗阳,张学良,等.固定结合面刚度分形模型[J].农业机械学报,2013,44(2):255-260.WEN ShuHua,ZHANG ZongYang,ZHANG XueLiang,et al.Stiffness fractal model for fixed joint interfaces[J].Transactions of the Chinese Society for Agricultural Machinery,2013,44(2):255-260(In Chinese).
[15] 杨建国,小波分析及其工程应用[M].北京:机械工业出版社,2005:41-46.YANG JianGuo,Wavelet analysis and its engineering application [M].Beijing:Machinery Industry Press,2005:41-46(In Chinese).
[16] 王安良,杨春信.小波变换方法评价曲线的分形特征[J].机械工程学报,2002,38(5):80-85.WANG AnLiang,YANG ChunXin.Wavelet transform method evaluate the fractal characterization of profiles[J].Journal of Mechanical Engineering,2002,38(5):80-85(In Chinese).
[17] 杨红平,傅卫平,王雯,等.小波系数表征机械加工表面分形特征的计算方法[J].仪器仪表学报,2010,31(7):1454-1459.YANG HongPing,FU WeiPing,WANG Wen,et al.Calculation method for fractal characteristics of machining topography surface based on wavelet coefficients[J].Chinese Journal of Scientific Instrument,2010,31(7):1454-1459(In Chinese).
[18] Wornell GW,Wavelet-based representations for the 1/ f family of fractal processes[J].Proceedings of the IEEE,1993,81(10):1428-1450.
[19] 杨福生.小波变换的工程分析与应用[M].北京:科学出版社,1999:40-50.YANG FuSheng.Engineering analysis and application of wavelet transform[M].Beijing:Science Press,1999:40-50(In Chinese).
[20] Robert L.Jackson.,Jeffrey L.Streator.A Multi-scale Model for contact between rough surfaces[J].Wear,2006,261:1337-1347.
[21] 樊计昌,刘明军,王夫运,等.浅析小波最大分解层[J].科技导报(北京),2008,26(10):40-42.FAN JiChang,LIU MingJun,WANG FuYun,et al.Analysis on maximum wavelet decomposition level from theory and application[J].Science & Technology Review(Bei Jing),2008,26(10):40-42(In Chinese).
[21] 郜峰利,郭树旭,张振国,等.1/f类分形信号的最小二乘法参数估计[J].电子与信息学报.2009,31(7):1746-1748.SHAO FengLi,GUO ShuXu,ZHANG ZhenGuo,et al.Parameter estimation of 1/ f-type fractal signal using least square method[J].Journal of Electronics & Information Technology.2009,31(7):1746-1748(In Chinese).
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