基于Copula函数的铣削力、振动与表面粗糙度的相关性分析
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摘要
探求切削力、振动和表面粗糙度之间的相互关系,对实现表面粗糙度的预测预报具有重要意义。以MQL铣削45钢为试验对象,进行了切削速度v、每齿进给量f_z、切削深度a_p的三因素四水平的64组切削试验,在线测量主切削力、轴向力和径向力及振动,对切削分力数据处理得到相应的平均值、标准差和均方根值,同时离线测量出二维粗糙度R_a、三维粗糙度平均值S_a和均方根值S_q。采用正态分布、指数分布、Gamma分布、Weibull分布和Cauchy分布等函数拟合,根据AIC准则确定出最优分布函数,采用极大似然法估计出未知参数。使用Gaussian Copula、t-Copula、Frank Copula、Gumbel Copula、Clayton Copula等Copula函数拟合铣削力、振动和粗糙度之间相关结构形式,采用AIC准则优选出最优Copula函数,并确定出参量。利用最优Copula函数导出的Kendall秩相关系数τ作为评价指标,分析比较了铣削力、振动与表面粗糙度的整体相关性。采用混合Copula函数对铣削力、振动与表面粗糙度的尾部相关性进行了分析。
To explore the relationship between cutting force, vibration and surface roughness is of great significance to predict surface roughness. In this paper, the 64 all-factor experiments of milling 45 steel were conducted with the control variable method of three factors and four levels of cutting speed v, feed per tooth fz and cutting depth ap. The main cutting force, axial force, radial force and vibration were measured on line, and the corresponding average value, standard deviation and RMS values of cutting force were obtained. At the same time, the two-dimensional surface roughness Ra, three-dimensional roughness average Sa and RMS Sq were measured off-line. Then five distribution functions such as Normal distribution, Exponential distribution, Gamma distribution, Weibull distribution and Cauchy distribution were used to fit the sample data. The optimal distribution function was determined by AIC criteria, and the unknown parameters were estimated by maximum likelihood method. The five Copula functions such as Gaussian Copula, t-Copula, Frank Copula, Gumbel Copula, and Clayton Copula were used to fit the related structural forms between milling force, vibration, and roughness, and the optimal Copula function was selected according to the AIC criteria and the parameters are determined. Deriving from the optimal Copula function, the Kendall rank correlation coefficient τ was chosen as the evaluation index to analyze and compared the overall relativity between milling force and surface roughness. A mixed Copula function was constructed to analyze the tail correlation between milling force and surface roughness.
To explore the relationship between cutting force, vibration and surface roughness is of great significance to predict surface roughness. In this paper, the 64 all-factor experiments of milling 45 steel were conducted with the control variable method of three factors and four levels of cutting speed v, feed per tooth fz and cutting depth ap. The main cutting force, axial force, radial force and vibration were measured on line, and the corresponding average value, standard deviation and RMS values of cutting force were obtained. At the same time, the two-dimensional surface roughness Ra, three-dimensional roughness average Sa and RMS Sq were measured off-line. Then five distribution functions such as Normal distribution, Exponential distribution, Gamma distribution, Weibull distribution and Cauchy distribution were used to fit the sample data. The optimal distribution function was determined by AIC criteria, and the unknown parameters were estimated by maximum likelihood method. The five Copula functions such as Gaussian Copula, t-Copula, Frank Copula, Gumbel Copula, and Clayton Copula were used to fit the related structural forms between milling force, vibration, and roughness, and the optimal Copula function was selected according to the AIC criteria and the parameters are determined. Deriving from the optimal Copula function, the Kendall rank correlation coefficient τ was chosen as the evaluation index to analyze and compared the overall relativity between milling force and surface roughness. A mixed Copula function was constructed to analyze the tail correlation between milling force and surface roughness.
引文
[1]刘献礼,刘强,岳彩旭,等.切削过程中的智能技术[J].机械工程学报,2018,54(16):45-61.LIU Xianli, LIU Qing, YUE Caixu, et al. Intelligent machining technology in cutting process[J]. Journal of Mechanical Engineering,2018, 54(16):45-61.
[2]LAURO C H, BRANDAO L C,BALDO D, et al. Monitoring and processing signal applied in machining processes a review[J]. Measurement, 2014, 58(58):73-86.
[3]LU X H, HU X C, JIA Z Y, et al. Model for the prediction of 3D surface topography and surface roughness in micro-milling Inconel 718[J]. The International Journal of Advanced Manufacturing Technology,2018, 94(5-8):2043-2056.
[4]ARAPOGLU R A, SOFUOGLU M A, ORAK S. An ANN-based method to predict surface roughness in turning operations[J].Arabian Journal for Sciences and Engineering,2017,42(5):1929-1940.
[5]MIA M, DHAR N R. Modeling of surface roughness using RSM, FL and SA in dry hard turning[J]. Arabian Journal for Science and Engineering, 2018, 43(3):1125-1136.
[6]SEKULIC M, PEJIC V, Brezocnik M, et al. Prediction of surface roughness in the ball-end milling process using response surfacemethodology, genetic algorithms, and grey wolf optimizer algorithm[J]. Advances in Production Engineering&Management, 2018, 13(1):118-130.
[7]ARRIANDIAGA A, PORTILLO E, SANCHEZ JA, et al. Recurrent ANN-based modelling of the dynamic evolution of the surface roughness in grinding[J]. Neural Computing&Applications, 2017, 28(6):1293-1307.
[8]SVALINA I, SIMUNOVIC G, SARIC T, et al. Evolutionary neuro-fuzzy system for surface roughness evaluation[J]. Applied Soft Computing, 2017, 52:593-604.
[9]MAHER I, ELTAIB M E H. Cutting force-based adaptive neuro-fuzzy approach for accurate surface roughness prediction in end milling operation for intelligent machining[J].The International Journal of AdvancedManufacturing Technology, 2015, 76(5):1-9.
[10]裴宏杰,李公安,付坤鹏,等.基于Copula函数的切削力与表面粗糙度的相关性[J].江苏大学学报(自然科学版),2018,39(2):174-178.PEI Hongjie, LI Gongan, FU Kunpeng, et al. Correlation between cutting force and surface roughness based on Copula function[J]. Journal of Jiangsu University(Natural Science Edition),2018, 39(2):174-178.
[11]JAWORSKI P,DURANTE F,HARDLE W K,et al. Copula theory and its applications[M]. Berlin Heidelberg:SpringerVerlag, 2010.
[12]DURANTE F, SEMPI C. Principles of Copula theory[M]. Boca Raton:CRC Press,2015.
[13]DEGROOT M H,SCHERVISH MJ. Probability and statistics[M]. 4th ed. Boston:Pearson Education, 2012.
[14]吴建华,王新军,张颖.相关性分析中Copula函数的选择[J].统计研究,2014,31(10):99-107.WU Jianhua, WANG Xinjun, ZHANG Ying. The choice of the Copula function in the correlation analysis[J]. Statistical Research,2014, 31(10):99-107.
[15]朱永生.实验数据分析(下册)[M].北京:科学出版社,2012.ZHU Yongsheng. Experimental data analysis(Second Volume)[M]. Beijing:Science Press, 2012.
[16]SHAW M C. Metal cutting principles[M]. 2nd ed. New York:Oxford University Press, 2005.
[2]LAURO C H, BRANDAO L C,BALDO D, et al. Monitoring and processing signal applied in machining processes a review[J]. Measurement, 2014, 58(58):73-86.
[3]LU X H, HU X C, JIA Z Y, et al. Model for the prediction of 3D surface topography and surface roughness in micro-milling Inconel 718[J]. The International Journal of Advanced Manufacturing Technology,2018, 94(5-8):2043-2056.
[4]ARAPOGLU R A, SOFUOGLU M A, ORAK S. An ANN-based method to predict surface roughness in turning operations[J].Arabian Journal for Sciences and Engineering,2017,42(5):1929-1940.
[5]MIA M, DHAR N R. Modeling of surface roughness using RSM, FL and SA in dry hard turning[J]. Arabian Journal for Science and Engineering, 2018, 43(3):1125-1136.
[6]SEKULIC M, PEJIC V, Brezocnik M, et al. Prediction of surface roughness in the ball-end milling process using response surfacemethodology, genetic algorithms, and grey wolf optimizer algorithm[J]. Advances in Production Engineering&Management, 2018, 13(1):118-130.
[7]ARRIANDIAGA A, PORTILLO E, SANCHEZ JA, et al. Recurrent ANN-based modelling of the dynamic evolution of the surface roughness in grinding[J]. Neural Computing&Applications, 2017, 28(6):1293-1307.
[8]SVALINA I, SIMUNOVIC G, SARIC T, et al. Evolutionary neuro-fuzzy system for surface roughness evaluation[J]. Applied Soft Computing, 2017, 52:593-604.
[9]MAHER I, ELTAIB M E H. Cutting force-based adaptive neuro-fuzzy approach for accurate surface roughness prediction in end milling operation for intelligent machining[J].The International Journal of AdvancedManufacturing Technology, 2015, 76(5):1-9.
[10]裴宏杰,李公安,付坤鹏,等.基于Copula函数的切削力与表面粗糙度的相关性[J].江苏大学学报(自然科学版),2018,39(2):174-178.PEI Hongjie, LI Gongan, FU Kunpeng, et al. Correlation between cutting force and surface roughness based on Copula function[J]. Journal of Jiangsu University(Natural Science Edition),2018, 39(2):174-178.
[11]JAWORSKI P,DURANTE F,HARDLE W K,et al. Copula theory and its applications[M]. Berlin Heidelberg:SpringerVerlag, 2010.
[12]DURANTE F, SEMPI C. Principles of Copula theory[M]. Boca Raton:CRC Press,2015.
[13]DEGROOT M H,SCHERVISH MJ. Probability and statistics[M]. 4th ed. Boston:Pearson Education, 2012.
[14]吴建华,王新军,张颖.相关性分析中Copula函数的选择[J].统计研究,2014,31(10):99-107.WU Jianhua, WANG Xinjun, ZHANG Ying. The choice of the Copula function in the correlation analysis[J]. Statistical Research,2014, 31(10):99-107.
[15]朱永生.实验数据分析(下册)[M].北京:科学出版社,2012.ZHU Yongsheng. Experimental data analysis(Second Volume)[M]. Beijing:Science Press, 2012.
[16]SHAW M C. Metal cutting principles[M]. 2nd ed. New York:Oxford University Press, 2005.