基于经验模态分解方法的加工误差溯源研究
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摘要
二十一世纪是“质量的世纪”,随着企业竞争的不断深化,质量越来越成为企业赖以生存和发展的基础。
加工精度是机械类产品质量的基石。被加工工件在多种多样的误差源综合影响下,难免会出现加工误差,当加工过程出现异常时,只有很少一部分时间用于进行异常的处理,80%以上的时间都被用来判断异常的来源。传统的以统计方法为基础的加工误差溯源方法需要大量的样本数据,很难适用于目前主流的多品种小批量生产方式。为克服传统方法的不足,本文提出了基于经验模态分解方法的加工误差溯源方法,对加工过程中的误差源进行追溯,以提出合理、准确的调整措施。主要研究内容包括三方面：
(1)对经验模态分解方法的理论进行了研究,并将其应用到加工误差信号处理当中。分析了端点效应产生的原因,提出了用极值点对称延拓法和灰色误差分离方法联合抑制端点效应的方法。用MATLAB对经验模态分解方法和其端点效应抑制方法进行了编程实现,并对模拟信号进行分解,验证了本文提出的端点效应抑制方法的有效性。
(2)用经验模态分解方法将工件加工误差进行分解,得到其形状误差曲线,并根据形状误差曲线特征进行误差溯源。提出用工件表面Hilbert谱进行加工误差诊断的方法。通过对机床主轴、导轨和传动链在加工过程中误差的频率特性进行分析,得出了当出现主轴不平衡和不对中等故障、导轨不平衡故障、传动链内部零件故障和切削力故障时Hilbert谱的频谱特征,进而进行加工误差的诊断,并用经验模态分解方法对工件表面加工误差进行了溯源。
(3)在轴承、主轴刚度分析的基础上,提出了主轴系统力变形的优化计算方法,建立了主轴的力变形误差模型。通过对导轨进行受力分析,建立了切削力和导轨五项几何误差的关系,从而建立了机床导轨力变形误差模型。当工件表面Hilbert谱高频部分出现高能量集中时,说明切削力为主要误差源,提出了用经验模态分解方法和机床误差模型对切削力产生的工件表面实际加工误差进行溯源的方法,并用模拟信号对切削力加工误差溯源的过程进行了模拟,通过对信号进行相关性分析,证明了基于经验模态分解方法和机床误差模型进行加工误差溯源的有效性。最后,对机床主轴的力变形误差模型进行了修正,使其能准确计算切削力静态部分引起的主轴误差。
The21st century is "The Century of Quality"', with the deepening of enterprise competition, the quality is becoming more and more important.
Machining precision is the base of mechanical product quality. Under the influence of various error sources, there might be machining errors on the parts. When the machining process is abnormal, only a little time will be spent in dealing with the abnormal factors, more than80percent time will be spent in finding them. The traditional error tracing methods based on statistical theory needs plenty of sample data, so it's difficult to be applied to the mainstream way of multi-varieties and small batch production mode. In order to overcome the deficiency of the traditional methods, the processing error tracing method based on Empirical Mode Decomposition (EMD) is proposed in this paper. In order to put forward reasonable and accurate adjustment measures, the error sources from the machine tools must be traced. The main research content includes three aspects:
(1) The EMD theory is researched and applied to the machining error signal processing. Analyzed the reason of endpoint effect and proposed the method of combining Extreme Point Symmetry Continuation method and Gray Error Separation method to suppress the endpoint effect. The program of EMD and Endpoint Effect suppressing method is developed with MATLAB. The Endpoint Effect suppressing method proposed in this paper is proved to be effective by decomposing simulation signal.
(2) The form error is gotten by the decomposition of the work piece machining error with EMD, and then the error sources are traced by the characteristics of the form error. The Hilbert spectrum is applied to the processing error diagnosis. The Hilbert spectral characteristics of spindle imbalance and other faults, slide way imbalance, transmission chain errors are analyzed by analyzing the frequency characteristic of spindle, slide way and transmission chain. And then the machining error of work piece is traced by EMD method.
(3) After a research on the stiffness of bearing and shaft, the paper proposed a simple method to calculate the deformation of the spindle under cutting force, so the spindle model is established. Then the slide way model is established on the basis of carrying out stress analysis for slide way. When the concentrated high energy appears in the high frequency part of Hilbert spectrum, the main error source is cutting force. The paper proposed a method to trace the error caused by cutting force based on EMD and machine tool model. Then a simulation signal is used to simulate the error tracing process, and the method is proved to be effective by correlation analysis. In the end, the spindle model is corrected by EMD method, so that the deformation caused by static force can be calculated correctly.
加工精度是机械类产品质量的基石。被加工工件在多种多样的误差源综合影响下,难免会出现加工误差,当加工过程出现异常时,只有很少一部分时间用于进行异常的处理,80%以上的时间都被用来判断异常的来源。传统的以统计方法为基础的加工误差溯源方法需要大量的样本数据,很难适用于目前主流的多品种小批量生产方式。为克服传统方法的不足,本文提出了基于经验模态分解方法的加工误差溯源方法,对加工过程中的误差源进行追溯,以提出合理、准确的调整措施。主要研究内容包括三方面：
(1)对经验模态分解方法的理论进行了研究,并将其应用到加工误差信号处理当中。分析了端点效应产生的原因,提出了用极值点对称延拓法和灰色误差分离方法联合抑制端点效应的方法。用MATLAB对经验模态分解方法和其端点效应抑制方法进行了编程实现,并对模拟信号进行分解,验证了本文提出的端点效应抑制方法的有效性。
(2)用经验模态分解方法将工件加工误差进行分解,得到其形状误差曲线,并根据形状误差曲线特征进行误差溯源。提出用工件表面Hilbert谱进行加工误差诊断的方法。通过对机床主轴、导轨和传动链在加工过程中误差的频率特性进行分析,得出了当出现主轴不平衡和不对中等故障、导轨不平衡故障、传动链内部零件故障和切削力故障时Hilbert谱的频谱特征,进而进行加工误差的诊断,并用经验模态分解方法对工件表面加工误差进行了溯源。
(3)在轴承、主轴刚度分析的基础上,提出了主轴系统力变形的优化计算方法,建立了主轴的力变形误差模型。通过对导轨进行受力分析,建立了切削力和导轨五项几何误差的关系,从而建立了机床导轨力变形误差模型。当工件表面Hilbert谱高频部分出现高能量集中时,说明切削力为主要误差源,提出了用经验模态分解方法和机床误差模型对切削力产生的工件表面实际加工误差进行溯源的方法,并用模拟信号对切削力加工误差溯源的过程进行了模拟,通过对信号进行相关性分析,证明了基于经验模态分解方法和机床误差模型进行加工误差溯源的有效性。最后,对机床主轴的力变形误差模型进行了修正,使其能准确计算切削力静态部分引起的主轴误差。
The21st century is "The Century of Quality"', with the deepening of enterprise competition, the quality is becoming more and more important.
Machining precision is the base of mechanical product quality. Under the influence of various error sources, there might be machining errors on the parts. When the machining process is abnormal, only a little time will be spent in dealing with the abnormal factors, more than80percent time will be spent in finding them. The traditional error tracing methods based on statistical theory needs plenty of sample data, so it's difficult to be applied to the mainstream way of multi-varieties and small batch production mode. In order to overcome the deficiency of the traditional methods, the processing error tracing method based on Empirical Mode Decomposition (EMD) is proposed in this paper. In order to put forward reasonable and accurate adjustment measures, the error sources from the machine tools must be traced. The main research content includes three aspects:
(1) The EMD theory is researched and applied to the machining error signal processing. Analyzed the reason of endpoint effect and proposed the method of combining Extreme Point Symmetry Continuation method and Gray Error Separation method to suppress the endpoint effect. The program of EMD and Endpoint Effect suppressing method is developed with MATLAB. The Endpoint Effect suppressing method proposed in this paper is proved to be effective by decomposing simulation signal.
(2) The form error is gotten by the decomposition of the work piece machining error with EMD, and then the error sources are traced by the characteristics of the form error. The Hilbert spectrum is applied to the processing error diagnosis. The Hilbert spectral characteristics of spindle imbalance and other faults, slide way imbalance, transmission chain errors are analyzed by analyzing the frequency characteristic of spindle, slide way and transmission chain. And then the machining error of work piece is traced by EMD method.
(3) After a research on the stiffness of bearing and shaft, the paper proposed a simple method to calculate the deformation of the spindle under cutting force, so the spindle model is established. Then the slide way model is established on the basis of carrying out stress analysis for slide way. When the concentrated high energy appears in the high frequency part of Hilbert spectrum, the main error source is cutting force. The paper proposed a method to trace the error caused by cutting force based on EMD and machine tool model. Then a simulation signal is used to simulate the error tracing process, and the method is proved to be effective by correlation analysis. In the end, the spindle model is corrected by EMD method, so that the deformation caused by static force can be calculated correctly.
引文
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[9]Gianantonio Magnani, Paolo Rocco. Mechatronic analysis of a complex transmission chain for performance optimization in a machine tool [J]. Mechatronics,2010,20 (1):85-101
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[2]张公绪.现代质量管理学[M].北京：中国财政经济出版社,1999
[3]W Hu, A G Starr. A Systematic Approach to Integrated Fault Diagnosis of Flexible Manufacturing Systems [J]. International Journal of Machine Tools & Manufacture [J],2000(40):1587-1602
[4]江平宇,刘道玉.数字化加工过程质量控制方法与技术[M].北京：科学出版社,2010
[5]Spur G.主轴—轴承系统的计算：利用结构修正法确定静态和动态性能[J].国外轴承,1991,(4)：6-11.
[6]Gagnol V, Le T P, Ray P. Modal identification of spindle-tool unit in high-speed machining. Mechanical Systems and Signal Processing,2011,25(7):2388-2398.
[7]J. Hjink. Analysis of A milling machine [J]. Computed results Versus Experiment Date.1973, (14):58-61
[8]Jaspreet Singh Dhupia, Bartosz Powalka. Effect of joint nonlinearities on the dynamic performance of a machine tool [J]. Journal of Manufacturing Science and Engineering,2007,129(5):943-950
[9]Gianantonio Magnani, Paolo Rocco. Mechatronic analysis of a complex transmission chain for performance optimization in a machine tool [J]. Mechatronics,2010,20 (1):85-101
[10]石世宏,颜竟成.机床主轴回转误差的分析建模与仿真[J].组合机床与自动化加工技术.1994,10：20-24
[10]陈世平,曹建国.机床主轴回转误差分析[J].机械.1998,25：385-387
[12]杨海.M115W外圆磨床主轴的动力学仿真分析及其参数反求[D].湖南大学硕士学位论文,2010.
[13]董献国.机床导轨结合部变形所产生的加工误差[J].陕西机械学院学报.1988,4(3)：19-27
[14]黄玉美.机床导轨结合部优化设计方法与程序[J].陕西机械学院学报.1989, 5(2)：125-129
[15]张广鹏,史文浩,黄玉美.机床导轨结合部的动态特性解析方法及其应用[J].机械工程学报,2002,(10)：114-117
[16]李锦西.机床传动链误差的形成机理及数学模型的探讨[J].设备管理与维修,2002,4：9-11
[17]Fang C Y, Fan K C. Development of multi-function error calibration system for NC machine tools[J]. In Proc.3rd ROC-ROK Metrology Symposium. 1990,3:163-171
[18]Chen J S, Yuan J, Ni J, Wu S M. Real-time compensation for time-variant volumetric errors on a machining center, Transactions of the ASME[J]. Journal of Engineering for Industry.1993(115):472-479
[19]Fan K C, Chen M J, Huang W M. A six-degree-of-freedom measurement system for the motion accuracy of linear stages[J].Int J.Manufact.1998,38(3):155-164
[20]H F F Castro. A method for evaluating spindle rotation errors of machine tools using a laser interferometer[J], Measurement,2008,41(5):526-537
[21]沈金华.数控机床误差补偿关键技术及其应用[D].上海交通大学博士学位论文,2008
[22]S Ibaraki, M Sawada, A Matsybara, and etc., Machine tests to identify kinematic errors on five-axis machine tools[J], Precision Engineering,2010,3(34):387-398
[23]Bryan J B.A simple method for testing measuring machine and machine tools[J]. Precision Engineering.1982,4(2):61-69
[24]Ziegert J C,Mize C D.The laser ball bar:a new instrument for machine tool merology [J].Precision Engineering.1994,16(4):259-267
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