大型立式超精密机床系统误差分析与辨识技术研究
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摘要
超精密加工技术是现代高技术战争的重要支撑技术,是现代高科技产业和科学技术的发展基础,是现代制造科学的发展方向。以超精密加工技术为支撑的半导体器件,为电子、信息产业的发展奠定了基础。现代科学技术的发展以试验为基础,所需试验仪器和设备几乎无一不需要超精密加工技术的支撑。当前超精密加工已进入纳米尺度,成为尖端技术发展中不可缺少的关键加工手段,不论是军事工业,还是民用工业,都需要这种先进的加工技术。
本文主要针对两轴立式大型超精密机床加工精度进行研究,采用传递矩阵法、有限元方法以及多体系统理论对影响加工精度的机床主要部件误差进行分析。为能够比较全面表征已加工表面形貌特征,本文选择小波方法、相关性分析方法和功率谱密度方法对机床已加工表面形貌进行分析,小波变换方法区别于传统傅立叶变化方法的主要特征是能够在时频域对信号进行全面表征,相关性分析可以对两个不同过程信号的相关性进行评估。功率谱密度方法可以全面反映检测信号中的小尺度波纹特征,据此对机床误差进行了辨识。
针对液体静压轴承结构,根据流体力学知识推导出轴承参数公式并与其他计算方法进行了对比。基于牛顿定律,建立了主轴系统平衡状态下数学模型,以此模型为基础推导了主轴加工过程中偏摆幅值与轴承刚度等参数关系,并给出了各个方向上运动刚度。通过建立主轴系统动力学模型研究了加工过程中质量不平衡引起的主轴受迫振动,并推导出了相应动态频率响应。从机床主轴系统的传热机理着手进行分析,建立了主轴系统的热-机械模型,推导出了主轴系统内部传递热量的计算依据。分析了在不同条件热误差影响下轴承特性的变化,从而推导出机床整个主轴系统的。
文中利用多体系统理论建立了机床X向和Z向导轨耦合的运动误差模型,针对空气静压溜板结构,根据气体润滑理论推导出了双排节流空气静压溜板的气膜压力分布,得出相应承载力公式,气膜刚度。给出了气膜厚度变化时整个溜板系统频率变化规律。建立了运动溜板和卸荷溜板刚度耦合的动力学模型,推导出了气膜厚度变化时溜板沿垂直方向的振动响应幅值变化规律,最后得出在整个气膜厚度波动范围内,刚度耦合的溜板系统响应频率的相应变化范围。
最后以小波变换为手段对检测信号进行处理。从主轴回转误差的检测着手进行分析,提出了以维尔斯特拉斯函数建立的主轴综合回转误差模型,与实际检测结果的对比验证了此模型的正确性与可行性。以互相关性分析为手段,分别分析了导轨系统和主轴系统误差与加工面形结果的相关性,从而推导出了各误差对加工精度的影响程度。以小波方法和功率谱密度方法相结合,从频域对导轨系统和主轴系统误差进行分析,提取出了机床相关振动信号的频域特征,从而根据频谱特征辨识出影响加工精度的各个误差源。
Ultra-precision machining technology is the development foundation for high-tech industries. The semiconductor device supported by ultra-precision machining technology, laid the foundation for the development of electronics and information industry. The development of modern science and technology based on the test, almost all of the test equipment needs the support of ultra-precision machining technology. Now ultra-precision machining has entered the nano-scale, and become an indispensable key means of developing high-tech. Whether the military industry, or civilian industry, all need such advanced machining technology.
The research on machining precision of a two-axis large ultra-precision machine tool, analyzing the errors of main components of machine tool by the transfer matrix method, finite element method and multi-body theory. In order to show the comprehensive characterization of workpiece, wavelet method, correlation analysis and power spectral density method are used to analyze the surface topography of workpiece, different from the traditional Fourier transfer method, wavelet method express the comprehensive characterization of the signal in time and frequency domain. Correlation analysis method can estimate the signal in two different processes. Power spectral density method can fully reflect the impact of small-scale waviness of surface morphology on the machined accuracy.
For the hydrostatic bearings, the parameters equation of bearings was deduced by the knowledge of fluid mechanics, and the calculated results were compared with other calculations. The mathematical model of spindle system in equilibrium was established according to Newton’s law, based on the model, the relationship between derivation angle and stiffness of bearing was deduced, and the stiffnesses in all directions are given. The forced vibration of spindle caused by unbalance during machining process was researched through dynamic model of spindle, dynamic frequency response was deduced according to the model of spindle. Thermal-mechanical model of spindle system was established, the calculation basis of the heat transfer in the spindle system was deuced, and thermal error was analyzed with heat transfer mechanism, the variation of bearing performance at the different conditions under the influence of thermal errors, and the impact on the machining accuracy was analyzed.
The coupling error model of guideways of machine tool was established with multi-body system theory. For the complex structure of guideway and unloading slide, the pressure distribution of gas film of guideway with double row orifices by gas lubrication theory, and corresponding load capacity and gas stiffness was obtained. The movement frequency with gas film thickness of entire slide system during machining process was showed. The coupling dynamic model of motion and unloading slides was established through corresponding frequency, the dynamic response of slide with the variation of gas film thickness was deduced. Finally, the variation of moving frequency in the whole gas film thickness was obtained.
Finally, the measured result of workpiece was processed by wavelet transfer. The rotation error model of spindle was proposed by Weierstrass function, and the correctness and feasibility of this model was verified by comparing with actual test results. The correlation between guideway, spindle system and measured result of workpiece was analyzed, thus the degree of influence of every error on the machining accuracy was deduced. Combained with wavelet method and power spectral density method, the errors of guideway and spindle systems was analyzed in frequency domain, the characteristics of vibration signal of machine tool in frequency domain was extracted, and various error that affect the machining accuracy were identified according to the spectral characteristics.
本文主要针对两轴立式大型超精密机床加工精度进行研究,采用传递矩阵法、有限元方法以及多体系统理论对影响加工精度的机床主要部件误差进行分析。为能够比较全面表征已加工表面形貌特征,本文选择小波方法、相关性分析方法和功率谱密度方法对机床已加工表面形貌进行分析,小波变换方法区别于传统傅立叶变化方法的主要特征是能够在时频域对信号进行全面表征,相关性分析可以对两个不同过程信号的相关性进行评估。功率谱密度方法可以全面反映检测信号中的小尺度波纹特征,据此对机床误差进行了辨识。
针对液体静压轴承结构,根据流体力学知识推导出轴承参数公式并与其他计算方法进行了对比。基于牛顿定律,建立了主轴系统平衡状态下数学模型,以此模型为基础推导了主轴加工过程中偏摆幅值与轴承刚度等参数关系,并给出了各个方向上运动刚度。通过建立主轴系统动力学模型研究了加工过程中质量不平衡引起的主轴受迫振动,并推导出了相应动态频率响应。从机床主轴系统的传热机理着手进行分析,建立了主轴系统的热-机械模型,推导出了主轴系统内部传递热量的计算依据。分析了在不同条件热误差影响下轴承特性的变化,从而推导出机床整个主轴系统的。
文中利用多体系统理论建立了机床X向和Z向导轨耦合的运动误差模型,针对空气静压溜板结构,根据气体润滑理论推导出了双排节流空气静压溜板的气膜压力分布,得出相应承载力公式,气膜刚度。给出了气膜厚度变化时整个溜板系统频率变化规律。建立了运动溜板和卸荷溜板刚度耦合的动力学模型,推导出了气膜厚度变化时溜板沿垂直方向的振动响应幅值变化规律,最后得出在整个气膜厚度波动范围内,刚度耦合的溜板系统响应频率的相应变化范围。
最后以小波变换为手段对检测信号进行处理。从主轴回转误差的检测着手进行分析,提出了以维尔斯特拉斯函数建立的主轴综合回转误差模型,与实际检测结果的对比验证了此模型的正确性与可行性。以互相关性分析为手段,分别分析了导轨系统和主轴系统误差与加工面形结果的相关性,从而推导出了各误差对加工精度的影响程度。以小波方法和功率谱密度方法相结合,从频域对导轨系统和主轴系统误差进行分析,提取出了机床相关振动信号的频域特征,从而根据频谱特征辨识出影响加工精度的各个误差源。
Ultra-precision machining technology is the development foundation for high-tech industries. The semiconductor device supported by ultra-precision machining technology, laid the foundation for the development of electronics and information industry. The development of modern science and technology based on the test, almost all of the test equipment needs the support of ultra-precision machining technology. Now ultra-precision machining has entered the nano-scale, and become an indispensable key means of developing high-tech. Whether the military industry, or civilian industry, all need such advanced machining technology.
The research on machining precision of a two-axis large ultra-precision machine tool, analyzing the errors of main components of machine tool by the transfer matrix method, finite element method and multi-body theory. In order to show the comprehensive characterization of workpiece, wavelet method, correlation analysis and power spectral density method are used to analyze the surface topography of workpiece, different from the traditional Fourier transfer method, wavelet method express the comprehensive characterization of the signal in time and frequency domain. Correlation analysis method can estimate the signal in two different processes. Power spectral density method can fully reflect the impact of small-scale waviness of surface morphology on the machined accuracy.
For the hydrostatic bearings, the parameters equation of bearings was deduced by the knowledge of fluid mechanics, and the calculated results were compared with other calculations. The mathematical model of spindle system in equilibrium was established according to Newton’s law, based on the model, the relationship between derivation angle and stiffness of bearing was deduced, and the stiffnesses in all directions are given. The forced vibration of spindle caused by unbalance during machining process was researched through dynamic model of spindle, dynamic frequency response was deduced according to the model of spindle. Thermal-mechanical model of spindle system was established, the calculation basis of the heat transfer in the spindle system was deuced, and thermal error was analyzed with heat transfer mechanism, the variation of bearing performance at the different conditions under the influence of thermal errors, and the impact on the machining accuracy was analyzed.
The coupling error model of guideways of machine tool was established with multi-body system theory. For the complex structure of guideway and unloading slide, the pressure distribution of gas film of guideway with double row orifices by gas lubrication theory, and corresponding load capacity and gas stiffness was obtained. The movement frequency with gas film thickness of entire slide system during machining process was showed. The coupling dynamic model of motion and unloading slides was established through corresponding frequency, the dynamic response of slide with the variation of gas film thickness was deduced. Finally, the variation of moving frequency in the whole gas film thickness was obtained.
Finally, the measured result of workpiece was processed by wavelet transfer. The rotation error model of spindle was proposed by Weierstrass function, and the correctness and feasibility of this model was verified by comparing with actual test results. The correlation between guideway, spindle system and measured result of workpiece was analyzed, thus the degree of influence of every error on the machining accuracy was deduced. Combained with wavelet method and power spectral density method, the errors of guideway and spindle systems was analyzed in frequency domain, the characteristics of vibration signal of machine tool in frequency domain was extracted, and various error that affect the machining accuracy were identified according to the spectral characteristics.
引文
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