双树复小波表面分析模型及加工过程形貌辨识方法研究
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摘要
机械制造业中90%的工件失效源于表面问题,对工程表面形貌的准确分析和评定是提高机加工产品质量的重要保证。将表面计量方法与加工过程相关联则是当前表面计量领域的研究重点。这种联系建立的前提是:对表面各种特征的准确提取; 对特征的有效分析方法,即建立起特征变化与加工过程条件变化之间的联系。
本文研究了用于工程表面分析的第一代和第二代小波模型,从幅度和相位传输特性的角度分析了不同小波基对工程表面分析评定的影响。指出基于提升格式算法的双正交小波由于具有线性相位、好的幅度传输特性以及较高的运算效率,从而是当前用于表面计量的最优小波滤波器之一。
为了解决基于实小波变换的第一、二代小波模型的平移敏感性和方向性差的缺点,本文将双树复小波变换引入到表面计量领域中,建立了工程表面分析的双树复小波模型。由于双树复小波变换具有近似的平移不变性以及改进的方向选择性等优点,从而成功地解决了实小波模型用于提取表面功能特征(如峰、坑、脊、谷等)时所存在的沿特征边缘的信号畸变问题。对复小波滤波器的表面计量特性进行了分析,结果表明其具有线性相位和近似理想的幅频传输特性,对于表面粗糙度等频率成分具有很好的分辨特性。计算机模拟与实际二维三维数据处理的结果验证了其特性。
本文提出了基于双树复小波变换的测量信号软阈值降噪方法。假定各层小波变换系数服从双指数分布、噪声服从高斯分布,采用最大后验估计方法推导了阈值计算方法,给出了该降噪方法的算法流程,模拟及实际数据的分析结果,验证了该方法的有效性。提出了复有限脊小波变换方法,通过对信号在有限Radon 变换上的投影进行双树复小波变换,将线奇异性转换为点奇异性,成功实现了对线特征的多尺度平移不变提取。
本文提出了基于表面计量的加工过程状态辨识方法。分析了表面空间参数、空间自相关谱、空间功率谱、角谱和半径谱的物理意义,以及与加工过程的条件变化之间的关系。对铣削加工过程中颤振和刀具磨损时表面形貌变化的研究表明:已加工表面的空间谱,尤其是空间自相关谱的模式能够反映铣削加工过程的颤振发生及其发展; 表面空间参数和空间自相关谱的联合分析可以确定刀具磨损的程度。
It has been shown that the 90% of all engineering component failures in practice are surface initiated. The exact analysis and characterization of the surface topography is important to ensure the quality improvement of the machined components. The investigation of combining surface metrology with the machining process has been emphasized in the field of the modern surface precision metrology. The preconditions of building this relationship are: to extract different surface features correctly; to create an effective analysis method for these features, i.e., to establish the relation between the variation of the surface features and the variation of machining conditions.
The first/second generations of wavelet surface analysis model based on the Real Discrete Wavelet Transform (real DWT) have been reviewed. The influences of different wavelet bases for surface analysis have also been investigated from the aspects of phase and amplitude transmission characteristics. It is pointed out that the second generation of wavelet model based on the lifting scheme and biorthogonal wavelet basis is currently one of the best wavelet filters for surface metrology, as it takes advantages of linear phase, near brick wall transmission and efficient algorithm.
To solve the problems of shift-variance and poor directional selectivity existing in the Real DWT model, the Dual-tree Complex Wavelet Transform (DT-CWT) has been introduced into the field of surface metrology. Accordingly the third generation of wavelet model for engineering surface analysis is also built by using DT-CWT. Due to the good properties of approximately shift-invariance and improved directionality, the DT-CWT can extract the morphological features (such as the peaks/pits and ridges/valleys) without aliasing along the edges of these features. The metrological characteristics of the DT-CWT filter for surface analysis are investigated, especially on the aspect of transmission characteristics analysis. The property of linear phase ensures filtering results with no distortion and good ability for feature localization, the property of near brick wall transmission of the amplitude transmission enables DT-CWT filter to separate different frequency components (such as roughness, waviness and form errors) efficiently. Both Computer simulation and experimental results of practical surface 2D/3D filtering prove that the DT-CWT filter is very suitable for the separation and extraction of frequency components such as surface roughness, waviness and form.
A soft-threshold method in the DT-CWT domain is proposed to reduce the noise of measurement signals. By using the Maximum Posteriori estimator (MAP) and presuming that the wavelet coefficient of the noisy signals obey double exponential distribution and the noise obey the Gaussian distribution respectively, the value of soft-threshold has been induced
and the procedure of algorithm to reduce the noise is also given. Simulated and practical denoising results have verified the effectiveness of the algorithm. A novel developed Complex Finite Ridgelet Transform (CFRIT), which provides approximate shift invariance and analysis of line singularities, is proposed by taking a DT-CWT on the projections of the Finite Radon Transform (FRAT). A surface metrology based machining-condition-monitoring methodology is proposed to analyse the change of the surface topography features during machining process. The physical meaning of the variation of the areal numerical parameters, Areal Autocorrelation Function (AACF), areal power spectrum density (APSD), angular spectrum and the radius spectrum has been analysed and associated to the variation of machining condition. Through a series of cutting experiments, the phenomena of Chatter and tool wear in peripheral milling have been investigated. The results show that the pattern of the areal spectrum, especially the AACF of the machined surface can reflect the chatter arising and development of milling process; the combination of analysis on the areal numerical parameters and the AACF can address the degree of tool wear.
本文研究了用于工程表面分析的第一代和第二代小波模型,从幅度和相位传输特性的角度分析了不同小波基对工程表面分析评定的影响。指出基于提升格式算法的双正交小波由于具有线性相位、好的幅度传输特性以及较高的运算效率,从而是当前用于表面计量的最优小波滤波器之一。
为了解决基于实小波变换的第一、二代小波模型的平移敏感性和方向性差的缺点,本文将双树复小波变换引入到表面计量领域中,建立了工程表面分析的双树复小波模型。由于双树复小波变换具有近似的平移不变性以及改进的方向选择性等优点,从而成功地解决了实小波模型用于提取表面功能特征(如峰、坑、脊、谷等)时所存在的沿特征边缘的信号畸变问题。对复小波滤波器的表面计量特性进行了分析,结果表明其具有线性相位和近似理想的幅频传输特性,对于表面粗糙度等频率成分具有很好的分辨特性。计算机模拟与实际二维三维数据处理的结果验证了其特性。
本文提出了基于双树复小波变换的测量信号软阈值降噪方法。假定各层小波变换系数服从双指数分布、噪声服从高斯分布,采用最大后验估计方法推导了阈值计算方法,给出了该降噪方法的算法流程,模拟及实际数据的分析结果,验证了该方法的有效性。提出了复有限脊小波变换方法,通过对信号在有限Radon 变换上的投影进行双树复小波变换,将线奇异性转换为点奇异性,成功实现了对线特征的多尺度平移不变提取。
本文提出了基于表面计量的加工过程状态辨识方法。分析了表面空间参数、空间自相关谱、空间功率谱、角谱和半径谱的物理意义,以及与加工过程的条件变化之间的关系。对铣削加工过程中颤振和刀具磨损时表面形貌变化的研究表明:已加工表面的空间谱,尤其是空间自相关谱的模式能够反映铣削加工过程的颤振发生及其发展; 表面空间参数和空间自相关谱的联合分析可以确定刀具磨损的程度。
It has been shown that the 90% of all engineering component failures in practice are surface initiated. The exact analysis and characterization of the surface topography is important to ensure the quality improvement of the machined components. The investigation of combining surface metrology with the machining process has been emphasized in the field of the modern surface precision metrology. The preconditions of building this relationship are: to extract different surface features correctly; to create an effective analysis method for these features, i.e., to establish the relation between the variation of the surface features and the variation of machining conditions.
The first/second generations of wavelet surface analysis model based on the Real Discrete Wavelet Transform (real DWT) have been reviewed. The influences of different wavelet bases for surface analysis have also been investigated from the aspects of phase and amplitude transmission characteristics. It is pointed out that the second generation of wavelet model based on the lifting scheme and biorthogonal wavelet basis is currently one of the best wavelet filters for surface metrology, as it takes advantages of linear phase, near brick wall transmission and efficient algorithm.
To solve the problems of shift-variance and poor directional selectivity existing in the Real DWT model, the Dual-tree Complex Wavelet Transform (DT-CWT) has been introduced into the field of surface metrology. Accordingly the third generation of wavelet model for engineering surface analysis is also built by using DT-CWT. Due to the good properties of approximately shift-invariance and improved directionality, the DT-CWT can extract the morphological features (such as the peaks/pits and ridges/valleys) without aliasing along the edges of these features. The metrological characteristics of the DT-CWT filter for surface analysis are investigated, especially on the aspect of transmission characteristics analysis. The property of linear phase ensures filtering results with no distortion and good ability for feature localization, the property of near brick wall transmission of the amplitude transmission enables DT-CWT filter to separate different frequency components (such as roughness, waviness and form errors) efficiently. Both Computer simulation and experimental results of practical surface 2D/3D filtering prove that the DT-CWT filter is very suitable for the separation and extraction of frequency components such as surface roughness, waviness and form.
A soft-threshold method in the DT-CWT domain is proposed to reduce the noise of measurement signals. By using the Maximum Posteriori estimator (MAP) and presuming that the wavelet coefficient of the noisy signals obey double exponential distribution and the noise obey the Gaussian distribution respectively, the value of soft-threshold has been induced
and the procedure of algorithm to reduce the noise is also given. Simulated and practical denoising results have verified the effectiveness of the algorithm. A novel developed Complex Finite Ridgelet Transform (CFRIT), which provides approximate shift invariance and analysis of line singularities, is proposed by taking a DT-CWT on the projections of the Finite Radon Transform (FRAT). A surface metrology based machining-condition-monitoring methodology is proposed to analyse the change of the surface topography features during machining process. The physical meaning of the variation of the areal numerical parameters, Areal Autocorrelation Function (AACF), areal power spectrum density (APSD), angular spectrum and the radius spectrum has been analysed and associated to the variation of machining condition. Through a series of cutting experiments, the phenomena of Chatter and tool wear in peripheral milling have been investigated. The results show that the pattern of the areal spectrum, especially the AACF of the machined surface can reflect the chatter arising and development of milling process; the combination of analysis on the areal numerical parameters and the AACF can address the degree of tool wear.
引文
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