Dual Tree Complex Wavelet Based Surface Analysis Model And Topography Recognition For Machining Process

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.