Full Length ArticleInvestigation of KDP crystal surface based on an improved bidimensional empirical mode decomposition method
Introduction
Optical products manufactured by ultra-precision cutting process were widely used in optics, photonics, and biomedical engineering, etc. KDP crystal used as optical switch was a typical kind of material for harmonic frequency converting in laser systems, the performances of optical components made from KDP crystal were determined by the surface quality [1]. Efficient identifying and evaluating texture features with different spatial frequencies would help to reveal the mechanism of product surface, and it was demonstrated that advanced signal analysis methods had much potential for the understanding of surface topography [2].
Texture features had great impact on the quality of KDP crystal surface. It was found that surface roughness with low frequency range was determined by feed marks, which were generated from the spindle-work piece system [3]. An investigation on the cutting process of KDP crystal by single point diamond flycutting, demonstrated that the cutting direction had great impact on the surface quality of KDP crystal [4]. The influence of waviness on the KDP crystal surface was carefully investigated through dynamics analysis, and the result indicated that the waviness with large wavelength were generated by the tool-machine-workpiece system vibration under the intermittent cutting force [5]. An experimental study on surface roughness in rotary ultrasonic machining process of KDP crystal showed that the surface quality was affected by different machining variables (spindle speed, feed rate, and ultrasonic power) [6].
The power spectral density (PSD) method was widely used to understand texture features of machined surface and analyze their effects. The PSD profile based fractal method and correlation analysis model were employed to quantify chemical composition and the environment of glass surface [7]. Texture features with low frequency and high frequency noises of a scanning profile were clearly identified by the PSD technique, then a low pass filter was employed to remove the high frequency noise [8]. The PSD method was used to describe rough surface in frequency domain, with the calculation of amplitudes and frequencies from PSD profiles, the surface was split into macroscopic and microscopic components [9].
Advanced signal processing methods were demonstrated to have excellent performance on analyzing texture features of machined surface [10]. The two-dimensional wavelet transform (2D-WT) based image texture analysis methods were developed for extracting features from turned surface images [11]. The 2D-WT technique was used to evaluate the roundness profiles of mechanical elements, and verified to be a useful tool for analyzing reliability and material strength [12]. Wavelet transform and fractal geometry were applied to process surface profiles and detect roughness trend from thin film surface [13]. An advanced signal processing technique based on continuous wavelet transform was proposed to investigate the correlation relationship between manufactured surface quality and the corresponding generation process [14]. The fractal analysis and box-counting methods were employed to characterize surface profile of ground mono-crystal sapphire [15]. A fractal root mean square deviation method was proposed to evaluate three-dimensional surface machined by rotary ultrasonic grinding process, and the results demonstrated that the developed method can get higher quality surface in practice [16].
Though the ability of digital signal processing methods on analyzing texture features were verified by many research, it was demonstrated that these techniques had shortcomings, such as employing fixed parameters and leakage problems [17], [18]. An advanced signal processing method called bi-dimensional empirical mode decomposition (BEMD) was developed for non-linear and non-stationary signal analysis, and demonstrated that the BEMD can overcome shortcomings of wavelet transform [19]. The BEMD method was indicated that the method had advantages in two dimensional signal processing and texture feature analysis [20], [21]. However, the classical BEMD method was developed based on envelope analysis and sifting process, which suffered from end effects and redundant intrinsic mode functions (IMFs). Large swings occurred at both the two ends of signal during the interpolation fitting process, and corrupted the whole iterative process [22]. Prediction approach was employed to deal with the end effect problem of BEMD method [21]. An improved one dimensional EMD method was developed for weak signal processing using wavelet transform embedded technique [22]. However, the performance of prediction based BEMD method was closely related to the surface quality, and the surface profile analysis by denosing embedded BEMD method has not been reported yet.
This paper developed a novel spatial-frequency analysis method based on improved bidimensional empirical mode decomposition to identify and evaluate the KDP surface profile, a denoising technique was embedded in the sifting iteration process to remove redundant information in decomposed sub-surfaces. Comparative study with the PSD method, two-dimensional wavelet transform, and the traditional BEMD method, was carried out on analyzing KDP crystal surface.
The remainder of this paper was organized as following. Section 2 introduced the experiment of machining KDP crystal. Section 3 presented results obtained from the PSD technique. Section 4 described the BEMD and IBEMD methods, as well as their application on extracting texture features. Section 5 carried out the comparative study with 2D-wavelet transform method. Section 6 discussed the results and findings. Section 7 drew the conclusions.
Section snippets
Experiment
The KDP crystal was processed by an ultra-precision flycutting machine, which was made by the Center for Precision Engineering at the Harbin Institute of Technology. Shown as Fig. 1, the machine tool consisted of diamond tool, worktable, flycutting head, and vacuum chuck, etc. A series of flycutting tests is carried out on the ultra-precision machine tool, under the cutting conditions: depth of cut of 15 mm, feed rate of 100 mm/s, and a spindle rotational speed of 390 r/min, and the tool
Influence of surface characteristics on PSD
The mathematical model of PSD is widely used for the quantitative description of surface roughness. For a discrete wavefront function z(m, n), the PSD can be calculated as following [23],Where, Δx is the pixel length in X direction, Y direction has the same pixel length, k and j are point indexes for two direction profiles, fm and fn are spatial frequencies, defined as fm = m/(NΔx), M and N are the number of pixel points in two directions.
Bidimensional empirical mode decomposition
The bidimensional empirical mode decomposition (BEMD) was a data driven method and developed based on envelope analysis and sifting process, which can decompose complicated signal into a number of IMFs with local characteristics of the signal. By analyzing each IMF component, texture features of the original signal can be effectively identified.
For a two dimensional signal f(m, n), the process of detecting texture features by BEMD method is as following [25],
- (1)
Initialization, set s(m, n) = f(m, n).
- (2)
Comparative study with the 2D-WT method on surface texture analysis
The developed improved BEMD method had a comparative study with the widely used two-dimensional wavelet transform (2D-WT) on analyzing the machined KDP crystal surface profile. Deduction of the 2D-WT method can be referred to [28], with multi-resolution decomposition and reconstruction technique of 2D-WT, the surface profile of KDP crystal was decomposed into sub-surfaces in four directions. The decomposition process employed the widely used sym8 wavelet function, the decomposition level was
Discussion
Texture features detection would help to understand the surface topography and identify defects in the machined surface. The IBEMD method developed in this paper devoted to provide a solution for the end effect problem of traditional BEMD method, as well as had applications on detecting texture features of machined surface. With embedded denoising technique in the iteration procedure, different spatial frequencies of the machined crystal surface were identified by the IBEMD method. Combined
Conclusions
In summary, this paper developed an improved BEMD method for texture feature investigation of machined KDP crystal surface in spatial frequency domain. By embedding a two dimensional denoising technique in the sifting process, the end effect and iteration errors were removed to improve the decomposed IMFs by the BEMD method. Comparative study with PSD method, traditional BEMD method, and 2D-WT technique on investigating texture features of machined surface demonstrated that, (i) the cutting
Acknowledgement
This research was funded by the National Natural Science Foundation of China (#51561125002, #51705106).
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