Shock and Vibration

Volume 2016 (2016), Article ID 1040942, 10 pages

http://dx.doi.org/10.1155/2016/1040942

## An Investigation into Error Source Identification of Machine Tools Based on Time-Frequency Feature Extraction

College of Mechanical Engineering & Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China

Received 19 June 2015; Revised 30 October 2015; Accepted 15 November 2015

Academic Editor: Toshiaki Natsuki

Copyright © 2016 Dongju Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a new identification method to identify the main errors of the machine tool in time-frequency domain. The low- and high-frequency signals of the workpiece surface are decomposed based on the Daubechies wavelet transform. With power spectral density analysis, the main features of the high-frequency signal corresponding to the imbalance of the spindle system are extracted from the surface topography of the workpiece in the frequency domain. With the cross-correlation analysis method, the relationship between the guideway error of the machine tool and the low-frequency signal of the surface topography is calculated in the time domain.

#### 1. Introduction

Machining accuracy is an important performance factor for machine tools, especially under circumstances in which relatively high precision is one of the basic requirements [1]. During the machining process, a variety of errors are in play at the same time, and this will be reflected in the surface topography of the workpiece with varying degrees. Errors of a machine tool include static errors and dynamic errors. Static errors are related to the structure of the machine tool, primarily caused by the geometric errors of the components of the machine tool; this part of the error can be identified from the experimental results by error shape. The dynamic errors of a machine tool are mainly the mechanical distortion of the workpiece and tool, the vibration of the structure of the machine tool, and the tracking error of the controller, which can introduce spatial frequency domain error; thus, this type of error should be identified from the frequency domain. The vibrations caused by the unbalance may destroy critical parts of the machine tool, such as bearings and couplings, which make up the major portion of the observed vibration frequency spectra of the machinery. These vibration spectra can be used to determine the error sources from the machine tool [2]. Before identification, the signal data should be processed first, and its main features should be extracted and determined.

Under certain machining conditions, the surface topography of the workpiece that turned by a machine tool is generated and then is measured through direct measurement of a profiler; thus, a fast and satisfactory identification method should be used. The premise of identification is processing the measured result first and extracting the important features in the signal. In conventional signal processing, the Fourier transform is a direct and commonly used method [3, 4]; a complicated high-order exponential function is used to transform the signal in the time domain into a function in the frequency domain, but the local signal cannot be well analyzed by this method. Local features can be described by the short-time Fourier transform [5], which appears subsequently, but the signal in the frequency domain cannot be localized in the time domain. For nonstationary signals, the wavelet transform is an effective method for processing the signal, which is an analysis method of a signal in the time and scale (frequency) domains. It is a multiresolution analysis method and is known as the microscopic representation of the signal. The biggest advantage is that, in the time and frequency domains, there is a good localized nature: the short time signal with high frequency can be localized, and there is also an accurate trend analysis for low-frequency signals, which provides a special advantage in terms of the measurement of the mutant signal and identification of the fault signal. Wavelet analysis in the field of manufacturing is applied in online monitoring of tool breakage and fault diagnosis of bearings and gears. Li et al. [6] researched the influence of machine vibrations on hard turned surface topographies based on the FFT and wavelet and analyzed the tool behaviour by spatial domain frequency analyses based on the fast Fourier transform, and wavelet reconstruction was used for profile filtering. Lingadurai and Shunmugam [7] proposed the metrological characteristics of the wavelet filter for processing of engineering surfaces and established a few typical manufactured surfaces and their reference surfaces by the wavelet filter and brought out the waviness content and phase matching by random process techniques. Antonino-Daviu et al. [8] studied the wavelet signals at different levels and applied the DWT to analyze numerical and experimental data for the diagnosis of dynamic eccentricities in induction motors. Chand [9] proposed SC- and SS-wavelet transforms that use the cosine and sine signals defined over the smaller intervals that help represent the Fourier transform of a signal in a better way. The SC- and SS-wavelet transforms provide not only sharper time-frequency localization but also much more information in a better localized form than the A-wavelet transform; Zhu et al. [10] reviewed the state of the art of wavelet analysis for tool condition monitoring (TCM), introduced wavelet approaches, and discussed the superiorities of wavelet analysis to Fourier methods for TCM based on the nature of monitored signals. Bhowmik et al. [11] used an electromagnetic transient program (EMTP) to model a real transmission system and MATLAB for DWT and NN, and various types of faults were identified. The Fourier transform cannot be directly used for the signals which are random in the time domain because the signals have no integral condition. The power spectral density (PSD) and autocorrelation functions are coupled with the Fourier transform. PSD describes how the power of a signal or time series is distributed over the different frequencies. As a spectrum function, PSD has a natural advantage in the evaluation of the frequency domain. Bonte et al. [12] proposed a new formula to consider phase differences in the determination of an equivalent von Mises stress power spectral density (PSD) from multiple random inputs. Yoshida [13] analyzed the data of acceleration broadband with PSD; the signal was analyzed according to the height of the peak, and the power spectrum with the statistical properties is generally used as the basis of spectral analysis. Lu et al. [14] analyzed the random vibration signals of a vehicle’s coupled longitudinal tracking system with PSD. Random vibration theory was used to obtain the response power spectral densities, by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation problem and then applying symplectic solution methodology.

With the provided analytical and numerical approaches, some researchers have studied the effects of the unbalanced parts on the machining process and the behaviour of the machine tools. Schulz and Würz [15] showed the system-specific limitations of the component focused balancing and discussed the requirements by means of analytical and numerical approaches. The dynamic unbalance of the spindle is evaluated by a double-rotor model of spindle-drawbar-bearing [16] and harmonic wavelet [17]. The fast Fourier transform (FFT) is used to process the signal to reduce computation time [18] and satisfy magnitudewise shift invariance [19]. Recently, correlation analysis has been used in many research fields. Wieleba [20] used the correlation analysis in tribological research, evaluating the coefficient of friction and wear rate of PTFE composite with steel counterface roughness and hardness. Lockwood and Reynolds [21] presented a technique for automatically characterizing the three-dimensional geometry of fracture surfaces and used digital image correlation (DIC) to provide an accurate and fast method for digitally reconstructing fracture surfaces.

From the above, the previous work merely measured or modelled the single component error of machine tools; these methods will introduce some errors, and the analysis results are different from the actual values. Some researchers analyzed and identified the motion errors of machine tools from several measured results; however, the measured signal from the components of the machine tools cannot represent the actual processing surface. Therefore, the method which identifies the dominant error from the surface topography of the workpiece is more accurate.

In this paper, the surface topography of the workpiece is transformed into a low-frequency part and a high-frequency part by wavelet transform method. Then, the main features are extracted from the high-frequency signal part in the frequency domain by a power spectrum analysis method; the correlation degree of the geometric error of the machine tool and the low-frequency part of the surface topography is calculated in the time domain by the cross-correlation method. Finally, the experimental scheme for the vibration signal of the spindle system in different measurement conditions is designed, and the numerical analysis is verified.

#### 2. Analysis of the Surface Topography of the Workpiece

##### 2.1. Surface Topography of Workpiece Generation

In the experiment, a cylindrical aluminum alloy is selected as the processing part for machining. The machining machine tool is a vertical two-axis lathe in the laboratory, its frame is shown in Figure 1, and it has and guideways. The workpiece (number 2) is supported by a hydrostatic spindle (number 1), and the lathe is used to turn the end face of the workpiece. The dimension of the end face includes a diameter of 20 mm; maximum rotating spindle speeds of 150 rpm and 110 rpm are used in the processing. The upper end face of the cylinder workpiece is turned by the tool (number 5), which is driven by (number 3) and guideways (number 4). The surface topography of the workpiece is measured by a profile testing instrument, and the type is PGI1240. The stylus moves along the radius from the centre of the workpiece to the edge. The displacement is 10 mm because the cylinder is symmetric; thus, the measured result shown in Figure 2 is approximately symmetric, and the horizontal coordinate, that is, the test range, is from −10 mm to 0 and from 0 to 10 mm. The result is a 2D image, and the ordinate coordinates represent the form and waviness of the surface. In Figure 2, the green curve shows the flatness and waviness of the surface turned by the machine tool in Figure 1. The red line expresses the standard centreline of the profile testing instrument, and the maximum form error is shown by the symbol or in Figure 2; the value is 2.0465 *μ*m.