Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition

doi:10.1007/s11465-020-0587-1

Front. Mech. Eng.

2020, Vol. 15

Issue (2) : 227-239 https://doi.org/10.1007/s11465-020-0587-1

RESEARCH ARTICLE

Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition

Jiasheng LI^1,², Xingzhan LI², Wei WEI²(

), Pinkuan LIU¹

¹. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². Institute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Chengdu 610200, China

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Abstract

In the process of cutting, the relative vibration between the cutter and the workpiece has an important effect on the surface topography. In this study, the bidimensional empirical mode decomposition (BEMD) method is used to identify such effect. According to Riesz transform theory, a type of isotropic monogenic signal is proposed. The boundary data is extended on the basis of a similarity principle that deals with serious boundary effect problem. The decomposition examples show that the improved BEMD can effectively solve the problem of boundary effect and decompose the original machined surface topography at multiple scales. The characteristic surface topography representing the relative vibration between the cutter and the workpiece through feature identification is selected. In addition, the spatial spectrum analysis of the extracted profile is carried out. The decimal part of the frequency ratio that has an important effect on the shape of the contour can be accurately identified through contour extraction and spatial spectrum analysis. The decomposition results of simulation and experimental surface morphology demonstrate the validity of the improved BEMD algorithm in realizing the relative vibration identification between the cutter and the workpiece.

Keywords bidimensional empirical mode decomposition spatial spectrum analysis boundary effect vibration identification surface topography

Corresponding Author(s): Wei WEI

Just Accepted Date: 09 April 2020 Online First Date: 28 April 2020 Issue Date: 25 May 2020

Cite this article:

Jiasheng LI,Xingzhan LI,Wei WEI, et al. Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition[J]. Front. Mech. Eng., 2020, 15(2): 227-239.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0587-1
https://academic.hep.com.cn/fme/EN/Y2020/V15/I2/227

Fig.1 Schematic diagram of boundary data continuation.

Fig.2 The improved algorithm flowchart. BIMF: Bidimensional intrinsic mode function.

Fig.3 Test principle and experiment site of machined surface topography.

Tab.1 Experiment parameters

Fig.4 Experimental surface topography of ultraprecision fly-cutting machining: (a) Square workpiece and (b) circular workpiece.

Fig.5 Experimental surface decomposition of the square workpiece: (a) The 1st BIMF, (b) the 2nd BIMF, (c) the 3rd BIMF, and (d) the residual term.

Fig.6 Experimental surface decomposition of the circular workpiece: (a) The 1st BIMF, (b) the 2nd BIMF, (c) the 3rd BIMF, and (d) the residual term.

Tab.2 Surface simulation schemes with different D values

Fig.7 Section profile curve and its spatial spectrum (D = 0.3, A_v= 10 nm, f_v= 29.4 Hz): (a) Section profile curve and (b) spatial spectrum of section profile curve.

Fig.8 Section profile curve and its spatial spectrum (D = 0.1, A_v= 10 nm, f_v= 37.8 Hz): (a) Section profile curve and (b) spatial spectrum of section profile curve.

Fig.9 Section profile curve and spatial spectrum (D = 0.3, A_v= 10 nm, f_v= 29.4 Hz; D = 0.1, A_v= 10 nm, f_v= 37.8 Hz): (a) Section profile curve and (b) spatial spectrum of section profile curve.

Fig.10 Section profile curve and spatial spectrum (D = 0.3, A_v= 10 nm, f_v= 29.4 Hz; D = 0.1, A_v= 2 nm, f_v= 37.8 Hz): (a) Section profile curve and (b) spatial spectrum of section profile curve.

Tab.3 Simulation parameters of machined surface topography

Fig.11 Obvious boundary effect in decomposition results: (a) The 1st BIMF, (b) the 2nd BIMF, (c) the 3rd BIMF, and (d) the residual term.

Fig.12 Decomposition results after boundary effect suppression: (a) Bidimensional diagram of the residual term and (b) the residual term.

Fig.13 The second BIMF contour curve and corresponding spatial spectrum: (a) Section profile curve and (b) spatial spectrum.

Fig.14 The third BIMF contour curve and corresponding spatial spectrum: (a) Section profile curve and (b) spatial spectrum.

$z v$	Displacement of mono-frequency vibration
$A v$	Amplitude of mono-frequency vibration
$f v$	Frequency of mono-frequency vibration
$ϕ$	Spindle rotation angular
$f s$	Spindle rotation frequency
$f r$	Frequency ratio
$I$	The integral part of the frequency ratio
$D$	The decimal part of the frequency ratio
$φ$	Phase shift
$S f n$	Feed per revolution
f	Feed speed of hydrostatic guide
$ω$	Spindle speed
$f n$	Spatial frequency
$l a$	Local amplitude
$l p$	Local phase
$l f$	Local frequencies

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