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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front Mech Eng Chin    2009, Vol. 4 Issue (2) : 179-183    https://doi.org/10.1007/s11465-009-0018-9
RESEARCH ARTICLE
Dynamic characteristics of an NC table with phase space reconstruction
Linhong WANG1(), Bo WU2, Runsheng DU2, Shuzi YANG2
1. Department of Electromechanical Engineering, Nanyang Institute of Technology, Nanyang 473004, China; 2. National Key Laboratory of Digital Manufacturing and Assembling Technology, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

The dynamic properties of a numerical control (NC) table directly interfere with the accuracy and surface quality of work pieces machined by a computer numerical control (CNC) machine. Phase space reconstruction is an effective approach for researching dynamic behaviors of a system with measured time series. Based on the theory and method for phase space reconstruction, the correlation dimension, maximum Lyapunov exponent, and dynamic time series measured from the NC table were analyzed. The characteristic quantities such as the power spectrum, phase trajectories, correlation dimension, and maximum Lyapunov exponent are extracted from the measured time series. The chaotic characteristic of the dynamic properties of the NC table is revealed via various approaches. Therefore, an NC table is a nonlinear dynamic system. This research establishes a basis for dynamic system discrimination of a CNC machine.
Keywords NC table      chaotic characteristic      phase-space reconstruction      correlation dimension      maximum Lyapunov exponent     
Corresponding Author(s): WANG Linhong,Email:wlhjdx@tom.com   
Issue Date: 05 June 2009
 Cite this article:   
Linhong WANG,Bo WU,Runsheng DU, et al. Dynamic characteristics of an NC table with phase space reconstruction[J]. Front Mech Eng Chin, 2009, 4(2): 179-183.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-009-0018-9
https://academic.hep.com.cn/fme/EN/Y2009/V4/I2/179
Fig.1  Iterated computing process
Fig.2  Testing system
S.N.statespeed/(mm?min-1)
123x axial motionx-y line interpolationx-y circular interpolation10-200010-200010-2000
Tab.1  Working condition for the test
Fig.3  Time-domain waveform in circular interpolation
Fig.4  FFT power spectrum chart in circular interpolation
Fig.5  directional phase trajectory chart
Fig.6  directional phase trajectory chart
Fig.7  directional phase trajectory chart
speed/(mm?s-1)state 1state 2state 3
1000.80041.05200.8779
2000.78060.80470.8691
3000.86430.84120.8995
4000.75910.83710.8631
5000.97540.81750.9117
6000.88350.90040.9381
7000.91071.01050.9711
8000.99941.12730.9018
9000.72220.88430.8916
10000.87400.86700.7281
Tab.2  Correlation dimension
motion stateLyapunov exponent
steady motionλi<0i=1,2,…,n
periodic motionλ1=0,λi>0i=2,3,…,n
quasi periodicλ1=0,λ2=0,λi<0i=3,4,…,n
chaotic motionλi>0,λi may be positive, negative or zero, i≠1
random motionλ1→∞,λi may be positive, negative or zero, i≠1
Tab.3  Relationship between motion state and Lyapunov exponent
speed/(mm?s-1)state 1state 2state 3
100-0.00730.0025-0.0075
2000.00000.0004-0.0013
3000.0032-0.0062-0.0023
4000.00010.00070.0000
5000.00180.00130.0001
600-0.00200.00100.0012
7000.0011-0.00100.0012
800-0.00260.00230.0008
9000.00120.0022-0.0033
10000.0006-0.00660.0016
Tab.4  Maximum Lyapunov exponent
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[1] WANG Linhong, WU Bo, DU Runsheng, YANG Shuzi. Dynamic characteristics of NC table with SVD[J]. Front. Mech. Eng., 2008, 3(4): 385-391.
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