The recurrence analysis method is used in the mechanical diagnosis of a gear transmission system using time domain data. The recurrence is a natural behavior of a periodic motion system, which tells the state of the system, after running some time, and will approach a certain past state. In this paper, some statistical parameters of recurrence qualification analysis are extensively evaluated for the use of mechanical diagnosis, based on fairly short acceleration time series; recurrence results are compared with those obtained from Fourier analysis, and the identification procedures for the failure gear transmission by recurrences is also presented. It is found that, using only fairly short time series, some statistical parameters in quantification recurrence analysis can give clear-cut distinction between a healthy and damaged state.

References

References
1.
Harris
,
S. L.
, 1958, “
Dynamic Loads on the Teeth of Spur Gears
,”
Proc. Inst. Mech. Eng.
,
172
, pp.
87
112
.
2.
Parker
,
R. G.
,
Vijayakar
,
S. M.
, and
Imajo
,
T.
, 2000, “
Nonlinear Dynamical Response of a Spur Gear Pair: Modelling and Experimental Comparisons
,”
J. Sound Vib.
,
237
, pp.
435
455
.
3.
Warminski
,
J.
,
Litak
,
G.
, and
Szabelski
,
K.
, 2000, “
Dynamic Phenomena in Gear Boxes
,”
in Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities
, edited by
M.
Wiercigroch
, and
B.
De Kraker
,
Series on Nonlinear Science A
, Vol.
28
,
World Scientific
,
Singapore
, pp.
177
205
.
4.
Guo
,
Y.
, and
Parker
,
R. G.
, 2010, “
Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters
,”
ASME J. Vib. Acoust.
,
132
, p.
011006
.
5.
Cooley
,
C. G.
,
Parker
,
R. G.
, and
Vijayakar
,
S. V.
, 2011, “
A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics
,”
ASME J. Vib. Acoust.
,
133
, p.
041004
.
6.
Kahraman
,
A.
, and
Singh
,
R.
, 1991, “
Interactions Between Time-Varying Mesh Stiffness and Clearance Nonlinearity in a Gear System
,”
J. Sound Vib.
,
146
, pp.
135
156
.
7.
Byrtus
,
M.
, and
Zeman
,
V.
, 2011, “
On Modeling and Vibration of Gear Drives Influenced by Nonlinear Couplings
,”
Mech. Machine Theory
,
46
, pp.
375
397
.
8.
Łazarz
,
B.
,
Wojnar
,
G.
,
Madej
,
H.
, and
Czech
,
P.
, 2009, “
Evaluation of Gear Power Losses From Experimental Test Data and Analytical Methods
,”
Mechanika
,
6
, pp.
56
63
. Available at: http://zurnalas.mechanika.ktu.lt/files/mech680/Lazarz680.pdf.
9.
Lin
,
J.
, and
Parker
,
R. G.
, 2002, “
Parametric Instability of Planetary Gears Under Mesh Stiffness Variation
,”
J. Sound Vib.
,
249
, pp.
411
429
.
10.
Litak
,
G.
, and
Friswell
,
M. I.
, 2005, “
Dynamics of a Gear System With Faults in Meshing Stiffness
,”
Nonlinear Dynam.
,
41
, pp.
415
421
.
11.
Jedliński
,
Ł.
,
Kisiel
,
J.
, and
Jonak
,
J.
, 2009, “
Diagnosing the Condition of Gear Transmission on the Basis of Periodic and Residual Components of the Signal Spectrum
,”
Diagnostyka
,
49
, pp.
57
61
.
12.
Lyons
,
R. G.
, 2004,
Understanding Digital Signal Processing
,
Prentice Hall
,
Englewood Cliffs, NJ
.
13.
Litak
,
G.
,
Sawicki
,
J. T.
, and
Kasperek
,
R.
, 2009, “
Cracked Rotor Detection by Recurrence Plots
,”
Nondestructive Test. Eval.
,
24
, pp.
347
351
.
14.
Litak
,
G.
,
Syta
,
A.
,
Gajewski
,
J.
, and
Jonak
,
J.
, 2010, “
Detecting and Identifying Nonstationary Courses in the Ripping Head Power Consumption by Recurrence Plots
,”
Meccanica
,
45
, pp.
603
608
.
15.
Nichols
,
J. M.
,
Trickey
,
S. T.
, and
Seaver
,
M.
, 2006, “
Damage Detection Using Multivariate Recurrence Quantification Analysis
,”
Mech. Syst. Signal Process
,
20
, pp.
421
437
.
16.
Eckmann
,
J.-P.
,
Kamphorst
,
S. O.
, and
Ruelle
,
D.
, 1987, “
Recurrence Plots of Dynamical Systems
,”
Europhys. Lett.
,
5
, pp.
973
977
.
17.
Webber
, Jr.
C. L.
, and
Zbilut
,
J. P.
, 1994, “
Dynamical Assessment of Physiological Systems and States Using Recurrence Plot Strategies
,”
J. Appl. Physiol.
76
, pp.
965
973
.
18.
Marwan
,
N.
, 2003, “
Encounters With Neighbours: Current Development of Concepts Based on Recurrence Plots and Their Applications
,” Ph.D. thesis, Universität Potsdam, Potsdam.
19.
Marwan
,
N.
,
Romano
,
M. C.
,
Thiel
,
M.
, and
Kurths
,
J.
, 2007, “
Recurrence Plots for the Analysis of Complex Systems
,”
Phys. Rep.
,
438
, pp.
237
329
.
20.
Marwan
,
N.
, 2009, “
Commandline Recurrence Plots
,” http://www.agnld.uni-potsdam.de/∼marwan/6.download/rp.phphttp://www.agnld.uni-potsdam.de/∼marwan/6.download/rp.php (Last accessed May 10, 2009).
21.
Sen
,
A. K.
,
Litak
,
G.
,
Edwards
,
K. D.
,
Finney
,
C. E. A.
,
Daw
,
C. S.
, and
Wagner
,
R. M.
, 2011, “
Cyclic Heat Release Variability With Transition From Spark Ignition to HCCI in Internal Combustion Engines
,”
Appl. Energy
,
88
, pp.
1557
1567
.
22.
Takens
,
F.
, 1981,
Detecting Strange Attractors in Turbulence, Lecture Notes in Mathematics
, Vol.
898
,
Springer
,
Heidelberg
, pp.
366
381
.
23.
Kantz
,
H.
, and
Schreiber
,
T.
1997,
Non-linear Time Series Analysis
,
Cambridge University Press
,
Cambridge
.
24.
Klimaszewska
,
K.
, and
Żebrowski
,
J. J.
, 2009, “
Detection of the Type of Intermittency Using Characteristic Patterns in Recurrence Plots
,”
Phys. Rev. E
,
80
, p.
026214
.
25.
Litak
,
G.
,
Wiercigroch
,
M.
,
Horton
,
B. W.
, and
Xu
,
X.
, 2010, “
Transient Chaotic Behaviour Versus Periodic Motion of a Parametric Pendulum by Recurrence Plots
,”
Z. Angew. Math. Mech.
,
90
, pp.
33
41
.
26.
Mo
,
E.
, and
Naess
,
A.
, 2009, “
Nonsmooth Dynamics by Path Integration: An Example of Stochastic and Chaotic Response of a Meshing Gear Pair
,”
J. Comput. Nonlinear Dynam.
,
4
, p.
034501
.
You do not currently have access to this content.