The early detection of failures in geared systems is an important industrial problem which has still to be addressed from both an experimental and theoretical viewpoint. The proposed paper combines some extensive numerical simulations of a single stage geared unit with localized tooth faults and the use of several detection techniques whose performances are compared and critically assessed. A model aimed at simulating the contributions of local tooth defects such as spalling to the gear dynamic behavior is set up. The pinion and the gear of a pair are assimilated to two rigid cylinders with all six degrees of freedom connected by a series of springs which represent gear body and gear tooth compliances on the base plane. Classical shaft finite elements including torsional, flexural and axial displacements can be superimposed to the gear element together with some lumped stiffnesses, masses, inertias, … which account for the load machines, bearings and couplings. Tooth defects are modeled by a distribution of normal deviations over a zone which can be located anywhere on the active tooth flanks. Among the numerous available signal processing techniques used in vibration monitoring, cepstrum analysis is sensitive, reliable and it can be adapted to complex geared system with several meshes. From an analytical analysis of the equations of motion, two complementary detection techniques based upon acceleration power cepstrum are proposed. The equations of motion and the contact problem between mating flanks are simultaneously solved by coupling an implicit time-step integration scheme and a unilateral normal contact algorithm. The results of the numerical simulations are used as a data base for the proposed detection techniques. The combined influence of the defect location, depth and extent is analyzed for two examples of spur and helical gears with various profile modifications and the effectiveness of the two complementary detection methods is discussed before some conclusions are drawn.

Issue Section:
Technical Papers
Keywords:
failure (mechanical), fault simulation, power transmission, variable speed gear, vibrations, numerical analysis
Topics:
Bearings, Degrees of freedom, Equations of motion, Failure, Gears, Helical gears, Modeling, Signals, Vibration, Stiffness, Stress, Computer simulation, Signal processing, Algorithms, Cylinders, Databases, Finite element analysis, Machinery, Simulation
1.
Alattass, M., 1994, “Maintenance des machines tournantes. Signature des de´fauts d'engrenages droits et he´licoi¨daux,” Ph.D. dissertation, INSA de Lyon, p. 198.
2.
McFadden
,
P. D.
,
1986
, “
Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibration
,”
ASME J. Vibr. Acoust.
108
, pp.
165
–
170
.
3.
Choy
,
F. K.
,
Polyshchuk
,
V.
,
Zakrajsek
,
J. J.
,
Handschuh
,
R. F.
, and
Townsend
,
D. P.
,
1996
, “
Analysis of the Effects of Surface Pitting and Wear on the Vibration of a Gear Transmission System
,”
Tribology Int.
29
, No.
1
, pp.
77
–
83
.
4.
Wang
,
W. J.
, and
McFadden
,
P. D.
,
1995
, “
Application of Orthogonal Wavelets to Early Gear Damage Detection
,”
Mech. Syst. Signal Process.
109
, No.
5
, pp.
497
–
507
.
5.
Brennan
,
M. J.
,
Chen
,
M. H.
, and
Reynolds
,
A. G.
,
1997
, “
Use of Vibration Measurements to Detect Local Tooth Defects in Gears
,”
Sound Vib.
31
, No.
11
, pp.
12
–
17
.
6.
Randall, R. B., 1980, “Cepstrum Analysis and Gearbox Fault Diagnosis,” Edition 2, Bru¨el and Kjaer Technical Bulletin, pp. 1–19.
7.
Mahfoudh, J., Bard, C., Alattass, M., and Play, D., 1995, “Simulation of Gearbox Dynamic Behavior with Gear Faults,” Proc. 2nd ImechE International Conference on Gearbox Noise, Vibration and Diagnostics, London, C492/95, pp. 91–100.
8.
Velex
,
P.
, and
Maatar
,
M.
,
1996
, “
A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behaviour
,”
J. Sound Vib.
191
, No.
5
, pp.
629
–
660
.
9.
Bogert, B. P., Healy, M. J. R., and Tukey, J. W., 1963, “The Frequency Analysis of Time Series of Echoes: Cepstrum, Pseudo-autocovariance, Cross-cepstrum and Saphe Cracking,” Proc. Symp. Time Series Analysis, M. Rosemblah, ed., New York, Wiley, pp. 209–243.
10.
Capdessus
,
C.
, and
Sidahmed
,
M.
,
1992
, “
Analyse des vibrations d'un engrenage:cepstre, corre´lation, spectre
,”
Traitement Signal
8
, No.
5
, pp.
365
–
372
.
11.
El Badaoui
,
M.
,
Guillet
,
F.
, and
Daniere
,
J.
,
1999
, “
Surveillance des Syste`mes Complexes a` Engrenages par l'Analyse cepstrale synchrone
,”
Traitement Signal
16
, No.
5
, pp.
371
–
381
.
12.
Cahouet, V., El Badaoui, M., Velex, P., Guillet, F., and Daniere, J., 1999, “Simulations nume´riques et de´tection d'avaries sur les dentures d'engrenages cylindriques,” Proc. 4th World Congress on Gearing and Power Transmission, 3, Paris, pp. 2359–2370.
13.
Drouiche
,
K.
,
Sidahmed
,
M.
, and
Grenier
,
Y.
,
1991
, “
De´tection de de´fauts d'engrenages par analyse vibratoire
,”
Traitement Signal
8
, No.
5
, pp.
331
–
343
.
Copyright © 2001
 by ASME
You do not currently have access to this content.