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A simple and compact model of defects and non-linear dynamicstiffness of a ball bearing

Published online by Cambridge University Press:  24 February 2010

Mourad Dougdag*
Affiliation:
COMENA/CRNB/DTN/Laboratoire des Études Mécaniques, CRNB BP 180 Ain-Oussera, 17200 Willaya de Djelfa, Algérie
Mohammed Ouali
Affiliation:
Département de Mécanique, Faculté des sciences pour l’ingénieur, Université Saad Dahlab Blida, BP 27, Route de Soumâa, Blida, Algérie
*
a Corresponding author:[email protected]
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Abstract

This paper presents a modelling study of a ball bearing dynamic behaviour with differentdefects types, which is part of an investigation related to the modelling of machineryrotating components. Our contribution in this work is a proposition of a five-degree offreedom model describing the nonlinear dynamic behaviour of a ball bearing. The aim is aparametric formulation of the ball bearing stiffness which allows the introduction of thedefects characteristics. This approach is a result of an intrinsic structural behaviourmaking it different from methods which introduce external impulsion to simulate defects.Hence, a more realistic dynamic ball bearing defect simulation is obtained for better usein design and maintenance domain. This simulation can be formulated by two methods. Thefirst, partial contact method, is based on elimination of some ball stiffness. The secondone imposes displacement in the system response. Obtained results give response formssimilar to standards and to different author’s results (theoretical and experimental)found in the literature. The developed model is simple, compact as compared to existingones and we can express our satisfaction about this promising model.

Type
Research Article
Copyright
© AFM, EDP Sciences 2009

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References

L. Bourgain, R. Dart, J. Bourgain, Machines tournantes et circuits pulsés. Applications Industrielles et médicales de l’analyse spectrale, Dunod, Édition Bordas 1988, pp. 392–411
J.E. Shigley, L.D. Mitchel, Mechanical Engineering Design. 4th Edition, McGraw-Hill, 1983, pp. 85–88, pp. 484–514
S. Timoshenko, Résistance des matériaux, Théorie élémentaire et problèmes, tome I, 1968, collection Dunod technique, pp. 2–19
A. Palmgren, Ball and roller bearing engineering, 3rd Edition, S. Burkank & Co, Philadelphia, 1959
T.A. Harris, Rolling Bearing Analysis, 3e edition, 1966, Lavoisier, 1991
P. Eschmann, L. Hasbargen, K. Weigand, Ball and roller bearings, Theory, design and application, R, Oldenburg Verlag, John Wiley and Sons, Inc, 1985
Kraus, J., Blech, J.J., Braun, S.G., In situ determination of roller bearing stiffness damping by modal analysis. Trans. of the A.S.M.E., J. Vibration, Acoustics Stress and Reliability in Design 109 (1987) 235240CrossRefGoogle Scholar
Drago, R.J., New approach for analysing transmission noise, Machine Design 52 (1980) 114115Google Scholar
M.D. Rajab, Modelling of the transmissibility through rolling-element bearing under radial and moment loads, Ph.D. thesis, The Ohio state university, Columbus, Ohio, 1982
W.B. Young, Dynamic modelling and experimental measurement of gear shaft and housing system, M.S. Thesis, The Ohio state university, Columbus, Ohio, 1988
T. Lim, Chin, Vibration transmission through rolling element bearings in geared rotor systems, the Ohio State University, 1989, pp. 12–60
De Mul, J.M., Vree, J.M.Maas, D.A., Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction. part I: general theory and application to ball bearings, Trans. of the A.S.M.E., J. Tribology 111 (1989) 149155CrossRefGoogle Scholar
Fukata, S.E.H., Kondou, T., Ayabe, T.Tamura, H., On the Radial Vibration of Ball Bearing, Bull. JSME 28 (1985) 899904CrossRefGoogle Scholar
Yhland, E., A linear theory of vibrations caused by ball bearings elasticity in gear at moderate speed. Trans. Of the A.S.M.E., J. Tribology 154 (1992) 348359CrossRefGoogle Scholar
I.S. Choi, Simulation des mécanismes complexes en C.M.A.O. étude des non linéarités de comportement. Application aux boîtes de transmission de puissance d’hélicoptères, Thèse de doctorat, INSA de Lyon, 1993 n°.93 ISAL, 0034, p. 224
B. Adelin, Modélisation dynamique globale des boîtes de vitesses automobiles, thèse de doctorat à INSA de Lyon, 1997, n° 97 ISAL 0084, pp. 23–42
M.L. Adams, Analysis of Rolling Element Bearing Faults in Rotating Machinery: Experiments, Modelling, Fault Detection and Diagnosis, Thesis for Doctor of philosophy in the case Western Reserve University, August 2001, pp. 12–13, 25–28, 50–53, 74–108, 147–183
B.T. Holm-Hansen, Development of self-diagnostic rolling element bearing, Thesis for Doctor of philosophy in the University of Massachusetts, 1999, pp. 12–30
M. Lelkes, Définition des engrenages klingelnberg, Thèse de doctorat présentée à l’INSA Lyon, N° d’ordre 02-ISAL-0012, 2002. pp. 106–110, pp. 125–127
F. Louf, Contact: théorie de Hertz, 2003, site Internet: http://agregb1.dgm.enscachan.fr/Documents/TheorieTP/files/Contact.pdf, pp. 1–7
Chevalier, Guide du dessinateur industriel, Classique Hachette, Édition 1979, pp. 188–189
M. Moret, Roulements et butées à billes et à rouleaux, Techniques de l’ingénieur, Vol. B5-I, août 1995
A. Palmgren, Les roulements description, théorie, application, SKF Paris 1967, p. 120
P. Estocq, Une approche méthodologique numérique et expérimentale d’aide à la détection et au suivi vibratoire de défauts d’écaillage de roulements à billes, thèse de doctorat, Université de Reims Champagne Ardennes, 2004, pp. 35–51
A. Allezy, Contribution à l’analyse du comportement dynamique de machines tournantes en régime transitoire, Approches métrique et expérimentale, Thèse de doctorat présentée à l’INSA Lyon, N° d’ordre 2006-ISAL-0013, 2006, pp. 146–150
M. Paz, Structural dynamics. Theory and computation, Van Nostrand Reinhold Company New-York, 1985 (2e Édition), pp. 389–397
P. Ladevèze, J.-P. Pelle, Mastering Calculations in Linear and Nonlinear Mechanics, Translated by Theofanis Strouboulis, Mechanical Engineering Series Frederick F. Ling, Springer Science+Business Media, 2005 Inc., p. 250
N.M. Newmark, A Method of Computation for Structural Dynamics, ASCE J. the Engineering Mechanics Division, 85 (1959)
G. Baratto, J.J. Guerin, J. Mongis, C. Toupnies, A. Vieu, Analyse morphologique des défaillances d’organes de machine, CETIM 1992, pp. 58–65
C.M. Harris, C.E. Crede, Shock and vibration Handbook, Second Edition, McGraw-Hill 1976, pp. 40-5–40-8
C. Marcovici, J.-C. Ligeon, Utilisation des techniques de fiabilité en mécanique, PSI techniques et documentations, Paris, 1996
I.A. Pasynkova, Bifurcations of Cylindrical Precessions of an Unbalanced Rotor, Technische Mechanik, Band 26, Heft 1, (2006), 1–10, Manuskripteingang: 12 Oktober 2005, pp. 1–10
M. Angelo, Vibration monitoring of Machines, Technical Review N°1-1987, Brüel & Kjaer, pp. 11–31
Brüel & Kjaer, Surveillance des machines, révision Sept. 1990, pp. 19–33
R.B. Randall, B. Tech, Frequency Analysis, 3rd edition, 1st print Brüel & Kjaer 1987, pp. 179, 288–295, ISBN 87 87355078
B.J. Trampe, Mechanical Vibration and Shock Measurements, Brüel & Kjaer, avril 1984, pp. 197–205
C.M. Harris, A.G. Piersol, Harris’shock and Vibration Handbook, Fifth Edition, McGraw-Hill, 2002, 1996, 1988, 1976, 1961 by The McGraw-Hill Companies, Printed in the United States of America., pp. 16-10–16-11
V. Barkov, N.A. Barkova, Non-linear Signal Models in Vibroacoustic Machine Diagnostics, 1996
V. Barkov, N.A. Barkova, The Artificial Intelligence Systems for Machine Condition Monitoring and Diagnostics by Vibration, Published in the Proceedings of the Saint Petersburg Post-graduate Institute of the Russian Federation Power Industry and Vibration Institute, USA, Saint Petersburg, 1999, Vol. 9
A. Liew, A study of a rotor system with ball bearing non-linearities; and the development of transfer matrix techniques suitable for analysing such systems, Thesis for Doctor of philosophy in New South Wales University, 2002, pp. 91–95
Kiral, Z.Karagülle, H., Simulation and analysis of vibration signals generated by rolling element bearing with defects, Tribology International 36 (2003) 667678CrossRefGoogle Scholar
Kiral, Z.Karagülle, H., Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force, Mechanical Systems and Signal Processing 20 (2006) 19671991CrossRefGoogle Scholar
Morhain Al-Ghamd, A.Mba, D., A comparative experimental study on the use of acoustic emission and vibration analysis for bearing defect identification and estimation of defect size, Mechanical Systems and Signal Processing 20 (2006) 15371571CrossRefGoogle Scholar
Chao-Shih Liu, Fault detection of rolling element bearings, Thesis for Doctor of philosophy in the University of Washington, 2005, pp. 96–98.