Abstract
A lumped parameter model (LPM) has previously been used to model gear and bearing faults in a gearbox. It was found that simulated signals for localized bearing faults had good correspondence with measured ones in a narrow high frequency band demodulated for envelope analysis. However, for extended faults, there is more interaction with the gearbox structure, as the fault modulates the gear meshing, and the correspondence was poorer. Forces at the bearings from the LPM model were applied to a finite element (FE) model of the casing, and the results improved but were still deficient. This paper has benefited from CMS (component mode synthesis) based FE model reduction techniques to reduce the FE model of a gearbox casing into manageable and well representative degrees of freedom of the casing. The reduced model of the casing was embedded with the LPM of the internals, which was previously obtained with the aid of Simulink® and has the capability of capturing time-varying stiffness nonlinearities arising from gears and bearings and has also the capability of simulating geometrical faults (spalls) for both gears and bearings. In order to extend the validity of the combined /reduced model, the forces are extracted from combined/reduced model and convolved with the impulse responses corresponding to the FRFs of the whole gearbox. The results show the improvements obtained through combining the reduced model of the casing with the LPM model giving a much better correspondence with measured signals. This has been verified for both the fault free and faulty cases.
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References
N. Sawalhi and R. B. Randall, “Simulating gear and bearing interactions in the presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults,” Mechanical Systems and Signal Processing, vol. 22, pp. 1924-1951, 2008.
N. Sawalhi and R. B. Randall, “Simulating gear and bearing interactions in the presence of faults: Part II: Simulation of the vibrations produced by extended bearing faults,” Mechanical Systems and Signal Processing, vol. 22, pp. 1952-1966, 2008.
Z.-Q. Qu, Model Order Reduction Techniques :with Applications in Finite Element Analysis Springer, 2004.
L. I. Myklebust and B. Skallerud, “Model Reduction Methods for Flexible Structures,” presented at the 15th Nordic Seminar on Computational Mechanics, Aalborg, Denmark, 2002.
N. Sawalhi and R. B. Randall, “A Combined Lumped Parameter and Finite Element Model of a Single Stage Gearbox for Bearing Fault Simulation,” presented at the COMADEM 2008 (Condition Monitoring and Diagnostic Engineering Management), Prague, Czech Republic, 2008.
N. Sawalhi and R. B. Randall, “Improved Simulation of Faults in Rolling Element Bearings in Gearboxes,” presented at the 9th International Conference on Vibrations in Rotating Machinery, 8-10 September, UK, 2008.
P. Sweeney, “Transmission error measurement and analysis “ Ph. D. Dissertation, Mechanical & Manufacturing Engineering, Faculty of Engineering, University of New South Wales, Sydney, Australia, 1994.
S. Du, “Dynamic modelling and simulation of gear transmission error for gearbox vibration analysis,” Ph.D. Dissertation, Mechanical & Manufacturing Engineering, Faculty of Engineering, University of New South Wales, Sydney, Australia, 1997.
H. Endo, “Simulation of gear faults and its application to the development of differential diagnostic technique “ Ph. D. Dissertation, Mechanical & Manufacturing Engineering, Faculty of Engineering, University of New South Wales, Sydney, Australia, 2005.
J. T. Young. (2000). Primer on the Craig-Bampton Method, (Based on input from William B. Haile).
P. Koutsovasilis and M. Beitelschmidt, “Model order reduction of finite element models: improved component mode synthesis,” Mathematical and Computer Modelling of Dynamical Systems, vol. 16:1, p. 57 — 73, 2010.
P. Koutsovasilis and M. Beitelschmidt, “Comparison of model reduction techniques for large mechanical systems,” Multibody System Dynamics, vol. 20, pp. 111-128, 2008.
R. J. Guyan, “Reduction of stiffness and mass matrices,” AIAA Journal, vol. 30, pp. 772-780, 1965.
B. M. Irons, “Structural eignvalue problems-elimination of unwanted variables,” AIAA journal, vol. 3, pp. 961-962, 1965.
S. L. Chen and M. Géradin, “An exact model reduction procedure for mechanical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 143, pp. 69-78, 1997.
J. C. O'Callahan, “A procedure for an improved reduced system (IRS) model,” in Proc. 7. International Modal Analysis Conference, Las Vegas, 1989.
M. I. Friswell, S. D. Garvey, and J. E. T. Penny, “Model reduction using dynamic and iterated IRS techniques,” Journal of Sound and Vibration, vol. 186, pp. 311-323, 1995.
C. Carmignani, P. Forte, and G. Melani, “Component modal synthesis modeling of a gearbox for vibration monitoring simulation,” presented at the The Sixth International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, Dublin, Ireland, 2009.
S. Ulf, “COMPONENT MODE SYNTHESIS - A method for efficient dynamic simulation of complex technical systems,” Technical Report, Department of Machine Design, The Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden2003.
H. N. Bayoumi, “Interfacing FEA and Multibody Simulation Through Component Mode Synthesis,” in ASME Conference Proceedings, 2005, pp. 1387-1392.
R. Craig and M. Bampton, “Coupling of substructures for dynamic analysis “ Amer. Inst. Aero. Astro. J., vol. 6, pp. 1313–1319, 1968.
N. Sawalhi, L. Deshpande, and R. B. Randall, “Improved simulations of faults in gearboxes for diagnostic and prognostic purposes using a reduced finite element model of the casing,” in 7th DSTO International Conference on Health & Usage Monitoring Melbourne, 2011.
J. Antoni and R. B. Randall, “Unsupervised noise cancellation for vibration signals: part I--evaluation of adaptive algorithms,” Mechanical Systems and Signal Processing, vol. 18, pp. 89-101, 2004.
J. Antoni and R. B. Randall, “Unsupervised noise cancellation for vibration signals: part II--a novel frequency-domain algorithm,” Mechanical Systems and Signal Processing, vol. 18, pp. 103-117, 2004.
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Deshpande, L., Sawalhi, N., Randall, R.B. (2011). Fault Simulation in a Gearbox Using Finite Element Model Reduction Techniques. In: Proulx, T. (eds) Linking Models and Experiments, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9305-2_30
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DOI: https://doi.org/10.1007/978-1-4419-9305-2_30
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