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Experimental determination of stiffness and damping in rotating systems using metaheuristic hybrid optimization and state observers

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Abstract

Recently, more research have been conducted on the analysis of the vibration response of rotors, so that new techniques, which are used to characterize the dynamic response of rotating machines, have been developed to aid and predict the lifespan of such systems. One of the vibration management techniques in rotating systems is the monitoring of stiffness and damping parameters of the bearings and system excitation forces. In this context, this paper aims to estimate the stiffness and damping of the bearings through a hybrid metaheuristic method. This uses a population-based search method as a starting point for direct search method, genetic algorithms and quasi-Newton method, respectively, in this work. The function to be minimized contains experimental bearing data. Moreover, the state observer is used to reconstruct all states of the system from the experimental data from the sensors. Thus, it is proposed to identify the excitation forces using orthogonal functions, Chebyshev polynomials specifically, and then, to verify the effectiveness of the method when compared to the calculated force excitation of the system.

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Abbreviations

[A]:

Dynamic matrix

[B]:

Input matrix

[C]:

Damping matrix

[D s ]:

Output matrix

[D me ]:

Measurement matrix

e :

Distance between the center and the unbalanced mass

[F], [X]:

Force and displacement coefficient to Chebyshev polynomials

[G]:

Gyroscopic matrix

[I]:

Identity matrix

J :

Cost function

[L ob ]:

Gain matrix of the observer

m o :

Unbalanced mass

[M]:

Mass matrix

[P]:

Operational matrix of integration

r :

Number of terms of Chebyshev polynomials

δ :

Nodal displacement vector for an element

Ω:

Angular velocity

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Acknowledgments

The authors thank INCT and CAPES for the financial support and the Department of Engineering Mechanics of Ilha Solteira for technical support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculdade de Engenharia de Ilha Solteira, UNESP-Univ Estadual Paulista, Ilha Solteira, SP, Brazil

    Lucas Rangel de Oliveira & Gilberto Pechoto de Melo

Authors
  1. Lucas Rangel de Oliveira
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  2. Gilberto Pechoto de Melo
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Corresponding author

Correspondence to Lucas Rangel de Oliveira.

Additional information

Technical Editor: Kátia Lucchesi Cavalca Dedini.

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de Oliveira, L.R., de Melo, G.P. Experimental determination of stiffness and damping in rotating systems using metaheuristic hybrid optimization and state observers. J Braz. Soc. Mech. Sci. Eng. 38, 59–66 (2016). https://doi.org/10.1007/s40430-015-0413-6

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  • DOI: https://doi.org/10.1007/s40430-015-0413-6

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