Experiments on routes to chaos in ball bearings

Mevel, Bruno; Guyader, Jean‐Louis

doi:10.1016/j.jsv.2008.04.024

Cited by 48 publications

(26 citation statements)

References 8 publications

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“…The maneuver load inducing response of the system performs as two typical patterns: One is the alternating of period 2 motion and period 1 motion for ω = 1,350 rad/s; the other is the alternating of quasi-periodic motion and period 2 motion for ω = 1,470 rad/s. These two ways have a certain similarity to the sub-harmonic route and the quasi-periodic route to chaos that are investigated in [36]. The quasi-periodic motions are due to the small damping considered in the simulating model, which is similar to the results of researches studying the effect of damping on the regular orbits and chaotic orbits of nonlinear systems (see [37][38][39]).…”

Section: Discussionsupporting

confidence: 55%

Turning maneuver caused response in an aircraft rotor-ball bearing system

et al. 2014

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This paper focuses on the nonlinear response caused by aircraft turning flight in a rotor-ball bearing system with internal clearances and Hertzian contact forces. The equations of motion are formulated by using Lagrange equation, where the aircraft turning flight is modeled as a maneuver load. Numerical analyses are carried out to detect the response of the system under maneuver load. The sub-harmonic resonance and irregular motions subjected to the maneuver load are obtained and presented by bifurcation diagrams, amplitude spectrum diagrams, Poincare maps and phase portraits. Two typical patterns that the maneuver load inducing response are found: one is the alternating of period 2 motion and period 1 motion for ω = 1,350 rad/s; the other is the alternating of quasi-periodic motion and period 2 motion for ω = 1,470 rad/s. Moreover, mass eccentricity shows a significant effect on the sub-harmonic resonance of the rotor-ball bearing system under turning flight, which is different from that without considering maneuvering flight condition (Bai and Zhang in Int J Nonlinear Mech 50:1-10, 2013). The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight.

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Section: Discussionsupporting

confidence: 55%

Turning maneuver caused response in an aircraft rotor-ball bearing system

et al. 2014

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“…Moreover, Harsha [17] investigated the effect of radial internal clearance for rotor bearing systems in which rolling element bearings show periodic, quasi-periodic and chaotic behavior by considering time response, Poincaré maps and power spectra. Mevel and Guyader [18] observed experimentally the existence of two different routes to chaos in ball bearing dynamic motion. Nataraj and Harsha [19] investigated the nonlinear dynamic behavior of an unbalanced rotor-bearing system due to cage run-out.…”

Section: Introductionmentioning

confidence: 99%

Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings

Sinou

2009

Mechanism and Machine Theory

101

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To cite this version:Jean-Jacques Sinou. Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings. Mechanism and Machine Theory, Elsevier, 2009, 44 (9) AbstractThis study deals with the non-linear dynamic response of a flexible rotor supported by ball bearings. The excitation is due to unbalance force. The finite element rotor system is composed of a shaft with one disk, two flexible bearing supports and a ball-bearing element where the non-linearities are due to both the radial clearance and the Herztian contact between races and rolling elements. A numerical analysis is performed to analyze the non-linear behavior of this bearing rotor by using the Harmonic Balance Method with appropriate condensation located only on the non-linear coordinates of the system in order to minimize computer time. The condensation process reduces the original non-linear rotor system by focusing only on the solution of the non-linear equations of the Fourier coefficients associated with the system's non-linear components. In this study, the procedure is developed for the estimation of the harmonic and super-harmonic responses of the complex rotor system. Consequently, the non-linear unbalance responses and the associated orbits of the bearing rotor will be investigated. Moreover, the transition from contact to no-contact states between rolling elements and races, and the associated restoring contact forces are calculated for different speeds of the unbalanced rotor. Finally, hardening-type nonlinearity or softening-type nonlinearity due to the effects of radial clearance and unbalance mass are examined.

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“…They further showed that complicated nonlinear motion can occur in systems supporter on ball bearings if the clearance becomes large enough. For a similar rotor system, supported by ball bearings, Mevel and Guyader [2] found different routs to chaos experimentally.…”

Section: Introductionmentioning

confidence: 95%

Approximated Stiffness Coefficients in Rotor Systems Supported by Bearings with Clearance

Karlberg

2010

International Journal of Rotating Machinery

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Many kinds of rotating machinery are supported by bearings with clearance, which are further clamped in a supporting structure. When designing such machinery it is important to be able to predict dynamics and hence valid models are needed. Due to gravity, the shaft often vibrates close to a static equilibrium position leading to a possibility to linearise the equation of motion. Although several studies on bearings with clearance exist, there are still no reports on how such clearances affects the stiffness coefficients close to a static equilibrium position. Therefore, analytical expressions for such approximated pedestal stiffness coefficients have been derived in this paper. By using such approximated pedestals in simple rotordynamical models, it was found that the eigenfrequencies decrease significantly with clearance. It is further shown that the approximated pedestal stiffness coefficients only will be valid for vibrations close to the static equilibrium position.

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Experiments on routes to chaos in ball bearings

Cited by 48 publications

References 8 publications

Turning maneuver caused response in an aircraft rotor-ball bearing system

Turning maneuver caused response in an aircraft rotor-ball bearing system

Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings

Approximated Stiffness Coefficients in Rotor Systems Supported by Bearings with Clearance

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