A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

Jin, Yulin; Lu, Zhenyong; Yang, Rui; Hou, Lei; Chen, Yushu

doi:10.1007/s10483-018-2308-9

Cited by 26 publications

(13 citation statements)

References 38 publications

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“…where FC is a component of the restoring force in the radial direction, δr is the deformation in the radial direction, Cb is the stiffness coefficient, c0 and c1 are stiffness coefficients for the linear and cubic terms, respectively. This expansion at δr < 1000 µm agrees with the experimental results in [18].…”

Section: Statement Of Problem and Equations Of Motionsupporting

confidence: 90%

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Multi-parametric Dynamic Analysis of a Rolling Bearings System

Kydyrbekuly

Ibrayev

Ospan

et al. 2021

SV-JME

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A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.

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Section: Statement Of Problem and Equations Of Motionsupporting

confidence: 90%

“…Radial compliance of bearings occurs due to deformation of the rolling elements and raceways at the contact points. In this case, the nonlinear restoring force in bearings can be generally described using the Hertz contact formula [14,18] 3 2 .…”

Section: Statement Of Problem and Equations Of Motionmentioning

confidence: 99%

Multi-parametric Dynamic Analysis of a Rolling Bearings System

Kydyrbekuly

Ibrayev

Ospan

et al. 2021

SV-JME

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“…ere is a mathematical relationship of the cubic nonlinearity, and the fitting results are compared with the traditional analytical model. It is proved that the cubic nonlinear fitting method is more suitable [30].…”

Section: Rolling Element Bearingmentioning

confidence: 99%

Nonlinear Dynamic Analysis of Rotor‐Bearing System with Cubic Nonlinearity

Nan

Zhu

Zhang

et al. 2021

Shock and Vibration

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Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

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“…However, the possibility that these two models are equivalent is in a wide range of deformation. Thus, the predicted maximum deformation value is 1000 µm based on the experimental Hertzian analytical formulation, and then the data are fitted by cubic polynomial [58]. In our case, we will call coefficients c0 and c1 are stiffness factors (or constants) of the rotor support (stiffness of the rolling bearing), c2stiffness coefficient of the foundation support; χ and χ0external friction coefficients acting on the rotor and foundation.…”

Section: Fig 1 Scheme Of a Rotor On Rolling Bearingsmentioning

confidence: 99%

Applications of Jacobi’s Elliptic Functions in Forced Vibration in Nonlinear Rotor Dynamics

Ibrayev

Elishakoff

Kydyrbekuly

2021

Preprint

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In this paper studied a rotary system with a nonlinearity, the equations of motion of which is one of the types of the Duffing’s equations with multidegree-of-freedom, and also consider the advantages of using the elliptic function method to solve problems of this type. The system studied in this paper is also distinguished by the fact that in addition to the rotor vibrations in elastic supports with a nonlinearity, the vibrations of the foundation are also taken into account. The article presents a comparative analysis of the numerical Runge-Kutta-Fehlberg's 4-order method with an error estimate of 5-order, the approximate analytical Van der Pol’s method and the elliptic function method proposed by the authors by comparing the obtained equations of motion of the system, as well as by comparing the constructed frequency response characteristic. From the results obtained, it follows that the method proposed by the authors can serve as a more accurate, general case of previously used approximate methods.

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A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

Cited by 26 publications

References 38 publications

Multi-parametric Dynamic Analysis of a Rolling Bearings System

Multi-parametric Dynamic Analysis of a Rolling Bearings System

Nonlinear Dynamic Analysis of Rotor‐Bearing System with Cubic Nonlinearity

Applications of Jacobi’s Elliptic Functions in Forced Vibration in Nonlinear Rotor Dynamics

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