Reliability and sensitivity analysis of an axially moving beam

Yao, Guo; Zhang, Yimin

doi:10.1007/s11012-015-0232-y

Cited by 21 publications

(8 citation statements)

References 21 publications

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“…The superposition principle cannot be used for the nonlinear system, and the accurate probability distribution function of g ( B , x ) is impossible to calculate. 37 Therefore, the first four moments of g ( B , x ) can be used to describe the statistic properties of state function…”

Section: Dynamic Reliability Model Of Matched Bearingsmentioning

confidence: 99%

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Zhang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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Bearings are the core components in various kinds of rotating machineries. With the increasing demand of reliable bearings in precision equipment, it is of great significance to analyze the motion error of bearings. In this article, a nonlinear dynamic model of angular contact ball bearings installed in pairs is constructed to describe its response characteristics. The definition of a failure mode in matched bearings is that the dynamic response of each inner race is larger than the allowed axial runout. This article introduces a feasible approach to evaluate the reliability of positioning precision of matched bearings with random geometric parameters. The statistical moments of dynamic response are calculated using stochastic perturbation method. The probability distribution function of state function relating to positioning precision is approached by Edgeworth series, from which the reliability and sensitivity are obtained. A pair of 7206B bearings is taken as an application instance of the proposed method. Monte Carlo simulation is employed to provide a benchmark on which to verify the precision and efficiency of the proposed method. In addition, the effects of mean values and variances of random geometric parameters on the positioning precision are analyzed, respectively.

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Section: Dynamic Reliability Model Of Matched Bearingsmentioning

confidence: 99%

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Zhang

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…Pakdemirli and Ozkaya [2] and Yang et al [3] have examined the behavior of traveling continua that maintained constant velocity. This axial velocity is modeled as a harmonic function in the investigations carried out in [4][5][6][7][8][9][10][11][12][13][14][15][16] by considering different beam materials; damping terms; linear and nonlinear models of the beam. Oz [4], Pakdemirli and Oz [5], and Oz et al [6] used elastic beam material with simply supported boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Saksa et al [11] compared the dynamic characteristics of steel and paper adopting Poynting-Thomson model of axially accelerating viscoelastic beam. Yao and Yimin [12] carried out reliability and sensitivity analysis on traveling beam and concluded that the reliability of the moving system decreases when traveling velocity increases, the length of the beam increases for a particular speed, and it increases when the thickness of the beam increases and mass density decreases. Chakraborty and Mallik [13] made free and forced nonlinear vibration analysis of a traveling system using complex normal modes.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

et al. 2022

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In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension of the beam is modeled as a function of the traveling velocity, support stiffness parameter as well as spatial coordinate. Geometric cubic nonlinearity appeared in the equation of motion due to elongation set in the neutral axis of the beam. The integropartial differential equation of motion of the axially accelerating beam associated with the simplysupported end conditions is solved analytically by adopting the direct perturbation method of multiple time scales (MMS). As a result, a set of complex variable modulation equations are generated, which governs the modulation of amplitude and phase. This set of modulated equations is numerically solved to explore the influence of the support stiffness parameter upon the stability and bifurcation of the beam which has not been addressed in the existing literature. Apart from this, the impact of fluctuating velocity component, viscoelastic coefficient, longitudinal stiffness parameter, internal and parametric detuning parameters on the stability and bifurcation analysis is studied, revealing significant dynamic characteristics of the traveling system. The Fourth-order Runge-Kutta method is applied is to find the dynamic solution of the system. The system displays stable periodic, quasi-periodic, and mixed-mode dynamic responses along with the unstable chaotic behavior for a specific set of system parameters. The results obtained through an analytical-numerical approach may help the design and operation of an axially moving beam.

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“…In many cases, due to initial, parametric, and external excitations, the generation of unwanted transverse vibrations may limit their applications. Therefore, the dynamic behaviors of such devices have been widely investigated by numerous scholars for the past decades and are still of interesting today [1][2][3][4][5][6][7][8][9][10]. Moreover, according to the demand of the actual engineering problems, some researchers have applied their theoretical results to design and optimize the axially moving structures [11,12].…”

Section: Introductionmentioning

confidence: 99%

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Li¹,

Tang²

2017

Mathematical Problems in Engineering

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The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton's second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff 's fractional material model are much larger than those predicted by Mote's fractional material model.

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Reliability and sensitivity analysis of an axially moving beam

Cited by 21 publications

References 21 publications

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Dynamic reliability analysis of angular contact ball bearings in positioning precision

Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

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