Motion Patterns at Rotor Stator Contact

Ehehalt, Ulrich; Hahn, E. J.; Markert, Richard

doi:10.1115/detc2005-84440

Cited by 12 publications

(9 citation statements)

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“…From a theoretical viewpoint, the rub phenomenon is a typical non-smooth nonlinear dynamic problem, which cannot be linearized even in the case of small perturbation. Many authors have studied the rub problem in rotordynamics [1][2][3][4][5][6][7][8][9][11][12][13][14][15][16]. Muszynska [16] presented a list of literature on rub-related phenomena up to 1989.…”

Section: Introductionmentioning

confidence: 99%

Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability

Zhang

et al. 2009

Nonlinear Dyn

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The nonlinear synchronous full annular rub motion of a flexible rotor induced by the mass unbalance and the contact-rub force with rigid and flexible stator is studied analytically. The nonlinear property is due to the dry friction force between stator and rotor. The exact solutions of the synchronous full annular rub motion and its run speed regions are obtained. The stability of the synchronous full annular rub motion is discussed analytically. The stability criterion and the stability regions of the synchronous full annular rub motion are obtained. A simplified approximate criterion formula for dynamic stability is also derived under the conditions of large impact stiffness, small damping and small friction. The simplified criterion formula can be used conveniently in engineering and matches the real situations of industry.eMass eccentricity of the disk E i , υ i The Young's modulus and Poisson ratios of rotor and stator at the contact point F n or N Normal contact force between rotor and stator at contact point F t Tangential rub force between rotor and stator at the contact point h Clearance between rotor and stator k or k r Stiffness coefficient of the shaft at the disk position k s Stiffness coefficient of the stator at the contact position k p The equivalent stiffness coefficient of the contact force model m or m r Mass of rotor m s Mass of stator r or r r Absolute radial displacement of the geometric center C or O r of the disk r s Absolute displacement of the geometric center O s of the stator r st Relative distance between O s and O r r 0 , φ 0 Non-dimensional amplitude and phase angle of unbalance response of disk center before contact R Radius of disk of the rotor t Time u 0 Initial normal impact velocity x, y Generalized coordinates of the geometric center O s of the stator θ Angular position of the geometric center C or O r of the disk 580 G.F. Zhang et al.μ Friction coefficient ξ , ξ 1 , ξ 2 The non-dimensional embedded displacements of synchronous full annular rub at the contact point ω, ω r √ k/m, √ k r /m r , natural frequencies of rotor without rub ω s √ k s /m s , natural frequency of stator without rub Ω Spinning speed of the rotor Definition of non-dimensional quantities: e = e/ h,r = r/ h,R = R/ h,x = x/ h,ȳ = y/ h, r sr = r sr /h, τ = ωt, φ = Ωt − θ ,m s = m s /m r , k p = k p /k(or = k p /k r ),Ω = Ω/ω (or = Ω/ω r ), ω s = ω s /ω r , ς = c/(2 √ mk), ς r = c r /(2 √ m r k r ), ς s = c s /(2 √ m s k s ).

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Section: Introductionmentioning

confidence: 99%

Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability

Zhang

et al. 2009

Nonlinear Dyn

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“…This simple model includes all effects for replicating the various motion patterns mentioned above [3]. The equations of motion for rotor and stator displacement r R and r S are…”

Section: Model and Analysis Methodsmentioning

confidence: 99%

“…Bifurcation analysis is not able to distinguish between forward and backward whirl, superharmonic motion and sideband motion around the synchronous motion. Beside Bifurcation Diagrams and phase-planes spectra [3] are helpful.…”

Section: Superharmonics Chaotics and Sidebandsmentioning

confidence: 99%

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Bifurcation of Contact Between Rotor and Stator

Alber

Markert

2012

MATEC Web of Conferences

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Abstract. The paper discusses Bifurcation Diagrams of rotor stator contact problems and the transition from synchronous whirl towards different asynchronous movement patterns. Bifurcation Diagrams based on Poincaré Maps are presented for the model consisting of a Jeffcott rotor and a flexible mounted rigid stator ring. The analysis methods are applied systematically with respect to various motion patterns that have been observed for rotor stator contact in the past. The type of motion is identified using the analysis methods. Also the influence of different parameters on the changes of motion patterns and the transitions that result are described. The unique identification of all motion patterns for rotor stator interaction based on Bifurcation Diagrams is focus of the paper. Further insight on the conditions that lead to the change of motion patterns is given.

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“…Recently, Ehehalt [3], Ehehalt et al [4], and Muszynska [5] analyzed orbit patterns of a synchronous forward whirl, subharmonic resonances, and chaotic motions caused by contact and rubbing. Li and Paidoussis [6] showed numerically that self-excited oscillations of a forward and backward whirling modes occur due to rubbing and collisions when a rotating disk flies in a cylinder colliding to its inner surfaces.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision

et al. 2009

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This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Y. Ishida Balance Method (HBM). As the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these oscillation are also clarified.

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Motion Patterns at Rotor Stator Contact

Cited by 12 publications

References 0 publications

Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability

Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability

Bifurcation of Contact Between Rotor and Stator

Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision

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