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

Abstract

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 ).

Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system

“…x The local contact stiffness coefficient can be determined by the equivalent stiffness of the contact linear spring force model [20],…”

The forward and the backward full annular rubbing dynamics of a coupled rotor-casing/foundation system

“…From the whirl frequency of the dry friction backward whirl, w , it is more easily found that the whirl frequencies increase with the rotation speed and have different ranges of values in the two existence regions when μ = 0.25. Actually, the magnitudes of the whirl frequencies in the two existence regions are limited respectively by the two natural frequencies of the coupled rotor-casing/foundation system with zero clearance as given by (3).…”

“…In this aspect three simplified rotor/stator models were studied. The first rotor/stator model consists of a Jeffcott rotor and a rigid stator that is rigidly fixed on a rigid foundation [1][2][3]. The second rotor/stator model still uses a Jeffcott rotor but the stator is modeled as an added stiffness.…”

Bifurcation analysis on full annular rub of a nonlinear rotor system

“…(8) and (9). For physical systems only stable solutions are of interest because they reflect the system response which can really occur.…”

“…The response and stability for both two cases were obtained, and the effect of parameters, such as mass unbalance, dry friction, rotor damping, and seal stiffness, on shifting from synchronous response to reverse rub were discussed. Zhang et al [9][10][11] studied the SFARM (synchronous full annular rub motion) of a single disk rotor and a flexible rotor, respectively. Perturbation method was employed to solve the exact solution and its stability regions.…”