Abstract
In this paper the global response characteristics of a piecewise smooth dynamical system with contact, which is specifically used to describe the rotor/stator rubbing systems, is studied analytically. A method to derive the global response characteristics of the model is proposed by studying each piece of the equations corresponding to different phases of the rotor motion, i.e., the phase without rubbing, the phase with rubbing and the phase of self-excited backward whirl. After solving the typical responses in each phase and deriving the corresponding existence boundaries in the parameter space, an overall picture of the global response characteristics of the model is obtained. As is shown, five types of the coexistences of the different rotor responses and deep insights into the interactive effect of parameters on the dynamic behavior of the model are gained.
Highlights
C Real constant in the solution part of backward whirl motionH Complex constant in the supposed solution R0 Non-dimensional clearance R Non-dimensional deflection of the shaft center Rdisk Non-dimensional radius of the disk W Complex deflection of the rotor, X + j Y X, Y Non-dimension displacements of the shaft center c Damping of the rotor e Rotor mass eccentricity ks, kb Stiffness of the rotor shaft and the stator m Mass of the rotor r0 Clearance between rotor and stator r Displacement of the shaft geometric center rdisk Radius of the disk at the contact point t Time x, y Horizontal and vertical displacements of the shaft center α Real part of exponent of the solution part of backward whirl motion β Stiffness ratio of rotor-to-stator, ks/kb φ Phase angle μ Coefficient of friction τ Non-dimensional time ω Rotating speed of the rotor ω0 Backward whirl “natural” frequency of nonlinear coupled rotor/stator system ω2 Natural frequency of the rotor system with zero clearance ωb Normalized whirl frequency of the rotor, ωb = ωw/ω2 ωw Whirl frequency of the rotor Ω Normalized rotating speed of the rotor, ω/ω2 Ωe Critical rotating speed for the start of dry friction backward whirl ζ Damping ratio of the rotor system
Rotor-to-stator rubbing is a malfunction in rotating machinery that degrades the machine performance and may lead to a catastrophic failure of a whole machine through dry whip in the worst case
This paper aims to depict the global response characteristics of a specific rotor/stator contact system by determining the existence conditions of the most typical rotor responses of the piecewise smooth nonlinear system
Summary
H Complex constant in the supposed solution R0 Non-dimensional clearance R Non-dimensional deflection of the shaft center Rdisk Non-dimensional radius of the disk W Complex deflection of the rotor, X + j Y X, Y Non-dimension displacements of the shaft center c Damping of the rotor e Rotor mass eccentricity ks, kb Stiffness of the rotor shaft and the stator m Mass of the rotor r0 Clearance between rotor and stator r Displacement of the shaft geometric center rdisk Radius of the disk at the contact point t Time x, y Horizontal and vertical displacements of the shaft center α Real part of exponent of the solution part of backward whirl motion β Stiffness ratio of rotor-to-stator, ks/kb φ Phase angle μ Coefficient of friction τ Non-dimensional time ω Rotating speed of the rotor ω0 Backward whirl “natural” frequency of nonlinear coupled rotor/stator system ω2 Natural frequency of the rotor system with zero clearance ωb Normalized whirl frequency of the rotor, ωb = ωw/ω2 ωw Whirl frequency of the rotor Ω Normalized rotating speed of the rotor, ω/ω2 Ωe Critical rotating speed for the start of dry friction backward whirl ζ Damping ratio of the rotor system
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