Study On Bifurcations And Chaos Of Coupled Bending And Torsional Vibration About Fan's Rotor System

The rotor system of fans has symmetry structure is taken as study object in this paper. Aft-er the purpose and significance of the study subject are expanded, research status and problems remained on the nonlinear rotor dynamics are summarized. On it, the nonlinear dynamics cha-racter of unbalance rotor, impact-rubbing rotor, coupled flexural and torsion vibration and the bifurcation and chaos motion caused by them are deeply studied. The main works of the paper are as flowers:1) Bases on the certain fan, pick up the parameter correlated and analyse its geometry str-ucture, then establish the mechanics model equivalent with it.2) To the mechanics model, give out the freedom differential equations of bending-torsion coupling vibration about damped rotor and ideal rotor. On the basis of it, analyse the forses of unbalance rotor and impact and rubbing rotor models.By using Lagrange Equation and Dalng-bel theory, the general differential equations of coupled bending and torsional nonlinear vibra-tion about rotor with unbalance character and rubbing character are deduced. For the conveni-ence of determine the nature research, change them dimensionless.3) Bases on given unbalance rotor mathematics model, find the balance point. Establish the First-Order approximate perturbed equation about balance point, when finding eigenvalues of Jacobi matrix know that: the eigenvalueλ_i isn't related with angle velocityΩ, but the eccen-tricitye , and are all negative. From Center Manifold Theorem, the geometry structure of bala-nce point nearby has asymptotic stablility, singular point bifurcation won't happen. Using the same theory, during calculating the eigenvalues of First-Order approximate perturbed equation of Jacobi matrix about impact and rubbing system find that: the eigenvalueλ_i is related with angle velocityΩ, also the eccentricitye , and follow the changes of velocityΩand eccentrici-tye and eigenvalueλ_i change from negative to positive. System near the balance point changed from asymptotically stable to unstable, singular point bifurcation will happen; then the nonlin-ear stability of the periodic motion of the rotor system with unbalance and rubbing is investiga-ted by using Floquet theory and the shooting method. The convert and evolution course of peri-odical motion, quasi-periodical response, double-periodical bifurcation and chaos of the system response are opened out. 3) For the two dimensionless general differential equations of coupled bending and torsi-onal nonlinear vibration about rotor, educe the numerical value result by using the numerical value analysis method. The bifurcation diagrams, poincarémaps, phase plane portraits, trajec-toryies of journal center, time-history curve of the rotor motion are used. The convert and evol-ution course of periodical response, quasi-periodical response, double periodical bifurcation, chaos of the system response is analyzed. Bifurcation and chaos behavior especially the influ-ence on bifurcation and chaos behavior of unbalance and impact-rubbing fault rotor system caused by the parameters of rotor rotating speed was analyzed, using numerical value analysis method and the conclusion that Floquet multipliers in accorded with the results by numerical value analysis method is also gained.