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Most rotating machinery consists of a driver coupled to a driven machine through mechanical couplings used to transmit torque from the driver to the machine. In these, angular and parallel misalignments of shafts are common with more or less degree due to system assembly or maintenance proceedings. Several mechanical couplings can be present in a long shaft-line and the misalignment between connected shafts causes vibration to the holy assembly.
In the literature, the vibration analysis of rotors with flexible coupling subjected to misalignment forces have been studied. Theoretical and experimental analyses were done in order to demonstrate the stability and misalignment effects on a rotor system. However, few studies have detailed this approach for simulating the effect produced by misalignment on rotating machinery. In special for the coupling, diagnostics concluded the majority of the misalignment forces induce higher harmonics. The dynamics of the coupling excitation on the rotor was captured by means of stiffness coefficients calculated to represent the coupling in the assembly model. Depending on the formulation of the coupling stiffness matrix cross-coupled coefficients appear indicating the possibility of coupled lateral-axial-torsional vibration response of the rotor due to the coupling.
In this work, the misalignment of a rigid coupling is analyzed and highlighted to give other diagnostic informations. In similar way, superharmonic components in the system vibration response are the most remarkable effects of rigid coupling misalignment and are due to the variable loading on the bearings. There are few studies about this phenomenon in the literature and these diagnostics leads us to nonlinear analyses. The stability and bifurcation analysis consider the nonlinear damping and stiffness of the journal bearings. The finite element method is used for modeling the rotating system. The nonlinear behavior of the journal bearings is analyzed as function of the periodical change of the bearing load after adding a significant level of coupling misalignment. The nonlinear effects are highlighted by the spectral analysis of the system response considering the nonlinear forces and their Jacobians as calculated simultaneously. The stability and bifurcation of periodic responses are performed. A jump phenomenon that typically occurs in the nonlinear system is detected from the unstable periodic orbit to the period-doubling orbit of the center of the rotor at the bearing station. With the rotating speed increasing a bifurcation occurs. Beyond the bifurcation point, unbalanced responses show torus attractors for the projection of the Poincar map. From these numerical results, rich and complex nonlinear behaviors are demonstrated.