Coupled bending torsional vibrations of non-ideal energy source rotors under non-stationary operating conditions

•A novel model for non-ideal energy source rotors operating at non-constant speed and very high regime is proposed.•The finite element model with 6 dof per node superimposes the torsional deformation and the nominal intrinsic rotation in one variable.•A particular attention is paid to the coupling between the lateral and torsional behavior induced by the gyroscopic effect and the mass unbalance.•The better estimation of the vibratory behavior obtained by the fully coupled new model is exhibited through the comparison of the numerical results with other uncoupled models.•The model is particularly suitable for the study and the design of multi rotors connected by gears or flexible couplings and going through several critical speeds. [Display omitted] In the automotive industry, high-speed elecrical engines will be used in a very large range of speeds, leading to non-stationary operating conditions. Thus more critical speeds may be crossed a very large number of times during the whole life-time of the engine. Therefore, estimating accurately the non-stationary loads and deformations during these transient regimes is of first importance for a correct design. In this paper, we propose a novel dynamic model for unbalanced high-speed rotors with less restrictive assumptions. The finite element model accounts for flexion, torsion and traction-compression leading to six degrees of freedom on each node. The non-ideal energy source is considered and the rotor is running under non-stationary operating conditions and crossing supercritical speeds. The angular displacement is defined in such a way that it combines simultaneously the intrinsic nominal rotation and the torsional deformation. The comparison of the proposed model with other models under different assumptions on the energy source and on the bending-torsion coupling shows that our model offers more accurate prediction for both lateral and torsional vibrations when crossing critical speeds. The ability of the proposed model to account for the mutual influence between lateral and torsional behavior is highlighted and is exhibited through time-frequency analyses.