Dynamics of a viscoelastic rotor shaft using augmenting thermodynamic fields—A finite element approach

Modelling viscoelastic materials is always difficult since such materials store energy as well as dissipate it to the thermal domain. Whereas modelling the elastic behaviour is easy, modelling the energy dissipation mechanism poses difficulty. This paper presents a theoretical study of the dynamics of a viscoelastic rotor-shaft system, where the internal material damping in the rotor-shaft introduces a rotary force well known to cause instability of the rotor-shaft system. An efficient modelling technique that assumes coupled (thermo-mechanical) augmenting thermodynamic field (ATF) to derive the constitutive relationships is found more suitable in comparison with the viscous and hysteric damping models, and is used to model the viscoelastic rotor material. Dynamic behaviour of an aluminium rotor is predicted through viscoelastic modelling of the continuum to take into account the effect of internal material damping. Stability limit speed (SLS) and unbalance response (UBR) amplitude are used as two indices to study the dynamics. It is observed that, the ATF approach predicts more reliable SLS and UBR amplitude in comparison with the viscous and hysteretic model of rotor-internal damping. Composite rotor-shaft assumed by reinforcing the aluminium matrix with carbon fibre is found to postpone the critical speeds and thus make available, higher speed of rotor operation and lower UBR amplitude in comparison with pure aluminium rotor-shaft. Finite element method is used for modelling and analysis.