Modelling and Analysis of Various Issues in Viscoelastic Composite Rotors

Abstract

Rotordynamics is a specific wing of science that deals with various issues related to rotating structures. The shaft or rotor is a rotating module that acts as the significant vibration source in most machines. Vibration brings in severe effects, and minimizing it is essential for the smooth and efficient operation of machines. Apart from balancing, replacing heavy metals with viscoelastic substances exhibiting lesser density and proficient material damping mechanism can stand as an alternative to reduce the excessive vibration. However, the main disadvantage of viscoelastic material is its low elastic modulus, which can be overcome by reinforcements. Composite materials have been extensively used for rotor design due to their lightweight, environment-friendly, low cost, quality, and better performance. Unlike a nonrotating system, material damping in the rotor shaft plays a significant role in deciding its dynamics. It produces a speed-dependent force acting tangentially and destabilizes the system after a certain spin speed. Hence, along with proper modelling of rotor systems with asymmetries due to internal damping, it also becomes essential to model the shaft considering the laminated nature of the composite that would satisfy both symmetric and non-symmetric stacking sequences. Further, under dynamic conditions, one of the main reasons for rotating systems' failure is the development of fatigue cracks. Considering the fact that breathing nature is indeed observed in the crack while the system is in operation, it is crucial to appropriately model the breathing behaviour of the crack and further study its effect on the rotating shaft dynamics. Along with the issues mentioned above, a common concern is observed in the large computational effort by the bulky and non-self-adjoint system, especially for more realistic models like submarine shafts, which considerably have a large continuum, lead to large and complex finite element models. The study based on the first issue proposes a novel mathematical technique named Equivalent Modulus Theory (EMT) to model viscoelastic laminated composite shafts and compare it with another method known as Direct Procedure Technique (DPT). The operator-based constitutive relationship is endorsed to each lamina to integrate the material damping, leading to a higher-order finite element (FE) model. Timoshenko beam theory is used in the finite element formulation to incorporate the shear deformation effect. Numerical results are acquired through eigenanalysis and unbalance response. On comparison, the results obtained out of the two procedures authenticate the suitability of EMT for complex heterogeneously laminated structures like rotor-shaft systems. The vital contribution of the study lies in the application of the novel mathematical formulation which uses the material properties of just the single lamina, eliminating the need for fabricating the whole composite irrespective of the stacking sequence. Further, the study has been continued to carry out the dynamic analysis of the composite rotor systems subjected to an important issue, i.e., cracks. Geometry based novel mathematical formulation for breathing mechanism is proposed. This introduces a time-varying stiffness matrix for simulating the breathing behaviour of the crack in a rotating composite shaft. The stiffness matrix is incorporated into the previously obtained higher-order FE model to study the effect of crack on stacking sequence and mode shapes of the heterogeneous laminated shaft. The issue of bulky and complex finite element models leading to higher computational time is dealt with using the reduction process, i.e., Modified SEREP (System Equivalent Reduction Expansion Process). The reduction process is applied over a realistic multilayer propeller shaft system exhibiting viscoelastic nature to check the efficiency of the process through computational time comparison. The carried out research work presents mathematical models that can be applied to any viscoelastic unidirectional composite shaft systems subjected to breathing cracks and exhibit complex and bulky nature