Dynamic Analysis and Active Control of Functionally Graded Rotor Shaft System

Functionally graded (FG) shaft finds applications in gas turbines and aircraft jet engine rotors to withstand the thermal and mechanical loads. The present work deals with the finite element modelling, and dynamic analysis and active control of different kinds of FG rotating shaft systems considering temperature-independent (TID) and temperature-dependent (TD) material properties. Aluminum oxide (Al2O3), stainless steel (SUS304), and titanium alloy (Ti-6Al-4V) are considered as the FG shaft materials. One dimensional (1D) and two dimensional (2D) distributions of material properties of the FG shafts have been obtained. Material properties of the FG shafts are determined based on the power-law distribution. A time-dependent two-dimensional (2D) temperature distribution problem is assumed for the FG shafts; it has been solved using the finite difference method (FDM). Based on the Timoshenko beam theory (TBT), a three noded beam element has been developed for the finite element (FE) modelling and dynamic analysis of the FG spinning shaft systems. The present FE modelling is based on the first-order shear deformation theory considering rotary inertia and gyroscopic effects. The governing equation of motion is derived using the Hamilton principle. In this present work, electromagnetic actuator (EMA) has also been used to provide the non-contact control force for actuation, which significantly can reduce the rotor vibration due to unbalance forces by enhancing the stability limit speed of the rotor-shaft system which can lead the safe operations at higher speeds. The mathematical model of the EMA has been carried out for the determination of input current and generated force. It has been found from the obtained results that eigenfrequencies, stability limit speed (SLS), maximum real parts, and frequency and time-domain responses have significantly been influenced by temperature variation, power-law index, and internal viscous and hysteretic damping. Proportional-derivative (PD) control scheme has also been implemented to control the above responses by varying the number of coil turns (N) and pole face area (Ap) of the EMA.