Study of dynamic stress and estimation of life for viscoelastic rotor-a finite element approach

Abstract

Firstly this work deals with the analytical study of stress developed in viscoelastic beam. Instantaneous stress is obtained by operating instantaneous strain. Modelling technique as ATF (Augmenting Thermodynamic Fields) displacements is used to represent the constitutive relationship in time domain by using certain viscoelastic parameters. This operator based constitutive relationship is used to bring the equations of motion. Finite element technique is used to discretize the continuum by using Euler Bernoulli Beam theory and study has been done for various cases of beams by applying different boundary conditions, under different loading situation. Time domain solution is calculated through state space representation of equation of motion which is further utilized for getting the dynamic stress. Further this study has been extended to develop a finite element mathematical model of internally damped viscoelastic rotor which is subjected to combined loading (i.e. due to bending and torsion) and also exposed to thermal environment. The shaft damping is incorporated by considering Kelvin – Voigt model. The bending stress & shear stress are calculated along various location as well as different instant of the rotor. Maximum stress location decides the failure point have also been calculated for our further design. Safe design of rotor parameters have been predicted by comparing failure stresses of the system with the Goodman diagram. Our thematic aim was to investigate fatigue behaviour and estimation of rotor life with the help of the S-N curve, which necessitate the calculation of endurance strength that can also be interpolated through Goodman diagram. Numerical results show that the life of the rotor is affected by the temperature but innocent with the axial torque in operating range. It has been concluded through the resultant stresses the design is safe and hence rotor has infinite life of operation.