Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients

Abstract

The dynamic stiffness matrix (DSM) method, an analytical method that provides exact solutions, has been used for the first time for the free vibration analysis of a functionally graded (FG) rotor bearing system subjected to temperature gradients and to investigate its application to FG rotors. The material gradation occurs based on the power law between the inner metal core and the outer ceramic rich layer of the FG rotor. The temperature gradation follows the Fourier law of heat conduction which leads to non-linear temperature distribution (NLTD) in the radial direction of the FG rotor. The development of the DSM formulations for Timoshenko FG rotor elements using the governing equations derived from translational and rotational equilibrium conditions is the novelty of the present work. The DSM of the FG rotor elements, rigid disk and linear isotropic bearings are assembled to obtain the global dynamic stiffness matrix of the FG rotor bearing system. The natural whirl frequencies are computed from the global DSM using the Wittrick–William algorithm as a root searching technique. The natural and whirl frequencies are validated with the results available in the literature and the exactness of the DSM method has been exemplified.

Stiffness characteristics of angular contact ball bearing considering thermal - mechanical coupling

“…The heat displacement of the bearing inner and outer rings in the axial direction can be expressed as follows: 11 22…”

“…Subsequently, Mi Wei et al [10] , from Xi'an Jiaotong University, established a transient thermal network model to account for heat-deformation coupling in shafting systems aiming to predict temperature fields more accurately within sphind-bearing systems while monitoring real-time temperature rise in key components.Their approach employed the thermal network method where key components were selected as temperature nodes,and characteristic parameters such as heat source and boundary conditions were modified dynamically to enable coupling analysis between temperature field and deformation. Bharath et al [11] employed the dynamic stiffness matrix (DSM) to conduct free vibration analysis of a functional classification (FG) rotor bearing system subjected to temperature gradient. The global dynamic stiffness matrix of the FG rotor bearing system is obtained based on Fourier's heat transfer law.…”

A Study on Dynamic Behaviour of Thermally Distributed Exponentially Graded Rotor System with Induced Porosities

“…Nguyen and Bui [21] carried out the dynamic analysis of a higher-order finite FG beam element under a thermal environment. Obalareddy et al [22] investigated the free vibration behaviour of an FG rotor-bearing system subjected to temperature gradients by employing the dynamic stiffness matrix approach. e effect of thermal gradients on the vibrational behaviour of the FG rotor system was analysed by Bose and Sathujoda [23].…”