Effect of Corrosion on the Natural and Whirl Frequencies of a Functionally Graded Rotor-Bearing System Subjected to Thermal Gradients

Abstract

Corrosion causes a loss of material resulting in the reduction of mass and stiffness of a component, which consequently affects the dynamic characteristics of any system. Fundamental frequency analysis of a corroded functionally graded (FG) rotor system, using the finite element method based on the Timoshenko beam theory, was investigated in the present paper. The functionally graded shaft consisting of an inner metallic core and an outer ceramic layer was considered with the radial gradation of material properties based on the power law. Nonlinear temperature distribution (NLTD) based on the Fourier law of heat conduction was used to simulate the thermal gradient through the cross-section of the FG rotor. The finite element formulation for a functionally graded shaft with a corrosion defect was developed and the dynamic characteristics were investigated, which is the novelty of the present work. The corrosion parameters such as length, depth and position of the corrosion defect in the shaft were varied and a parametric study was performed to investigate changes in the natural and whirl frequencies. An analysis was carried out for different power indexes and temperature gradients of the functionally graded shaft. The effects of corrosion were analysed and important conclusions are drawn from the investigations.

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

“…The variables 𝑥 and 𝑦 are eliminated from the equilibrium condition equations of the planes (x,s) and (y,s) given in Equations ( 12), ( 13), ( 18) and (19), respectively. The resultant equations are combined by introducing a complex variable 𝜃 = 𝜃 𝑦 − 𝑖𝜃 𝑥 , to obtain the governing equation for the Timoshenko FG rotor element in terms of bending slope θ as: In (x, s) plane:…”

“…The free vibration analysis of the FG rotor bearing system having hysteresis and viscous damping effects has been carried out in refs [15,16] using FEM. The free vibration behavior of thermally loaded FG rotor-bearing systems having defects, such as transverse crack [17], porosities [18] and corrosion defect [19] have been investigated, and the influence of these defects on the natural and whirl frequencies has been studied in detail in the literature.…”

Functionally graded materials (FGMs): A review of classifications, fabrication methods and their applications

“…In addition to the above applications, the FGMs are widely used in various industries [269,270]: industrial tools such as cutting tools, heat-resistant coatings, abrasion, corrosion, but also in other fields [271][272][273][274][275][276][277][278][279][280][281][282][283][284][285][286][287][288]. Tian et al [289] investigated the thermal and mechanical shock resistances of a newly developed Si 3 N 4 /(W,Ti)C graded ceramic tool material using the water quenching methods and intermittent cutting test, respectively.…”

Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

“…A vibration analysis of an FG rotor-bearing system whose FG shaft had a transverse crack and a surface crack was performed using finite element formulation [27,28]. Sathujoda et al [37] investigated the natural and whirl frequencies of a corroded FG rotor-bearing system using the finite element method (FEM). Even though a few works on the natural frequency analysis of cracked and corroded FG rotor systems are available [27,28,37] in the literature, to the best of the authors' knowledge, research on the dynamic analysis of a porous FG rotor system is rarely found.…”

“…Sathujoda et al [37] investigated the natural and whirl frequencies of a corroded FG rotor-bearing system using the finite element method (FEM). Even though a few works on the natural frequency analysis of cracked and corroded FG rotor systems are available [27,28,37] in the literature, to the best of the authors' knowledge, research on the dynamic analysis of a porous FG rotor system is rarely found. Recently, an attempt was made by Bose and Sathujoda [38] to analyse the natural frequencies of a porous FG rotor-bearing system without thermal effects using ANSYS three-dimensional finite elements.…”