Abstract
Functionally graded material shafts are the main part of many modern rotary machines such as turbines and electric motors. The purpose of this study is to present an analytical solution of the elastic-plastic deformation of functionally graded material hollow rotor under a high centrifugal effect and finally determine the maximum allowed angular velocity of a hollow functionally graded material rotating shaft. Introducing non-dimensional parameters, the equilibrium equation has been analytically solved. The results for variable material properties are compared with the homogeneous rotor and the case in which Young’s modulus is the only variable while density and yield stress are considered to be constant. It is shown that material variation has a considerable effect on the stress and strain components and radial displacement. Considering variable density and yield stress causes yielding onset from inner, outer, or simultaneously from both inner and outer rotor shaft radius in contrast to earlier researches that modulus of elasticity was the only variable. The effects of the density on the failure of a functionally graded material elastic fully plastic in a hollow rotating shaft are investigated for the first time in this study with regard to Tresca’s yield criterial. Numerical simulations are used to verify the derived formulations which are in satisfying agreement.
Highlights
Graded materials (FGM) are finding vast applications in different rotary systems such as DC motors with a magnetic membrane and chemical resistant hydraulic motors (Mahamood & Akinlabi, 2017), gas turbine rotors (Bahaloo, Papadopolus, & Ghosha, 2016; Klocke, Klink, & Veselovac, 2014; Lal, Jagtap, & Singh, 2013), and modern vehicle drive train systems (Kaviprakash, Kannan, Lawrence, & Regan, 2014; Lee, Kim, Kim, & Kim, 2004; Moorthy, Mitiku, & Sridhar, 2013)
ZamaniNejad and Rahimi studied the elasticity of an Functionally graded materials (FGM) rotating cylindrical pressure vessels (ZamaniNejad & Rahimi, 2010)
In the present article, elastic-plastic behavior of a rotating shaft made of FGM under high centrifugal forces is investigated for the first time
Summary
Graded materials (FGM) are finding vast applications in different rotary systems such as DC motors with a magnetic membrane and chemical resistant hydraulic motors (Mahamood & Akinlabi, 2017), gas turbine rotors (Bahaloo, Papadopolus, & Ghosha, 2016; Klocke, Klink, & Veselovac, 2014; Lal, Jagtap, & Singh, 2013), and modern vehicle drive train systems (Kaviprakash, Kannan, Lawrence, & Regan, 2014; Lee, Kim, Kim, & Kim, 2004; Moorthy, Mitiku, & Sridhar, 2013). Density variation is considered with variable density and radius ratio of a hollow rotor on elastic and plastic behavior and maximum allowed angular velocity are discussed (Fig. 1). Yielding occurs when above equation equals zero for the corresponding load parameters such as angular velocity ω, yield stress σ0, and modulus of elasticity E These parameters are rearranged and defined together as non-dimensional loading parameter (NLP): NLP 1⁄4 pωffiffiffiffiffi ð14Þ σ0. By knowing general stress-strain relations and using Hook’s general law and Tresca’s yield criterion, the stress-displacement equation becomes: Fig. 5 Ωfp and Ωy to the loading parameter exponent nj (h = 0.5)
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