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TECHNICAL PAPERS

Annular Component Transient Thermoelastic Analysis Using a State Space Approach

[+] Author and Article Information
Woon Yik Yong

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom

Patrick S. Keogh

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdomenspsk@bath.ac.uk

J. Tribol 129(4), 818-828 (Mar 15, 2007) (11 pages) doi:10.1115/1.2768082 History: Received September 21, 2006; Revised March 15, 2007

Annular components are used widely in engineering systems and include bearing bushes and races, which may be exposed to extreme operating conditions. A method to establish the localized transient thermoelastic deformation of a homogeneous two-dimensional annular component is developed. The analysis is based on solving the thermoelasticity equations using a state space formulation for the Fourier components of the radial and tangential displacements. Two boundary conditions are considered, namely, rigid and resiliently mounted outer boundaries, both associated with stress free inner boundary conditions. The thermoelastic solution is then demonstrated for a transient temperature distribution induced by inner boundary frictional heating due to rotor contact, which is derived from a dynamic Hertzian pressure distribution. The application is to a relatively short auxiliary bearing for which a state of plane stress is appropriate. However, the thermoelastic analysis is generalized to cover cases of plane strain and plane stress.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Mounting configurations for annular component: (a) rigid outer boundary and (b) resiliently mounted outer boundary

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Figure 2

Coordinate systems for superimposed annular and half space regions. The line source location is the axial line through O′.

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Figure 3

Normalized solutions and relative errors between finite element and analytical solutions: (a) rigid outer boundary and (b) resilient outer boundary

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Figure 4

Time variation of inner surface temperature at contact point θ=0 together with the associated heat flux. The data in Table 1 apply.

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Figure 5

Contact induced temperature distributions at (a) t=1ms, (b) t=10ms, and (c) t=100ms

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Figure 6

Comparison of inner surface radial and tangential thermoelastic displacements of Green’s function evaluated at t=10ms. The dashed line corresponds to a truncated series of 50 harmonics from Eq. 46, while the solid line corresponds to a truncated series of 50 harmonics from Eq. 50.

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Figure 7

Time variation of thermoelastic radial displacements at θ=0. The data in Table 1 apply.

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Figure 8

Thermoelastic surface distortion of the rigidly mounted bearing at (a) t=1ms, (b) t=10ms, and (c) t=100ms

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Figure 9

Thermoelastic surface distortions of the resiliently mounted bearing at (a) t=1ms, (b) t=10ms, and (c) t=100ms

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Figure 10

Thermoelastic radial stress distributions for the rigidly mounted bearing at (a) t=10ms and (b) t=1s

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Figure 11

Thermoelastic von Mises stress distributions for the rigidly mounted bearing at (a) t=10ms and (b) t=1s

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Figure 12

Thermoelastic radial stress distributions for the resiliently mounted bearing at (a) t=10ms and (b) t=1s

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Figure 13

Thermoelastic von Mises stress distributions for the resiliently mounted bearing at (a) t=10ms and (b) t=1s

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