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TECHNICAL PAPERS

# Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

[+] Author and Article Information
Jun Wen

Louisiana State University, Department of Mechanical Engineering, 2508 CEBA, Baton Rouge, LA 70808

M. M. Khonsari1

Louisiana State University, Department of Mechanical Engineering, 2508 CEBA, Baton Rouge, LA 70808Khonsari@me.lsu.edu

1

Corresponding author.

J. Tribol 129(3), 517-527 (Feb 24, 2007) (11 pages) doi:10.1115/1.2736435 History: Received August 14, 2006; Revised February 24, 2007

## Abstract

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency $ω¯=ωl2∕4α$ and the dimensionless oscillation amplitude $A¯=A∕l$, whose product can be interpreted as the Peclet number involving oscillatory heat source, $Pe=ω¯A¯$. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

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Topics: Heat , Temperature

## Figures

Figure 1

Semi-infinite body subjected to an oscillating heat source

Figure 2

Heat source configurations: (a) Circular heat source: (b) Rectangular heat source: (c) Elliptical heat source

Figure 3

Cases where sin(Φ−ϕ) is not positively or negatively defined: (a) before adjusting Φ*; (b) after adjusting Φ*

Figure 4

Comparison of surface temperature for a moving uniform circular heat source on a semi-infinite medium. ξ is the axis passing through the center of the heat source along the sliding direction. Pe=UR∕2α, here R is radius of the circular contact area, q0=μp0U.

Figure 5

Temperature variation up to steady state at the center of the contact area for a moving uniform circular heat source on a semi-infinite medium. Pe=UR∕2α, here R is the radius of the circular contact area, q0=μp0U.

Figure 6

Comparison of maximum steady temperature variations at different γ for oscillating uniform circular heat source on a semi-infinite medium, q0=μp0Aω, γ=Rω∕α

Figure 7

Comparison of the maximum overall temperature at different γ for oscillating uniform circular heat source on a semi-infinite medium, q0=μp0Aω, γ=Rω∕α

Figure 8

Effect of the dimensionless frequency ω¯ on the maximum dimensionless temperature for uniform square heat source. (a) Dimensionless temperature as a function of cycles, ω¯=ωl2∕4α; (b) Steady state versus the dimensionless frequency, ω¯=ωl2∕4α.

Figure 9

Maximum dimensionless overall temperature variation at steady state at different dimensionless frequency ω¯ for uniform square heat source, ω¯=ωl2∕4α

Figure 10

Distribution of dimensionless overall temperature for oscillating uniform square heat source along the sliding direction with the center of the contact region as the origin, ω¯=ωl2∕4α

Figure 11

Distribution of dimensionless overall temperature for oscillating uniform circular heat source along the sliding direction with the center of the contact region as the origin, ω¯=ωl2∕4α and l=R

Figure 12

Distribution of dimensionless overall temperature for oscillating parabolic heat source along the sliding direction with the center of the contact region as the origin, q0=2qm∕3 and qm=μpmAω, ω¯=ωl2∕4α, and l=R

Figure 13

Effect of the dimensionless amplitude A¯ on the maximum dimensionless temperature for uniform square heat source. (a) Dimensionless temperature as a function of cycles at ω¯=190, A¯=A∕l. (b) Steady state versus the dimensionless amplitude at ω¯=190, A¯=A∕l.

Figure 14

Maximum dimensionless overall temperature variation at steady state at different dimensionless amplitude A¯ for uniform square heat source, A¯=A∕l

Figure 15

(a) Maximum dimensionless steady temperature versus ω¯ and A¯ for parabolic heat source. (b) Residuals of maximum dimensionless steady temperature versus ω¯ and A¯ for parabolic heat source.

Figure 16

Comparison of maximum dimensionless overall temperature predicted by the fitting solution and by Greenwood and Alliston-Greiner (10) with different ω¯ for the parabolic heat source

Figure 17

Comparison of maximum dimensionless overall temperature predicted by the fitting solution and by Greenwood and Alliston-Greiner (10) with different A¯ for the parabolic heat source

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