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Research Papers: Hydrodynamic Lubrication

Theoretical Study of Static and Dynamic Characteristics for Eccentric Cylinders Lubricated With Ferrofluid

[+] Author and Article Information
Kadry Zakaria, Magdy A. Sirwah, M. Fakharany

Department of Mathematics, Faculty of Science, Tanta University, Tanta 11511, Egypt

J. Tribol 133(2), 021701 (Mar 17, 2011) (18 pages) doi:10.1115/1.4003481 History: Received April 27, 2010; Revised December 28, 2010; Published March 17, 2011; Online March 17, 2011

The aim of this study is to explore the static and dynamic performance characteristics of finite journal bearings lubricated with a non-Newtonian ferrofluid in the presence of an external magnetic field using the spectral method technique. The modified Reynolds equation governing the film pressure, coming out from the combination of the momentum and continuity equations, is derived. We use the pressure distribution function to study the static and dynamic characteristics and the stability of the given system. Numerical applications are achieved in order to investigate the influence of the various parameters on the stability behavior of the system. For instance, it is observed that the journal loci get stable as the magnetic force increases. The non-Newtonian, the distance ratio, and the magnetic parameters play an important role in administrating the stability behavior. The non-Newtonian parameter is found to stabilize the system, while the magnetic force coefficient destabilizes it. Furthermore, for law eccentricity ratios, the stability of this system is significant.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Finite journal bearing geometry and its velocities

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Figure 4

(a) Plots of F̂μ versus ε0 for various values of the ferrofluid parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) Comparing plots of F̂μ versus ε0 for several values of the magnetic parameter α, while the fixed parameters are Lr=1, R̃=1.6, and σ=2.6.

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Figure 5

(a) Plots of cμ versus ε0 for varying values of the ferrofluid parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) Graphs of cμ versus ε0 for different values of the magnetic parameter α, while the fixed parameters Lr=1, R̃=1.6, and σ=1.4.

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Figure 6

(a) Comparing plots of Ŝrr versus ε0 for different values of the ferrofluid parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) The behavior of Ŝφφ versus ε0 for varying values of the non-Newtonian parameter σ. For a diagram having Lr=1, R̃=1.6, and α=0.05. (c) Comparing plots of Ŝrr against ε0 for several values of the distance ratio R̃, while the fixed parameters are Lr=1, α=0.05, and σ=2.6. (d) Plots of Ŝφφ versus ε0 for varying values of the distance ratio R̃, while the fixed parameters are Lr=1, α=0.05, and σ=2.6.

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Figure 7

(a) Graphs of Ŝφr versus ε0 for different values of the ferrofluid parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) Ŝrφ plotted against ε0 for several values of the ferrofluid parameter. For a diagram having Lr=1, R̃=1.6, and α=0.05. (c) Graphs of Ŝφr plotted against ε0 for different values of the distance ratio R̃. For a system having Lr=1, α=0.05, and σ=2.6. (d) The variation of Ŝrφ with ε0 for several values of the distance ratio R̃. For a diagram having Lr=1, α=0.05, and σ=2.6.

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Figure 8

(a) Comparing plots of D̂rr versus ε0 for different values of the ferrofluid parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) Plotting D̂φφ against ε0 for various values of the ferrofluid parameter σ. For a diagram having Lr=1, R̃=1.6, and α=0.05. (c) Graphs of D̂rr plotted against ε0 for different values of the magnetic coefficient α. For a system having Lr=1, R̃=1.6, and σ=1.4. (d) The variation of D̂φφ with ε0 for different values of the magnetic coefficient α. For a system having Lr=1, R̃=1.6, and σ=1.4.

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Figure 9

(a) Graphs of D̂φr plotted against ε0 for different values of the non-Newtonian parameter σ. For a system having Lr=1, R̃=1.6, and α=0.05. (b) Plotting D̂rφ versus ε0 for several values of the ferrofluid parameter σ. For a diagram having Lr=1, R̃=1.6, and α=0.05. (c) The variation of D̂φr versus ε0 for various values of the magnetic coefficient α. For a system having Lr=1, R̃=1.6, and σ=1.4. (d) Comparing plots of D̂rφ versus ε0 for different values of the magnetic coefficient α. For a diagram having Lr=1, R̃=1.6, and σ=1.4.

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Figure 10

For a diagram having Lr=1, R̃=1.6, and α=0.05 reveals the variation of Ŵℓ versus ε0 for different values of the ferrofluid parameter σ

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Figure 11

Sample plots of Ŵℓ against ε0 for various values of the magnetic parameter α. For a system having Lr=1, R̃=1.6, and σ=1.4.

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Figure 12

Influence of α on Ŵℓ for different values of ε0. For a system having Lr=1, R̃=1.6, and σ=2.6.

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Figure 13

Plots of Ŵℓ versus R̃ for several values of ε0, while the fixed parameters are Lr=1, α=0.05, and σ=2.6

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Figure 14

The behavior of external load Ŵ, friction force F̂μ, and attitude angle φ versus the eccentricity ratio for several values of non-Newtonian parameter σ, in light of Fourier spectral technique

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Figure 2

(a) Journal loci for finite journal bearing for various values of the ferrofluid parameter σ, while the fixed parameters are Lr=1, R̃=1.6, and α=0.1. (b) Journal loci for finite journal bearing for various values of the magnetic parameter α. For a system having Lr=1, R̃=1.6, and σ=1.4.

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Figure 3

(a) Graphs of S plotted against ε0 for different values of the ferrofluid parameter σ, while the fixed parameters are Lr=0.05, R̃=2.6, and α=0.05. (b) Comparing plots of S versus ε0 for various values of the geometric parameter Lr. For a diagram having α=0.05, R̃=1.6, and σ=1.4.

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