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RESEARCH PAPERS

Grain Flow for Rough Surfaces Considering Grain/Grain Collision Elasticity

[+] Author and Article Information
Yeau-Ren Jeng

Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, Taiwanimeyrj@ccu.edu.tw

Hung-Jung Tsai1

Department of Mechanical Engineering, WuFeng Institute of Technology, Chia-Yi, Taiwanhjtsai@mail.wfc.edu.tw

1

Author to whom correspondence should be addressed.

J. Tribol 127(4), 837-844 (Mar 22, 2005) (8 pages) doi:10.1115/1.2005287 History: Received October 01, 2004; Revised March 22, 2005

Previous work by this group on an average lubrication equation for grain flow with roughness effects is extended to include grain-grain collision elasticity ranging from perfectly elastic to perfectly inelastic. The average lubrication equation is based on Haff’s grain flow theory, with flow factors from Patir and Cheng and Tripp’s use of perturbation. The derived flow factors are obtained as functions of rough surface characteristics, grain size, and collision pattern. As collision energy loss approaches zero, the inelastic results approach those for perfectly elastic grain collision. The mathematical formulas for flow factors, grain/grain collision elasticity, grain size, and roughness are presented and discussed. Predicitons for the elastic and inelastic cases are graphically demonstrated and compared. The derived average lubrication equation for grain flow shows good agreement with the theoretical and experimental data of Yu, Craig, and Tichy [J. Rheol., 38(4), 921 (1994)].

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of grain flow film between two rough surfaces

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Figure 2

(a) Variation of normal stress with normal shear rate for smooth stationary surface (HP=5.10): comparison of grain flow theory to the analysis and experiment by Yu, Craig, and Tichy (see Ref. 10). (b) Variation of normal stress with normal shear rate for rough stationary surface (HP=5.10): comparison of grain flow theory to the analysis and experiment by Yu, Craig, and Tichy (see Ref. 10).

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Figure 3

The inelastic-elastic grain flow function ratio (Ψine(HP,w∕k)∕Ψe(HP)) as function of film particle ratio (HP) with variation of dimensionless ratios (w∕k)

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Figure 4

(a) Grain size coefficients f as functions of film particle ratio (HP) with variation of dimensionless ratio (w∕k). (b) Grain size coefficients g as functions of film particle ratio (HP) with variation of dimensionless ratios (w∕k).

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Figure 5

(a) Variation of pressure flow factors (Φ¯xxP) with film thickness ratio (HS) for various dimensionless ratios (w∕k) with surfaces (γ1=γ2=9,σ1=σ2,Hp=500). (b) Variation of crosspressure flow factors (Φ¯xyP) with film thickness ratio (HS) for various dimensionless ratios (w∕k) with surfaces (γ1=γ2=9,σ1=σ2,HP=500).

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Figure 6

(a) Variation of pressure flow factors (Φ¯xxP) with film thickness ratio (HS) for various Peklenik numbers (γ) and dimensionless ratios (w∕k) with surfaces (θ1=θ2=0°,σ1=2σ2,HP=500). (b) Variation of crosspressure flow factors (Φ¯xyP) with film thickness ratio (HS) for various Peklenik numbers (γ) and dimensionless ratios (w∕k) with surfaces (θ1=θ2=45°,σ1=2σ2,HP=500).

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Figure 7

(a) Variation of pressure flow factors (Φ¯xxP) with roughness orientation angles (θ) for various dimensionless ratios (w∕k) with surfaces (γ1=γ2=9,HS=3,σ1=2σ2,HP=500). (b) Variation of crosspressure flow factors (Φ¯xyP) with roughness orientation angles (θ) for various dimensionless ratios (w∕k) with surfaces (γ1=γ2=9,HS=3,σ1=2σ2,HP=500). (c) Variation of shear flow factors (Φ¯xxS) with roughness orientation angles (θ) for various dimensionless ratios (w∕k) with surfaces (γ1=γ2=9,HS=3,σ1=2σ2,HP=500).

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Figure 8

(a) Variation of pressure flow factors (Φ¯xxP) with film particle ratio (HP) for various dimensionless ratios (w∕k) and roughness orientation angles (θ) with surfaces (γ1=γ2=9,HS=3,σ1=2σ2). (b) Variation of crosspressure flow factors (Φ¯xyP) with film particle ratio (HP) for various dimensionless ratios (w∕k) and roughness orientation angles (θ) with surfaces (γ1=γ2=9,HS=3,σ1=2σ2).

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