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Analysis of the fluid pressure, load capacity, and coefficient of friction of an elliptic machine hammer peened surface structure in hydrodynamic lubrication

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Abstract

Recently, the velocity distribution within an elliptical machine hammer peened (MHP) surface structure was discussed by solving analytically the Reynolds equation using Full-Sommerfeld boundary condition (Trauth et al. in Tribol Lett 60(19):1–13, 2015). However, in order to design the MHP process to obtain defined friction characteristics and load capacities of a fluid film, the pressure distribution has to be analyzed as well. Thus, in this contribution, the fluid pressure is discussed using Full-Sommerfeld first, then the previous work is extended by the Swift–Stieber boundary condition to account for cavitation effects. Thereby, the influence of geometry and process parameters on the fluid pressure, load capacity and coefficient of friction will be analyzed both using an approach based on absolute and dimensionless numbers. To asses the influence of lateral effects, the semi-analytic 1D results are compared to numerical 2D results based on the Raimondi approach. Thereby, a recommendation for a surface design manufactured by machine hammer peening is formulated.

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Abbreviations

a :

Longer semi-axis of the ellipse (mm)

b :

Shorter semi-axis of the ellipse (mm

\( C_1, C_2 \) :

Constant of integration (–)

d :

Diameter of the MHP head (mm

f :

Frequency of the MHP head (Hz

F :

Impact force of the MHP head (N)

\( F_L \) :

Load bearing capacity (N)

\( \tilde{F_L} \) :

Dimensionless load capacity (–)

\( F_T \) :

Shear force (N)

h, h(x):

Height of the dimple (mm)

\( h_0 \) :

Fluid film thickness (mm)

\( h_p \) :

Maximum structure depth (mm)

\( \tilde{h} \) :

Dimensionless structure depth (–)

l :

Length of the computational domain (mm)

\( l_p \) :

Line pitch (mm)

p, p(x):

Fluid pressure (MPa mm)

\( p_1, p_2 \) :

Inlet (1) and outlet fluid pressure (MPa mm)

\(\tilde{p} \) :

Dimensionless fluid pressure (–)

\( r_p \) :

Structure length (mm)

s :

Substitution variable (–)

t :

Substitution variable (–)

\( U_1, U_2\) :

Longitudinal velocity of contact body 1 or 2 (mm/s)

v :

Machine feed (mm/s)

\( W_1, W_2 \) :

Longitudinal velocity of contact body 1 or 2 (mm/s)

\( x* \) :

X-coordinate of intersection of the ellipse (mm)

\( \tilde{x} \) :

Dimensionless length (–)

\( y* \) :

Y-coordinate of intersection of the ellipse (mm)

z :

Z-direction (–)

\( \alpha \) :

Structure density (–)

\(\eta \) :

Dynamic viscosity [\(\hbox {Ns}/\hbox {m}^{-2}\)].

\(\tau _L(x)\) :

Frictional shear stress (MPa mm)

\(\lambda \) :

Texture aspect ratio (–)

\(\mu \) :

Coefficient of friction (–)

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Acknowledgments

This work was partly supported by the European Union, Investing in our Future, European Regional Development Fund within the Initiative ’Ziel2.NRW’ [Grant Number: 21060207612] and the German Research Foundation (DFG) [Grant Number: KL 500/135-1].

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Authors and Affiliations

  1. Laboratory for Machine Tools and Production Engineering (WZL), RWTH Aachen University, Steinbachstr. 19, 52074, Aachen, Germany

    D. Trauth, J. Stanke, A. Shirobokov, P. Mattfeld & F. Klocke

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  1. D. Trauth
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  4. P. Mattfeld
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Correspondence to D. Trauth.

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Trauth, D., Stanke, J., Shirobokov, A. et al. Analysis of the fluid pressure, load capacity, and coefficient of friction of an elliptic machine hammer peened surface structure in hydrodynamic lubrication. Prod. Eng. Res. Devel. 10, 539–550 (2016). https://doi.org/10.1007/s11740-016-0696-1

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