A Model for Junction Growth of a Spherical Contact Under Full Stick Condition

[+] Author and Article Information
V. Brizmer, Y. Kligerman

Department of Mechanical Engineering, Technion, Haifa 32000, Israel

I. Etsion1

Department of Mechanical Engineering, Technion, Haifa 32000, Israeletsion@technion.ac.il


Corresponding author.

J. Tribol 129(4), 783-790 (Jul 12, 2007) (8 pages) doi:10.1115/1.2772322 History: Received February 12, 2007; Revised July 12, 2007

The evolution of the contact area (junction growth) of an elastic-plastic preloaded spherical contact subjected to an additional tangential loading is investigated theoretically. The normal preloading, under full stick condition, leads to the formation of a junction that can support additional tangential load. A gradual increase of this tangential load, while the normal preload remains constant, can incept plasticity of the contact zone in case the initial normal preload was elastic or enhance an existing one, thus lowering the tangential stiffness of the junction. Finally, the tangential stiffness approaches zero, which corresponds to sliding inception (i.e., loss of stability). The evolution of the contact area during the tangential loading prior to sliding inception reveals an essential junction growth which depends on the magnitude of the normal preload. The mechanism causing this junction growth seems to be new points of the sphere surface, which originally lay outside of the initial contact area that are coming into contact with the rigid flat during the tangential loading. The theoretical results for the junction growth obtained in the present work correlate well with some limited experiments.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A model of a deformable sphere in contact with a rigid flat under combined normal and tangential loading

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Figure 2

Contact area boundaries under normal preload alone and at sliding inception: (a) present theoretical results for P*=200 and (b) experimental results for P*=210(25)

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Figure 3

The evolution of the dimensionless contact pressure distribution in the symmetry plane for increasing tangential loading at P*=10

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Figure 4

Relative junction growth, As∕A0, versus the dimensionless normal preload, P*: best fit of the numerical results (Eq. 1, solid line) and preliminary experimental results (triangles)

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Figure 5

Three stages of the combined loading showing: (a) normal preload alone; (b) tangential loading tending to bend the sphere and its axis of symmetry as well as tilting the flat; and (c) restoring moment returns the flat to its horizontal position, increasing the interference. The initial symmetry axis is shown by the dashed line.

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Figure 6

The evolution of the plastic region in the symmetry plane, for P*=100 at the completion of normal preload (dashed line), and at sliding inception (solid line) (30)

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Figure 7

The growth in dimensionless interference, Δω*=(ω−ω0)∕δc, versus the initial dimensionless interference, ω0*=ω0∕δc

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Figure 8

The dimensionless tangential displacement of the initial axis of symmetry of the sphere ux∕(ux)max versus the dimensionless vertical coordinate z∕R, within the upper 2% of the sphere’s height, for P*=100

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Figure 9

Dimensionless vertical displacement change, Δuz∕Δω, during the tangential loading, for P*=100: (a) in the xz plane and (b) the symmetric distribution in the yz plane

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Figure 10

Dimensionless gap change, Δh∕h0, close to the original contact boundary, during the tangential loading, for P*=100: (a) at the leading edge; (b) at the trailing edge; and (c) at the lateral edges

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Figure 11

Instant junction growth, A∕A0, versus the instant dimensionless tangential load, Q∕P, for different dimensionless normal preloads, P*



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