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RESEARCH PAPERS

# Improvement of Punch Profiles for Elastic Circular Contacts

[+] Author and Article Information
Marilena Glovnea

Department of Mechanical Engineering, University of Suceava, 1 University Street, 720225, Romaniamlg@fim.usv.ro

Emanuel Diaconescu

Department of Mechanical Engineering, University of Suceava, 1 University Street, 720225, Romaniaemdi@fim.usv.ro

J. Tribol 128(3), 486-492 (Mar 21, 2006) (7 pages) doi:10.1115/1.2197522 History: Received February 24, 2004; Revised March 21, 2006

## Abstract

Machine design and electrical contacts involve frequently elastic circular contacts subjected to normal loads. Depending on geometry, these may be Hertzian or surface contacts. Both possess highly nonuniform pressure distributions which diminish contact load carrying capacity. The achievement of a uniform pressure distribution would be ideal to improve the situation, but this violates stress continuity. Instead, the generation of a uniform pressure over most of contact area can be sought. Generally, equivalent punch profile which generates this pressure is found by numerical evaluation of double integrals. This paper simplifies the derivation of punch profile by using an existing correspondence between a polynomial punch surface and elastically generated pressure. First, an improved pressure profile is proposed seeking to avoid high Huber-Mises-Hencky stresses near contact surface. Then, this is approximated by the product between typical Hertz square root and an even polynomial, which yields directly the punch profile. Formulas for normal approach and central pressure are derived.

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## Figures

Figure 1

Proposed dimensionless pressure distribution (x¯=x∕R; y¯=y∕R)

Figure 2

Auxiliary geometrical construction

Figure 3

3D plot of dimensionless HMH stress in a radial plane: (a)c¯=0; (b)c¯=0.2 (r¯=r∕R; z¯=z∕R)

Figure 4

Variation of dimensionless HMH stress with depth: (a) on central axis; (b) at radius au(z¯=z∕R)

Figure 5

Variation of the depth of maximum HMH stress at radius au with c¯(z¯m=zm∕R)

Figure 6

Proposed, p(r¯)—dotted line, and approximating, pa(r¯)—solid line, dimensionless pressure profiles for n=5 and c¯=0.2(r¯=r∕R)

Figure 7

Dimensionless diametric profile of improved punch (r¯=r∕R, z¯a=za∕ηp0R)

## Errata

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