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A higher dimensional theory of electrical contact resistance
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10.1063/1.3148289
/content/aip/journal/jap/105/12/10.1063/1.3148289
http://aip.metastore.ingenta.com/content/aip/journal/jap/105/12/10.1063/1.3148289
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

True points of contact occur only at the asperities of the contacting surface, leading to high contact resistance.

Image of FIG. 2.
FIG. 2.

The classical model of a cylindrical current channel of radius joint by a zero-thickness circular hole of radius a (-spot).

Image of FIG. 3.
FIG. 3.

A rectangular current channel with a constriction of ZBL.

Image of FIG. 4.
FIG. 4.

A rectangular current channel with a finite axial length of in the direction of current flow.

Image of FIG. 5.
FIG. 5.

A connecting bridge in the form of a cylinder of radius and a finite axial length in the direction of current flow.

Image of FIG. 6.
FIG. 6.

A connecting bridge in the form of a funnel with a total axial length in the direction of current flow.

Image of FIG. 7.
FIG. 7.

The normalized contact resistance of a rectangular current channel with ZBL. Also shown is the asymptotic formula for (dash curve).

Image of FIG. 8.
FIG. 8.

Timsit’s normalized contact resistance of the -spot. Holm’s classical result, , is recovered in the limit .

Image of FIG. 9.
FIG. 9.

The normalized contact resistance as a function of at various values of for a rectangular current channel. The squares show values according to conformal mapping, Eq. (A4), at some random combinations of and .

Image of FIG. 10.
FIG. 10.

The normalized contact resistance as a function of at various values of for a rectangular current channel. The squares show values according to conformal mapping, Eq. (A4), at some random combinations of and .

Image of FIG. 11.
FIG. 11.

The normalized rate of increase in the contact resistance with respect to the bridge length for a rectangular channel, extracted from numerical data according to the exact theory, Eq. (A4). Also shown is the analytic formula (dash curve).

Image of FIG. 12.
FIG. 12.

The normalized contact resistance as a function of at various values of for a cylindrical channel with a cylindrical bridge. The squares show values according to spot checks with electrostatic code at some random combinations of and .

Image of FIG. 13.
FIG. 13.

The normalized contact resistance as a function of , at various values of for a cylindrical channel with a funnel shaped bridge. The squares show values according to spot checks with electrostatic code at some random combinations of and .

Image of FIG. 14.
FIG. 14.

(a) The half rectangular current channel in the plane and (b) its map onto the plane.

Image of FIG. 15.
FIG. 15.

as a function of for a rectangular current channel with ZBL, according to the exact formulation, Eq. (A6). The dashed curve shows the asymptotic formula for , Eq. (A7).

Image of FIG. 16.
FIG. 16.

A branch cut for , joining and . The line integral of equals zero on contours and , and on any path on which .

Image of FIG. 17.
FIG. 17.

Alternate contour to evalaute Eq. (B1).

Image of FIG. 18.
FIG. 18.

The contours and , which lie just above and below the branch cut.

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/content/aip/journal/jap/105/12/10.1063/1.3148289
2009-06-17
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A higher dimensional theory of electrical contact resistance
http://aip.metastore.ingenta.com/content/aip/journal/jap/105/12/10.1063/1.3148289
10.1063/1.3148289
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