A Study of the Approximate Expressions for Constriction Resistance of Multitude Conducting Spots

Hitoshi NISHIYAMA  Isao MINOWA  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E82-C   No.1   pp.25-32
Publication Date: 1999/01/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Electromechanical Devices and Their Materials)
Category: 
Keyword: 
multitude conducting spots,  Greenwood's expressions,  constriction resistance,  boundary element method,  partial resistance,  contact surface,  

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Summary: 
Simple expressions for constriction resistance of multitude conducting spots were analytically formulated by Greenwood. These expressions, however, include some approximations. Nakamura presented that the constriction resistance of one circular spot computed using the BEM is closed to Maxwell's exact value. This relative error is only e=0. 00162 [%]. In this study, the constriction resistances of two, five and ten conducting spots are computed using the boundary element method (BEM), and compared with those obtained using Greenwood's expressions. As the conducting spots move close to each other, the numerical deviations between constriction resistances computed using Greenwood's expressions and the BEM increase. As a result, mutual resistance computed by the BEM is larger than that obtained from Greenwood's expressions. The numerical deviations between the total resistances computed by Greenwood's expressions and that by the BEM are small. Hence, Greenwood's expressions are valid for the total constriction resistance calculation and can be applied to problems where only the total resistance of two contact surfaces, such as a relay and a switch, is required. However, the numerical deviations between the partial resistances computed by Greenwood's expression and that by the BEM are very large. The partial resistance calculations of multitude conducting spots are beyond the applicable range of Greenwood's expression, since Greenwood's expression for constriction resistance of two conducting spots is obtained by assuming that the conducting spots are equal size. In particular, the deviation between resistances of conducting spots, which are close to each other, is very large. In the case of partial resistances which are significant in semiconductor devices, Greenwood's expressions cannot be used with high precision.