There has been increasing demand to research the measuring method to characterize the batch consistency of contact rivets. An automated test equipment has been described that makes it possible to measure the electrical contact resistance with high efficiency. The relationship between contact force and contact resistance during the loading and unloading process was measured explicitly using AgPd alloy, stainless steel and sapphire substrate material with Au coatings as sphere indenters separately. To explain the phenomena of contact resistance decreasing more slowly than the traditional theoretical results during loading, the indenter with coating and rivet are modeled by using the commercial FEM software COMSOL Multiphysics. Besides the constriction resistance, the transition region Au coating resistance and the bulk resistance of the substrate are deduced from the simulated current lines profiles and iso-potentials. The difference of electrical conductivity between indenter material and gold coating is the reason for the occurrence of the transition region.

Constriction resistance is calculated by numerical analysis using Laplace's equations for electric potential of steady state in many cases of contact spot dispersion-status. The results show that contact resistance does not increase beyond 1.5 times even if the total real contact area is about 15% of the apparent contact area. When real contact area is at least about 60% of the apparent contact area, the contact resistance is approximately the same as the constriction resistance acquired from the apparent contact area. When the real contact area is about 50% of the apparent contact area, the contact resistance is approximately constant without regard to the contact shape and contact-point dispersion layout. Therefore, it is proved that contact resistance can be practically calculated using apparent contact area instead of real contact area when there are many contact points caused by metal to metal contact.

Contact resistance is caused by constriction resistance and film resistance through contact layers. It is well known that a surface film causes non-linear voltage and current characteristics. The origin of non-linearity is caused by tunneling electron through thin insulation barrier or jumping over the thick barrier (Shottky barrier) on the contact surface. In this paper, a new idea causing nonlinear property by only current constriction which flows through very small contact spot area, if there is no film layer, is proposed by the two dimensional contact model. The contact model, used in this paper, is a two dimensional type narrow path of contact area (short bridge) made by thin copper foil of 0.035 mm on a glass epoxy resin board. The contact part is made by scraping with an electric drill as a single bridge shape of 0.1 mm wide and 0.3 mm long on the centre of a board (100 mm100 mm). The 3rd harmonic distortion voltage was measured by using a Component Linearity Test Equipment (Type CLT1 made by Radiometer Electronics Company) which the system supplies a pure sine wave current of 10 kHz and detects a distortion voltage of 30 kHz by a narrow band pass filter circuit. The sensitivity of the Component Linearity Test Equipment (CLT1) is under a 10-9 volt. Four bridge samples were examined for the comparison of nonlinear distortion voltage. The distortion voltage of a sample (A) (0.1 mm wide, 0.3 mm long) is too larger than the one of the sample (B) (0.2 mm wide, 0.3 mm long) at the same applied voltage which resistance is not so different each other. It seems that current constriction to the spot (A) may heat up higher and cool down lower than (B). It would be also guessed that the power dissipation of 20 kHz cause temperature oscillation of 20 kHz, then it causes a component of contact resistance of 20 kHz, and therefore the product of 10 kHz current and 20 kHz resistance component cause 30 kHz component distortion voltage.

In this presentation the authors consider in detail the problems relating to parameters like contact normal force, the effective contact areas and the surface plating, which have significant influence onto the surge current strength of electrical power contacts. Obtaining the behaviour of machine turned pin and socket contacts with different pin diameters the parameters of the active contact area radius, the constriction resistance and the constriction temperature are calculated by using FEM for elastic/plastic surface deformation. With the knowledge of the constriction radius the temperature curve of the contact area was determined by coupled electrical/thermal FE calculation. Laboratory tests were carried out in order to verify the FE-calculation.

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.

The electric or electronic circuits have many contact devices such as relay and switch. The contact between two nominally conducting flat surface has a lot of micro contact spots. The constriction resistance of the contact is known to determine the sum of the parallel resistance of the micro contacts and the interaction of them. The constriction resistance of two circular conducting spots was approximately formulated by Greenwood. This formulation shows that the interacted resistance of two circular spots is in inverse proportion to the distance between two conducting spots. It was known that this effect is introduced by the interaction between two conducting spots. However, the condition of interaction in the spots is not clear. Calculating the current density distribution in the spots is important to clarify the condition of interaction. The numerical analysis is very suitable to calculate the current density in the spots. In the fundamental case of the computation of the current density the boundary element method (BEM) is more efficient and accurate than that of the finite element method (FEM) because the boundary condition at the infinite is naturally satisfied and is not required a great number of the element in a wide space. In this paper the current density in the square spots is computed by the BEM. As the distance between two conducting spots becomes small, the current density in the two spots decreases. It becomes clear that the constriction resistance of conducting spots is increased by this effect. The decrease of current density by interaction is not uniformly, that at the near location to the opposite spot is larger than that at the far location in the same spot. In this paper the constriction resistance of two conducting spots is also considered. It was known that the constriction resistance of one conducting spot is not influenced by the form of spot very much. However, that of two conducting spots is not clear. The constriction resistance of two square spots is also computed by the BEM. The computed values of the constriction resistance of two square spots are compared with that of two circular spots by Greenwood's formulation and other results. As the result, it is clear that they have the considerable discrepancy. However, the trend of the variations is almost agree each other.