Analytical Nonlinear-Probabilistic Model of the Equivalent Electrical Resistance of a Layer of Metal Granules

Abstract

As a result of processing the experimental data, an analytical continuous nonlinear-probabilistic model of the equivalent electrical resistance of a layer of metal granules in the working liquid was created. It is described by four equations: the modified Gaussian distribution and the dependences on the instantaneous values of the discharge current in the layer of metal granules of the mathematical expectation, dispersion and correction coefficient of the range of its equivalent electrical resistance. Based on the form of the dependences obtained during the experiments and the physics of the processes that occur in this case, two main groups of analytical functions are considered that approximate the obtained dependences. Criteria and methods for finding the optimal values of their coefficients are described. The adequacy of the approximation of each of the three obtained dependences by several analytical functions was investigated, the optimal values of the coefficients of which were found by the described method. Analytical functions was compared, which approximate the dependence of the mathematical expectation of the equivalent electrical resistance of a layer of metal granules on the instantaneous values of the discharge current in it with the known nonlinear models of the resistance of such a medium. References 33, figures 3, tables 3.