Equivalence Relation and Scaling in Solving Engineering Problems of the Magnetic Materials

New algorithm for optimizing technological parameters of soft magnetic composites has been derived
on the base of topological structure of the power loss characteristics. In optimization magnitudes
obeying scaling, it happens that one has to consider binary relations between the magnitudes having
different dimensions. From mathematical point of view, in general case such a procedure is not
permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that
in such systems, the binary relations of magnitudes of different dimensions is correct and has
mathematical meaning which is important for practical use of scaling in optimization processes. The
derived structure of the set of all power loss characteristics in soft magnetic composite enables us to
derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a
relation of the hardening temperature, the compaction pressure and a parameter characterizing the
power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the
best values of technological parameters.