Novel algorithm for designing values of technological parameters for production of Soft Magnetic Composites (SMC) has been created. These parameters are the following magnitudes: hardening temperature $T$ and compaction pressure $p$. They enable us t
o optimize of power losses and induction. The advantage of the presented algorithm consists in the bicriteria optimization. The crucial role in the presented algorithm play scaling and notion of pseudo-state equation. On the base of these items the mathematical models of the power losses and induction have been created. The models parameters have been calculated on the basis of the power losses characteristics and hysteresis loops. The created optimization system has been applied to specimens of Somaloy 500. Obtained output consists of finite set of feasible solutions. In order to select unique solution an example of additional criterion has been formulated.
Assuming that Soft Magnetic Material is a Complex System and expressing this feature by scaling invariance of the power loss characteristic, the unified model of the temperature dependence of Core Losses in Soft Magnetic Materials Exposed to Nonsinus
oidal Flux Waveforms and DC Bias Condition has been constructed. In order to verify this achievement the appropriate measurement data concerning power losses and the all independent variables have been collected. The model parameters have been estimated and the power losses modeling has been performed. Comparison of the experimental values of power losses with their calculated values has showed good agreement.
Assuming that core loss data of Soft Magnetic Materials obey scaling relations, models describing the power losses in materials exposed to non-sinusoidal flux waveforms and DC Bias conditions have been derived. In order to test these models, the meas
urement data for two materials have been collected and the core losses calculated. Agreement between the experimental data and the model predictions is satisfactory.
Optimization of power loss in soft magnetic components basis on the choice of the best technological parameters values. Therefore, the power losses have been measured in Somaloy 500 samples for a wide range of frequency and magnetic induction. These
samples have been prepared under a wide range of the hardening temperatures and pressures. The power loss characteristics have been derived by assuming that investigated samples obeyed the scaling law. Agreement obtained between experimental data and the scaling theory has confirmed this assumption. Moreover, the experimental data of the given sample have been collapsed to a single curve which represented measurements for all values of frequency an magnetic induction pick. Therefore, the scaling transforms the losses characteristics from the two dimensional surfaces to the one dimensional curves. The samples were produced according two methods: for different pressures with constant temperature and at different temperatures with constant pressure. In both cases the power losses decrease with increasing pressure and with increasing temperature. These trends in decreasing losses stopped for certain critical values of pressure and temperature, respectively. Above these values the power losses increase suddenly. Therefore, the mentioned above the critical pressure and the critical temperature are sought after solutions for optimal values. In order to reduce the parameters values set the limit curve in the pressure-temperature plane has been derive. This curve constitutes a separation curve between the parameters values corresponding to high and low losses.
Definition of frustration is expressed by transitivity of binary entanglement relation in considered complex system. Extending this definition into n-ary relation a hierarchy of frustrations is derived. As a complex system the U.S. Intermarket is cho
sen where the correlation coefficient of intermarket sectors plays the role of entanglement measure. In each hierarchy level the frustration and the transitivity are interpreted as values of an order of measure for corresponding subsystem. The derived theory is applied to 1983-2012 data of the U.S. Intermarket.
Data collapse enables comparison of measurement data measured in different laboratories on different samples. In the case of energy losses in Soft Magnetic Materials (SMM) the data collapse is possible to achieved only if the measurement data can be
described by the two components formula. For more complicated cases we propose to perform data collapses sequence in the two-dimensional subspaces $L_{i,i+1}$ spanned by the appropriate powers of frequency ${f^{i},f^{i+1}}$. Such approach enables the data comparison in the different two-dimensional subspaces. This idea has been tested with measurement data of the four SMM-s: amorphous alloy textrm{Fe}_{78}textrm{Si}_{13}textrm{B}_{9}$, amorphous alloy $textrm{Co}_{71.5} textrm{Fe}_{2.5} textrm{Mn}_{2} textrm{Mo}_{1} textrm{Si}_{9} textrm{B}_{14}$, crystalline material -- oriented electrotechnical steel sheets 3% Si--Fe, iron--nickel alloy $79% textrm{Ni}-textrm{Fe}$. Intermediate calculations revealed interesting property of the energy losses in the cristalline and amorphous SMM-s which lead to the following hypothesis. Let $P_{tot,1,2}=f_{1,2}(1+f_{1,2})$ be scaled two-components formula for the energy loss in SMM, where $f_{1,2}$ is the corresponding scaled frequency. Then the scaled energy losses values in amorphous SMM are below the second order universal curve $P_{tot,1,2}=f_{1,2}(1+f_{1,2})$, whereas the scaled energy losses values in crystalline SMM are above that universal curve.
