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The analysis of the physical processes at various combinations of external impacts on the material in microplazmaspark alloying (MPA, MPA + USM, USM + MPA + USM) has been carried out in the present paper. Physical models for the microplasma electrode erosion and the cooling down of a droplet of the molten anode material in the MPSA process have been developed. As a result of the analysis of a numeric solution of the problems on heat conduction with a powerful point heat source of heat release and cooling down without sources, it has been established that the droplet cooling time for the eroded anode is markedly less than the other time parameters specifying the alloying process. There has been solved the problem of the determination of the optimum values of the pulse duration and the pause between the electrospark discharges that provide for the maximum anode erosion rate. A physicomathematical model in the form of the small vibrations’ theory with the corresponding algorithm and software realized in the Mathematica software pack age have been developed for the experimental data interpretation from the positions of the physical mecha nisms. With the optimality methodology application, the possibility for the solution of the multifactor (the input parameters are the volt–ampere and time specifications, and the output parameters are the anode ero sion rate and the fraction of the hardened droplet of the eroded anode material) problem of the control of the MPSA + USM joint process for obtaining a quality strengthened surface has been demonstrated.
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