In order to perform an optimal design of electromechanical system, the designer must take into account ever more stringent constraints and many physical phenomena from electric, magnetic, aeraulic, thermic, electronic, mechanic and acoustic. The originality of this thesis is to put forward a multi-physic design based on lumped models: halfway between analytical and numerical modeling. These models allow sizing a permanent magnet synchronous machine under constraints for rail traction. The results are validated with finite element simulations and experimental analysis. The multi-physic modeling is fully automated, parameterized, in order to combine the model with the optimization tool. We used here particle swarm optimization to search compromises between several objectives (Pareto Front). In this paper, we focus on electromagnetic torque and electromagnetic noise. Finally a sensitive study validates the robustness of selected design when it is subjected to manufacturing constraints. The aim of this work is to propose a decision tool to size electrical machines
