The purpose of the present project is the design and optimization of a fifth teen-slot ten pole permanent magnets synchronous machine with interior magnets and concentrated windings. Stator and rotor armatures are taken from an existing motor of different characteristics, which is actually in production. The main motivation of building different types of motors with the same materials is to reduce the costs and to simplify the production process, increasing at the same time, the variety of products offered. The start points are the needed characteristics and the existing motor. The stator and rotor armatures are taken, modifying slightly the rotor frame in order to reduce the cogging torque and to optimize the motor operation. Then, the calculations of the design parameters are made, and finally the simulations to obtain the motor characteristics. The project contains a memory, which describes the followed methodology to study and design the motors, with theoretical explanations of the calculations y simulations performed. It also contains annexes of the calculations done, their justifications and the results obtained.