###### Abstract  
The use of electric motors, and particularly, Permanent Magnet Synchronous Motors, is increasing in recent years, and their vibration response is one of the most crucial aspects regarding their behaviour. Thus, the reduction in vibrations is one of the key objectives when optimizing electric motors. In an initial design state, the influence of the main design parameters on the behaviour of the machines is not always clear. For that reason, this work presents a global sensitivity analysis procedure that allows identifying the most influential design parameters and determining guidelines to optimize the design of Permanent Magnet Synchronous Motors. First, the analytical calculations employed to estimate the electromagnetic torque and the vibration response of the machine are described. Then, the sensitivity analysis procedure, based on the Monte Carlo method, is presented, and the conditions to apply the method successfully and accurately are analysed. Finally, the sensitivity analysis is performed for a particular electric motor design, and some general design guidelines are deduced, which can be extrapolated to similar machines.  
electrical machines; design; vibration; electromagnetic forces; sensitivity analysis; Monte Carlo +
Footnote †: journal:  
0000-0001-5000-0001-5000]M.M.  
Regarding the stator, several authors propose modifying the shape of the teeth [10; 11; 18; 19], or varying the width [11; 20; 21] of both the teeth and the slots. Other approaches are to include notches in the teeth [12; 14; 16; 22] or to modify the width of the stator [18; 19; 21].  
In addition, some authors propose modifying the length of the air gap [12; 23], implementing a skewed rotor [24], or changing the slot and pole number combination [25; 26] in order to reduce the vibrations and noise of the electric machines.  
In those works, interesting conclusions were obtained regarding the optimization of the design of electric machines. Multiple influential parameters were observed, which affect several aspects of the behaviour of a machine, but the effect of these parameters depends on the typology and dimensions of the motor.  
For that reason, when developing a new machine design, or when optimizing an existing one, the influence of its design parameters needs to be analysed in detail. In the literature, numerous authors perform Finite Element calculations with that purpose, but when a high number of influential parameters is considered, the computational cost of Finite Element calculations becomes excessive.  
Moreover, in an initial design state, the accuracy of the results is not usually the main objective, as it is more interesting to obtain general trends of how the behaviour of the machine changes with each of the input parameters. Therefore, in this type of optimization problem, fast analytical calculations must be used.  
In this work, an optimization tool is presented, which consists of a global sensitivity analysis that studies the effect of various design parameters on the torque and vibration response of the machine. This tool can be useful when defining new machine designs, as it allows performing fast calculations and observing the trends of the behaviour of the machine in the function of the input parameters. Moreover, the optimization tool is applied to a specific PMSM, and certain design rules are concluded, which can be extrapolated to similar machines.  
Previously developed analytical models are employed in order to estimate the electromagnetic torque and the vibration response of PMSMs. The analytical models are described in Section 2. Based on those models, a sensitivity analysis procedure is developed in order to study the influence of several design parameters on the behaviour of the machines. The procedure employed to define the sensitivity analysis is described in Section 3. Finally, the results of the sensitivity analysis are shown and discussed in detail in Section 4.