The main aim of this article is to achieve predictive maintenance by proposing reliable residuals specific to outer ring bearing faults. Our work falls within the general context of maintenance, with particular emphasis on vibration analysis techniques. For an in-depth study of the fault, we use spectral analysis of electromagnetic torque, which gives very satisfactory results compared with work based on line current or neutral voltage fault signatures due to the similarity in the mechanical nature of the fault and the signal to be studied. In fact, an analytical calculation of the electromagnetic torque has been developed to obtain the specific frequencies of the fault under consideration. To highlight our results, the simulation of the analytical calculation of this fault was implemented in MATLAB/SIMULINK using the Fast Fourier Transform method to extract fault signatures. The induction motor's performance was analyzed under various operating conditions, including both healthy and faulty states. Finally, an experimental study will support our analytical developments.