*2.2. Bearing Fault (BRN)*

Characteristic frequency components are generated on the stator current when an SCIM has a faulty bearing. These specific frequency components can be predicted since they are related to both the power supply frequency and the mechanical system frequency. When there is a fault in any component of a bearing, for instance, its inner raceway, outer raceway, or rolling elements, specific components are induced in the vibration and current signals of the machine. These characteristic frequencies associated to the bearing faults depend directly on the bearing geometry and the machine rotating speed. A defect on the outer race will cause an impulse every time the rolling elements make contact with the defect. The outer raceway-related frequency can be theoretically determined by

$$f\_o = \frac{n}{2} f\_r \left[ 1 - \left(\frac{BD}{PD}\right) \cos(\beta) \right] \tag{2}$$

where *n* is the number of balls (rolling elements), *fr* is the shaft rotating frequency, *BD* is the diameter of the balls, *PD* is the bearing race diameter, and *β* is the angle between the ball in the race [20].
