<p>Deep groove ball bearings, as critical precision components in rotating machinery, are primarily used to support shafts and reduce friction. Its performance depends critically on geometric integrity and material properties. This study establishes a nonlinear dynamic model for ball bearings with localized defects on rolling elements and innovatively integrates it with a non-intrusive polynomial chaos expansion framework to achieve efficient uncertainty quantification. The validity of the model is confirmed through comparative analysis. The results not only verify established deterministic characteristics-such as the dominance of the ball pass frequency in the periodic vibration response and the significantly higher vibration amplitude in the load direction compared to the non-load direction-but also include an in-depth uncertainty analysis. Uncertainty analysis reveals that the load, stiffness coefficient, and defect edge length collectively account for 68.3% of the uncertainty in the outer race displacement response. Among these factors, the sensitivity index of load is close to 0.6, making the load the dominant factor affecting uncertainty. When the mean value of the defect edge length increases, the growth rate of the outer race displacement mean is significantly higher than that of the inner race, and the coefficient of variation of the displacement exhibits multiplicative growth; Increasing the standard deviation of the defect edge length primarily amplifies the displacement response dispersion.</p>