This paper presents mathematical expressions to identify the existence of localized surface defects on the raceways of the deep groove ball bearings. For the formulation of the mathematical expressions, matrix method of dimensional analysis based on force, length, time, and temperature (FLTϴ) system of unis is used. The model is based on the complete set of physical dimensions and operating parameters of the deep groove ball bearing in that the spall size is directly allied with vibration responses. The formulated governing model equations are solved numerically by applying a scheme of empirical modeling through multiple factorial regression analysis. Experiments are performed on the laboratory test rig to verify the results obtained from the developed model equations. For the experiments, deep groove ball bearings designated as SKF 6307 are used. These bearings are having artificially induced square-shaped surface defects of different sizes on the outer and inner races and are analyzed for different operating speeds. A good similarity between the predicted numerical values and the experimental results is noticed. This study showed that the proposed methodology can be successfully used for the characterization of the localized surface defects on the raceways of the deep groove ball bearings.

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