Roller bearings are essential parts extensively used in many industries such as automobile, sugar factories, cement industries, weaving mills, chemical industries, and other process industries. The catastrophic failure of such bearings results into unplanned shutdowns, discontinuity of manufacturing process, and heavy maintenance cost. The vibration analysis of the roller bearing is a vital factor in the rotating machines because its performance significantly affects the safety and operational life of the rotating machines and subsequently entire plant. The object of this paper is to study how to predict the vibration characteristics of the rotor-bearing system by using the mathematical model. In the present research work, a empirical model for the vibration characteristics of the roller bearing has been established using FLTθ system. The new mathematical model considers the influences of the bearing variables on the vibration of the rotor system. Furthermore, a new model on bearing system is carried out by using dimensional analysis (DA) and the defect frequencies and vibration characteristics of the bearing system are obtained. The effects of speed and load along with other variables on vibration characteristics have been studied by establishing an empirical model. Experiments were conducted to validate the developed empirical model. The method proposed in this paper is based on FLTθ method of DA. The vibration characteristics thus obtained provides a complete and systematic theory and technique in this aspect.