Many industries make wide use of rotor bearing systems such as high speed turbines and generators. However, the vibration of antifriction rotor–bearings is a key factor in reducing the life of the bearings; thus significantly influencing the performance and working life of the whole power plant. In earlier research on the vibration characteristics of high speed rotor–bearing systems, such as in induced draft (ID) fans, an application used in sugar cane factories, the supporting antifriction bearings were simplified as a particle on a shaft with radial stiffness and damping coefficient. However, such simplification neglects the effects of the bearing structure on the vibration performance of the rotor–bearing system. This paper demonstrates the benefits of a more holistic approach and establishes a numerical model of the stiffness of the spherical roller bearing through Buckingham's π theorem (BPT). On the basis of this model, we argue for the benefits of a new dimensional analysis (DA) technique for rotor–bearing systems. Our new DA also considers the influences of the bearing structure parameters on the vibration of rotor–bearing systems. We demonstrate the effectiveness of our approach by conducting a comparative BPT study using an ID fan, a rotor–bearing system in use in sugar cane factories. We first analyzed an ID fan using the simplified model to obtain the defect frequencies and vibration amplitude responses of the ID fan system. Subsequently the same ID fan rotor was also analyzed using our new multivariable regression analysis (MVRA) approach to verify the validity of our new and holistic BPT. The results indicate that the new method we propose in this paper for the calculation of vibration characteristics of a high speed rotor–bearing (ID fan) is credible and will save time and costs by the accurate detection of imminent bearing failure.