Roller Bearings are the prime component in the condition monitoring of high-speed industrial machines. Even a smaller malfunction may cause the failure of the system and leads to unscheduled maintenance or shut down. This paper presents the development of a mathematical model using dimension theory (DT) which considers structural, material, and thermal parameters of the roller bearings. The vibration response of damaged bearings is investigated for validation, and regression analysis is performed to illustrate its effectiveness in the damage detection. Results indicate the simple and time-saving nature of the model. © 2020 American Institute of Physics Inc.. All rights reserved.