Dynamic Response Analysis of a Deep Groove Ball Bearing Supported Rotor Under Unbalance and Coupling Misalignment

Abstract The reliable operation of rotating machinery largely depends on the early detection and accurate diagnosis of dynamic faults such as rotor unbalance and shaft misalignment, which often act simultaneously and interact nonlinearly. This study presents a model-based and experimental investigation into the influence of progressive angular misalignment on the vibration response of a rotor–bearing system under unbalanced conditions. Controlled experiments were carried out using a laboratory-scale rotor–bearing test rig equipped with precisely aligned couplings, where misalignment levels and unbalance masses were systematically varied across a range of operating speeds to replicate real-industrial conditions. An empirical dimensionless analysis (EDA) model was formulated using the Buckingham π method to establish functional relationships among vibration amplitude, unbalance mass, misalignment angle, and rotational speed. The developed model incorporates nonlinear parameters such as bearing and coupling stiffness–damping, contact stiffness, and backlash effects, representing the inherent complexities of rotor–bearing interactions. Experimental vibration spectra revealed that while unbalance primarily excites the 1X frequency component, angular misalignment dominates the 2X harmonic, and their coexistence produces strong nonlinear coupling, leading to amplitude modulation and harmonic distortion. Validation against experimental data showed that the EDA model accurately predicts vibration amplitudes at characteristic frequencies with a deviation of less than 8%, confirming its robustness and reliability. The proposed approach bridges a critical gap in understanding the coupled dynamics of unbalance and misalignment by integrating nonlinear effects within a scalable dimensionless framework. The article aims to enhance vibration reliability by developing and validating an EDA model that accurately predicts dynamic behavior under combined unbalance and angular misalignment defects.