Critical speed and forced vibration analysis of rotor-bearing systems with asymmetric elastic bearings

Vibration in rotor-bearing systems critically affects reliability of rotating machinery. In industrial machines (gin machines, compressors, turbines), transverse vibrations increase due to asymmetric bearing supports and external excitation. This paper presents a dynamic model of a massive rotor with asymmetric elastic bearings using Lagrange equations. Equations of motion are derived in matrix form considering stiffness of elastic elements between bearings and housing. Natural frequencies and critical speeds are determined. Influence of asymmetric stiffness on dynamic characteristics is analyzed. Forced vibrations from rotor unbalance are investigated. Results show operating speed of gin machine shaft is significantly below first critical speed, ensuring stable operation. Elastic polyurethane elements effectively reduce vibration transmission and improve dynamic stability. Unlike existing studies, this work considers asymmetric elastic supports and offset excitation forces within a unified analytical framework. The proposed approach can be applied to a wide range of rotating machinery systems with asymmetric support conditions.