Vibrations caused by noncircular shaft journals — a mathematical model for rotordynamic analysis of electrical motors with sleeve bearings

摘要

The paper presents a mathematical model for theoretical rotordynamic analysis of electrical motors with sleeve bearings, regarding excitation due to noncircular shaft journals. It is shown, that noncircular shaft journals lead to kinematic constraints regarding the movement of the shaft journals on the oil film of the sleeve bearings and therefore excite the rotordynamic system to vibrate. The rotordynamic system is mathematically described by a system of linear differential equations, considering the rotor mass, the rotor structural stiffness, the oil film stiffness and damping of the sleeve bearings, the structural stiffness of the sleeve bearing housings with the end shields, the electromagnetic coupling between rotor and stator in the air gap and the excitation due to noncircular shaft journals. The solution of this differential equation system leads to the mathematical description of the movement of the rotor centre, the shaft journals and the sleeve bearing housings. Additionally, the relative movements between the shaft journals and the bearing housings can be calculated, as well as the bearing housing vibration velocities. A four-pole induction motor is analyzed, to also show numerical results.