Rotor Bearing System Analysis Using the Transfer Matrix Method with Thickness Assumption of Disk and Bearing

One of the methods to find the natural frequencies of rotating systems is the application of the transfer matrix method. In this method the rotor is modeled as several elements along the shaft which have their own mass and moment of inertia. Using these elements, the entire continuous system is discretized and the corresponding differential equation can be stated in matrix form. The bearings at the end of the shaft are modeled as equivalent spring and dampers which are applied as boundary conditions to the discretized system. In this paper the dynamics of a rotor-bearing system is analyzed, considering the gyroscopic effect. The thickness of the disk and bearings is also taken into account. Continuous model is used for shaft. Results Show that, the stiffness of the shaft and the natural frequencies of the system increase, while the amplitude of vibration decreases as a consequence of increasing the thickness of the bearing.