The effect of changing disk parameters on whirling frequency of high speed rotor system

The requirement for efficiency improvement of machines has caused machine rotor to be designed to rotate at high speeds. It is known that whirling natural frequency of a shaft changes with the change of shaft speed and the design needs to avoid points of resonance where the whirling frequency equals the shaft speed. At high speeds, a shaft may have to carry a huge torque along and this torsional effect has been neglected in past shaft analyses. Whirling behaviour of high speed rotating shaft is investigated in this study with consideration of the torsional effect of the shaft. The shaft system under study consists of a shaft, discs and two bearings, and the focus is on the effect of the disc parameters. A finite element formulation is developed based on Nelson's 5 degrees of freedom (DOF) per node element that includes the torsional degree of freedom. Bolotin's method is applied to the derived Mathieu-Hill type of equation to get quadratic eigenvalues problem that gives the forward and backward frequencies of the shaft. Campbell's diagrams are drawn in studying the effect of discs on the whirling behaviour of the shaft. It is found that the addition of disks on the shaft decreases the whirling frequency of the shaft and the frequency is lower for mass located at the centre of the shaft compared to the one located near to the end. The effect of torsional motion is found to be significant where the difference between critical speed of 4DOF and 5DOF models can be as high as 15%