Natural Frequency Analysis of a Jeffcott Rotor Having Stepped Shaft
The Rotating shafts are mechanical elements used to transmit power or motion. A shaft with a step or steps is widely used instead of a shaft with a fixed (non-variable) diameter when operating at high speeds. The aim of this research is to study the effect of the step amount and its location in the shaft on the natural frequencies of the Jeffcott rotor model. Analytical methods are used to find an approximate formulation to obtain the natural frequencies of the Jeffcott rotor model neglecting the shaft mass. Lagrange equations are used to develop dynamic equations assuming elastic shaft with steps carrying a disk. The finite element method by using ANSYS is used to validate and compare the results obtained in the analytical method. The results obtained analytically and numerically were compatible and in good agreement. In addition, some parameters such as the step amount and the stepped shaft length are changed to check its effects on the natural frequencies. the results showed that the natural frequencies increase with an increase in the amount and length of the stepped part, while they decrease the closer the disc position to the center.
Dynamics of Rotors and Foundations by Erwin Kramer (1993) published by Springer-Verlag Berlin Heidelberg GmbH (pp.4-44).
Dynamics of Rotating Shafts by Robert G Loewry, Vincent J Piarulli (1969) (pp. 5-20).