A partial similitude method considering variable powers in scaling laws and applied to rotor-bearing systems

Abstract Similitude theory is used to establish the necessary conditions between the enlarged or reduced model and the original structure, and has been widely applied to vibration and impact tests of large structures. However, several limitations and difficulties still persist in partial similitude for complex structures. In this paper, a partial similitude method to obtain scaling laws is proposed. The powers in scaling laws are variables against the scaling factors, and the coupling effect among design parameters is considered in the powers. The accuracy and applicability of the proposed method are demonstrated in two case studies. The first case study discusses the partial similitude of a single rotor-bearing system. The single rotor-bearing system is scaled with distortion in the geometrical dimension and boundary conditions. It is found that the proposed method predicts the critical speeds and unbalance responses with good accuracy. Furthermore, the proposed method can improve the prediction accuracy by comparing with the methods in current literatures. The second case study comprises a dual-rotor system to demonstrate the accuracy and applicability of the proposed method for more complex rotor-bearing system. The speed ratio, excitation position, co-rotation, and counter-rotation are discussed in predicting the critical speeds as well as unbalance responses. It is also found that the proposed method can improve the prediction accuracy.