6. Analysis of the Dynamic Response of Coupled Coaxial Rotors

The fundamental dynamics of a single rotor are very well understood, and extensively covered in the literature. However, many rotating machines such as aircraft engines consist of multiple shafts, which are often directly coupled by inter-shaft bearings. This paper aims to provide better insight into the underlying dynamics of such systems by analysing a simple but representative model of a rigid dual-rotor system. The modes and natural frequencies were computed numerically and it was found that the different modes could be classified by the following criteria: (i) relative phase of the motion of each rotor, (ii) whirl direction of the rotors, and (iii) presence of rotational or translational motion. The high-speed mode shapes could also be classified into (i) “static” modes with very low frequencies, (ii) “flat” modes which tend towards constant frequencies, and (iii) “precessional” modes which have a frequency which linearly increases with speed. A parameter study was performed in order to obtain a better understanding of the sensitivity of the modal properties. It was found that increasing the inter-shaft bearing stiffness can raise the natural frequencies of the modes at low speeds as well as the critical speeds, but has less influence at high speeds. The speed ratio influences the whirl direction of the modes and hence plays a crucial role in determining how each mode varies with speed. Since the speed ratio also controls the frequency of excitation from unbalances, it has a particularly profound effect on the critical speeds, and extra ones can arise. The importance of considering the dynamics of the complete system in the design of turbomachinery with multiple-shafts was highlighted.