Analysis of the Dynamic Behavior of a Rotating Composite Hollow Shaft

Abstract

In the present paper, a simplified homogenized beam theory is used in the context of a numerical investigation regarding the dynamic behavior of a rotating composite hollow shaft. For this aim, a horizontal flexible composite shaft and a rigid disc form the considered simple supported rotating system. The mathematical model of the rotor is derived from the Lagrange's equation and the Rayleigh-Ritz method, which is obtained from the strain and kinetic energies of the disc and shaft, and the mass unbalance. In this case, a convergence procedure is carried out in terms of the vibration modes to obtain a representative model for the rotor system. Therefore, the proposed analysis is performed in both frequency and time domains, in which the frequency response functions, the unbalance responses, the Campbell diagram, and the orbits are numerically determined. Additionally, the instability threshold of the rotor system is obtained. This study illustrates the convenience of the composite hollow shafts for rotor dynamics applications. KeywordsRotor dynamics, composite hollow shaft, Rayleigh-Ritz method, numerical investigation. the dynamics of rotating machines was studied by Jeffcott (1919). The work of H.H. Jeffcott led to the development of other essential studies, such as the Campbell diagram, which was first presented by Wilfred Campbell, from General Electric. More effective methods of balancing were proposed and the behavior of rotors supported by hydrodynamic bearings was further investigated, leading to the design of lighter rotating machines operating at higher speeds.The mathematical representation of the specific physical phenomena that involve rotating machines requires a reliable design tool. In this context, the finite element (FE) method appears as a largely used technique for rotordynamics design. Nelson and MacVaugh (1976) were among the first researchers to include the effects of rotational inertia, gyroscopic moment, and axial force in the FE models. Before the FE method, the so-called transfer matrix method was used to determine the dynamic behavior of rotating machines considering the system as being continuous (Lallement, Lecoanet, and Steffen Jr, 1982). In this context, the modern rotating systems currently employed in various industrial sectors were developed, such as steam turbines, hydro power units, and aircraft engines. These machines present high associated costs and operate under great responsibility and some of them have already composite material components.Following the growing evolution of the materials used in rotating systems (i.e., materials associated with high performance and low weight), investigations on the dynamic behavior of composite shafts seems to be an important issue. Mazda Motor Corporation adopts hybrid glass and carbon fiber shafts in their cars since 1982. The use of this new technology aims at reducing weight of the rotating system, the cost of maintenance, noise, vibration level, and, at the same time, to increase efficiency as compared with the same compone...

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