Rotordynamical Aspects of High-Speed Electrical Machines
For very high-speed machines study of rotordynamics becomes very important. Rotors of today’s high-speed machines regularly operate in supercritical regime, therefore, issues such as unbalance response and stability of rotation need to be addressed early
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Rotordynamical Aspects of High-Speed Electrical Machines
5.1 Introduction For very high-speed machines study of rotordynamics becomes very important. Rotors of today’s high-speed machines regularly operate in supercritical regime, therefore, issues such as unbalance response and stability of rotation need to be addressed early in the design phase to prevent machine’s failure. Naturally, the field of rotordynamics concerns with a great number of rather complex problems, study of which goes well beyond scope of this thesis. Still, machine geometry, construction, even magnetic field have great influence on dynamical behavior of the rotor and that influence is particularly important when designing high-speed machines. In this chapter, a qualitative insight into important dynamical aspects of high-speed rotors will be given through analytical modeling. The goal of the chapter is to define the dynamical limits for the rotor speed and to correlate those limits with machine parameters. The phenomenon which is of practical concern is rotor vibrations, their cause and influence on the system. Two types of vibrations can be distinguished: resonant and self-excited [1]. Resonant vibrations are excited by an oscillating force whose frequency coincides with one of the natural frequencies of the rotor-bearings system. Vibrations that are caused by an (external) oscillating force are generally referred to as forced vibrations. Typically, the oscillating force comes from the rotor mass unbalance. Influence of the rotor unbalance (which is inevitably present in realistic rotors) can be modeled as a force which rotates around a perfectly balanced rotor and has the same rotational frequency as the actual rotor frequency. Therefore, the rotor unbalance will excite the resonant vibrations when rotational speed is equal to a natural frequency of the rotor-bearings system. Those rotational speeds are referred to as critical speeds. Evidently, resonant vibrations occur at certain frequencies and are influenced by the amount of unbalance. They can be damped by external damping and may be passed if sufficient energy (dissipated in bearings’ dampers) is invested. However, not only mass unbalance of the rotor can cause resonant vibrations. Circulating fluids in the bearings or harmonics of unbalanced magnetic pull of the A. Borisavljevi´c, Limits, Modeling and Design of High-Speed Permanent Magnet Machines, Springer Theses, DOI: 10.1007/978-3-642-33457-3_5, © Springer-Verlag Berlin Heidelberg 2013
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5 Rotordynamical Aspects of High-Speed Electrical Machines
electrical machine whose forces may not be synchronous with the rotor can also excite resonant vibrations. Nevertheless, these phenomena will not be analyzed in detail in this chapter and the reader will be referred to literature. Self-excited vibrations, on the other hand, require no external force for inception1 [1, 2]. They arise within range(s) of rotational speed, usually after a certain (threshold) speed which is correlated with intrinsic properties of the system. The extern
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