Dynamics of Rotors and Foundations by Erwin Krämer

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By Erwin Krämer

Rotordynamics are of significant significance within the layout, manufacture and meeting of turbomachines in addition to in making sure their secure operation. additionally very important are the dynamics of the root and its interplay with the dynamics of the rotor. This booklet is split into 4 elements. Following a presentation of the elemental conception the dynamics of rotors supported on a number of bearings. The 3rd half describes the dynamics of foundations of turbine line-outs and the calculations for a turbomachine coupled with its origin. The final half incorporates a part on estimation methods, a entire presentation of the theoryand perform of rotors having a transverse crack, a bit at the mathematical basics and an outline of the pc software used for the examples within the booklet. The publication addresses either the sensible engineer and the theoretician and may offer brands, operators, college and polytechnic teachers and scholars with an knowing of the vibrations of turbomachines. the implications are defined in any such manner that they are often simply understood and applied.

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11). Reference [19] contains charts, from which the behaviour can be numerically portrayed. In [20], it is shown that one can calculate the behaviour of a realistic rotor, using the results for a leffcott rotor found in reference [19]. 3 Jeffcott Rotor with Flexible Bearings 29 Angular velocity Fig. 10. leffcott rotor. Amplitudes and angular velocity for startup with constant torque [19] Angu lar ve locity / Displacement Time - Fig. 11. As in Fig. 3 J effcott Rotor with Flexible Bearings Up to now in this chapter the bearings supporting the rotor have been assumed to be rigid .

The number of revolutions Zn turned by the rotor up to an angular velocity CP = Wn is a better measure than is the non-dimensional angular acceleration o = a/w~. From the above equations, Zn = (1/471")0. The scale assigned to Zn in Fig. 9 shows that the effect displayed is stronger where fewer rotor revolutions are necessary up to cp = w n • Turbomachines are as a rule started up or shut down so slowly that they display resonance as if with a non-accelerating drive. 4). The more difficult case of a given torque has been investigated by Gasch, Markert and Pjiitzner in references [19] and [20].

5 Ip Fig. 22. r. n. _ Q, Fig. 23. Orbit radius for unbalance excitation. 05 = 10e and the error is -6 %. For the second, the eigenvalues and modal damping ratios of the model were calculated (Fig. 24). Of these D2 is significant at resonance. 6 e, exactly the same as the value obtained by lengthy calculation although such accuracy, is a coincidence. 39) is discussed in Chap. 21. The behaviour for an unbalance moment will be considered in Chap. 5 for short and long rotors, and by so doing the rotor length will be shown to playa decisive role.

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