Critical Speeds of Gyroscopes: Course Held at the Department by Gerhard Schweitzer

By Gerhard Schweitzer

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That cancel two roots of the denomi- nator so that indeed there remain only two resonance frequencies or critical speeds at Only the natural modes of the forward whirl are excited here. The hidden resonance at 2 112 - ± Vc/(A+c)' is called apparent resonance as the amplitudes remain finite here. The normal modes of the reverse whirl are not excited and do not lead to resonance. One conclusion following from it is that it does not in general suffice to study the denominator of a resonance function in order to obtain from its roots resonance frequenciesone has to consider the numerator as well.

Where A results from (4. 1) and (4. 11) and is given by and a0 is the coefficient of the highest power of the corre- sponding characteris tic polynomial . (o) and the weighting matrix 8 are taken into account. An effect, not considered in the aforesaid criteria, is that of parameter sensitivity. For this reason some theoretical results could not be verified by experiment . As ar. example Fig. 11 (see next page) shows the IE~value depending on the damping parameter d 0 mum 1 0 • It is reasonable that the absolute opti- for low damping is of practically no use and that the optimal damping parameter d 0 is determined by the relative but nevertheles s true optimum Oz • The correspond ing IE a -op- timal parameters are given in Fig.

9 lower end rotor lower bearing 4. 2 Optimization of parameters. The free parameters of the system have to be determined so that its dynamic behavior will be optimal in a. sense that has to be specified [13]. A measure of the quality of an optimum is given by an optimization criterion that weights the technical performance requirements in a suitable way. The 47 Elastically supported rotor system has eight free parameters : the two damping coefficients of the bearings, the masses of the two bearings and the four elasticity coefficients of the support.

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