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

By Gerhard Schweitzer

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Extra info for Critical Speeds of Gyroscopes: Course Held at the Department for General Mechanics September 1970

Example text

8 shows amplitude curves with the lowest possible resonance peak together with the amplitude curves for the initial parameter set of the model. In this case the maximal resonance peak of the upper rotor end reduces to 29o/o of the initial maximum. 2 IE - criterion. For the continuous operation of the gyro at constant rotor speeed its behavior as caused by impulse-shaped disturbances may stand for its general behavior. The impulse response is very suitably characterized by the generalized integral of square error ( IE 2 -criterion).

16) exists. etA• 0. This can only occur if the system is undamped and the exciting frequency is equal to a natural frequency w t. n Then, the particular solu- tion increases unboundedly in the case of resonance (the statement (3. 13) is then not valid). In the case of apparent resonance it takes finite values as shown below. Resonance occurs when the resonance function (3. 15) as a function of the exciting frequency Q becomes a maximum. This is the case when the denominator comes to a minimum unless it is cancelled by a minimum of the numerator reached at the same time.

13. The measured variables of the gyroscopic model are of mechanical nature being displacements and angular velocities. They have to be transformed by suitable pickoffs into electrically measured values. In order to obtain a defined connection between the original mechanical and now electrical values the measuring program has to care for calibration procedures. Hence, for the purpose of calibration a defined input signal acts on the model. For analyzing the measured values as well and for the param~ ter identification a defined input signal, for example a harmonic vibration, is very useful.

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