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Dino Bousso (1933-1971)
● TITLE: A stability criterion for rotating shafts
● AUTHOR: Bousso, D.
● SOURCE: D.Sc. thesis, Technion, Haifa, Israel (1963).
● LANGUAGE: Hebrew.
● SUPERVISOR: B. Popper (1927-2012)
● SYNOPSYS: The stability of an inertia mounted on a rotating flexible shaft is dealt with by means of a perturbation method. This case serves only as an example and the method can be used for more complicated systems.

In contrast to the linearization of the equations of motion required before use of the Routh-Hurwitz stability criterion, this method is based on direct analysis of the forces and moments acting on the inertia after it has established precession at each of its natural frequencies as a result of a random disturbance.

These forces and moments are divided into two groups; those necessary for maintaining a steady state of precession and the rest due to internal and external friction and load moment. Since the first group is in equilibrium with the inertia forces it is possible to concentrate ourselves on the second group whose influence is decisive in this aspect and examine if the work done by them is positive or negative. In the first case the amplitude of the precession must increase and in the second case it must decrease. The boundary of stability is reached when the total work done by the second group equals zero when the rotor is precessing.

In the absence of friction and load moment the precession will maintain itself indefinitely. Both forward and backward precession is possible. Both internal and external friction tend to damp out the backward precession. However for the forward precession to be damped out the external friction forces must exceed the internal friction forces. Since no linearization of the internal friction force is made, the stability criterion obtained will depend also on the amplitude of the initial disturbance. Thus factors which disappear because of linearization manifest themselves when a more realistic internal friction law is assumed.

As a further stage the effect of the load moment on the stability is examined. It appears that when the rotor precesses the resultant of the input and output moments has a component in the direction of positive precession. This component will do work on the system and will increase the amplitude of vibration if there is insufficient external friction. When the rotor is the driver (in turbine for example) the moment will tend to decrease the amplitude of forward precession but will increase the back precession amplitude. It is shown that with sufficient internal and external friction the amplitude of back precession will either reach a certain limit or damp itself out.

Within the framework of engineering examples, a method for static and dynamic self-balancing of rotors on flexible shafts is described. The instability of a driven rotor is analyzed. Finally an explanation is given to the phenomena of back precession in turbines, a phenomena hitherto unaccounted for. The self-balancing and instability have been verified experimentally in the Mechanics Department of the Technion and Research Department of the Defence Ministry.

The linearization of the equations of motion and the application of the Routh-Hurwitz criterion require work which is not only lengthy and tedious but often leads to erroneous conclusions as shown by experiments. This is due to the excessive idealization of the problem by linearization resulting in the lose of its inherent properties.

The method propounded here maintains a closer touch with reality and requires little mathematics with the result that a deeper understanding of stability phenomena is obtained. These properties should help increase the use of the method by engineers and designers. They also increase its pedagogical value.


Ben-Amots, Netsivi., "The dynamical behavior of a rotor on a belt suspension drive," M.Sc. thesis, Technion, Haifa, Israel (1969). Supervisor: Bousso, Dino (1933-1971). (HEBREW with English summary). Abstract in English Abstract in Hebrew

Porat, I. (1934-2012), "Optimal damping of flexibly-mounted rotor," Israel J. Technol, v. 7, p. 235 (1969). Abstract in English

Ben-Amots, Netsivi., "The motion of a high-speed rotor under the influence of a moment perpendicular to the axes of precession and nutation," D.Sc. thesis, Technion, Haifa, Israel (1975). Supervisors: Bousso, Dino (1933-1971), and Porat, Itzhak (1934-2012). (HEBREW with English synopsis). Abstract in English Abstract in Hebrew

Cohen, R., "Effect of the coupling between flexural and torsional vibrations on rotors driven by a flexible shaft," DSc. thesis, Technion, Haifa, Israel (1982). Supervisor: Porat, Itzhak (1934-2012). (Hebrew with English abstract). See p. 11, 203 Abstract

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