Ein Reibschwinger mit Selbsterregung ohne fallende Reibkennlinie

Abstract

Es wird ein System vom Freiheitsgrad drei entwickelt, das auch dann selbsterregt schwingen kann, wenn die Reibkennlinie monoton mit der Reibgeschwindigkeit steigt.

On the minimal model for the low frequency wobbling instability of friction discs

“…It is proportional to the friction force, which can be easily seen in (14) because this matrix is multiplied by the friction coefficient µ . The physical explanation of this basic effect can be found for example in [15]. However it is not the only matrix proportional to the friction.…”

“…These terms describe the friction induced damping. They influence significantly the stability of the friction disc and were unfortunately overlooked in previous publications [15,16].…”

“…The second one is the mode coupling which was investigated extensively in connection with the break squeal problem [15 -18]. The models [15] and [17] are quite general and mainly oriented on the principal effect of the non-symmetric stiffness matrix generated through friction forces. The models [16] and [18] are more specific and concentrated on specific properties of the brake, i.e.…”

Gyroscopic Stabilization

“…A counterexample in R 5 , where tr D, tr QDQ > 0 and no gyroscopic stabilizer exists, has not yet been found. We therefore formulate our missing case in R 5 as an open problem.…”

“…The motion of the system sustains itself, an effect which is called self-excitation or self-induced vibration. The reason behind this effect is the presence of negative damping, which results for example from dry friction, see [1], [5], [18]. Another example is the Van der Pol Oscillator (see [13], p. 9), which due to a non-constant damping coefficient, locally has negative damping.…”