In order to increase the efficiency of airplane engines, the clearance is reduced between the rotary portions formed by bladed wheels (or rotor stages) and the stationary portions surrounding them and constituted by casings that also support series of stationary vanes (or stator stages).
Nevertheless, this reduction in clearance increases the risk of contact being made between the moving blades of the bladed wheel and the facing casing segments, and some such contacts can lead to systems instabilities.
FIG. 1 shows such a casing 10 provided with a layer of abradable material 12 on its inside face, shown together with a bladed wheel 20 mounted in the housing defined by the casing 10.
Such contacts take place in particular at transient speeds as a result of local or continuous interference between the tip of a blade and the facing track of the casing. When such contact is made, it will be understood that the blades can be subjected to high levels of stress presenting a vibratory nature, and that under such circumstances they can be caused to vibrate in one of their resonant modes. Under such circumstances, the level of vibration increases very quickly, subjecting the blades concerned to deformations that are liable to exceed their endurance limit, thereby leading to degradation of the abradable tracks and to damage to the blades (blade tip heating, fatigue cracking, permanent deformation, . . . ) that can lead to blades breaking. As a general rule, the phenomenon is very short lived, either because some external event puts an end to it (change of speed of rotation of the rotor, thermal transient, . . . ), or else because the resonant frequency of the damaged blade is changed, thereby putting the system out of tune.
The phenomenon might involve a single blade, a set of blades, or the entire wheel, i.e. all of the blades, where the all-blade phenomenon occurs rarely, simply because of dispersions in blade length due to fabrication.
In general, in order to limit such damage, the leading edge and/or the trailing edge is offset so that contact does not take place in those locations but rather in zones where the blade is more robust: this is to the detriment of performance.
FR 2 869 069 discloses taking consideration of the vibratory phenomenon due to the blades of a bladed wheel and avoiding resonance phenomena by deliberately de-tuning the bladed wheel.
Nevertheless, under such circumstances, no account is taken of rotor and stator interactions, also known as “coupling phenomena”, that occur between the vibratory modes of the bladed wheel and the vibratory modes of the assembly formed by the casing and the bladed wheel.