Helicopter Forced Vibrations

There are in the helicopter many sources of exciting forces which cause forced vibrations. Such sources include: main and tail rotors, powerplant,

transmission gearboxes, and transmission shafts.

Each of these sources creates exciting forces with a definite frequency.

The lowest exciting force frequency is that of the main rotor. It may be found from the formula

where n^r is the main rotor exciting force frequency; ng is the main rotor rps; к is the number of main rotor blades.

The frequency of the main rotor exciting forces varies in the range of 8-16 vibrations per second. The tail rotor excites forces with a frequency of 10 – 60 vibrations per second. The transmission shafts and gearboxes create a still higher frequency of the exciting forces: from 50 to several

hundred vibrations per second. The powerplant yields a broad spectrum of exciting forces with frequency of 600 – 1000 vibrations per second.

The primary forced vibration source is the main rotor with hinged blade support. Blade oscillations relative to all the hinges are also the source of many vibrations.

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Vibrations from the blades of the main and tail rotors are transmitted through the hubs and the airstream deflected by the blades. This slipstream strikes the tail boom and tail fin in the form of periodic pulses and causes vibrations.

All parts of the helicopter are subjected to forced vibrations, but the amplitude of these vibrations differs. The amplitude magnitude depends on the stiffness of the structure, the closeness of the source of the exciting forces, their magnitude and points of application, and on the degree of close­ness to resonance. The degree of closeness to resonance is determined by the relative frequency v, equal to the ratio of the exciting force frequency to the natural vibration frequency

v = —- •

n

nat

The amplitude of forced vibrations can be expressed graphically, plotting the structure deformation vertically and the relative frequency horizontally (Figure 110). The relative deformation is the ratio of the deformation caused /180 by the dynamic load to the deformation created by the static load. From this graph we can draw the following conclusions:

The largest deformation or the largest amplitude occurs at resonance (v = 1). Therefore, resonant vibrations are very dangerous: they can lead

to structural failure due to material fatigue;

For v > 0.5 the vibration amplitude increases very rapidly and the structural deformation increases sharply;

For v > 1.5 there is a reduction of the structural deformation in com­parison with the deformation caused by a static load of the same magnitude.

Thus, to reduce the structural deformation it is necessary to reduce the degree of closeness to resonance by altering the natural vibration frequency.

If the exciting force frequency is high, the natural vibration frequency must be reduced. Rubber vibration dampers are used in mounting the engine to the frame to avoid resonance. The use of shock mounts reduces the stiffness of the frame-engine structure, which leads to reduction of the natural vibration frequency and increase of the relative frequency (v > 1.5).

Another example. The main rotor provides low-frequency exciting forces. The main rotor gearbox is mounted rigidly to the gearbox frame, without shock absorbers. This type of mounting increases the natural vibration frequency, and as a result the relative frequency is considerably less than

0.5.

The helicopter control linkage rods are most frequently subjected to forced vibrations. Therefore, it is particularly important to prevent resonance of the control rods. To this end the natural frequency of the rod is determined. If this frequency is close to the exciting force frequency in the region where the rod is located, the natural frequency must be changed. This frequency can be found from the approximate formula

where D is the rod cross-section diameter; l is the rod length;

E is the longitudinal elastic modulus; у is the specific weight of the material.

We see from this formula that the rod diameter must be increased or its length must be reduced in order to increase the natural vibration frequency.

If the rods are long, roller type supports are used to increase the frequency. When it is not possible to determine exactly the possibility of the occurrence of resonance, use is made of rods with inertial dampers. The inertial damper is a weight located inside the rod close to its midpoint, between two rubber plugs. The presence of the damper leads to rapid decay of the vibrations.

Under normal conditions the forced vibrations of the various parts of the helicopter are small; their amplitudes are measured in hundredths or tenths of a millimeter. However, in certain cases they may become hazardous if the normal operating conditions are exceeded.

Most frequently, magnification of the vibrations is caused by the failure of individual structural elements (stiffness is reduced and resonance occurs), by improper the adjustment of structural parts, and by mass unbalance. The acceptable vibration limit is determined by their effect on the structure and on the human organism. Vibrations are considered acceptable if they do not lead to structural failure and do not cause discomfort to the personnel (Figure 111). The higher the vibration frequency, the lower the vibration amplitude which can be endured by the personnel without pain.