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Aviation History
1964
1964 - 0402.PDF
SUPPORT STRUTS 751 879 924 973 IOI4 IO52 IO89 M7O 1437 1652 FREQUENCY C.RS. MODE C 853 929 955 9 84 IO28 IO97 1169 1324 1916 2962 FREQUENCY C.P S CROSS-OVER AP 3.45/ MODE B MODE t FREQUENCY Fig 14 Flap and torsion vibrations of compressor blades is set up. Since a high amplitude of oscillation in any part implies a high stress, such oscillations must be prevented. When dealing with compressor blades, then we must start by examining what resonances are possible. After that we must consider how they can be excited. Modes of Oscillation The simplest mode of oscillation, which we call "first flap" is just what its name implies. It is the oscillation of a diving board after the diver has left it. The maximum stress in the board or blade occurs at the fixed end, and this is where break- age is most likely to occur. At a rather higher frequency one can excite "second flap," in which the free end of the blade moves in one direction, while the inner two-thirds moves in the opposite direction. There is a stationary point, or node, about one-thiid of the way from the free end. In a similar way one can get third and higher flaps at even higher frequencies. Another possible mode of oscillation of a strip clamped at one end is a torsional one. This could be excited by twisting one end of the strip and then letting it go. One edge then moves in the opposite direction to the other, and the nodal line, on which stresses are highest, runs along the centre line of the strip. Again we can get a higher mode, of the so called "tramline" type, with two nearly parallel nodal lines. A long, narrow strip has a relatively low frequency of flap compared with its frequency of twist; a short, wide strip has a relatively high flap frequency (Fig 14). At intermediate lengths the frequencies are similar and combine to form coupled modes with diagonal nodal lines. The actual blade, of course, is not a plain strip but is a bent and twisted aerofoil of varying section. Its modes of oscillation are therefore much more complicated than those for simple strips such as I have discussed, and coupled modes abound particularly at the higher frequencies. The nodal lines can produce all sorts of delicate patterns. The frequencies are slightly affected by centrifugal effects when the blade is being whirled round in the engine. They are also affected by the fact that the disc on which they are supported is slightly flexible and has its own modes of vibration. It is therefore a very complicated matter to calculate all the possible frequencies, and every now and then testing discloses a resonance that was not foreseen. Resonances How are such resonances excited ? There are three main causes, which are illustrated in Fig 15: circumferential variations in airflow; rotating stall; and self-excitation. As a blade moves round it passes through the wakes behind the stationary vanes in the preceding row. Like a motor cyclist driving Past a convoy of lorries on the M1 in a strong wind, it experiences INCIDENCEINCREASED] INCIDENCE REDUCED LIFT j^STALLED // BLADE (s ^ UNSTABLE' REGION INCIDENCE ROTATION Fig 15 Causes of compressor-blade excitation in turbojet engines a fluctuating side force which tends to make it wobble. If the number of wakes is small, low frequencies such as first flap are excited; if the number of wakes is high, resonances in the higher frequency coupled modes may occur and lead to blade failures. The low-frequency resonances are easily calculable and an engine is always designed to keep them as far as possible out of the normal running range. We ourselves usually fix our blades to the disc with thick pins, so that they can roll freely in the plane of the disc. The natural frequencies, particularly of the first-flap oscilla- tion, then increase markedly with speed, so that we can avoid resonance over a much wider speed range than is possible with rigidly fixed blades. Rotating Stall Rotating stall is a phenomenon that was illustrated by Professor Hawthorne in a Royal Institution discourse some years ago. When the compressor is running at its designed speed the air is several times as dense at outlet as it is at inlet, so the outlet passage is made much smaller, and the blades shorter. But at low engine speeds the compression is less, so the air tends to flow relatively slowly at the front of the compressor and relatively fast at the back. The moving blades at the front then find that the air is coming towards them at a much steeper angle than usual, and so they "stall"—that is, the air does not follow the contour of the blade, but breaks away from it, leaving a turbulent wake of "dead" air—the same thing happens to an aeroplane wing if the pilot tips its nose up too far when trying to fly slowly. The blades do not all stall together, however. When one stalls, the airflow pattern changes in a way that makes conditions easier for the blade in front and more difficult for the one behind. The latter then stalls in its turn, while the first blade is relieved and unstalls. As a result a spiral "cell" of the turbulent air produced by the momentarily stalled blades moves round the compressor at a speed about half that of the blades themselves. Remembering Gumperson's statement of the unco-operativeness of nature—"if an event is possible, it will occur at such a time and in such a way as to maximise the inconvenience"—one can see that the rotational speed of the stall cell or cells may well lock on to a natural resonance of the blade. The inevitable result is a fatigue failure. Various ideas have been suggested to avoid this: one is differ- ential spacing of the blades to fix the stall position. But the most reliable method seems to be to avoid those conditions where stall is likely, either by splitting the compressor into two and running the back end relatively faster than the front at low powers, or by bleeding air from the middle stages to increase the flow at the front. Self-excitation This occurs under conditions of negative aero- dynamic damping. Normally, if a blade is perturbed in one direc- tion the aerodynamic forces on it are changed in a way that tends to move it back again. But under certain circumstances—for example, if the blade is nearly stalled—a movement in one direction increases the force in that direction, so an oscillation is excited. Experience has shown us certain ranges of operation in which such instability is likely, and these must be avoided. Damping In general there are so many rows of blades, each with so many possible modes of vibration, and there is such an abun- dance of exciting forces, that one is left in some surprise that the blades are ever unexcited. The happy fact is that damping, in the material itself, in the blade fixings, and from the surrounding air, exerts a generally benign influence and seems to limit dangerous vibrations to a few cases in each new design: these are immediately discovered by testing long before an engine enters airline service.
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