GB2090339A - Damping vibration in turbomachine blades - Google Patents

Abstract

The blade is provided with a vibration damper for damping a predetermined vibration of the blade comprising a closed chamber 14 within the aerofoil portion 13 adjacent the tip of the blade, and liquid 15 within the chamber 14. The volume of liquid 15 is less than the volume of the chamber 14. The chamber 14 is shaped, positioned, and aligned relative to the blade, so that in use the liquid 15 is constrained to form a column which oscillates the chamber 14 in radial directions and in the same directions as the vibration to be damped. The volume, mass, and viscosity of the liquid are all chosen in relation to the frequency vibration (WB) of the vibration to be damped and the rotor speed (WB) so that, in use, the length (L) of the column of liquid is such that <IMAGE> wherein R = the blade tip radius. In this way the liquid 15 is caused to oscillate, under centrifugal loads, at a natural frequency which matches, or is close to, the resonant frequency of the vibration to be damped. <IMAGE>

Description

SPECIFICATION Vibration damped rotor blades for turbomachines This invention relates to blades for use in turbomachines, and is particularly concerned with damping vibrations induced in such blades.

With large compressor blades, for example, fan blades of a by-pass type gas turbine engine, it is known to use platforms, commonly called snubbers, at locations along the aerofoil portion to damp vibrations due to twisting, flutter and flapping of the blade. These snubbers interact with one another to form effectively a continuous platform which damps the vibrations. Such snubbers add undesirable weight therefore the blade roots and the discs or drums on which the blades are mounted, have to be considerably strengthened to withstand the high centrifugal forces on them. Furthermore, the provision of snubbers complicates the manufacturing and machining processes, compromises the aerodynamic efficiency of the blade, and introduces highly stressed zones at vulnerable regions of the blade. Therefore, there is a strong incentive to eliminate snubbers.

It is also known to provide turbine blades with tip shrouds which serve to minimise gas leakages at the blade tips, and provide damping of vibrations of the blades in much the same way as the snubbers do on compressor blades. Here again turbine rotor assemblies embodying blades with tip shrouds suffer from many of the disadvantages enumerated above, and there is a strong incentive to eliminate the use of tip shrouds and to deal with the problems of vibration damping and controlling tip seal clearances separately.

It is also known to damp shroudless blades by resilient blocks fitted under the root platform but this requires a larger chord bladeto obtain sufficient flexure to enable damping to be effective. This in turn results increased disc rim loads.

The claimed invention offers a way of damping vibrations induced in blades of turbomachines which do not have snubbers, tip shrouds, or other known vibration dampers.

The advantages offered by the claimed invention are mainly that the vibration damper is contained within the blade and so therefore does not compromise the aerodynamic efficiency of the blade.

Furthermore, the design of vibration damper enables adequate damping to be achieved without imposing undue centrifugal forces on the blades and rotor assemblies on which the blades are mounted.

In addition, the blades of the claimed invention are easierto manufacture and machine and hence are less costly to manufacture than blades provided with snubbers or tip shrouds.

The invention will now be described by way of-an example with reference to the accompanying drawings in which: Figure 1 illustrates a blade for a turbine rotor of a gas turbine aero engine constructed in accordance with the present invention.

Figure 2 illustrates in more detail a further form of vibration damper suitable forthe blade Figure 1.

Figures 3 and 4 are graphs illustrating the relationship between turbine speed, frequency of vibration to be damped and the different damping characteristics for changes in the shape of the chamber and mass of the liquid.

Referring to Figure 1 of the drawings there is shown a blade for a turbine or compressor rotor of a gas turbine engine.

The blade comprises a root portion 11, a platform 12 and an aerofoil portion 13.

The root 11 is of dovetail configuration whereby the blade may be mounted in a complementary shaped, axially extending, shaped slot in the rim of the respective compressor or turbine disc, or drum.

Other shapes of root portions are possible and the slots in the disc or drum may extend axially or circumferentially.

Located within the aerofoil portion 11 adjacent the tip of the blade is a closed chamber 14 which is partially filled with a liquid 15. The term "liquid" as used herein is taken to include liquid metals such as mercury, materials such as lead or sodium, which at the operating temperature of the blade become liquid, or liquids such as glass which become less viscous at the operating temperature of the blade. The chamber 14 is dimensioned and shaped, and the volume of liquid and its-mass and viscosity chosen, so that in use the resonant frequency of oscillation of the liquid 15 in the chamber 14, under centrifugal loads, matches, or is close to, the frequency of the principal mode vibration of the blade.The chamber 14 is shaped to provide, in use, a column of liquid 15 extending predominantly radially so that centrifugal loads on the column of liquid as the liquid oscillates, provides a large restoring force on the oscillating column of liquid thereby to damp the principal mode of vibration of the blade.

The chamber 14 is aligned so that the liquid 15 oscillates in the same direction as the principal mode of vibration of the blade; that is to say the region 19 where the radially extending portions of the chamber 14 are interconnected is aligned so that the liquid oscillates in this region 19 in the same direction as the principal mode of vibration of the blade.

The liquid does not fill the chamber 14 and any resistance to motion in the liquid results in energy being dissipated as heat. Since the chamber 14 is located at the position of maximum amplitude of the principal mode of vibration this is conductive to high energy absorbtion. Furthermore, wear which would occur with othertypes of devices employing solid components in frictional engagement or solid oscillating masses is eliminated, or at least greatly reduced. Damping should also be obtained over a wide range of frequencies. If desired a blade may incorporate two or more chambers 14 each being partially filled with a liquid and each being tuned so that the combined damping due to the oscillating liquids in all the chambers of each blade matches the resonant frequency of each blade.

It has been found that a liquid mass of 1% of the mass of the aerofoil portion of the blade can give a logarithmic decrement of 0.35 corresponding to a Q value of 9.0, assuming that the viscous resistance to oscillation is within predetermined limits. Damping would be obtained at a particular predetermined R.P.M. and would decrease as the R.P.M. varied from the particular R.P.M.

The invention will now be described in fuller detail with reference to Figure 2 which shows a particular design of chamber 14 for a specific blade.

It is assumed that the chamber, stationed at the blade tip is vibrating in simple harmonic motion and that the relativeiy small liquid mass does not affect blade frequency. The effect of this vibration on the liquid is taken into account by applying acceleration forces to the liquid, equivalent to the container acceleration and in the opposite direction.

Amplitude of liquid oscillation relative to contain mentchamber 14 is obtained from:

Damping Logarithmic Decrement 8, is obtained from:

Where aR = amplitude of liquid oscillation relative to chamber 14.

a5 = bladetipamplitude B = distance apart of 'limbs' of chamber 14

L = length of liquid column M = liquid mass

Mg = blade aerofoil mass K5 = BLADE VIBRATIONAL ENERGY ENERGY OF AEROFOIL MASS VIBRATING AT TIP AMPLITUDE b = Kvg MWB Where Kv = viscous force on fluid per unit velocity relative to chamber.

g = gravitational acceln. (non dimensional numerical value).

M = Liquid mass W5 = Vibrational circular frequency (Rads/unit time) = 27rxfrequency Where

Where R = blade tip radius WE = Turbine rotational speed (Rads/unit Time) Referring now to Figures3 and 4.

are functions of

and are plotted in Figures 3 and 4 against

Kv g MWB and against

ratherthan

in order to show, more directly the effect of variation in relative engine rotational speed and blade are quency.

It is seen that the maximum liquid relative amplitude and the maximum damping for given liquid B and blade masses and K5 and- values are obtained L when

this being when the natural frequency of the liquid in its U chamber in the centrifugal "g" field at the blade tip, is equal to the blade frequency.

The effect of decreasing the value of

T Kvg MWB is to increase maximum relative amplitude and damping at

but with the damping falling off more rapidly with changes in this function.

In the design of a damper there is then the choice of very high damping for a narrow range of engine R.P.M. and blade frequency or lower maximum damping, less sensitive however, to variation in these quantities.

It is necessary for the length of the fluid column L, to be such that

and the effectiveness of the damper will depend largely on how th is length compares with the thick nessofthe blade tip in which the liquid is housed.

If Lturned out to be much greaterthan the tip thickness the 'limbs" of the U shaped liquid column would have to be relatively long, the resulting low value of (BL)2 giving comparitively low damping. Thick tip section blades would be preferable for this form of damper.

It is difficult to calculate the viscous resistance to motion of a given liquid in its chamber. In other words it is difficult, without experimentation to ensure that a required value of Kv would obtain in practice. It may be that to obtain the required value, a liquid of considerably higher viscosity than the molten lead envisaged would be necessary - molten glass for instance. However, the comparitively low density of glass would reduce damping for a given volume. In the above described embodiment the required resistance to liquid motion has been assumed to be provided by viscous forces, but it might be possible and even preferable to obtain this resistance by providing some kind of restriction to the liquid motion in the containment chamber. Restriction by a small orifice might be more practicable than having to depend upon viscous forces.

With this arrangement, flow resistance would not then be directly proportional to velocity and the foregoing analysis would be invalid. However, it is believed that the energy dissipated by resistance to the damping liquid flow would be much the same if the mean resistances were about equal for the orifice restricted and the viscosity restricted cases.

The viscous resistance analysis will be used in the following example of practical application, in relation to a turbine blade having an Aerofoil Mass M5 = .036 lb.

Assume: Turbine R.P.M. = 17000 Tip Radius = 9.3 in.

Blade frequency 3350 hz-1F For maximum damping

Assuming this is required at 17000 R.P.M. then: 1700x 2x93 =1 60 x 3350 x L Required length of fluid column L = 0.13 in.

KvE A suitable value of MW has to be chosen. It is observed from graph 2 that a value of.1 would give high maximum damping, this falling off more however, with reduction in WE 2R W5 L Let us assume a value of.2 for

Kv g MWB lMWB j Even if this varied in practice over a range .1 to .3 the damping at

would be little affected, and small variations in R.P.M. or blade frequency could easily give continuous running at this condition.

From Graph 1 we obtain:

raR L7 L aB Bj SxMpximum at Kvg =0-2 MWB We need an estimate of the liquid amplitude aR to decide the chamber additional volume necessary to allow motion. Assume blade tip amplitude x frequency = 1.5 ft./sec. (This is considered to be about the maximum value for acceptable fatigue life).

Then Tip Amplitude ae = .0048 in. and liquid amp little at = 0.24 B ins.

L As B < 1 then aR < .024 in.

L It is seen that very little extra chamber volume is needed to accommodate the liquid amplitude.

Assuming a basic semi-circular shape forthe chamber.

Then for a length of liquid L = .13 in. (measured at the mean diameter).

Mean diameter = .13 x 2 = .083 in.

The radial thickness of the liquid needs to be sufficientto give an effective liquid mass but not so great as to invalidate the assumption made in the analysis, that the liquid could all be considered as subject to the same dynamic conditions.

The following dimensions appearto be suitable.

Achamber length of .25 in. could be accommo- dated in the blade tip.

Then for lead as the liquid.

Liquid Mass M = .13 x .03 x .25 x .4 = .00039lib.

Then from Graph 2 we obtain

i.e., at 17000 R.P.M.

WehaveM =.00039=.108 Me .036 B = .083 = .64 r .13 KE = .2 (Approximate value) This gives: logarithmic decrement = .35

at 15300 R.P.M. forthe same blade frequency W5.

giving8=.19 These give 0 factors i.e., Ir 8 of 9 and 17 at 17000 and 15300 R.P.M. respectively.

These results require that: Kvq = .2 MWe i.e., Kv = .2 MWB = 0.0042 lbflinlsec.

g High damping is seen to be theoretically obtainable from a small liquid mass (about 1% of aerofoil mass) over a useful engine R.P.M. range, and it appears that the chamber dimensions desirable are compatible with the space available.

The chamber 14, instead of being a generally "U" shaped tube may be formed by two spaced walls; the radially outer one of which is concave and the radially inner one of which is convex. In one specific construction the inner and outer walls may be spaced hemispheres thus effectively forming a chamber which in any radial plane is substantially "U" shaped.

In a further embodiment the chamber 14 may be a right-circular cylinder arranged with its axis normal to the direction of the vibration to be damped, and in this case the centrifugal loads on the liquid urges it into contact with the circumference of the cylinder so that effectively a generally "U" shaped liquid column is formed.

The volume of the chamber 14 not occupied by the liquid 15 is preferably evacuated or at least contains air or gas at a reduced pressure. In the case where the chamber 14 is a hollow cylinder (Figure 2) or formed by spaced convex and concave walls, the chamber may contain air or gas providing that the liquid can displace the air or gas or compress it without impairing the operation of the damper.

Claims (7)

1. A blade for a turbomachine having an aerofoil portion and a root portion, the blade being provided with a vibration damper for damping a predetermined vibration of the blade, the damper comprising a closed chamber within the aerofoil portion adjacent the tip of the blade, and a material within the chamber which, at least in use, is a liquid, the volume of liquid being less than the volume of the chamber, the chamber having a concave surface that faces towards the root portion and extends in a direction along the length of the aerofoil portion to define a path along which the liquid is constrained to oscillate, and the chamber being shaped, positioned, dimensioned and aligned relative to the blade so that the liquid forms a column which oscillates in the chamber in radial directions and in the same direction as the vibration to be damped, and the volume, mass and viscosity of the liquid being chosen in relation to the frequency (We) of the vibration to be damped, and the rotor speed (WE) SO that, in use, the length (L) of the column of liquid is such that

where R = the blade tip radius, thereby to cause the liquid to oscillate under centrifugal loads, at a natural frequency which matches, or is close to, the resonant frequency of the vibration to be damped.

2. A blade according to Claim 1 wherein the chamber is shaped to define two radially extending limbs interconnected at their ends nearest to the tip ofthe blade, so that in use centrifugal forces on the liquid cause it to oscillate from one limb to the other.

3. A blade according to any one of the preceding claims wherein the chamber is of cylindrical shape with a longitudinal axis of the cylinder extending transverse to the predetermined direction of vibration to be damped so that the liquid oscillates around part of the circumference of the cylindrical chamber.

4. A blade according to Claim 1 or Claim 2 wherein the chamber is defined by the gap between a concave wall which is spaced from, and faces, a convex wall, and in use the concave wall faces radially inwards.

5. A blade according to any one of the preceding claims wherein the liquid is a liquid metal.

6. A blade according to any one of Claims 1 to 4 wherein the liquid comprises a material which is a solid when not in use and liquid at the operating temperature of the blade.

7. A blade substantially as herein described with reference to any one of the accompanying drawings.