Underwater propeller vibration tests and Propeller blade vibrations

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UNDERWATER.

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nJTcP-PR OPE4LER. V.IBRATIO1N I11E-ST S.

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Prof. .L. C. BURRILL, M.Sc,. Ph.D., Member of council

AND

PROPELLER BLADE. VIBRATIONS.

B

W. L. HUGHES, B.E., B.Sc., Associate Member

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Papers read before the North East Coast Institution of Engineers and Shipbuilders -in Newcastle upon Tyne

on the 11th February, 1949, with the discussioi and

correspondenèe upon them, and the Authors' replies

thereto.

(Excerpt from the Institution Transactions,

Vol. 65).

NEWcAStLE UPON TYNE

PUBLISHED1 RY THE- INSTITUTION

OF ENGINEERS AND SHIPBUILDERS, BOLBEC HALL

LONDON - --- -

-'

E & 1' N spoN; LIMITED, '57, HAYMARKET, S W I

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THE INSTITUTION IS NOT RESPONSIBLE FOR THE STATEMENTS MADE, NOR FOR THE OPINIONS EXPRESSED, IN THESE PAPERS, DISCUSSION AND AUTHORS' REPLIES

PARTICULARS OF MEMBERSHIP of The Institution will be supplied on application to The Secretary (for address, see cover).

MADE AND PRINTED IN GREAT BRITAIN

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UNDERWATER. PROPELLER VIBRATION 'IESTh

By Prof. L. C. BTJRRILL, M.Sc., PhD., Member of.ouncl

11th February, 1949

SyNopsis This.paper describes the results of some initial tests on the vibration

of a marine propeller under water. The vibration patterns obtained show that

the same modes of vibration occur in air and in water, and that the corresprnding

nodal patterns are also similar, although the transverse nodal lines across the blades appear to be slightly nearer to the shaft axis for the tests in air than for

those in vater.

It is also shöwAihat while the effect of vdter damping an the resonant frequencies in the lower modes of vibration is considerable, this effect diminishes for the

frequency in water

higher modes. The ratio

_{frequency in air}

appears to increase in

approxi-mately linear manner as the number of nodes on each blade increases.

The results of some farther tests in air on a flat-plate model resembling this.

marine propeller, carried out by Mr. B; Grinstead of the Dc Havilland Engine

Co., Ltd., are also included, and throw some new light on the earlier tests with

full-size marine propellers in air. In discussing these latter, results, scime tentative.

conclusions are drawn regarding blade sensitivity to "singing ".

Introduction . .

THE

teSts which are the subject of this short paper are a

con-tinuation of the work which was carried out by the Author on

the vibration of full-size marine propellers in air, atid which was

the subject of a paper entitled "Manne Propeller Blade Vibrations

read before this Institution in 1946 *

The present tests have been

carned out for the British Shipbuilding Research Association and they

represent only the initial stages of a long-term research intQ the effect

of systematic changes in blade form on the frequencies and modes of

vibration of marine-propeller blades.

At the same time, these tests do answer some of the major questions raised in the discussion of the previous paper, and as our knowledge of the effect of water damping on the modes of vibration of propeller blades is so yew

small, it is hoped that the publication of these initial results will be of assistance

to investigators who may be engaged in attempting to obtain a mathematical solution to the as yet obscure problCm of propeller '.' singing."

Testing Arrangements

The propeller chosen for these tests. was a four-bladed bronze propeller

designed for 450 b h p at approximately 500 r p m The thameter was

4 ft.4 in. and the blade surface 772 sq. ft. giving a disc-area tatio Of 0525. The blades were approximately of elliptical shape and the blade sections of

aerofoil type Details of the blade design, pitch variation etc are shown in

Fig I

the propeller being the same as that shown as propeller' M' in the

earlier paper;.

.

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302 UNDERWATER PROPELLER VIBRATION TESTS

The instruments used in -carrying out these new tests were similRr to those previously, employed for the tests lii air, excepting that the loudspeaker-type vibrator was specially manufactured to work under water, and the pick-up

was also made watertight so that records of the blade vibrations could be taken

direct from the blades with the propeller under water.

For the-purpose of these tests, the propeller was set up in' the cenfre of a tank 21 ft. square by 4 ft. deep which had been erected specially for carrying out underwater tests of this kind, in the, Research Laboratory of the Naval Architecture - Dept. at' King's College Newcastle upon Tyne. Two . heavy timber baülks each 1 ft. square in section with a base made Of 2 in phnks,

were used to support the propeller. The propeller was seated on the forward

or larger end of the boss with the driving face of the blades uppermost, and.

ti vibrator was arranged.to stand on the same base as shown in Fig..2 which

shows the propeller in position in the tank This was the arrangement which

had been found to be most suitable, in the earlier tests, and was such that tle experiments 'in air and the experiments in water could be carried out without

moving or disturbing the propeller, so that the conditions were exactly similar

for' both series of experiments, apart from the effect of water damping. The tests in water proved .to be 'much more difficult to carry otit than the

tests' in air. In the' first place, it was' found to be rather more difficult to find

the' resonant frequencies and to, set, the' blades vibrating at resonance, and secondly the mapping of the model patterns was a much more lengthy and

painstaking task.

This was, in fact, done by marking the propeller blade

with a fairly close grid, and the observer in diving dress in the tank then had to report the position of the point Of the 'pickup to another observer outside

the tank in crossing each line of the grid. The pick-up was then moved to and

frO along the particular line chosen,. and was' finally positioned so that the

Lissajou figure obtained was' horizontal in'each case. The several crossing,

points for tlie different lines of'the grid were then marked on a plan such as. that shown in Fig. 3 and the nodal lines were plotted by joining the various

points as shown. ' ' '

The underwater pickup has worked satisfactorily throughout' the tess, but unfortunately the underwater vibrator broke down after part of the tests had been carried out as water had leaked into the body of the loudspeaker

Unit.

'It was' found that the rubber diaphragm protection for the top part'

of the instrument, which' could be inflated to prevent the ingress of water,, had been entirely satisfactory, but water had unfOrtunately leaked in through-the electrical connexions at through-the base of through-the vibrator. As a result, through-the: work was' held up for a considerable time as the, coils had- to be rewound and the;

instrument had to be almost re-made before, it was satisfactory. Following

this experience, the vibrator has been examined frequently during the progress of'the tests, and although there-is still a light leakage it can now be iatisfactorily controlled

'When the initial'tests were carried out, the depth of water in the tank was, varied, and experiments were made to,check the effect of the head' of Water

above the blades on the modes of vibrations and frequencies recorded. It

was, found that with a very small head of waler above the top of the boss the existence. of, resonant vibrations could be observed - by the appearance of a

crOssed-wave pattern on the surface of the water, which was excited locally over

each of the 'four blade ekttemitiós. These1ocal wave áttems took tha form'

df'a'g±id,ofvCry finn'waves which occtipied.an area approximately 4 in. to 6'in.'

in diameter and the existence of such patterns was very sharply defined, the

tuning being. very.delicate anl sharp. At the same time, the 'intensity Of the.

soi.ind rose considerably, and -the propeller could be heard to be "singing"

quite clearly at the point of resonance. Later the depth of water over the blades'

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tJNDERWATER PROPELLER -VIBRATION TESTS ₃₀₃ or could only be seen if the gain of the. amplifier was increased to a vely, high'

level,, considerably above the normal working value.

_{It was found that tle}

difference in the resonant frequencies was not sensitive to the head of water above .the boss, and that the differences could not be observed within, the

accuracy of the oscillator setting.

It was, however, felt that it was most

satisfactory to use the larger head of water so that the surface was not disturbed,

and the depth of water in the tank for the tests reported herein was about

40 in.,, the top of the' boss being about 12 in below the Surface. Ordinary tap water was used at room temperature, ' and the mean head above the b1ad

surface would be about 18 in. It is. cOnsidered that this head was sufficient

to represent fully immersed conditions.

Testing Procedure

The vibrator- was first attached to the' 'tip of one of the blades, usinga

universal ball-joint clip, and the whole range of input frequencies from about

20 cp.s. -uj to 2,000 -c.p.s. was slowly traversed with a view, to picking out the

resonant frequencies. As the frequency of the vibrator was increased, successive

modes of vibration were excited; and at resonance all blades were 'set freely

in vibration in each case. Each mode was then carefully studied to establish

the nodal pattern and the exact frequency at resonance. The resc nant vibrations

recorded were quite sharp and clearly defined, and the nOdal patterns were 'plotted by, traversing the pick-up across the blade opposite tQ that which had the vibrator attached to it, this being the procedure which had been found

to be most satisfactory during the previous tests'. Many 'of the tests:.were

repeated several times to make sure that there was no possibility of error, and

'the repeat testswere, in fact,' 'satisfactory. ' At a later stage during'the

experi-ments the point of apphcation of the vibrator was moved to several points on the trailing edgn Of the blade in' an attempt .to excite the torsional modes

more satisfactorily; but this did not have any effect oji the modes and frequencies recorded, and the torsional modes in water have prOved vet)' difficult to excite.

The current for the moving coil of the vibrator was fed from the B.S.R.

Beat Frequency Oscillator, described 'in the earlier paper, through a power

amplifier which was capable of delivering about 50 watts. The power output

was very much greater than that required, to vibrate 'the blades without,

over-loading the oscillator, thus avoiding any possibility of. distortion.

The pick-up used was-of-- the-De -Havilland -piezo-electric acceleration type,

and in order to enable the nodal lines to be -identified clearly, thetime base

of the Mullard -E800' oscillograph -was-disconnected and-a' voltage' was-supplied

direct from the beat-frequency oscillator to. these deflecting, plates. _The

pick-up was' then used to supply the vertical-deflecting plates with'a 'voltage

corresponding to the blade vibrations by means of a suitable amplifier and the resultant pattern shown on the screen 'of the oscillograph 'tepresented

these two voltages set at right angles to each other. Horizontal movements

of the spot therefore represented variations in the inputenergy to the propeller

blade wi-Ole vertical mOvements represented variationS in th' Output energy

corresponding to the movement of the propeller blade at the point of contact

of the pick-up. With ihe-propeller blades vibrating near true resonance;'- the

picture obtained in the' osdillograph .vas a cirCle or. an ellipse depending upon the' relative phase displacement of the input and. output energies. ,1f a certain input frequency were 'to have caused the blades. to vibrate at twice .thatfrequency,

the figure obtained would, of course, have ben a figure eight, and otler

Lissajou' figures would appear for higher harmonics, but in carrying out these investigations such harmonically excited' modes were ignored and only directly

excited frequencies were studied. _{AU the patterns shown were obtained by}

traversing the pick-up to and fro across the lines of no. vibration- (i.e., nodal

lines) in such a way that a fine ellipse-in the-dscillograph was caused to change

from' a position in which it sloped from righi to left to, a position in *hich- it slped:., from left to, right,, the zero point,- or position of the nOdal line ax

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304 UNDERWATER PROPELLER VIBRATION 'rESTS

resonance, being identified by the position of the pick-up for which the picture

was a straight horizontal line, representing input energy only with no output.

Under water, the position of the nodal lines at the blade edges was capable of

very accurate determination, but as these lines were followed into the central

and thicker root parts of the blade, they were

sometimes rather difficult to

determine with great accuracy.

So far as the experiments carried out in air were concerned, it was found to

be very easy to excite all the flexural and torsional modes of vibration up to the fifth mode of vibration with four nodes on the blade with the vibrator

located at a p dint near the blade tip. in water, however, it was found to be

very difficult to excite the torsional vibrations with the exciter placed near the tip of the blade, and it was, therefore, necessary to move the exciter to

various positions on the trailing edge in order to obtainsatisfactory records

of the torsional vibrations.

Even so, it was found impossible to identify

clearly any torsional mode above the second mode. Curiously enough, the

pattern with the crossed nodes at the tip shown in Fig. 16 was found to be readily excited both in air and in water.

Discussion of Results

Table 1 and Table 2 show the frequencies of the flexural and

torsional

vibrations respectively. The frequencies in air are shown in column 2, while

those in water are shown in column 3, and column 4 shows the ratio between

- . . frequency in water

the water and air frequencies. It will be seen that the ratio -_{frequency in air}

varies from P625 for the fundamental mode of vibration in flexure up to 98O for the 5th mode, with 4 nodes on each blade,, and that this ratio varies in a

linear manner with the number of nodes. That is to say, the effect of water

damping on the resonant frequencies, although appreciable for the fundamental

or lower modes of vibration, disappeared almost entirely for the higher and

more complicated patterns. Figs. 3, 5, 7, 9, 14 and 16 represent the patterns

which were identified when the propeller was vibrated under water,and Figs.

4, 6, 8, 10, 12, 13, 15 and 17 show the nodal patterns for the modes of vibration

identified in air.

TABLE 1 .Flexural Vibrations

TABLE 2.Torsional Vibrations

It will be seen from these diagrams that the same modes of vibration were

identified both in air and in water, that the nodal patterns were

generally

similar for both conditions, but that for the vibrations

in air the position of

No. of Nodes Frequency in c.p.s. FW/FA In air In water Fundamental 160 230 100 161 625 '70 2 460 375 '815 3 710 625 - 8 4 1,020 1,000 980 No.of Nodes Frequency in c.p.s. FW/FA In air In water 2 3 400 670 840 265 490

-

'732662

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-LJNDERWAThR PROPELLEF. VIBRATIOI 'TESTS 05

the nodal lines, was closer ta the shaft centre-line. .than was the caiefoi the

corresponding vibrations in water. This . is true not. only of the .fle,iural

vibrations, but to a lesser degree in the. case of the torsional vibrations.. Figs.

-1 8-21 show the frequencies plotted- to a base of the number of nodes on the

blade for. both flexural and torsional vibrations. . Fig. 22 shows the comparison between the flexural vibration frequencies in air and in water, from whichit will

be seen that the curve of frequencies plotted to a base of the number of nodes follows the same general line both in ar and in water. This was not found

tQ be so fOr. the frequencies of the torsional modes...

it will be seen from- Fig. 20 that the curve 'for the tdrsiotiál frequencies obtained in ar tends to bend towards the base for the third torsional mode T.3 and would, therefore, most probably, have interse ted and crossed the

corresponding line for the flexural vibrations if it had been extended to a

higher torsional mode. This is a curious result, and raises the question Of

whether the frequency for T 3 is reliable On this pomt it can only be stated

at present that the pattern for T.3 shOwn in Fig. 13 was quite clear, and that

it is believed that the frequency of 840 c.p.s. is correct for this mode. In view

of this result, it is considered advisable to., investigate this matter further, as

it i

important to determine' whether, 'in' fact the' curve drawn through. the.

frequencies of the torsional modes can intersect that drawn through the

frequencies of the flexural modes. Unfortunately, the higher torsional modes

are difficult to excite, and it may be necessary to test several propellers before

this point can be settled, and the conditions under which such an intersection of these two curves is likely to occur can be established.

This is important in view of the possibility that interference between torsional and fiexural modes may have some 'bearing, on the occurrence of singing.

,'Another point to note is the large difference between the air and water

frequencies for the cross-node patterns shown in Figs. 16 and. 17 respectively. This difference is much greater than thet for the air 'and Water frequencies for the flexural modes F.4 shown in Figs. 14 and 15 for which the water 'frequencies

are very similar. The mode of vibration in water shown in,Fig ,l 6: has been

checked a number of times by different observers. Fig. 1.7 has also been

checked several times, and so far as the experimental results are concerned,

it would appear that this targe difference between the air and water frequencies of the cross-node patterns 'is correct..

This is difficult to understand, and no explanation can at present be given for this result, other than a suggestion that the water damping for the quasi-torsional motion of the cross-node pattern is much greater than that for the

straight-forward flexural motion in Fig. 4.' II

It inay be that Fig. 16 does not correctly correspond with Fig. 17. in' view of the rather different disposition of the inner nodes, or that the combinatioi

between the lateral Or torsional and fiexural motions which this mode involves

is different in air and 'in water. ,

'.

. . . .

-In this' connexion, the Author has very kindly been granted permissibn by

Jr. W. Ker Wilson ofThe Dc Havilland Engine' Co., Ltd., to include as Fig. 23

the results 'of-some interesting tests carried out by Mr. B. Grinstead with a small model of a flat-plate of effiptical shape which closely resembles the

propeller blades under discussion. . :

'in these iests, the plate 'was flimly seOued at the root and th 'various modOs

of vibration in air were excited by bowing with the aid of a rotating dis,

the corresponding nodes' being established by means of sand patterns.' The

resonant frequencies Obtained are, of course, much' highCr han thOse for' the full-size propeller, and would require to be corrected 'by means Of a 'scale

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306 UNDERWATER PROPELLER VIRRAflON TESTS

The point of major interest in these tests is that they establish the nature of the cross-node patterns which were obtained in the Author's earlier work

with full-size propellers, and which were then not clearly understood. For

example, the patterns with frequencies of 2,155 c.p.s. and 2,418 c.p.s.,

respec-tively, in this plate model series, are caused by a combination between the

pattern 0/3 at 2,202 c.p.s. with another pattern having two-nodes running

along the length of the blade, rather like that shown for 1,365 c.p.s.

In this Fig. 23, the flexural modes are shown as 0/0, 0/1, 0/2, etc., and the torsional modes are shown as 1/0, 1/1, 1/2, etc., and the true nodes with two nodes along the length of the blade would have been 2/0, 2/1, 2/2, etc.

It will be seen that the pure modes 2/1, 2/2, etc., do not appear, owing to the

closeness between their natural frequencies and those of the flexural modes

0/3 and 0/4. What does happen, in fact, is that as the exciting frequency is

increased, the modes for 2,155 c.p.s., 2,202 c.p.s. and 2,418 c.p.s., for example,

succeed each other very rapidly, and are sometimes difficult to maintain

separately.

This phenomenon had in fact been observed by the Author in carrying out the earlier tests on propellers such as propellers F to M, and it was mentiojed

that these modes, then designated as cross-modes and diaphragm-modes

respectively, were found to be the most noisy, and were also very likely modes

for exciting sustained vibrations.

There is evidence that such modes of

vibration have occurred in a number of cases of singing propellers (see p. 255 of earlier paper) and this would suggest that one possible cause of sensitivity

to singing would be the possibility of interference between what may be termed

the secondary lateral modes with two longitudinal nodes and the flexural

modes with several transverse nodes.. This is not inconsistent with previous

conclusions, in that it seems possible that apart from any hydrodynamic causes sensitivity to singing may be due to

Torsional-flexural coupling due to lack of mass-balance about a

central torsional axis.

interference between torsional and flexural modes, leading to mixed

patterns.

interference between ihe secondary lateral flexural modes, and the

ifexural modes with several transverse nodes.

-. . .: Conclusions

The work described in this paper shows that for the propeller tested the effect of water damping was to decrease the natural frequencies of both the

lower flexural and torsional modes very considerably, but that this effect

diminished for the higher modes of vibration. It also indicates that similar

patterns are produced in air and in water, but that the nodal lines are somewhat

closer to the shaft axis for the vibrations in air than for the corresponding

modes in water. Consideration of the work carried out by Mr. B. Grinstead,

in conjunction with the earlier work on full-size propellers, indicates that cross-modes and diaphragm modes may be present if the frequencies for the secondary lateral modes are similar in value to those for the natural flexural

modes. -

-Acknowledgments . .

-The Author is very greatly indebted to Mr. A. G. Boggis, B.Sc., (Eng.) and

Mr. W.Vasey of the Naval Architecture Department, King's College, for their very

painstaking and careful work in carrying out these underwater vibration

tests in very difficult conditions. He also wishes to thank the Manganese

Bronze and Brass Co., Ltd., for their considerable assistance in lending some

of the equipment for these tests to the Naval Architecture Department, and for

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Fig. 1Details of Propeller tested in Air and in Water DIAMETER

433ft.

PITCHvarying,

294ft;to 235ft.

PITCHmean

282ft.

SUPFACE 7 72sq. ft. BLADES 4 RH. & 4Lltt -1rr

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308 UNDERWATER PROPELLER VIBRATION TESTS

Fig. 3Fl in Water.

Frequency 161 cp.s.

Fig. 2Propeller and Vibrator in the Tank

I

---i

-\ ' I I \ -.-_.t-.-j..__L

--'\

\ I / _/

Fig. 4Fl in Air.

Frequency 230 c.p.s.

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Fig. 7F2 in Water.

Fig. 9fl in Water.

Frequency 490 c.p.a.

Fig. 8F2 In Air.

Fig. 1OT2 In Air.

Frequency 690 c.p.a.

U24DERWATER PROPFLLE VIBRATION TESIS 309

Fig. 5T1 in Water.

Fig. 6TI In Air.

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-Fig. i1F3 in Water.

Fig. I 3T3 in Air. Frequency 840 c_p.s.

1 not obtained in Water

Fig. 14F4 in Water.

Frequency 1,000 c.p.s.

Fig. 12F3 in Air.

Fig. 15F4 in Air.

Frequency 1,020 c.p.s. 310 UNDERWATER PROPELLER VIBEATION TESTS

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RR

fr

ti

800'-C)

Ha

I-400

-2OO.

0. I. 2. 3. 4. NUMBER OF NODES Fig. 1 8Flexural Vibrations in Air

UNDERWATER PROPELLER VIBP.ATION TESTS 311

Fig. 16Cross-Node in Water.

Fig. 17Cross-Node in- Air.

Frequency 1,060 c.p.s. Frequency 1,275 c.p.s.

1600

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---In 1600

--I: 1200 oö 3. PIUMBER OF NODES.

Fig. 1 9Flexural Vibrations in Ware,

1600 1400 1200 I0 eoo U-

[600

200 0

P

-0. 2. 3. NUMBER OF NODES

Fig. 20iorsional Vibrations in Air

2.

I.

0.

5.

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1600 .400 1200

bOO-

800 600 0 w IL 400 200

hE

600

_{1400 -}

ZOO

_b000-

800 U 6OO UI 400 200

-0. 2. 3. 4. S. 0. 2. 3. NUMBER OF NODES NUMBER OF NODES

Fig. 21Torsional Vibrations in Water

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314 UNDERWATER PROPELLER VIBRATION TESTh 249 i/o 415 1819 /2 2155 2J1.0/3 2202 0/3 2418 2/1-013 3o09 1/3 o/l 889 i/I 1135 c'2(+t) os 4000 3000

I2°0c

1000 2/i, 2/0(-0/2) 0 0 2 3 4-0/Ti:

NUMBER OF NODAL LINES

'n Fig. 23Flat Plate Model Test Results

-r;4

2fI21

W4

"22P.

!:pl5

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PROPELLER : BLADE VIBRATIONS

By W. L. HUGHES, BE., B$c., Associate Member

11th February,.1949

SYNoPSIS :The paper describs experiments carried. out on a series of model propeller blades in order to investigate, their behaviour when vibrated at different

freqzthncies by eleciro-magnetic methods. The experimental apparatus is described

Vibration patterns are given for excitation both in air and in water,, including specimen diagrams showing the amplitude of vibration at different points of the

blade surface. The various resoAant frequencies are plotted as curves to a base

of mean width ratio of blade

Damping of vibrations is discussed, and typical response curves are inclithed. Attention is drawn to the surprising effect on damping of the presence of small

air bubbles on the surface of the blade.

1. Broad Outline of Work

THE

tests to be described in this paper have been. carried out in

the Engineering Laboratory of the University of Oxford as part

of a programme of work for a research degree.

Previously

published investigations on the same subject

. have been performed,

in the main, on isolated propellers or blades bearing little relation to

each other, such work often being done in support of some particular

theory of the nature and causes of . "singing".

Coming to the subject

"with an entirely open mind, it was considered that it, would .be of value

to conduct a systematic series.of experiments on a set of related blades

in which one factor at a time was variedin this case. blade outline

and to follow the changes that occurred in resonant frequencies and

nodal patterns.

Thus, ultimately, it should be possible to plot charts

of resonant frequency for the type of bla4e under review, similar to'

those widely used in other aspects of propeller design. The aim was

not to discover (jious hope') the cause of "singmg", but to make some

contribution to the ever-growing fund of knowledge of the behaviour

of vibrating blades.

.

Two blades. have been used, of identical outline and section, one being flat

'and the other having a pitch ratio of unity. Side by side with the experimental

work, frequency calculations were perforthed, the results being checked by

experiment on the flat blade. Such calculations even for simple modes are

extremely tedious and laboriotis, and of, doubtful practical value, and the, Author is firmly convinced that the only practicable method of investigating'

vibratiOnal modes is by experiment. For systematic experiments it would.

appear that work on model scale is the best solution from the point of view

of cost and eguiprnent required. _{The full-scale 'patterns, are geometrically}

cimibr to thoseof model, while the frequencies are those of the model divided.

by the lineaz. scale ratio. In this work, models of single blades of a built-up

propeller have been used, results being obtained both in air and under water.

In addition to the customary nodal patterns, contours of amplitude of ''ibration have, also been plotted for a large. number of cases.

In so far as the, question of singing is concerned, this paper deals exclusively

with the so-called bell aspect under the artifical conditions of non-rotation

and still' watet.. The " clapper" aspect does not enter.

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274 PROPFT 'JR BLADE VIBRATIONS

2. Description of Apparatus

(A) Blades

Fig. I depicts the blades used.

They were cast an4 dressed by Messrs.

J. Stone and Sons, Deptford, to whom the Author and the department are

greatly indebted for the generous gift of the blades. They are of manganese

bronze, for which the density is 3O lb. /cu. in. and the modulus of elasticity

(E) l34 x 100 lb./sq. in.

It will be seen that the blade outline is symmetrical,

and it is in fact given by the equation x = A (y+b) (1 5y)r, which gives outlines

fairly representative of practical designs. Circular-backed sections and flat

driving face, with linear thickness taper to the tip, were adopted to simplify

the frequency calculations, as well as for ease in manufacture. For the pitched

blade, a regular series was formed by progressively cutting away the outer

parts of the blade and reshaping the sections, keeping the centre-line thickness unaltered.

Table 1 gives range of disc-area ratios covered by series: TABLE 1

Mounting

The blades were mounted horizontally on the side of heavy concrete block,

being drawn up hard by four in. bolts on to a mild-steel face plate cast into

the side of the block. As the heaviest blade weighed 40 lb. while the weight of the block was about 500 lb., it was considered that the blade thus mounted was fixed rigidly at the root. This was checked by the addition of several

50 lb. weights to the block, which caused no apparent alteration in either

resonant frequencies or nodal patterns.

For vibrating under water, the blade projected through the side of a tank, the centre-line of the blade being 6 in. below the surface and 14 in. above the

tank bottom, with a minimum clearance all round of 7 in. on the largest blade.

The tank itself was supported on wooden baulks, and was nowhere in contact with either block or blade, the joint between blade palm and tank side being

made watertight with Bostik. Excitation

Power for the excitation of the blade was supplied by a B.S.R. TypeL.O.

800A beat-frequency oscillator, with a frequency range of from 0-25,000 cycles. By further sub-division of the existing low-frequency scale it was easily possible

to read changes of frequency to one cycle per second. The instrument has a very slight frequency drift which is unimportant except in cases where the resonance peak is very sharp, and even here the difcuIty is easily overcome.

As singing seems rarely to have been experienced with a frequencyabove

300 cycles per second, in this work the upper limit was taken at 3,000 cycles per

second in air, i.e., 400 cycles per second on full scale with a scale ratio of 75

to I (corresponding with a built-up screw diameter of 20 ft. 6 in.) or 500 cycles

per second with 6 : I scale ratio (16 ft. 6 in. diameter screw). Even when these

frequencies are lowered by the presence of water, it is considered that they cover the modes most likely to be associated with singing in practice.

The output from the oscillator was used to actuate a small telephone earpiece

magnet which acted on a tiny piece of soft iron soldered on to the surface of

the blade. In the normal telephonic use of such a magnet its permanent field

is much stronger than that due to the exciting current, resultingin practically

pure sinoidal forces on the diaphragm. In the present application, however,

Blade .. A B C M.W.R. .. 42 29 2l D.A.R.

85

59 42 4 blades.. D.A.R ..

4

.44 32 3 blades..

(19)

PROPELLER BLADE VIBRATIONS ₂₇₅

the exciting currents were, abnormally large, leading to the introduction of

liarmonics in the force dnving the blade, and often producing vibration patterns whose frequencies were two, three or four times the frequency of the oscillator,

in many cases superposed upon a stroiiger mode Of the same frequency -as

the oscillator. _{This was considered by no means undesirable, as it is extremely}

unlikely that any disturbing factor in practice will be

purely sinoidal in

character.

(D) Detect iOn

-Several different pick ups were used each havmg features which rendered

it more suitable for certain applications.

Location Of nodes. For this purpose, the commercial ROthermeif

Brush VP5 piezo-electrjc type pick-up was employed.

_{This is an}

extremely sensitive acceleration-type instrument, ideal for the abOve

puriiose, but,, by virtue of its comparatively large mass (8 oz.),

unsuitable for the measurement of amplitudes on small-scale work.

Measurement of amplitudes. Two'" home-made" pick-up's

were

developed for this job, which demands that the added _{-tháSs due tO}

the pick-up be so small that its application to the surface ofthe blade

does not appreciably disturb the natura,l frequency of

vibration.

The first consisted simply of a telephone magnet, across the pole faces of

which was laid. a strip Of rubber to serve as a spring for the moving element. _{This latter was a thin flat piece of soft irOn to which was}

soldered a 2 _{in. length of stiff steel wire to act as a prod, the whole}

assembly being held together by tubber bands.

In this instrument the mass of the moving parts was less than 1 g. and it was found quite átisfactory fOr measuring amplitudes of vibration in air.

The second pick-up, which was much more sensitive, consisted _{of an}

ordinary telephone receiver with a prod attached normal to the surface

of the diaphragm. _{With the blade vibrating in air, it was found that}

the sound waves caused vibration of the diaphragm, giving_{false signals.}

However, with the blade immersed, most of the sound energy is

reflected-at the wreflected-ater surface, and this effect becomes negligible. _{This instrument}

was thus employed for amplitude measurements of vibrations in _water.

In this connexion it should be pointed out that the_{amplitude measurements.}

were in general taken with the blade vibrating a few cycles Off actual resonance.

When the damping is very low, the response curve is vety steep at resonance so that the addition of even a very small mass (i.e., pick-up), even though

altering the natural frequency by onlyone or two cycles; may cause an appreciable

diminution in amplitude. _{If, however, the readings are taken at}_{a few cycles}

off resonance, the response curve is much less steep and so the. effect of a small change in frequency is greatly reduced, thereby allowing consistent and reliable

readings to be obtained _{The pattern of vibration remains, of course practically}

identical with that which would be obtainedactually at resonance

Amplification

In all cases the output e.rn.f. from the pick-up was fed to a cathode-ray oscillograph, and its magnitude determined from the resulting pattern on the

screen _{When using the piezo-electric pick-up, a single tube was sufficient}

but with the less sensitive types another tube was used m series with the first

to provide greater amplification. _{Under these circumstances, with gains of}

'the order of 50,000, very careful screening of all leads was necessary, and in addition, a high-pass filter was employed at thd input to the second tube to reduce the 50-cycle hUm to a- ha±tuléss level.

Signals .

As m Burnil s previous work the oscillator voltage was applied to horizontal plates and .the pick-tip voltage tO the vertical platin Of the-oscillograph, giving

(20)

276 PROPELLER BLADE VIBRATIONS

the familiar elliptical trace when the frequencies of vibration and excitation

are the' same. The sign of the slope of the major axis changes as the pick-up

crosses a nodal line due to the 180 degree change of phase of motion; On the nodal line itself the trace should be a horizontal line, since the amplitude

of motion ought to be zero. 'More generally it is fotind to consist of a

horizontal effipse. The explanation lies in the fact that true nodes are only

possible in systems having no dampingin all practical systems some damping

exists, and under such conditions the nodal lines are replaced by lines of

minimum (but not zero) amplitude. By the same token, due to the phase shifts

between successive points along the body caused by the' presence of damping,

readings of amplitudes at different points do not give a true instantaneous picture of the shape of the vibrating blade, as the various maxima occur at

different instants of time.

The occurrence of resonance could generally be detected easily enough by' ear, but in all cases it was indicated by the rapid increase in the amplitude of oscillograph signal as resonance was approached. A knowledge of some of

the fundamental combinations of Lissajous figures with different phase

differences was of great advantage in discriminating between pure resonances and those in which. a fundamental mode was combined with or even obscured by a mode of higher frequency.

3. Experimental Results

Effect of Pitch on Frequency

The comparison of frequencies of flat and pitched blades has been made only for the widest Outline. The effect of pitch is considerable only at low frequencies, diminishing as the frequency is increased and the blade begins to

vibrate in the more intricate modes rather as a flat plate than as a twisted blade.

At such high frequencies the observed "pitched" frequency is generally one

oE two per cent. higher than that for the flat blade, but this is in all probability

due more to slight differences in thickness of the respective blades than to the

influence of pitch. At low frequencies the results are erratic and do not lend

- themselves to plotting, but Table 2 contains the data for some of the modes. TABLE 2

Frequencies in Cyc!es per Second

It will, be seen that the effect is most marked for the first torsional mOde, and comparatively small for the other types. The added mass due to water is practially the same for both flat and pitched blades, as is evident from the values iii columns 4 and 7.

Effeët. of Sharp Edge on Frequency

The edge of blade A was modified by filing off the radius frOm the back

to give a straight taper from a sharp edge to a line in. in from the edge all

round. It was found that this alteration raised the frequencies of all modes,

the difference being greatest at higher frequencies as shown in Fig. 2. In cases

where singing has been reported cured by a similar modification., it may well.

Vibration Mode In Air

In Water

.

-Flat Pitched Ratio Fith Pitched . Ratio

1st Flexural

..

152 165 108 120 128 l'07

1st Torsional

..

189 310

l64

125 200 160

Plate Type ..

..

344 395 115 240 280

l-i6

2nd Torsional

..

497 550'

1l0

360 395

ll0

3rd Torsional

..

755 805 107 570 605

l06

(21)

1'

PROPELLER BLADE' VIBRATIONS 277

be that the natuia1 frequency hàs been altered sufficiently -to remove it from

that of any synchronous disturbing force, quite apart from any -possible increase in hydrodynarnic damping.

Effect of immersion in Water-on Frequency ;

-When a vibrating blade is immersed in water its apparent mass increases

due to the inertia of water set in motion by the blade This causes a reduction

in frequency which is illustrated graphically in Fig. 3, where the corresponding

frequencies in air and water are plotted for blades A, AB B and C

By

"corresponding" frequencies of course is meant frequencies for which the nodal pattern on the blade surface is the same.

The reduction in frequency is practically independent of blade outline, ad, except for one or two cases, the plotted points cluster very closely about the

mean line drnwn through all of them. If we consider the blade at each- critical

frequency as a single degree of freedom system, the following relatioti holds:

Fróquency in air

₅

Equivalent mass + added mass due to water

Frequency in Water. Equivalent mass

₅

added mass

(I + fii- where 8

Equivalent mass

Hence fi Frequency in air -

-L Frequency m water j

The quantity fi is also p1otted -on Fig. 3, showing a marked decrease with

increasing frequency. This is in line with the fact that, as the blade surface

becomes divided up by more and more nodal lines, the virtual inertia of the

sUrrounding water is decreased due to the occurrence- of increased cross-flow

between adjacent areas which are moving out-of phase with each other. It

will be seen that a large change infl is necessary to produce a comparatively small change in the ratio of frequencies in air and- water.

The above generalizations are drawn from consideration of the mean line

as drawn on Fig. 3. Little is known regarding the pressure and velocity field

in- a medium surrounding such a complex system as a many-noded blade, and

it is not surprising that some scatter shows up in the points as plotted. The

effect of water on the frequency is no doubt closely connected with the actual vibration pattern, especially in the vicinity of the blade edge, where the

cross-flow referred to above will operate to an important degree. Thus, in individaal

cases, the actual reduction in frequency will depend upon the particular pattern,

and modes whose frequencies are widely spaced in air may fall much closer

together in water, and vice versa. Furthermore, some modes which occur

in' air are not excited under water, while others which are very weak in air

becomequite-strong in water. In view of these factors, it is considered desirable

that for results of practical interest vibrations should for the most part be

studied under water rather than iii air.

Blade Patterns

Figs. 4 to 8 show representative patterns obtained from each of the pitched

blades A, AB, B, BC and C. Blades A; B and C are as depicted in Fig. I,

while blade' AB has the outline of blade A on one side, and that-of blade B on the other, thus representing in some degree an unsymmetrical blade with

the pdints of maximum thickness of sections on a radial straight line. Similarly

blade BC is a cross between blades B and C. In the interests of space some of

the modes have been omitted from the figures, but all the strong and easily

excited modes are included. These diagrams only depict that part of the -blade

clear of the fillet at the root, which accounts for the fact that the blade width

apparently varies at the' base. In actual fact all the forms have the same width

(22)

From this Table it is evidefit that, assuming the presence ofharmonics in

a sustained exciting disturbance, the frequency of such disturbance may have

any of a very large iumber Of values and still be such as to be capable of

exciting a resonant oscillation in the blade. Admittedly. the amplitudes of

Exciting Frequency

c.p.s.

. Notes

68 Mode 13.6 excitedIst overtone

136 Fundamental flexure

213 Mode 425 excitedIst overtone

230 Mode 458 excitedI st overtone

305 . Mode 915 excited-2nd overtone.

360 Mode 1080 superposedonMode 425 370 Mode 740 superposed on MOde 425 425 Fundamental torsiOn: Very strong signal

458 Strong signal .

540 Mode 1080 excited

5 . Mode 1670 excited 725 Mode 1445 excited

740 "Dirty" signal. Contains sothe of Mode 2250

758 Mode 1520 excited "Dirty" signal

915 Very strong clear signal. Secondary torsion 1,080 Strong clear signal

1,125 Mode 2250 excited

1,445 Very strong signal. Diaphtagm mode 1,520 Strong signal. Some mixture qfMo.de 3020

1,670 Very strong

2,250 Very strong

2,320 Strong clear signal. Diaphragm mode 2,525 . Strong signal

30i 5 Intense ear-piercing whistle .

278 PROPELLER BLADE .vIBRArION5

In generl it will be Seen that the complexity of the nOdal pattern increase

-with frequency and -with blade width At high frequencies, especially in the

wider blades, the pattern is characterized by numerous "lobes" round the

blade edge, which sometimes coalesce to give completely enclosed" diaphragms" within the blade, surrounded by a flapping edge comparatively free from

inter-ruptions by nodal lines At the lower frequencies the modes of pure torsion

and pure flexure are easily distinguishable, but m the wider blades a third type

of flappmg motion occurs in which the leadmg and trailing edges move

in phase while the tip is 180 degrees out of phase with both

In the

un-symmetrical blades, the torsional axis follows approximately the geoxtietrical

centi-e line. . .,.

As previOusly mentioned, the.excitation of the blades was such as to produce.

frequencies ofvibration which are multiples of the exciting frequency. This means that as the exciting frequency is gradually raised resonances occur at much closer intervals than indicated by the diagrams, it may be of interest

to foll&.v through the complete series of resonances for one blade, say blade C,

when excited at the point P marked in Fig. 8. Table 3 is actually an extract

from the log coverin the first exploration of the vibrations of this bae un4er

water.

TABLE 3

(23)

PROELL5R BLADE VIBRATiONS 279

the oieftoñe mOdes ar generally smaller than those of the fundamental -modes, but their audible effect on the human ear is often much greater, since the lower

limit of audibility decreases rapidly as the frequency increases up to about

2000 cycles per second Considered in this light practically every propeller

should sing at some frequency or other if singing is due to the maintenance

of forced vibration by a sUstaitied exitãtiOh such as eddy-shedding. The

fact that thiS iS b nO means the ôãSe tendS to disëount the value of this theory.

The relative strengths of the various modes depend, of course, upon the

location of the excltmg point P. bemg greatest when P is near an antinode and

least when P is near the node of the mode under consideration Where P

is near an ant node of each of two modes, the frequency of one being almost a simple multiple. of the other1 the resultant mode consists of a combination of both modes, each of which can be traced by its own Lissajous figure in the

oscillograph signal. Such a case occurs above at 1,520 cycles per second,

where, at the nodes of mode 1,520 there is still some motion due to mode 3,015. The pure mode can generally be produced by exciting on a node of the

other mode, and all the patterns are plotted under conditions approximating

to this.

A "dirty" mode is one in which the nodal signal is not clear-cut, thus

indicating high damping, or one in which the signal shows the presence Of

harmonics.

The blade patterns have been numbered simply in ascending order of

frequency in air, e g Al A2

In general this gives ascending frequencies

under water, but in some cases, e.g., Cl and C2, the order is reversed, indicating

much greater added mass in the case of the primary torsional mode C2. The

patterns are mostly self-explanatory but attention may be directed to some

interesting features.

-In general the nodal lines in air and water correspond very closely. The complexity of the patterns at higher frequencies indicates the hopelessness of calculation as a method of investigation.

(iii) As a general rule the most noisy modes were torsional, e.g.,. A3, A4, A7, AB3, AB9, B3, BC3, C2, C3, but no comparative measure. ments of sound intensity were taken, judgment being purely, by ear. The sound field near the blade is very complicated and the intensity of noise from the blade varies as the ear is moved- from point to

point in the vicinity. The mpst distressing note of all was produced

by pattern Cl0.

(iv) SOme modes are shown which do.not correspond to the condition of

absolute fixity at the blade root, i.e., they do not have a node in

this vicinity. In practice, perfect rigidity Of the propeller boss can

never be attained, and so these modes are quite likely to appear.

v) Patterns 44 and A5 indicate two quite different patterns at practically

the same frequency in air, but here again the added mass for the

torsional mode is evidently greater, resulting in considerable separatioti

of the frequencies under water.

(vi) In some cases nodal lines under water appear as mirror images of

those in air as illustrated by pattern C2. The nodal line in this

case should obviously follow the blade centre-line:

the fact that

it does not mdicates thatinthis condition the blade is very sensitive

to asymmetry, no doubt due to small errorsin blade finish in one

case, and to small differences in added mass -of water in the other. With the simplr tyoes of vibration it is eay to trace a partiàulàr mode from blade to blade, but with the more complicated forms considerable judgment, with a touch of imagination, is necessary. -This is no doubt due to the fact that the difference in blade outline between successive blades is fairly great,

(24)

and the process would be easier had the reductions been carried.out in smaller

steps. However, his considered that a reliable comparison can, be, made, and

Figs. 9 to Ii indicate the method of arriving at the curves of Fig. 12, which

showsthe variation of frequency of a particular mode plotted against mean width

ratiO, for blades vibrating under waters Broadly speaking, the ppints lie

on regular curves, all showing an increase of frequency with decrease of blade width, ihe slope of the curves varying so that in two instances they cross. each

other. Some modes occur only in one or two of the blades and are shown

either as isolated points or as short curves. In general, however, it Will be

seen that 'the same types of vibration occur in all blades of the type under consideration, and that. their frequencies vary regularly from blade to blade. The critical frequencies are more widely spaced for the narrower blades, but here it must be remembered that only resonances of the same frequency as the exciting forces are plotted: if all resonances were included, as in Table 3,

the diagram would be much more congested. Amplitude Contours

Contours of amplitude were plotted.for a large number of modes, typical

results being shown in Fig. 13. Comparative measurements in air and in

water failed to reveal any measurable difference in distributioti, thus confirming that modes giving the same nodal pattern really are identical forms of vibration.

The figures given on the various diagrams of Fig. 13 bear no relation to the

relative, intensity of vibration between different frequencies. They merely

serve to give an approximate (see Section 2(F)) instantaneous picture of the

shape of the blade surface.

At. the time. of writing, the actual values of

amplitude have not, been determined, but it is hoped' to do this in the near

future. Indications are that the maximum amplitudes are only of the order

of a few thousandths of an inch, although they are quite appreciable to the

touch.

In determining these patterns, excitation and magnification were

simply adjusted to give approximately the same scale reading in each .case at the point of maximum amplitude.

The most interesting feature of all such diagrams is the fact that, as the

frequency of vibration increases, the movement of the blade becomes relatively

more and more confined to a narrow strip round the edge of the blade. At

a given frequency the effect of an element of blade area as a source of sound is

proportional to the square of the amplitude, so that it may be said that, in any but the simplest modes, practically all the sound energy comes from the

edges of the blade. Whether this fact is significant in.the matter of the

intro-duction of damping by sharpened blade edges remains as a subject for future

investigation.

Damping .

From many points of view the study of the damping associated with the various modes of vibration is perhaps the most important aspect of research in this subject. It seems inevitable, regardless of special precautions taken

in the design of blades, that the resulting form will have certain resonant

frequencies at which strong vibrations will be produced, given a suitable relation

between exciting forces and area of application to the blade.

Even so, if

the damping is high, objectionable vibration will be reduced, whether it occurs in the fOrm of an intermittently excited free vibration, or as a forced vibration

sustained by steady periodic exciting forces. In the first case,'the free vibrations

will be rapidly damped out, while in the second case the resonant amplitude will be greatly dmunished. Perversely. enough, it has proved particularly difficult

to obtain reliable comparative, measurements of damping under

different conditions, due to the large number of variable quantities involved, and the data here 'presented must 'be regarded as interim qualitative results rather than hard and fast measurements of damping. Even so it is considered thatthey may be of some interest.

(25)

P.

C

or

x + 2yx + o2x = sin pa', where 2y =

-k

Wa = -

_m

The resultant steady-state forced vibration is given by x = b sin (pt - 0)

Prn

where the amplitude I

- [(22)2 + 42)]

Thus b is a function both of p, the exciting frequency, and of y, the damping

term, and Fig. 14 shows the general form of the response curves for such a system.

If y is smallas it generally isthe maximum value of b occurs when

p = w, and is given by

i.e., the amplitude at resonance is inversely proportional to the damping

coefficient, which illustrates the value of high damping in preventing large

resonant vibrations.

Similarly, if the exciting- force suddenly ceases, the amplitude of free vibration

decays with time according to the equation

b = boeft

a decay which will be much more rapid the higher the value of y, i.e., of c. Defining the logarithmic decrement (8) of the decay as the logarithm of the ratio of the amplitudes of successive oscillations we have

8 =

where Jo natural frequency.

Now from the equation of the response curve it can be shown thai

8 iT

7=_j_

where

f = the frequency difference between the two points a

which the

amplitude is half the resonant amplitude at the natural frequency f. Thus 8,

and hence y and c, are directly proportional to the breadth at half height of the response curve, which value can therefore be used as a measure of the damping

associated with any particular form of vibration.

In directly extending this analysis to the case of a continuous system with an infinite number of degrees of freedom it is tacitly assumed that, in the vicinity of each resonance, the blade behaves as an equivalent single-mass system, and also that the associated damping is of viscous type, i.e., proportional to velocity. While not strictly correct, it is considered that these assumptions do not impair the value of the method.

With the ordinary form of underwater excitation, i.e., with the poles of the

magnet close to the soft iron strip on the blade surface, it was found impossible

to obtain consistent figures for B, the breadth at half height of the response curve. This was due to the fact that the thin layer of water between the faces

presented an acoustic impedance to the passage of sound waves through the

water, which impedance reacted upon the motion of the blade itself; the effect

varying both with amplitude of vibration and with the distance of the pole

PROPELLER BLADE VIBRATLONS 281

The method of approach v'as the study of the response curve (amplitude p.

frequency) in the neighbourhood of resonance. Considering a simple

single-mass system under the action of a sinoidal exciting force and in the presence of viscous damping, the equation of motion is

(26)

faces from the blade. This impedance had bcith resistance and reactance

components which were revealed respectively by changes in the shape of response

curve and in the resonant frequency. Similarly, the pick-up itself affected the

motion, due both to its added mass and to its inherent damping, in different

degrees according to its point of application on the blade surface. Theáe

difficulties were na1ly overcome by soldering to the blade two stiff wires

bearing, at the upper end thin plates of soft iron. whith projected clear of the

water surface. Oii was usedfor excitation; and the other for detection, each

in association with a. magnet. ha air, the acoustical impedance mentioned

above is negligible, and with this arrangement consistent results were obtained

on blade C.

Fig. 15 shows typical curves obtained in this way, the corresponding values

of

and 8 being given in the Table. Curves 2,4, 8 and 10 give reasonably

consistent values for 8 which are of the correct order when compared with published results for brasS, where the values range from practically zero up

to 005 depending upon the previous history of the metal. Curves X and 6,

however, give 8 values some ten times as great. A likely explanation is that modes X and 6 are of the type involving an antinode in the palm of the blade

which in turn demands some motion of the supporting concrete block. The

value of 8 for concrete is some thirty times that for brass, and under these conditions it is probable that most of the damping measured occurs in the

concrete itself. On the other hand, modes 2, 4, 8. and 10 cause negligible

vibration in the block, and so give a much lower value for 8 In this connexion

it should be mentioned that when very heavy damping was artificially introduced

in the form of rubber strips between the palm of the blade and the face plate on the block, the only modesof all those previously observedwhich appeared when the blade was vibrated in air were 2, 4, 8 and 10, indicating an almost

complete absence of motion at this surface. All other modes were suppressed

or weakened so much as to be barely noticeable, indicating much greater

sensitivity to conditions of end fixing. From this it would seeth that purely

"reactionless" modes will persist in practice independent of conditions of attachment of blade or bos, and thus may reasonably be expected to 6e of

major inportance from the point of view of singing. The similarity between

patterns 4, 8 and 10 and those found in actual singing propellers and illustrated

by Burrill in his paper ofMarch, 1946* will at once be apparent.

It should be noted that even in curves Xand 6 of Fig. 15 which are broadened

on account of higher damping, the frequency of an exciting force must lie between very narrow limits to cause vibrations of amplitude greater than half

the resonant value. The frequency range is fifteen cycles per second, becoming

only two or three cycles per second on full scale, which decreases the likelihood that sustained forced vibratiOn is the cause of singing.

The discussion so far has neglected two other obvious forms of energy dissipation, namely, the production of eddies round the vibrating blade edge and the radiation of energy through the surrounding medium in the form of

sound waves. Of the former it may-be said that its effect appears to be small,

although it may be accentuated by sharpening the blade edge and increasing

the athplitude of vibration above its present very small value. If time permits

it is hoped to extend the work along these lines. With regard to the latter, its

effect irigenoral will also be vety small, due to the fact that in all but the simplest

modes the blade is divided into many different areas, each vibrating out of phase with its neighbour m addition, considermg both sides of' the blade each of these areas is acting as a double source of sound, which means a much smaller radiation of energy than would be the case were one side only of the

blade in contact with water. However, it does appear that this form of damping

is of great importance under certain special conditions, which will be discussed in the following section

(27)

PROPELLER BLADE VIBRATIONS 283

(G) Effect of Air 'Bzthbles

The sensitivity of damping to small extraneous influences was demonstrated

by such crude tests as the slackenmg of bolts, the insertion of paper between the surfaces of palm and face plate and the addition of non ngidly attached mass at vanous pomts of the blade, all of which showed a marked increase

in damping. However, even with all conditions apparently identical, in the

early stage of the workconsistentrestilts ëöttldnOt be obtairiedfor the response

curves under water Ultimately this was found to be due to the presence of

minute bubbles of air which had come out of solution in the tp water as its temperature rose to that of the room and had attached themselves to the under

surface of the blade. This was proved by the dc-oxidation of the water with

sodium sulphite, whereupon consistent results were obtained over long periods

of running, with complete absence of bubble formation. In view of the fact that this phenomenon is a case where an apparently minute factor exercises

a large controlling effect, it was decided to investigate it further. Several

tests were run, in all of which the effect was qualitatively the same. The first

consisted merely of filling the tank with fresh tap water and plotting response

curves at half-hourly intervals. The initial value of 8 was P011, which increased

teadily to a value of 031 after two hours running, by which time about 10 per cent.. by area of the blade surface was coveted with tiny air bubbles, the

estimated diameter of these bubbles ranging from O1 mm. to 05 mm.

At the same:time the maximum signal obtainable at resonance fell from 40 mm. initially to 14 mm. at the end of the run, i.e., in the inverse ratio of the damping

coefficient.

In another test the blade B was artificially covered yith bubbles of somewhat

larger size, rangng from 05 mm. to 3 mm. in diameter, and covering about

40 per cent. of the blade surface on both sides. Table 4 shows the effect on

some of the modes of vibration.

TABLE 4

Mode Blade free. of Bubbles Blade covered with Bubbles Frequency c.p.s. 8 Fr'equency c.p.s. 6

B2 400 01'5

390.

067

B3 635. 0045 615

B4 932 0039 885

B5 1,045 0052 965 i23

As before, the maximum amplitude obtainable at resonance fell off roughly

in the inverse ratio of the damping and as was to be expected the nodal

pattern in all modes became much less definite, with considerable motion in

the "nodal " areas.

At frequencies higher than that of mode B5 it was

im-nossible to excite any recognizable resonance.

In passing it may be mentioned that any possibility of temperature effects coming in was ruled out by a ten-hour run with dc-aerated water of which the

temperature was raised by immersion heater from 17 degrees C. to 29 degrees C.. without any measurable effect on the value of 8.

The diminution in resonant frequency is greater than can be accounted for

merely by the increase m 8 and at present remains unexplained In the same

way, at the tithe of writing a satisfactory theory for the action of the bubbles

in causing such a tremendous increase in damping has not. been developed, but

it Is thought probable that the explanation hes m the fact that elementary

portions of the blade now tend to act as simple, instead of double, sources, with a very great attendant increase in the radiation of sound. energy in the

surrounding water.

As a rough illustration, a simple point source in an

infinite medium at a frequency of 1,000 cycles per second radiates about 1,6Q0

tithes as much energy as a double source of the sam&strength. Even though the. actual system bears little relation to this theoEetical consideration, .yet the illustration may serve to show the order of the quantities involved...

(28)

Regardless of theoretical justification, the definite existence of the above

fact -leads to at least one important conclusion. Namly, that it

is most

unhkely that singing will occur in a blade which is operating under cavltatmg

conditions especially if the cavitation is in the full-developed sheet form

m which the back of the blade is practically covered by a layer of air, or mpcture

of water vapour and air. This appears to be in line with general experience,

where severe cavitation often does occur wthout any trace of singing. Agaii,

it. is. very tempting to suggest that the presence or absence of such bubblçs in

blades in service may well have some bearing on the critical, or borderline,

aspect of singing. Thus two apparently identical blades may differ slightly

in smoothness of surface finish and in working conditions of wake, with the

result that in one slight cavitation is produced from which the other is entirely

free.. This is ratheran imaginative statement, and is conditional upon whether

the effect of air on damping is equally definite in the case otthe lower frequencies

associated with toll-scale propellers.

In this connexion it would be most

interesting to investigate the effect on full-scale blades, since from the results of the present experiments it is impossible to say whether the effect depends

on (a) frequency of. vibration or (b) complexity of blade pattern.

The effect of bubbles. moving across the surface of the bladeas would

occur in the practical case of cavitationwas checked by blowing air bubbles

from a rubber tube across the under surface of the blade. During their passage,

the amplitude was considerably decreased, rising again to its original value when

the last bubble had traversed the blade. It was not possible to obtain a damping

curve under these unsteady conditions, and so the reduction in amplitude may be due to (a) increased demping or (b) the variation in mass distribution of the

blade as affected by the varying location of the moving bubbles. This variation

would be such as to prevent the building up of a steady resonant vibration of

considerable amplitude.

In any case, whether the bubbles are stationary or moving relative to the

blade, the effect is qualitatively the same: the amplitude of vibration is greatly reduced.

4. Conclusion

In reviewing the results of the tests described herein, and in attempting to

deduce general principles therefrom, it must be borne in mind that the findings

are subject to several limitations. First, the work has been done on model

scale and, although the results for frequency, and vibration pattern may readily be translated to full scale, the values for damping and the effect of air bubbles

really require verification by full-scale work. Secondly, the experiments were

performed in still fresh water, with the blade stationary, conditions far different

from actual operation of a marine propeller. Thirdly, the results refer only to models of built-up screws under special conditions of fixing at the root. Fourthly,, the tests have been carried out on a particular form of blade, which

is apparently infrequently associated with trouble due to singing. Bearing

these points in mind, it is still thought that the publication of the results may

interest thoseçoncerned, with the operation of marine propellers, and they are' presented with this object in view.

There is a great temptation to venture to propound a theory for the occurrence

of singing propellers, but in view of the Author's complete lack of personal

experience, with such monsters it is considered wiser to refrain from so doing.

Purely on consideration of the results of this work,it would appear that :-Singing is not caused by' sustained forced vibration.

"Reactionless" diaphragm-type modes may well be the means of

causing objectionable noise.:

The critical nature of singing is perhaps connected with the formation of bubbles on the back of the blade under working conditions.

However, it may well be that the data presented here may assist others far more competent to develop a more closelyknit explanation of this baffling

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PROPELLER BLADE JBRATINS 285

BIBLIOGRAPHY

L. C. BURRILL. "Marine Propeller Blade Vibrations," N.E.C. Inst., Vol. 62 1946 W. J. DUNCAN. "Torsion and Torsional Oscillations of Blades," N.E.C. Inst.,

Vol. 54, 1938.

W. KERR, J. F. SHANNON and R. N. ARNOLD. "The Problems of the Singing

Propeller," last. Mech. E., VoJ. 144, 1940.

A. L. KIMBALL. "Vibration Problems," Jour. App. Mechs., March and September.

1941.

H. LAMB. "On the Vibrations of an Elastic Plate in Contact with Water," Froc,

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Fig. 1Model Blades

Two blades, one flat and the other with P.R. = 1.0 Blade thickness fraction = 045 Material = Mn. Bronze

Sections = Circular backed

0.10

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-uk--U U

PROPELLER BLADE WBRAT1ONS 287

2000 V a. U 7 III WOO bi 50 ii 40 Iii U. ₃₀ INCASB IN 20 REçUENCY. l0 0 1000 2000

FI4uRMcy WiT ROUNa -C.PS.

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3000

r

_ICC

288 PROPELLER BLADE VIBRATIO1

Bo

1- Bi..og C BI.AOE A AB B

c

A

4/'

/

OF

_.6

A, -1000 2000 3000 P'RQUSr1CY IN AIR -C.PS. Fig. 3Effect of Immersion

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AtO

ASS