Thrust and torque fluctuations for APA 249, TMB model 4414

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HYDROMECHANICS o AERODYNAMICS o STRUCTURAL MECHANICS o APPLI ED MATH EMATI Cs

THRUST AND TORQUE FLUCTUATIONS

FOR APA 249, TMB MODEL 4414

by

H.Y. '(eh

HYDROMECHANICS LABORATORY

RESEARCH AND DEVELOPMENT REPORT

1b. y.

Sche.psboui

Tcchnsche Hoesch

Dell I

!eME!T O! Th

(2)

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THRUST AND TORQUE FLUCTUATIONS FOR APA 249, TMB MODEL 4414

by

H.Y. Yeh

(4)

ABSTRACT

A velocity survey was conducted on Model 4414 to obtain data needed to

calculate the thrust and torque fluctuations due to nonuniform wake distribution over the propeller disk for the APA 249. Detailed calculating procedures are

given in ari .-\prendix

I N T R O DU CII ON

In connection with checking propeller shafting stresses the Bureau of Ships requested

that the David Taylor Model Basin calculate the thrust and torque fluctuations due to non-uniform wake distribution over the propeller disk for the APA 249 (converted MAllAD type

C4-S-la). The ship conditions for the calculation are given by Buships as 21-ft draft at even keel, with the propeller delivering 22,000 shp at 106 rpm for 22 knots ship speed.

Thrust and torque fluctuations, position of off-center thrust force, and horizontal and vertical bearing forces can be estimated by calculating quasi-steady-state propeller forces2.

(See Appendix A.) In order to obtain the proper wake distribution for this calculation, a

veloc-ity survey was conducted on TMB Model 4414 representing the C4-S-la type of ship. The

re-sults of the velocity survey are given in Figure 1. The thrust and torque of the propeller vary

with blade position due to nonuniformity of the inflow velocity; this can be shown in Figure 2

which gives the total thrust and torque at various blade positions. The locus of the center of application of the thrust force is given in Figure 3; the positive angle is measured from upward vertical in the direction of propeller rotation and in magnitude is in percentage of radius. The vertical and horizontal bearing forces from torque are shown in Figure 4. The positive signs denote direction upward and toward the starboard. Since the propeller used in this calculation

is a 4-bladed propeller (M.A. Plan No. 1-25-S44-0-1), the values of thrust and torque repeat themselves every 90 degrees (assuming all blades are made identically). Consequently, the results of the calculation have a period of 90 degrees and are plotted from upward vertical

to 90 degrees, where the angle is measured in the direction of the propeller rotation. The

re-sults compared very well with those for the T2 tanker as reported by Neifert and Robinson in their 1955 paper.3 The detailed calculating procedures _{are given in Appendix A and are based} on the method described in a paper by L. C. Burrill.2

ACKNOWLEDGMENTS

The author wishes to extend his thanks to Mr. W. B. Morgan for using his material for

Appendix A, and to Miss M. Cavanaugh and Miss N. Hubble for carrying _{out the detailed}

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RE FE FEN CES

Bureau of Ships ltr S43-1 (436) Ser 436-67 of 3 Apr 1959 to David Taylor Model Basin.

Burrill, L.C., "Calculation of Marine Propeller Performance Characteristics," Trans-actions North East Coast Institute of Engineers and Shipbuilders, Vol. 60 (1943-44).

Neifert, HJ. and Robinson, J.H., "Further Results from the Society's Investigation of Tailshaft Failures," Transactions of The Society of Naval Architects and Marine Engineers,

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APPENDIX A

CALCULATION OF THRUST AND TORQUE FLUCTUATION

ASSUMING QUASI-STEADY-STATE CONDITIONS

Each propeller bláde section rotating in uniform inflow, or circumferentially uniform

in-flow, operates as an airfoil which is subject to a uniform velocity composed of essentially two components: (a) the velocity V in the axial direction and (b) the tangential velocity xrnd.

irnd

The fact that there is a change in momentum of the water as it flows through the pro-peller results in a velocity change. This momentum change is due to the energy that must be transmitted to the water in order to obtain the desired thrust. The components of this velocity are known as axial induced velocity ua and tangential induced velocity _{u. The modifications} to the propeller section velocity V,. are shown in the sketch below.

Other corrections must be made to the velocities since the blade is three-dimensional and is influenced by the proximity of the other blades. These corrections are usually consid-ered as changes in the airfoil operating characteristics (lift and drag) for _{a given inflow}

ve loe ity.

When a propeller is rotating in a circuniferentially nonuniform velocity, such as at the

stern of a ship, there is a resultant fluctuation in Vr which affects the characteristics of a

blade section (lift and drag) and hence the thrust and torque of the propeller. The problem of

the characteristics of an airfoil subject to oscillating velocities is an extremely difficult one.

A reasonable approximation to the solution to this problem can be made, if the frequency of the oscillations is small, by assuming that the magnitude of the forces on the blade section are the same as if the blade were at steady-state conditions at each velocity encountered.

The change in the inflow velocities at the various blade positions is determined from the wake survey. (See Figure 1.) The velocity component_{W V is subtracted from tzrnd if} the tangential component of the wake is in the direction of rotation and added _{to xirnd if the} opposite is true.

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V (1 WL)

To calculate the quasi-steady-state thrust and torque fluctuation on a propeller, a num-ber of propeller sections are investigated at various blade positions. For each section the thrust and torque contribution is calculated, and for each position these contributions are in-tegrated to determine the total blade thrust or torque at that position. The calculations can be somewhat simplified by calculating the performance of the blade sections over range of

inflow angles and plotting the resulting section thrust and torque versus this angle. Since this relationship is linear, only four angles, covering the range of operation, need be calculated. The angle is then calculated for each position from the wake survey, and the section thrust and torque are read from the charts at the corresponding angle.

The method of determining the section characteristics used here is that of Burrill's, and TMB Form 600 is based on this method. The number of radii investigated depends on the distribution of the wake. For most surface ships 0.4 R, 0.7 R, and 0.95 R will suffice. For the unflow angle, tan Ji ₌ J / ITX, usually four values which cover the range determined by the

wake survey will suffice.

Following is a step-by-step procedure for making the calculations using Burrill's method of calculating propeller performance (TMB Form 600). The first problem is to determine the section geometric characteristics - camber, thickness, pitch, etc. (All figure and table

num-bers in this procedure refer to Reference 2.) - assumed (based on wake tests)

t/c

- maximum thickness of section - chord

- solidity = B . C / nctd where B = No. of blades and C = Chord

- from Figure 7

k' - from Figure 6

gao" from Figure 15

' _{1'gs -} from Figure 16

8. - actual angle of zero lift =

o h from Table 1

for round back sectionsa0

= - ()

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9. a, - angle between pitch line and nose-tail line

o

= (Kgao) (00th) 11.00

=O+0o0nt0g

01 = (0

-

ú) (0.52 - 0.2 x) first approximation Calculation of final a. ¡Ç - from Figure 3 C2 = (2) (57.3)/A's a Kgs

for round back sections C2 = (2) (57.3) /K5 . _{o. Kgs . KR}_/3

where KRB = i - 0.02

L' - from Figure 3 tan /3

16.a

₃

_{=0 (1L' )}

₂ a

tan 2

If estimate of a is correct, a should equal 03; if not, make second estimate where

17. a1(second estimate)= a + (03

-R + 03 When ₀₁ = 03 9 percent, proceed to calculate

18. (6'L)l _{= "gs .} K 2 0°f._mal/57.3

For round back sections CL = Kgs K 217 . 0°f KRB/57.3 (also see Figure 13)

5C =

_L _- h'_gs . C_D tan 13

CL

= (CL)l +CL

Calculation of CD

CLOPt = (12.7 48t/c) (max camber/chord)

CD min = 0.0056 + 0.01 t/c + 0.1 (t/c)2 + K2

A2 obtained from Figure 10.

For round back sections 6'D _min(GDI) is obtained from Figure 14

CD = h'3 (CL - CL opt2 K3 from Figure 11 or 12

=CD minCD

₀

For round back sections CD _{= CD + CL}

573

25. tan _{= CD /CL}

The rest of the calculations for the thrust and torque coefficients follow directly from

TMB Form 600. Once KQX and LT are calculated for different values of J for each section

they are plotted versus tan t''.

)

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of rotation.

With the value of tan mL' from the above table the KT and KQ for each value of tan çt,

is read from the previously plotted curves of and K0 versus tan fr.

The values of T and Q should be calculated next from KTX and KQX. In these cal-culations the change in the tangential component must be taken into consideration. The change can be considered as an equivalent rps (n').

n =

rrnda, ± VW

nt

_rrxdVIVE

With this equivalent n' TX and are then calculated from KT and KQ.

2 d4 K

= p(m') _Tx = p(n')2 d5 KQ

The values of T, and Q at each blade position O'are then plotted versus the propeller radius x. These plots give the thrust and torque grading curves for each blade position and the area under each curve must be integrated to obtain the thrust, torque, eccentricity of thrust, and the torque bearing forces. For each blade position, T and Q are read from the plots at

a number of X-values and integrated by Simpson's rule.

O' WL * Vt V(1WL) VW rrndx± tan ti'

_'Tx

KQX 150 3600 Ø0 I

*Qbtained from wake survey data.

!tQx KQX

constant

K_Tx

tan mir

The next step is to determine the of each section (radii) at each blade position (from wake survey). A table, one for each radius, of W and WL at each position is made and

tan çb = V (lWL) / irndx VW is calculated. The sign in the denominator is minus if the tangential component is in the direction of rotation and positive if opposite to the direction

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Tb _{= (1/'3) (0.1) (1/B)} _{[.f(T)1 = thrust per blade}

where B = No. of blades

XTb = (1/3) (0.1) (1/B) [f(XT)1 = moment of thrust per blade

The above table is repeated for Q to obtain Qb and XQb, the calculations again repeat-ed for each blade position.

The values of Tb and Qb are then plotted versus blade position O.. The total thrust T and torque Q on the propeller is equal to the summation of the thrust and torque on each blade at its particular blade position. The fluctuation of thrust and torque repeats itself every 360/B degrees so it is necessary to investigate only this number of degrees. Thus, for a 4-bladed propeller with one blade at O degree the total thrust on the propeller is obtained by adding Tb at 0, 90, 180, and 270 degrees.

The torque for the different positions of rotation follows in the same manner. The plot of T and Q versus O'gives the thrust and torque fluctuations that occur every 360/B degrees

of revolution of the propeller.

The eccentricity (center) of thrust is calculated next. This is divided into two parts: (1) the radius to the center of thrust force and (2) the location in degrees from the vertical. A plot of XTb (moment of thrust per bladepreviously calculated for each blade position) versus O' is made, and the horizontal and vertical moments of the thrust _{(41Th and MTV) of the} propeller calculated over a range of blade positions from O to 360/B degrees.

X T XT S.41.

f(T)

f(XT) 0.2 0.3 1 4 I 2 4 - -I 2 4 I 10

[(T)

f(XT)

0' 00 100 _(360/B)° Tbl Tb2 Tb_Z ota1

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270°

= (XT

coS[0+

z=B r

MTV = (XTb)B Slfl [0' +

(XTb)B = XTb at O = 0' +

O' is Q (angle of rotation) of first blade.

The above calculation is made for each blade and their sum obtained for each value

of Q'.

From the horizontal and vertical moment of thrust, the radius of thrust eccentricity and

angular position are obtained.

0° 180° z=B (z-1) 3600] (2-1)360°] (z-1) 360° B MT = J(4ITv)2 + (MTh)2 MT

Final plots are then made of the eccentricity and the angle of eccentricity.

The vertical and horizontal bearing forces are calculated in similar manner. The torque

per blade Qb and XQb have been calculated for various blade positions, and the tangential

force per blade from torque P

(0') is given by

0' (XTb)B (z-1) 360 Q'+ cos 01+ (z-1) 3601 sin

r

_(z-1)3601

0+

Th MT.. B B L B J 0° 100

0

o

0'

MTL, MTh MT T Eccentricity MT,,

-

MTh 0° 10°

()°

B T Eqcentricity = M_Tv

Angle of eccentricity °e = arctan

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A plot is made of (O') versus 0', and using this plot the horizontal bearing force and the vertical bearing force Vb are calculated from

z=B Hb = _ZB

[

(Z-1)360]

+ B value. Vb z=B ZB ZB =

at 0= O'+

(Z-1) 360 B

This calculation is repeated for each blade (1 to Z) and the sum obtained for each O' Final plots of and Vb are then made.

2 Qb

(0') =- x

x Qb d XQb

[

(Z_1)360]

B

'

Qb XQb (Qb)2

()(xQb

(0') 00 300

i

3600

'

Í"ZB (Z-1) 360

0+

cos(T7'\ sinÇ Hb Vb B 00 100

I®

X X /360'°

B)

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NOT! LENGTH (tUL) BEAM ORANT OISPLACEREGT (5.W.) TRIM SPEED t'AS! 0F TERT

Figure 1 - Velocity Survey for APA 249, Model 4414

523.3 TEIS 76.0 FEET 21.0 FEET 14,140.0 TONS ZERO 22.0 KNOTS 21 APRIL 1959

THE VELOCITY MEASUREMENTS WERE MADE IN A PLANE WHICH IS

PERPENDICULAR TO THE LONCITUOINAL AXIS AND 4.0 YT FORWARD

0F STATION 20. V IS THE SHIP SPEED.

V,, IS THE NORMAL COMPOSENT 0F VELOCITY IN THE PLANE 0? THE SURVEY ARI) IS P051TTYR IN THE ASTERN TIRRITION.

Vr IS TSE RADIAL COMPONENT OF VELOCITY IN TOI! PUNE 0F THE SURVEY AND IS POSITIVE TOWARD THE ShAFT CENTERLINE. IS TER TANOEBTIAL COMPOSENT 0F THE VELOCITY IN THE PLISE TV THE SDRVES AND IS POSITIVE IN TN! COUNTERCLOCKWISE DIRTIOM. Ntr IS THE VETTOR SUOI OF THE Vt AND Vr, THE ONOTO?. SHOWN IS

55, Vr, V AND 5tr ARE RELATIVE TO THE SHIP.

TABLE OP COMPONENT RATIOS POSITION NUMBER V,,!? _5/0 _5r'M 1 36 0 -.02 2 37 0 .06 3 30 0 .13 4 58 -.11 -.01 5 49 -.07 .01 6 34 -.01 .09 7 60 -.13 -.02 8 59 -.11 -.01 9 39 -.04 .06 10 67 -.14 -.04 11 69 -.14 -.01 12 47 -.06 .05 13 80 -.15 -.01 14 79 -.16 -.01 15 55 -.09 .05 16 88 -.14 .02 17 86 -.16 .01 18 64 -.10 .06 19 91 -.11 .11 20 90 -.13 -.04 21 70 -.11 .08 22 92 -.10 06 23 91 -.11 .06 24 76 -.10 .10 25 91 -.08 .0 26 90 -.09 .0 27 76 -.07 .12 28 91 -.06 .08 29 90 -.07 -.09 30 71 -.02 .14 31 91 -.04 .08 32 91 -.05 .09 33 61 .04 .11 34 89 -.01 .09 35 91 .01 .1.3 36 42 .04 .05 37 85 0 -.02 38 47 O .03 39 32 O .01

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(17)

CALCULATION OF THRUST, TORQUE, EFFICIENCY

PRNC-TNB-600

r (Tan .' - Tan ') Tan ( + y)

(

I(,)(.'i3)

i + Tan Tan (. + V) g

+ ('7/)(i3)

(i - a') =

.?/ 9/

= C3

(i -

a')° (i + Tan2) CL Sin ( + V)

Coo V = 'TX '7 21,, X I Tan (4, + V) =

(.7sV)(13!)

2 _{(,7.4a.t-)(.oz../3)} SAMPLE CALCULATION = 13/ (.LIJ(. '813)

,erof,j/ SeD0

X =

-(1,)

= =

)( 97)

= 3,i/L/ nd*VJ,, n =

at

= i. o3 V4 (i.W)/nt V0.W = _{Tan 8 =} _P/3,rr

. 7J3

= 3'? ôo = = _9'3S + o ₊ _iit

'.

17 R R

(7X37')

a = 'go R ea =

,,

2

()(573)

- JX/' Tan 4, -= H.

5o(.

CL ott. =

#90a1

_.7.9!

CL = 73 CL CL opt. R

-;r

E = 4' + $ '13 . _q3,.cC CD HIS =

'D (cXó.i'.7

Sin 4' _{CD =} . Tan ß 1)3 /I Tan V = ' =

= C2 0Sin 4' Tan $ _{Cou V =}

,,ç

4' + = Tan 4,

7J

Tan (4' + 7) = _g/3 Sin (4' + Y) = 1+ . 7 - 7 _,73 x4 Tanß 8 (i-Ii) _Tan , 02 03

CL = (43a)(.î3X

_32(.)/('573)

. 73o = 733 S C )(. //o)(.3(ooZ1) = ,oc o CL

= .738

77 Tan

= 738

Tan (4, + V)

(18)

CALCULATION OF THRUST, TORQUE, EFFICIENCY PRNC-TIIB-600

a =

'TX

(Tan <b - Tan <b) Tan (<b + Y)

i + Tan <b Tan (<b + Y) 2K X X Tan (<b + Y) 7, JX 'TX -

(gto) C. '17/)

2io K,

¡99O

(.7) (.ys.)

(,17S)(V.?)

/ L

(i -a) =

_q3cr SAMPLE CALCULATIO4 7 = Tan (<b + Y) Va (i-WL) 0 = =

ndtyw

= = = Va (1-WL)/ndtva.W.,. _S.Sb Tan 9 = P/2',rr 8 ₌ 0 = 8 + +

at

= z = _Ua0

-a

= (.J32_)(,qs) = 32-= 95/7 = 7412.. 6 = C2 = Tan <b = X/ = . <b = -=

8-

<b = al _ÇOO CL o't. = <b = 8, -. o CL ₌

,3q

- i(.. CL -CL ø$'t. = ,ö73 3o.3

3,OO

C» Wfl = / ,7.5

AC» = (oe)(. ô7)

Sin <b 3/ C» =

Tan ß _içi _{Tan Y =} Y ₌

= C2 K Sin <b Tan ß 3.941

l,38' Cos Y = <b + Y =

Tan <b

1o' ¿J Tan (<b + Y) = '- Sin (<b + Y) =

¡4, .<97 _. _ir3 _z Tan ß cte / C3 = = 8 (i-14,) Tan <b C2 =3 _3.&o CL

= (7V)(9V7)(.)(V2c2)/(573

8 CL = (±)/.cI)(7 X0Q7/) = CL =

= C3 (1 - a)2 (1 + Tan2<b) CL Sin (<b + Y)

Cor Y = _(5v)Cr7//.

/S)C3)C4h/2)/(,9)

₌

..7ys_

Tan = =

Aroo,/

5ecM 8= -. öC<V (1 - a') = 17/s

(19)

CALCULAflON OF THRUST, TORQUE, EFFICIENCY _{SAMPLE CALCULATION}

PRMCTNBßOO

(Tin 4 - Tin 4,) Tan (4, + ")

(I7)(377)

a

- i + Tin 4' Tin (4 f V) - / ,' C 32.7)( i7)

(1 - a') = _.9579 'TX = 2I X I Tin(4, + y)

_{(.,sX 377)}

(5?7) (2H)

(.2.?.3)(. 4r/7)

= .53/

(1 - a')2 = =

d - Eak Sea'in

Tin 4,

=53,

Tan (4, + 'a = = = /. Vc a _ant = = 'a (1.wi)/na±y&. Tan 9 n /21rr = =

/? 7/

= _{8 + a0 + ant}

//

= . -An g = = = = ₈ ₌

,,

=

()(.c7.3)

.177.7 Tin Si _- /orI = 4 n

_//

_/

a = 8. - Si n . a1 _.o3 _{CL opt.} - a _CL i = 4, - 4, 5' 77 CL - CL 0*t. = 4, + 8 , ,ç CD tin = Wo

,S

. Sin 4, so?e»-C2.o(.tov D3),/c7,D Tin ß

_/03

Tan V = y = a2 C2 I,Sin 4, Tin ß ;&.a./ Co. V = 4, + V n

oV

Tan 4, _{Tin (4, + y) a} , 377 Sin (4, + V) =

I,

'ii?' Tinß 4'?' C3= ₌ 8 a2 a3 _L

-

(øo5s,)(/o/(o)

a (w)C.9) - ,.

_+o CL = ₍ _qy)(

32.ôW)(4$ß)/s7. a)

8CL = CL = C3(1 - a.)2 (1 + Tsn24,) CL Sin (4, + V) Coi Y =

= .oS/7

77 JX 1TX 2ir Iç X

(20)

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