1. Introduction
In designing a marine propeller, there are two important aspects to be considered: i.e., the hydrodynamic aspects, including efficiency, propeller excitation, cavitation erosion
and propeller rpm matching; and the strength aspect caused by
hydrodynamic and centrifugal forces on propeller blades.
Since the latter, i.e., the strength of the propeller blade, is fatal to the reliable operation of ships, great efforts have been made
to establish a standard method to ensure the strength of propellers. For this reason classification societies have been involved in this matter".
A marine propeller operates in the wake of a ship's hull. Since the wake is not uniform, the propeller blade load varies during each revolution of the propeller. This dynamic blade load causes periodical changes in blade stress during each revolution of the propeller. The strength of the propeller is
determined by the geometry of the blade, the level of dynamic
blade load and the mechanical properties of the material. Strength design of propeller blades has been based mainly on the mean blade estimated from the engine output
characteris-tics. The effect of dynamic load has only been taken into
account as the empirical safety factor of the design stress of the material. The corrosion fatigue strength of the material,
such as Nickel aluminum bronze (NiAlBz), is considered to be the basis for design stress by all classification societies(2)-(6),
since a propeller operates in corrosive sea water under
periodically varying loads.
After high speed single screw container ships were put into service in the late 1960's some cases of propeller blade fracture
due to fatigue were reported in the early 1970's(7)-1". Even
though certain casting defects or thermal residual stress at spots repaired by welding are responsible for the initiation of fatigue fractures, it was concluded that dynamic load on propeller blades was closely related to the fatigue fracture of the blades. Thus the estimation of dynamic blade stress has been recognized as being important in the course of propeller
design.
In order to understand the actual conditions of the blade
stress of a propeller, full-scale measurements were carried out
on the container ship "HAKONE MARU" during service.
This was done as part of a research project of the Shipbuilding
Research Association of Japan". The most difficult problem
in conducting full-scale measurements of propeller blade stress
Nagasaki Research & Development Center, Technical Headquarters
Dynamic Blade Stress on Marine Propellers Operating in Wake of Ship's Hull
Takao Sasajima*
In order to achieve reliable ship operation, it is indispensable to check the dynamic strength of propeller blades in the early design
stages. For this purpose, a modified quasi-steady approach was proposed for conventional propellers. This approach includes the
introduction of an averaged wake with weight function along the chord, contraction effect on the wake and a modification of
Kito-Izubuchi's beam theoly.
Comparison with full-scale data, obtained previously during a voyage of the container ship 'HAKONE MARU", showed
agreement with the results of the above approach. Also, the study was extended to cover Problems with the strength of highly skewed
propellers, which have recently become widely used to reduce propeller induced excitation forces. Due to the complexity of their
geometry, highly skewed propellers require careful strength design. By applying a propeller lifting surface program and the finite
element method, criteria were proposed for selecting skew. These criteria were shown to be useful by the blade stress measurements
of a skewed propeller series in non-uniform flow and also in transient conditions.
was to protect the strain gauges and lead wires against
corrosive sea water and hydrodynamic forces acting on the protruding parts of the strain gauges. This was solved by applying a new method and full-scale data were obtained successfully on the propeller mounted on the container ship.By referring to these full-scale data, a simple and useful
method of estimating dynamic blade stress was proposed. This
method comprised the beam theory, a modified quasi-steady approach to estimating propeller load and the estimation of wake distribution. Even though recent high speed computers enable us to use the unsteady propeller lifting surface theory and finite element method, the method proposed for
conven-tional propellers is a useful tool in the early stages of propeller design.
On the other hand, in the late 1970's vibration problems in ships became one of the most serious concern due to the strong
demands of ship owners to make ships comfortable in their
accommodation of crews("). There are two ship excitation
sources related to the propeller, i.e., shaft force and surface force. Shaft force consists of 6 elements of fluctuating forces and moments, caused by dynamic blade load, which are transmitted to the ship's hull through the stern tube bearing.
The surface force acts on the ship's hull at the stern as pressure
fluctuations induced by the unsteady cavitation of the
propel-ler. Both forces are related directly to the geometry of the propeller, the loading of the propeller and the wake of the ship's hull. In the early 1970's, the idea of highly skewed propellers was introduced to reduce shaft force("). Judging from the interaction process involving a skewed propeller and
the wake of ship's hull, it is reasonable to believe that highly
skewed propellers are also effective in reducing surface force. However, in designing highly skewed propellers,
consider-ation of
strength becomes most important due to
its`boorneran'-type geometry. Not only bending, but also
tor-sional, moment ad on the blade, and blade stress distribution on the propeller blade becomes quite complicated. Thus, the
simple beam theory cannot be applied and a more sophisticated
blade stress calculation method is needed.
In such circumstances, a series of skewed propellers for a
full ship was experimentally examined by measuring dynamic
blade stress in the wake in a cavitation tunnel and in transient
conditions in a towing tank. On the basis of the results, criteria
blade strength were proposed. Then, based on these criteria, survey design was conducted using the lifting surface theory
and finite element method, and practical guidance in selecting
the skew angle of highly skewed propellers was proposed. As an example of the application of this method, a highly skewed propeller was designed for a container ship. Model
tests were conducted in a simulated wake in a cavitation tunnel. The results were discussed focussing on the fatigue strength of the material and it was shown that the criteria and
guidance were useful.
In this paper, two kinds of topic relating to blade strength are discussed. In Chapter 2, a method of estimating the
dynamic blade stress of conventional propellers is discussed in
reference to full-scale measurement data. In Chapter 3, the strength design criteria for highly skewed propellers and a practical guidance in selecting skew angle are both proposed on the basis of ex-periments and design studies. Finally, the conclusions obtained from these studies are summarized and
proposals are made for the scope of future works which should be conducted.
2. Estimation of dynamic blade stress on conventional
propellers2.1 Introduction
In order to estimate the dynamic blade stress on a
full-scale propeller operating in the wake of a ship's hull, there
are three steps to be considered. These are:
estimation of the ship's wake
estimation of the dynamic blade load of a propeller
operating in the ship's wakeestimation of the blade stress on a propeller
The flow chart for dynamic blade stress estimation is summa-rized in Fig. 1.
(1) Estimation of ship's wake
The first step is to estimate non-uniform velocity or wake distribution in the propeller plane. Due to the spatial non-uniformity of axial and tangential velocities caused by the separation of the boundary layers on a ship's hull, the angle of attack of the relative flow to the propeller blade section changes during each revolution of the blade, which
induces unsteady pressure distribution and thus, force on the
blade. This unsteady force or spatially changing load to the blade is called dynamic blade load.
Usually, nominal wake distribution in the propeller plane of the model of a ship is measured using a 5-hole or 8-hole Pitot tube') and recently using an LDV system in a towing
Wile's). If we consider the large difference between the
Reynolds number reached in model tests (-107 range) and that reached in full-scale conditions (-109 range), it can easily be expected that correction is to be introduced to the result of model tests.
Sasajima et al."6) were the first to introduce the method of
estimating the wake distribution of a ship from model test results, taking into account the difference in boundary layer thickness and frictional resistance. This method, with those used by Hoekstrau7) and Dyne", is called extrapolation-type and used today, since direct calculation of the wake field using the viscous flow theory is still beyond our
I-Propellercharts Principal specifi-cations of ship IOpen -wa er characte istics Averaged wake distribution Design conditions ship's hull. propeller
Quasi -steady calculation of torque, Thrust fluctuations of one btade
Radial load distribution
Blade stress calculation
Fig. 1 Flow chart of dynamic blade stress estimation
I
means"9) . In this paper, Sasajima's method was simplified
so that it could easily be used in the early stages of propeller
design"(20.
Estimation of dynamic blade load
In estimating dynamic blade load, there are three methods, the quasi-steady method, the unsteady lifting line theory
and the unsteady lifting surface theory. The quasi-steady
method, which was first introduced by Lewis(77) in the field of ship hydrodynamics, was extended by MaCarthy(73) in 1961
to estimating thrust and torque changes of propellers in a
wake. The advantage of this method is simple and still gives good approximation if the unsteadiness is not so great. Even
though a more rigorous unsteady lifting line theory(24) and unsteady lifting surface theories(")-("), are available nowa-days, this method is still useful for checking propellers in their early design stages, since detailed data are not always available in the early stage of propeller design and high speed computer calculation requires a lot of time. That is why, in this paper, modification of the quasi-steady method
was proposed.
Estimation of blade stress
Blade stress calculation methods have changed from the beam theory(") to the shell theory(3)(32) and to the finite
element method (FEM)(33)(34). This movement is closely
related to changes in the type of marine propellers being used. For conventional propellers, the beam theory gave a
good estimation of the blade stress around the root, but with
the increase in the area of propeller blades doubt arose as to
whether the propeller blade could be represented by a simple cantilever. So attempts were made to represent the propeller
blade as part of a shell. These attempts, however, were not
so successful(32) and the FEM, which was developed and used
for structural analysis, was introduced into blade stress
Principal specifi -cations tf prOpeller iWake data I I Model wake I distribution Ship's wake I distribution t't Effective wake distribution IWeighted average wake distribution
Table 1 Principal dimensions of the "HAKONE MARU" and its propeller
calculation with a computer code. The FEM is indispensable
to designing highly skewed propellers, but for conventional propellers, the beam theory is still useful if the load
distribution in a radial direction is properly used(35)(36). In
this context, Kito-Izubuchi's method") was modified.
In this chapter, full-scale measurements of blade stress on
a propeller are discussed first, because
this study was
motivated by the occurrence of blade fractures in the early 1970's. It was thought that it was important to understand the blade stress level of a high speed container ship in service. Full-scale measurements of blade stress on propellers are notnecessarily new. In 1959, the 30th Committee of the Japan
Shipbuilding Research Association conducted full-scale mea-surements of blade stress on a propeller mounted on a small training ship("), but the data were limited due to the shortage of measuring techniques and instruments. Also, Wereldsmes) conducted full-scale measurements of blade stress on a
propeller mounted on a 42 000 DWT tanker in 1964 and in the early 1970's in view of the same kinds of blade fracture trouble
experienced by high-speed ships. Full-scale measurements were also conducted in the U.S.A.19' and in West
Germany (7)(8)(10).
Based on these full-scale data, a simple but useful method
of estimating dynamic blade stress was discussed. For this
purpose an averaged wake along the chord was introduced into
quasi-steady calculation, and the simplified wake estimation
method and beam theory were used(")(") as mentioned before.
For further improvement, an averaged wake along the chord with weight function and the introduction of effective wake was discussed")(").
2.2 Full-scale measurements of blade stress on marine propeller
2.2.1 Methods of measurement
Full-scale measurements of blade stress were conducted using the container ship "HAKONE MARU"(2°)(21). The principal dimensions of the ship and the propeller are shown in Table 1.
The arrangement of 28 strain gauges (9 three-component
strain gauges and 1 single strain gauge) on the face side of the
propeller blade are shown in Fig. 2. The points of measure-ment were so chosen to avoid cavitation from the gauge and lead-wire coatings based on cavitation tests on a model propeller. The radial components of gauges No.1 through No. 5 were fixed along the tangent to the maximum thickness line of the blade, while those of the other gauges were fixed in a radial direction. 0.9 R 1.0 R 0.7 R 0.50 Trailing edge 0.3R Generating line Line of maximum thickness Leading edge Strain gauge R marks
Fig. 2 Arrangement of strain gauges on blade
Fig. 3 Strain gauges and coating after completion
The strain gauges and lead-wires were protected against sea water corrosion by a double coating method, which was
newly developed through experiments in high-speed cavitation tunnel and in preliminary full-scale application.Fig. 3 shows a
photograph of the blade treated in the above manner. All the data measured by the strain gauges were recorded on two paper-oscillographs and data recorders for later detailed analysis, together with data specifying the measuring
conditions.
2.2.2 Full-scale measurements
Measurements were conducted during the 39th voyage of the "HAKONE MARU" in August, 1972, between Kobe and the west coast of the U.S.A.
The insulation resistance and zero point of the strain gauges were checked whenever possible. The insulation resistance of the strain gauges became almost constant at
about 400 KS2 after gradual fall in 10 days' submergence of the
propeller, shortly before departure from the port of Tokyo for Los Angeles. Fluctuations in blade strain were measured with sufficient accuracy, though the drift of zero point was inevi-table to some extent.
Sea conditions were generally calm on the voyage and a
lot of data on the fluctuations in blade strain due to a
non-uniform wake were obtained. On the day before arrival in
Tokyo, the sea became quite rough and valuable data on the fluctuations in blade strain due to the ship's motion were
obtained. Furthermore, turning tests with 4 rudder angles
Hull Propeller L(m) 175.00 D(m) 6.700 Direc. Right a.u.D(m) 26.00 P(m) 6.700 P/D 1.000 dm.(m) 9.50 A.,(m') 35.257 A p/ A. 0.834 (ton) 24 810 A,(mz) A(m2) d(m) 23.000 19.200 1.280 21./A, APIA., d/D 0.652 0.545 0.191 Engine
Type MAN K101 93/107E Power Rev. (MCR) 27 800BHP (MCR) 115rpm Rake(deg.) 5 8.0 t/c) 0., Material 0.051 NiAlBz Sec.
Torque Thrust
Synchronous mark Gauge mark : IOR
IT IS
IR
Propeller top mark
Rolling Acceleration
Propeller top mark
Rudder angle0 L revolution
a.
0 8 00 0 4411114t PitchingSea -water level detector
Gauge mark : 4R
Gauge mark :IR
CM. Al
o Sea trial Kobe -Nagoya o Tokyo -Los Angeles
°max QA ° 0,1 A 0 O41=1 0 A 1 revolution a caN2 0 0 A
Z.
t
at..r
1.'6 A da419
...,/ aI
-7,#
reA,/;I
aYr.:
i
a A 1 ATorsional vibration of propeller shaft II
7
2 od mode/141h order1st mode/4th order
601 80 - 100
N (rpm)
Fig. 5 Changes in blade stress during revolution of propeller(1R)
0
120
were performed to examine the effect of oblique flow on blade
strain.
Typical examples of the measured data are shown in Fig. 4. By multiplying the Young's modulus of the blade material,
i.e., E = 1.25 x 104 kg/mm2, the .measured strain is transformed
into stress.
2.2.3 Results and discussion
From the data obtained from routine measurements,
changes in maximum blade stress am. and double amplitude of
blade stress ZIG,- at propeller shaft speed N were plotted first and are shown in Fig. 5.
From these results, it was shown that if we consider a higher propeller shaft speed range, say N>80rpm in view of the accuracy of the data, the relation between cr and N can be
expressed as follows:
'---111. Fig. 4 Typical data reproduced
from data recorder
0.2 0.4 0,6 0.8 1.0
r/ R
Fig. 6 Radial distribution of blade stress
cr cc N2 (1)
This tendency is reasonable, since usually thrust T is roughly proportional to N and thus
a « T CC Kr leas CC NO (2)
and blade stress due to centrifugal force is
0. oc w . 632 cc N2
(3)
Thus, we can generally assume
a oc N2 (4)
Fig. 6 shows the radial components of blade stress measured along the maximum thickness line compared with those calculated using the beam theory. Both the time-mean value a and fluctuations in blade stress Zia have the same tendency in a radial direction, and the time mean blade stress calculated using the beam theory is a little lower than that
measured.
The radial components of blade stress at blade section 0.3 R are shown in Fig. 7. The maximum stress occurred between
the maximum thickness point and the mid-chord point, and this
agrees with the results of examinations on the fractured section of the propeller blades") and the results of other
full-scale rneasurements"°).
Fig.'8 shows an example of the fluctuations in principal blade stress around the maximum thickness point of 0.3R
Tokyo -Los Angeles 64%, D.W. Load N=11Orpm 0 0 8 6 4 2
10
5
8R 7R 1R.IS.IT 6R Gauge mark 0.215 0.43 0.65 0.825 1.0 x/cFig. 7.Chordwise distribution of blade stress 0 41-Kobe -Nagoya , c/R= 0.3 . N= 107 rpm 0 Gauge 1 Gauge 7 Face Back L E. 90 180 270 360 8 ( deg.)
Fig. 8 Change in blade stress during one revolution of propeller
during one revolution of the propeller. The blade stress measured shows a high peak value at =0° (12 o'clock position) and not so distinct peak value at 0=180° (6 o'clock position). From this figure, the mean value of principal blade stress at 0.3R was read as 5.7 kg/mnf
Turning tests were conducted after departure from Tokyo with four rudder angles. Blade stress patterns in steady turn with a rudder angle of 30° to port and 30° to starboard are shown in Fig. 9, in comparison with those of straight run measured a few minutes before the turning tests. The
following features are to be noted:
(1) The maximum stress an,ux and the double amplitude of fluctuations in blade stress ZI a decreased in comparison
"L
Tokyo -Los Angeles, 64% D.W. Load Rudder angle 8= port 30°
Gauge mark Straight run ( N= 110 rpm) IR -- Steady turn ( N= 92.2 rpm)} Measured r1R= 0.3
Steady turn ( N= 92.2 rpm)I Calculated Straight run ( N -= 110 rpm)
I I I I I
60 120 180 240 300 360
8 ( deg)
2
Tokyo-Los Angeles 64% D.W. Load Rudder angle 8 =Starboard 30°
Gauge mark Straight run ( N= 108.5 rpm) I Measured
1R -- Steady turn (N= 89.9 rpm)
r/R = 0.3 Straight run ( N= 108.5 rpm) }Calculated Steady turn ( N= 89.9 rpm)
II
i I
60 120 180 240 300 360
8 (dog)
of blade stress in turning Fig. 9 Comparison
conditions
with those in straight run.
Though the propeller revolutions decrease in steady turn,
time-mean stress aincreases considerably.
In the turn to starboard, a decrease in the fluctuations in blade stress is dominant. In the turn to port, on the other hand, an increase in time-mean stress is dominant. In both cases, stress on the port side of the propeller disc plane is considerably affected by the turn of the ship.
Blade stress measurements in the following sea conditions and ship motion were obtained:
Date : August 23, 1972 Sea : Rough
Beaufort scale : 5 (S. B. 150°) Swell : 4 (S. B. 90°)
Ship motion : Pitching 1.3° (Tp = 12 sec.) Rolling 4.4° (T, =15 sec.)
The maximum stress amax and double amplitude of blade stress fluctuations LI a at gauge mark 6R are plotted together with the ship's motion in Fig. 10. It can be said that the
fluctuations in blade stress in the period nearly equal to that of
the ship's motion are superimposed on those due to the non-uniform wake. A comparison of the blade stress patterns
with those of straight run in a calm sea shows clearly the effect
of ship motion on blade stress. Time-mean stress Fr and amax
show a tendency to increase.
T.E. tmax.
Kobe -Nagoya N=107 rpm, 0.3R
4 2 6 ^ 4 4 2 6 4
Oakland -Tokyo 57% OW. Load Sea state : Rough, Swell state: 4
Ship motion measured using vertical gyroscope
°;,: 0 _ a Phase mark 6max eld 't4 2.5
Propeller blade stress of gauge mark 6R
0
llllllllllllllllllll
k 1 revolution20 revolultions
Calm sea : r=3.63. d,= 6.07 , cla = 3.37 (kg/mm2)
6 8=4.16. e., =6.38. =3.08 (kg/mm2) 8=-4.27, w,,,a =6.50, ,dd =3.05 (kg/mm2) 4 21 1 0 90 180 8 (deg.)
Fig. 10 Changes in blade stress due to ship motion
The ship motions recorded on this voyage were not so severe compared with those occurring in winter". So it is very important to see how the mean blade stress increases in
higher seas.
2.3 Estimation of dynamic blade stress 2.3.1 Estimation of ship's wake
In order to estimate the ship's wake distribution from the model wake measured in a towing tank, a one-directional contraction method was used.
The width of the wake in full-scale is narrower than that measured on the model in the towing tank. The ratio of the width of the wake may, in the first approximation, be taken as the ratio of the boundary layer thickness at the end of the plates with the same length and Reynolds number for the model and ships. Thus, the ratio can be expressed as follows:
K =
(5)6'n4 - S
where,
d : displacement thickness of turbulent boundary layer at
the end of a flat plate
= 0.37 LRe-"5 (6)
: length of the corresponding plate
Re : Reynolds number
: scale ratio (Ls/Li)
(suffix s ships, M model)
Vs= 22.6kn : Full load, even keel
Measured Estimated
on model for ship
Fig. 11 Model and estimated ship's wake for "HAKONE MARU"
Wake distribution measured on the model is transformed into full-scale wake distribution by the following formula:
ws (y', z) = wm (y, z) (7)
where,
y' = Ky
The tangential component of the wake in the propeller disc plane, which was measured on the model, is used in this calculation without any correction.
Fig. 11 shows the estimated ship wake for the "HAKONE MARU" under fully loaded conditions, in comparison with that
measured in the towing tank.
2.3.2 Estimation of dynamic blade load
(1) Quasi-steady method of obtaining dynamic blade load
The quasi-steady method assumes that the characteristics
of a propeller at each phase of unsteady motion are
approximated by those at the same phase in uniform flow. Thus, if we know the non-uniform flow field around the propeller, the flow speed and angle of attack of the flow at each phase can easily be calculated. The characteristics of the propeller at each phase of unsteady motion areinter-polated from the open-water characteristics.
If we choose a representative radius rp, hydrodynamic pitch angle fl(0) at angular position 0 can be expressed as
follows:
fl(0) = tan-1 -is (1 Wa(9)) (8)
nVP+.18 Wt (0)
where,
= nD . advance coefficient xp = rp/ R
: ship speed
: rotational speed of the propeller : diameter of the propeller ws = 1 . axial wake fraction
s
: axial speed at position (xp, 0)
v,
W=-Vs
tangential speed at position (xp, 8) 1.0 R
360 270
7.5
Generating line
fe,(8) (b) Changes in angle of attack
Fig. 12 Schematic explanation of quasi-steady method
The local advance coefficient can be obtained using local hydrodynamic pitch angle g(e) as follows:
J(6)= rxptan)6(0) (9) 1 - wa(0) = .1s
1 + tan,
w,(0) where, /30 = -b--- (10) 7tXpThe relation is schematically illustrated in Fig. 12. If we
obtain the local advance coefficient, the thrust and torque coefficient at each angular position can easily be obtained from the open-water characteristics of the peopeller.
Introduction of averaged wake along blade chord In order to include the effect of in-flow velocity changes along the blade chord, an idea to average the wake change along the chord was introduced as follows:
1 r 6+6c
w(6,)d0, (11)
M(6) =
al_ 1- v7-.1 e-or
where,
CL : angle between the generating line and leading edge
67- : angle between the generating line and trailing edge
Fig. 13 shows the idea of an averaged wake and also an
example of an averaged wake for the estimated ship wake at 0.7 radius of the propeller.
Estimation of radial distribution of blade load
The radial load distribution explained below was used. It
was derived by modifying Kito-Izubuchi's method(36).
The modified method is based on the following two
assumptions:
C) Circulation distribution in radial direction;
= coR2A0(J) X (1 -e) (12) Trailing edge 0.10 0.08 0.06 0.04 0.02 0.015 0.01 0.005 Leading edge dK do Present method Lifting surface theory .1=0.76 2.0 1.0 0 1.0 0/R
Fig. 13 Concept of averaged wake along chord 2.0
Drag-lift ratio of the blade section;
e = constant for radial direction (13) where,
x = r / R
co = 27rn
n : propeller revolutions m = 4
: parameter determined by the advance coeffi-cient J of the propeller
The turust and torque distributions are expressed as follows:
dT(x, J) = pca2R4AAnx20 _x4)(1 ___fPH dQ(x, J)
dx = Peo2R5240(f)x2(1 x4)(-P+ e)7CC
An integration of (14) and (15) in a radial direction and
summation for the number of blades yield thrust T and
torque Q, which must be equal to those given by the
propeller open water characteristics at J.
Thus, the unknown parameters A0 (I)and e can be determined.Fig. 14 shows a comparison of the radial thrust and torque 1.0
0.191 0.4 0.6 0.8
= r/R
Fig. 14 Radial thrust and torque distribution
04)
0.8
0.6
21.° 0.4
0.2
Present method 0 Measured in. cavitation tunnel
(Uniform flow) J = 0.76 0 _ 0.4 J = 0.95 6 0 0. 0.1 I 0.191 0.4 0.6 0.8 1.0 r / R
Fig. 15 Comparison of radial blade stress .distribution
distribution calculated by the method mentioned above and
by available lifting surface calculations(42) for the propeller.
2.3.3 Estimation of blade stress
Blade stress was calculated using the beam theory, first
developed by Taylor("), and then modified by Kito-Izubuchi(36).
In the beam theory, the maxinnun stress at the line of the
maximum thickness due to hydrodynamic force is expressed as follows: =
4./y
Mtcostgi + Mosinflf (16) where,M, : bending moment due to thrust
Mg : bending moment due to torque
fif pitch angle of the face tgi=
nx
second order moment of inertia of area of the blade
section
y : height from the face to the neutral axis at the point of maximum thickness of the blade section
The bending moment due to centrifugal force on the raked blade is expressed as follows, disregarding the effect of skew,
Mc = Ws02R2.2.,3(.4 - x)tanOR cost?). (17) where,
xo : representative working radius of centrifugal force OR: rake angle
W : weight of the blade in the outer radius than the radius
at which the stress is calculated.
So, including the homogeneous tensile stress due to centrifugal
force, the total blade stress due to centrifugal force
isexpressed as follows: Mc rco2 W =
4./y
+ °
A Tokyo -LoS.Angeles 64.% D.W. Load N = 110 r pm , r/R=0.3Principal stress ai }Measured - Gauge mark : IR
ws estimated Calculated
---
mu averaged over the blade using Wake width at each blade position distribution-- as measured at 0.7 It
where, A is the sectional area of the blade section.
Thus, the stress on the blade is obtained as the sum of (16)
and (18),
= at +
(19)Fig. 15 shows a comparison between the radial distribu-tion of blade stress calculated using the beam theory and that measured in uniform flow. In this calculation, loading is
estimated by the method described in reference (42). It is shown
that the beam theory gives a slightly higher value at the blade root, but this is not significant.
2.3.4 Comparison with full-scale data
Fig. 16 shows a comparison of the blade stress changes during one revolution between full-scale measurement and
calculation by using the method mentioned above.
In the figure, both cases where the model wake and estimated full-scale wake were used are also included. From the figure, time-mean, the maximum and double amplitude of fluctuations in blade stress are taken and shown in Table 2.
The following should be noted:
There is a clear improvement in the accuracy of estimat-ing blade stress by introducestimat-ing an averaged wake along the chord in the quasi-steady approach, if we look at the blade stress patterns around the 180 degrees position.
The time-mean blade stress measured was higher than that
calculated. One of the reasons for this may be the inaccu-racy of estimating the operating conditions of the propeller
in full-scale operation.
As for the dynamic blade stress component, i. e., the double
Measured Ca1culted Principal stress Radial stress wm 2- 8 . Time-mean stress i (kg/mm) 4.93 4.28 - _ 4.14 4.14. 4.14
Maximum stress cr...(k.ginun2) 8.10 7.2-5 8.07 8.07 6.85
Double amplitude of fluctuation of 26(kg/mm2) blade stress 4.64 4.55 5.20 5.87 _ _ 4.05 120 180 240 300 360 8 (deg)
Fig. 16 Comparison of blade stress changes during one revolution
Table 2 Comparison of mean, maximum and double amplitude of fluctuating blade stress
1.4
1.2 Eq. ( 20)
1.0
4 6 8 10 12
CT= 7(1 /2)rp172R2
Fig. 17 Relation between the contraction of flow and propeller thrust loading coefficient
amplitude of blade stress fluctuations, conventional quasi-steady calculation overestimates about 25% in case of the
model wake and about 37% in case of the ship wake. On the
other hand, the introduction of an averaged wake gives
values closer to those measured (10% underestimation).
2.3.5 Further improvement
Fig. 16 shows rather good agreement between the full-scale measurements and the calculations using the averaged
wake along the chord, but there is still room for improvement.
If we check the dynamic blade stress estimation process, the following can be related to the remaining discrepancy(").
Accuracy of ship wake estimation
Introduction of effective wake in calculation
Inclusion of unsteady effect
Even though the measurements of a ship's wake have been
reported recently("), a more sophisticated method than those mentioned above is as yet unavailable. Thus, in this section,
items (2) and (3) will be discussed.
(1) Effective wake
An effective wake is a wake in which the effect of
propeller suction is included. The wake distribution measured at the propeller plane is called the nominal wake. It is understood that, due to the effect of propeller suction, the boundary layers of a ship's hull towards the stern of theship change, and consequently the wake distribution
changes.
Based on experimental observations and theoretical considerations, a simple method, was tried here(40). The nominal wake in the propeller plane of radius Rs is assumed
to contract uniformly to the propeller disc of radius R according to the relation given by the simple momentum theory, since the contraction of the approaching flow to the propeller in the plane just one propeller diameter before is well approximated by the following equation:
R 0.5 1 (1 ± + CT) } 2 (20) where,
Cr =
r.p 17.2R22T T : propeller thrust : ship speedThis equation is shown in Fig. 17 with data obtained by the measurements in uniform and non-uniform flow in the
cavitation tunnel.
The estimated effective ship wake was then averaged in a radial direction at each angular position to obtain the local
1.0 -F+ + Yamazaki , Z = 4 0.8 0.6 0.4 0.2 f3(x) 'IV 6'Zt. 43, Tanibayashi, 1 1 -0.08k2
\ Two- dimensional theory, IS (k)i
0.0
0 1 2 3 4
Reduced frequency k
Fig. 18 Amplitude of two-and three-dimensional response advance coefficient.
(2) Inclusion of unsteadiness
The introduction of the idea to average the wake along the
blade chord considerably improved the estimation of the dynamic blade load. Nevertheless, if we consider the chordwise load distribution due to the steady motion of an
airfoil in an unsteady flow field, the two-dimensional
unsteady theory produces an additional vortex distribution, which has the shape of a vortex distribution of a flat plate.
This means that, in averaging the wake along the chord, it is
worth introducing a weight function which includes the effect of unsteadiness in the flow field.
Three kinds of weight function can be expected, including
the one already used.
1
fi(x) = ; Uniform weight (21)
fs(x) = (1 .X2)°'5 8 = ; Elliptic weight 2 1 - x 1'1.5 cL 1 + x =
2 cot-1
'Flat plate-type weight
c 2
where,
c : chord length
2x
x -=
= cosch
Here 11(x) corresponds to the averaged wake already tried.
To see the improvement in quasi-steady response by
adopting these weight functions, the response of an airfoil to sinusoidal gust was calculated and compared with that using
unsteady theories(27x43), as shown in Fig. 18. Also a
comparison of the difference in phases is shown in Fig.19. In
these figures, an approximated curve of Tanibayashi's
three-dimensional response(") is also shown. It can be seen that the quasi-steady response of the airfoil using the averaged wake gives a good approximation to the
three-dimensional response of the airfoil, if the reduced frequency is relatively small. This explains why a good prediction was
obtained in the quasi-steady calculation of the blade stress on the propeller of a container ship. Of the three weight functions, Mx) is considered the most suitable, since it not
1.6
0 Uniform flow In wake
200
loo
r/2
Three-dimensional theory, Arg:F(k)
0 Breslin, Z=3 4- Yamazaki, Z=4 (1, Koyama, Z=5 - .
/
-0 3 4 Reduced frequency kFig. 19 Difference between two-and three-dimensional response phases
Single screw container ship(Service condition) Modified (Weight function : f3(r))
0.10 , ,, Quasi-steady
-- Modified (Weight function :ft trn methbd
- Conventional
0.08 --- Unsteady lifting surface theory 0 Measurements
90 180 270 360
8 (degree)
Fig. 20 Comparison of thrust fluctuations of one blade
only gives the closest response to that using Koyama's
three-dimensional unsteady theory(27) and the approximation
by Ta.nibayashi("), but also predicts the phase difference, which also approximates well with that using the three:
dimensional unsteady theories.
Thus, it can be concluded that the wake averaged along the chord with weight function Mx), which is similar to the expression for the vortex distribution of a flat plate, will further improve the quasi-steady calculation of propeller blade dynamic load and give more realistic results.
(3) Results of calculation
To see the effectiveness of the idea of the wake averaged along the chord with weight function Mx) in calculating propeller blade dynamic loading, the results of the
calcula-tions were compared with those using the unsteady propeller
lifting surface theory and model test data.
Fig. 20 shows the thrust fluctuations of the one of the blades of the container ship propeller. Measurements were conducted in the towing tank, using a one-component blade
dynarnometer(45). Calculation was performed using the same
wake distribution as that shown in Fig. 11. Three kinds of calculated results are shown in the figure, i. e., results using the conventional quasi-steady method, the quasi-steady method with averaged wake with weight function and the
7 6 5 4 3 2
Measurements (Tokyo -Los Angeles,1979)(el Modified cjuisi -steady .caldulation
1 I I i I
Ii
0 60 - 120 - - 180- - 240 ' 360
8 (degree)
Fig. 21 Comparison of dynamic blade stress
unsteady theory(27). It is evident that the quasi-steady
method with the averaged wake with weight function f3(x) gives the most realistic results of the three weight functions Even though this improved method overestimates a little on the port side in comparison with the test data, almost the same level of accuracy is achieved as by the unsteady propeller lifting surface theory.
Using this improved method and the effective wake
estimation method, the dynamic blade stress on the propeller
of the "HAKONE MARU" was calculated and coMpared with full-scale data. The results are shown in Fig. 21. Prediction was considered to be very good from a practical point of view, even though the calculated results Show a
slightly sharp stress peak, raising the question as to Whether
the estimated ship wake was contracted excessively. Thus, it is shown that an averaged wake with weight function Mx) works well in propeller dynamic load calcula-tion and that the improved quasi-steady method is effective in practical application.
2.3.6 Estimation of dynamic blade stress due to ship
motion
The quasi-steady approach alloWs the dynamic blade
stress on a propeller to be calculated during ship motion, if the
additional axial and tangential velocities induced by tinning, pitching, heaving etc., are properly estimated. The quasi-steady approach assumes the following local advance
coeffi-cient:
Is {1 w0(0) + u(0)} (24)
J (61
{1 + --.12(w1(0) + z4cos8 + uzsint71
ux, uy, uz : additional velocities due to ship motion
non-dimensionalized by
To see the usefulness of this method, calculation was conduct-ed assuming the drift angle for the turning conditions (see Fig:
9) and relative speed of the aft-part of the ship in pitching
conditions (see Fig. 10).
Results are also shown in Fig. 9 for turning conditions and
in Fig. 22 for pitching conditions.
For simplicity, the conventional quasi-steady approach
was used It can be qualitatively pointed out, the quasi-steady
calculation estimates the change in blade stress, except in the
Single screw container ship (Service condition)
N=110,prn, rIR =0..3 300
Calm sea Phase a bIMeasured c (gauge mark : 68) 1,,,= 1.14 m/s Calculated =0 ( r/R =0.3) = 1.14 m/s Oakland -Tokyo 57% D.W. Load N= 109 rpm Definition
Skew angle : 0, degrees Skew : 8,18 X 100% 8,= 360/z degrees : Number of blades Skew :s =(-8,/r/180) X ( 100/cosfif ) % Mid -chord line (Skew line) Skewed propeller Perspective view Generating line Leading edge Trailing edge Projected view Fig. 23 Definition of she*
0.5R 20°0PSI Chord _500
)500
0.0 500 3500(a)Principal stresses on the back side.
7111./11.11111111111
16
000 0.45R 8200 (MAX) 0.9 Chord 4 000 31500 415°°( b) Principal stresses on the face side
Fig. 24 Blade stress distribution of highly skewed propeller for San Cremente Class Ore/Bluk/
Oil Carrier(48)
skewed propeller is not a new type of propeller, since, in reference (50), Bourne already pictured a highly skewed
propeller in 1861. Since designing procedures had not then
been established in those days, the idea of a highly skewed propeller remained only an idea.
In the early 1970's, Morgan reintroduced highly skewed
propellers with a design procedure based on the lifting line and lifting surface theories113). The idea was applied to propellers
for San Cremente class Ore/Bulk/Oil carriers. The results of full-scale tests showed that highly skewed propellers were effective in reducing shaft force and pressure fluctuations
Unskewed propeller Leading edge 120 180 240 300 360 8 (deg.)
Fig. 22 Comparison of blade stress in ship motion
blade angle range in which the wake distribution in the propeller plane is considerably disturbed by the aft-part of the
ship's hull.
2.4 Concluding remarks
Full-scale measurements of blade stress on the propeller of
a container ship revealed several important results.
The level of mean blade stress on the propeller of the container ship was almost the same as had been assumed in the design stage. The double amplitude of fluctuating blade stress was at almost the same level as the mean stress.
The increase in dynamic blade stress due to ship motion is
not necessarily greater than that during the operation of the ship in calm sea. The mean blade stress increases with the
increase in ship motion.
In order to estimate dynamic blade stress in the early design stages of conventional propellers, the modified
quasi-steady method with the introduction of an averaged wake with
weight function was studied in combination with the ship's wake estimation method and beam theory.
It is worth noting that for conventional propellers, the modified quasi-steady method gives almost the same level of
accuracy as the unsteady lifting surface theory does in
estimating dynamic blade load. Fatigue fracture of the blade always starts in certain defects in the propeller, which cannotbe avoided in casting products such as propellers. The method proposed here for estimating dynamic blade stress provides an
opportunity to check the extent of allowable defects for the reliable operation of a ship.
3. Dynamic blade stress on highly skewed propellers
3.1 Introduction
In view of the recent demand for reductions in shipboard vibration in the shipping world, extensive investigations have been made on the hydrodynamic mechanism of
propeller-induced pressure fluctuations, and devices for reducing excita-tion levels have also been produced and applied to ships(46)(4).
Of these devices a highly skewed propeller (the definition of skew is shown in Fig. 23) has been recognized as an effective
countermeasure in reducing cavitation-induced pressure
Propeller 'A Propeller B Propeller C Propeller D
CA( 10) =5.4 kgimm2
Fig. 25 Principal stress distribution of propeller Propeller : C Ael
GT
T.E. 25% chord length from T.E. 5% chord length from T.E.BACK KYOWA FACE
KFC 2 -D17 -23
Fig. 26 Arrangement of active strain gauges on blade
induced on a ship's hull as expected, but that the blades were damaged in reverse operation.
Looking at the blade stress distribution on the blade, which is shown in Mg. 24, it was thought that the blade stress concentration near the trailing edge was responsible for the damage to the blade.
Thus, a skewed propeller requires more care in its strength
design than a conventional propeller, since both bending and torsional moments due to hydrodynamic loading act on the blade because of the geometry of the skewed blade. Based on the blade stress measurements of a series of highly skewed propellers(5"-("1, the criteria for designing highly skewed
propellers were proposed. These criteria can easily be checked in the early stages of geometric design using an FEM program
for the design condition of the propeller. Then, based on the systematic design of highly skewed propellers, a practical guidance to selecting the amount of skew will be proposed
Table 3 Principal specifications of 75 KDWT bauxite carrier
from the point of view of strength. The usefulness of the guidance was demonstrated by applying it to the design of a propeller for a container ship.
3.2 Highly skewed propeller series
In order to understand the blade stress distribution of highly skewed propellers, a series of propellers, of which the skew angle was systematically changed, were designed and blade stress measurements *ere conducted in uniform and simulated wake flows in a cavitation tunnel.
The ship, for which the skewed propeller series was designed, was a 75 KDWT bauxite carrier("). The principal dimensions of the ship and its engine are shown in Table 3.
At first, a conventional propeller was designed using an available propeller chart. The conventional propeller also had a certain amount of skew 19 degrees (26%). The skew angle Was then changed to 36, 46 and 59 degrees, corresponding to
50%, 64% and 82% skew.
The principal specifications of the propellers designed are shown in Table 4. Blade stress distribution calculated using the propeller lifting surface theory by the quasi-continuous method (QCM)(54) and an FEM program (NASTRAN)(55) is shown in
Fig. 25. The level of non-dimensiotialied stress on the blade is shown as equistress lines. Stress concentration tended to
appear when the skew angle exceeded 46 degrees (64%). I-9A Lpp BINLO AM) I 255.00m 248.00m 35.35m 18.30m
Full load draft Design 12.20m
Strength 12.80m Dead weight Approx.75 500t at de ,= 12.20m
Approx.80 500t at 4,.= 12.80m Main engine Mitsubishi MS-21-2 turbine x 1 Max. output: 19 000PS x 80rpm Normal output: 19 000PS x 80rprn
Speed Max. speed in sea trial : Approx.16.9kn
Full load service speed: 16.1kn
Propeller Highly skewed propeller
Diameter: 7.8m No. of blades: 5
No. a/aA(10) NO.alaA( 10) N°. 6/6A( 10) No. a/6(10)
2 0.06 2 0.06 2 0.05 2 0:05
4 0.24 4 0.24 4 0.25 4 0.37
6 0.42 6 0.42 6. 2.45 6 0.68
8 0.61 8 0.61 8 0.65 B 0.99
10 1.00 10 0.79 10 0.85 10 1.30
C,,.ev, e,, n rps in air C,. e n rps and J in water eh eh eh, eh = e e,
Table 4 Principal specifications of propellers
Diameter of model propeller (m) : 0.25
3.3 Measurements of dynamic blade stress in simulated
wake
To check the behavior of dynamic blade stress with skew,
blade stress measurements were conducted in a simulated wake in a cavitation tunnel.
Six 3-component strain gauges (KYOWA KFC-2-D17-23)
were fixed to the propeller blades as active gauges. Fig. 26
shows an example of the strain gauge arrangement on the
blade. All the gauges were coated with epoxy resin for
water-proofing. In order to avoid the effect of water
tempera-ture changes on the strain gauge outputs, 6 sets of three dummy
gauges were also fixed to the hub of the propeller in the same way as the active gauges.
In measuring the blade stress, a special procedure was
used to scale up the measured data to full-scale. By combining the blade stress measurements in air and water, and also at the
extremely low propeller shaft speed and at the specified propeller shaft speed, blade stresses due to centrifugal and hydrodynamic forces are separated and scaled up.
The block diagram of the measurements, the procedure of analyzing and scaling up the blade stress are shown in Fig. 27.
Axial wake distribution for the estimated full-scale wake
of the subject ship was simulated using wire mesh screens and crmls, Cr I
a X a,
bx.,
Principal stress analysis
62
61)=A/(1v)±(1+v)
46 = 1/2 tanl(A/B) A =(ari a,)/27
B=(6,;)/2 C = (err+cf,2a,) Definition LFig. 27 Flow chart of blade stress analysis
90 180 270 360
8 ( deg)
Fig. 28 Changes in blade stress during one revolution of propeller
a plate representing the stern part.
Fig. 28 shows the change in blade stress during one revolution of the propeller. It is interesting to note that even though high skew with unloading near the blade tip was applied to propellers C and D, the blade stress along the
trailing edge increases considerably, when the blade tip passes
through the high wake zone.
In Fig. 29, the mean and amplitude of blade stress were plotted for propellers A, B, C and D, together with the line
representing the relation between the corrosion fatigue
strength and mean tensile strength of the propeller
material-NiAlBz(56). The mean and amplitude of blade stress at gauges Nos. 5 and 6 of highly skewed propellers .0 and D are very large
and these data points are far away from the limit line. This means that propellers C and D are not safe from the point of view of fatigue strength. On the other hand, in the case of
conventional propeller A or the highly skewed propeller B, all
the data points are under the limit line.
The same tendency was reported by Yamasaki et al. in
their study on the strength of skewed propellerg5". A propeller with 100% skew was designed for a container ship. The stress
distribution of the blade calculated by the FEM showed the
Propeller A B C D D(m) 7.80 " II 7.80 PID).., 0.8141 0.8629 0.8713 0.8782 14,,/Ad 0.8057 v 0.8057 d /D 0.1846 II II 0.1846 Z II II 5 Rake angle(deg) 0 3.0 3.0 2.0 Skew(deg) 19 36 46 59
Pitch distribution Const. Tip unloaded Tip unloaded Tip unloaded P).0/ter 1.0 0.627 0.627 0.507 e : Blade strain a : Blade stress E :Youngs modulus v : Poisson ratio
Suffix T s, t. 3components D : Propeller diameter Scaling2
h; Hydrodynamic force Suffix M; Model (
c ; Centrifugal force s:Ship I a n ) kDm) I
pm: Density of prop, material n: Shaft speed (model, rps) (N/60\2(Ds\2
P.:Density of water N :Shaft speed (ship, rpm) n ) kDm)
Symbol Propeller Measuring point 2.0 A 'IR =0.25, s/C = 0.5'/R0.25. s/C =0.5 r/R=0.59. s/C = 0.95 .n/R=0.59, x/C =0.95 D 0 A(8 = Cr). = 10.7 kg/mm 2 EM,cM Pms.N 6, cr,,, ahr. 61,, ant
10 15 20 7 (kg/mm2)
tests in non-uniform flow showed that the blade stress near the
trailing edge increased considerably when the blade passed through the high wake zone. The mean and the amplitude of
the blade stress for the 100% highly skewed propeller, together
with that for the conventional propeller, were analyzed from
reference (57) and plotted in Fig. 30. Even though the data are for the model scale, the same tendency as that for propellers C
and D can be seen clearly.
From the results, it can be seen clearly that the dynamic blade stress of the highly skewed propellers, with stress concentration near the trailing edge, becomes very high and dangerous from the point of view of fatigue failure.
3.4 Measurements of dynamic bla.de stress in transient conditions
In the case of highly skewed propellers, it is generally understood that blade stress may be critical in transient conditions such as crash astern and crash ahead(58), but no quantitative verification exists. Calculation of blade stress distribution during transient conditions is usually quite
diffi-cult due to the complexity of the flow field around the
propeller.
To oyercome the difficulty in simulating flow fields in transient conditions, a quasi-steady approach was utilized in
model tests in a towing tank(59).
(1) Transient conditions
In order to simulate these transient conditions in a towing tank, a 7m long model of a ship was used for the tests. The
150 100 5b 0 50 100 05 06 06 05
Crash astern test
Prepeller, Tension Compression
A 0
0
Relation between corrosion fatigue strength up to 108 cycles and mean tensile strength
115 KDWT Bulk carrier
Conventional propeller
Crash ahead test
10 15
T (min.)
2.6%c
322xx o Face plane
3i%C © Back plane
0.7R Highly
- skewed propeller
Fig. 31 Example of crash astern and crash ahead tests With 115
liDWT Bulk carrier.
1
Fig. 29 Mean and amplitude of blade stress of highly skewd 3 a/
propeller series
existence of stress concentration with almost the maximum
value near the trailing edge around 0.7R. The results of model
0.2
0 0.2
MPNo.80 -3 MPNo.80 -5
MP No.80-3 1 0.3R max, thickness point 2 0.4R max. thickness point 3 0.5R max. thickness point
MP No.80 -5 4 0.5 R 80%C from LE 5 0.6R 50%C from L.E 6 0.6R80%C from LE. 7 0.712 80%C from L.E. 5 Ci I , 0.4 0.6 W ( kg/mm2)
Fig. 30 Mean and amplitude of blade stress of highly skewed and conventional propellers07)
principal specifications of the model are shown in Table 3. The typical transient operation of a bulk carrier is
shown in Fig. 31. It can easily be seen that since the speed
of the ship is low in comparison with the speed of the propeller tip, the quasi-steady approach to simulating tran-sient conditions is reasonable.
Three of the series of highly skewed propeller models, the principal specifications of which are shown in Table 4, were fitted to this model. Assuming a series of full-scale
skewed propellers was fitted to the ship, transient ship speed
and propeller shaft speed were estimated using the typical relation shown in Fig. 31 and Pig. 32.
The numbers marked in the figure correspond to C) : Steady ahead conditions
e - 0 : Crash astern conditions
0
: Steady astern conditions C) - C) : Crash ahead conditionsBlade stress measurements were conducted at transient points for (j) - S. 3-component strain gauges were applied to 4 points on both the face and back side of the propeller blades. The procedure for measuring blade stress was the same as that described earlier.
(2) Results and discussion
0.6
100
o
100
\ Vs
Test condition
0 (2) 0 0 0
®0
0 oFig. 32 Estimated transient operating conditions of the ship Propeller A Propeller B Propeller D 20 10 10
Fig. 33 Mean thrust and torque changes in transient conditions
Fig. 33 shows the changes in mean thrust and torque during crash astern and crash ahead conditions. Thrust and torque change with the propeller shaft speed, except in the range in which propeller is accelerating the ship in crash
ahead condition O. At point
8,
the torque value is higherthan that under the normal operating conditions of the ship. The maximum torque is 12% higher than that under normal
operating conditions. The torque value at is a little
exaggerated, say about 15%.
Both mean principal stress and double amplitude of the fluctuating component were analyzed and shown in Fig. 34 at a point of the maximum thickness of 0.25R (root) and in Fig. 35 at points near the trailing edge of 0.5R - 0.6R, where the
20
Fig. 34 Dynamic blade stresses in transient conditions(0.25R, face, point of max. thickness)
10 20 10 10[ 0 Gauge position : 1 Gauge position : 3 20 10 MOW
Propeller A (a51 R, mid -chord)
---- Propeller B (051 R, 95% chord length from L.E.) --- Propeller D ( 0.59 R 95 % chord length from LE.)
Fig. 35 Dynamic blade stresses in transient conditions(face)
high peak blade stress was expected. The results can be
summarized as follows:
As to the blade stress near the root on the face side, the
dynamic blade stress behavior is similar for all propellers. The mean principal stress Er near the trailing edge in the mid-radius area becomes extremely high (it becomes close
to the yield strength of the material) in case of the
propeller D, while increase in Z/ o- is small.
Thus, it can be concluded that a highly skewed propeller
10 Propeller A
-- Propeller B -- Propeller D
Abbreviations : T.U. : Tip Unloaded, L.I. : Linear Increasing L.D. : Linear Decreasing
with stress concentration near the trailing edge in
the mid-radius area should be avoided.3.5 Criteria for selecting skew angle
(1) Criteria
From the results of the model tests reported in 3.3 and 3. 4, the following criteria are recommended from the point of
view of strength design.
Any stress concentration with the maximum stress on the
blade near the trailing edge around the mid radius area
should be avoided.
Stress concentration patterns with a low stress level on
the blade near the trailing edge around the mid-radius area
are acceptable.
Based on these results, a systematic design study of highly
skewed propellers was conducted to obtain guidance for
selecting skew angle.
(2) Design procedures for highly skewed propellers
Propeller C, which was used in the study described in section 3.2, was chosen as a base for the systematic design study. The design procedure was as follows:
a) The basic geometric parameters were kept the same for propeller C. The same ship performance data as those for
propeller C were used.
® Thickness design was carried out under a design stress of 5.3kg/nrun2.
0 A pitch ratio of 0.7R was chosen so that open water characteristics at the design point were equal to that of
propeller C.
Table 5 Parameters and operating conditions of
systematically changed skewed propeller
4.90kg /mm2 Propeller : e 'Skew deg.(%), s =S/ Rh. = 4.98kg/mm2 Propeller dmax = 5.07kg/mm 2 Propeller : g Propeller
Fig. 36 Example of principal stress distribution:
C) The lifting surface program QCM was used to obtain pressure distribution on the blade, while the NASTRAN program was used to calculate the blade stress
distribu-Propeller Z A.M. Po., Design param. Skew KT
Base 5 0.806 0.814 T.U.p=0.63 46(64%),s = -0.145 0.21 a 0.806 adjusted T.U. p = 0.63 46(64%),s = -0.145 0.20 b 5 0.806 adjusted T.U. p=0.60 46(64%),s = -0.145 0.20 c 5 0.806 adjusted L.I. p= 0.85 46(64%),s= -0.145 0.20 d 5 0.806 adjusted L.D. p =1.15 46(64%),s = -0.145 0.20 e 5 0.806 adjusted T.U. p =0.60 25(35%),s = -0.3 0.20 f 5 0.806 adjusted T.U. p= 0.60 33(46%)s= -0.4 0.20 e 5 0.806 0.863 T.U. p =0.6o 41(57%),s = ', 0.5 0.20 h 5 0.806 adiusted T.U. p=0.60 49(68%),s = -0.6 0.20 i 5 0.806 1.035 T.U. p =0.60 41(57%),s = -0.5 0.20 j 5 0.806 0.947 T.U. p0.60 41(57%),s = -0.5 0,20 k 0.806 0.776 T.U. p= 0.60 41(57%),s = -0.5 0,20 m 5 0.806 0.863 T.U. p = 0.60 41(57%),s = -0.5 0.22 n 5 0.806 0.863 T.U. p =0.60 41(57%),s= -0.5 0.18 g' 5 0.75 adjusted T.U. p=0.60 41(57%),s= -0.5 0.20 le 5 0.70 adjusted T.U. p =0.60 41(57%),s = -0.5 0.20 g 5 0.65 adjusted T.U. p =0.60 41(57%),s = -0.5 0.20 o 5 1 0.65 adjusted 'f.O.p=o.so 25(35%),s = -0.3 0.20 P 5 0.70 adjusted T.U. p =0.60 33(46%),s = -0.9 0.20 q 5 0.65 adjusted T.U. p =0.60 33(46%),s = -0.4 0.20 4a 4 0.6 adjusted T.U. p0.60 91(46%), g type 0.20 4b 4 0.7 adjusted T.U. p=0.60 49(55%), h type 0.20 4c 4 0.5 adjusted T.U. p=0.60 33(37%), f type 0.20 4d 4 0.65 adjusted T.U. p =0.60 91(46%), g type 0.20 4e 4 0.74 adjusted T.U. p=0.60 49(55%), h type 0.20 9f 4 0.56 adjusted T.U. p=0.60 33(37%), g type 0.20
Table 6 Results of systematic blade stress -calculations
1: Propeller C (See Table 4) 2: Blade stress (kg/min')
m.b.s.: Maximum blade stress at root or x.xR near trailing edge
b.s.(n.t.e.): Blade stress (near trailing edge)
Comments:
Pitch distribution changed Skew distribution changed
changed from g Loading changed from g
Expanded blade area ratio changed from g
Combination of expanded blade area ratio and skew distribution
For 4-bladed propeller
1.0 0.5 ....,.....,
.,s
... =.'..- .. ..3...r... ... ... .. .... .,.. .../..\ 4
.../
....,.._ ... ., ...''''''' ,t. N V Propellera - c
---b d 0.2 0.4 0.6 0.8 1.0 r/RFig. 38 -Skew distribution Skew series propeller
z=5- =4
0 @ A Without stress concentration ® Stress concentration
near trailing edge @ 80 a,=0.8 (Ad Aa-0.55)X100 h @C e' g Container ship 4b,"if_ 4e
IDEl 4a Qs Op f 4c A4f 0 0 e Safe zone @A 0.4 01.6 01.8 I I i j AdAd
Pig. 39 Guidance for selecting maximum .skew
1.0
skew (see Fig. 38), effect of pitch, effect of loading, effect of
blade area, and the effect of the number of blades were studied. As a result, the following guidance for selecting skew was
proposed. If we assume a skew and pitch distribution, the
parameter which plays the most important role in selecting the
applicable skew is the blade area ratio. Thus, the data shown
in Table 6 are plotted in relation to skew s' (%) and blade area
ratio Ac/Ad, and shown in Fig. 39. In the figure, the data for skewed propeller series A, B, C and D are also plotted, since the skew and pitch distribution is not so different from that of
a g-type series propeller.
From this figure, the maximum applicable skew s' (%) can be expressed as follows:
s'
=0.8(Ae1Ad -0.55) x 100(%) (20This relationship was deduced from the criteria under the
m.b s.3 b.s.(n t.e)4 Evaluation Comments r/R ce. r/R a" Base' 0.55R
-
X a 0.5R 4.9-
X 1 b root 4.8 0.5R 4.30
c 0.6R 7.9-
X d 0.6R 5.1-
X e root 4.9-
0
2 f root 5.0-
0
g root 5.1 0.5R 3.60
h 0.5R 5.5-
X i root 5.2 0.6R 3.40
3 j root 5.1 0.6R 3.60
k root 4.9 0.55R 4.00
an root 5.5 0.55R 3.60
4 n root 4.3 0.5R 3.60
g' root 5.4 0.5R 4.8 X 5 87 0.5R 5.9-
X g' 0.5R 7.0-
-
X o root 5.8-
0
6 P root 5.6 0.6R 3.80
9 root 5.9 0.6R 4.80
4a root 4.9 0.6R 4.6 X 7 4b root 4.4 0.6R 4.2 X 9c root 5.5 0.6R 5.3 X 4d root 4.6 0.6R 3.7.0
4e root 4.2 0.6R 3.30
4f root 5.1 0.55R 3.90
01.2 0.4 06 08 1 0 I II1
I r/RFig. 37 Pitch distribution tion.
Table 5 summarizes the systematic change in the propeller
parameters and loading conditions, and Table 6 summarizes the results of blade stress calculations. Examples of blade stress distribution are shown in Fig. 36. As shown in both tables, the effect of pitch distribution (see Fig. 37), effect of
40
No. cr(kg/mm2)
2 0.15
4 1.24
6 2.33
8 3.43
10 4.52 Fig. 40 Principal stress
distribution
0.25R, face, mid -chord
--- 0.6R, face. 10% chord length from T.E.
KT=0.173
270
90 180
8 (leg.)
Fig. 41 Change in blade stress during one revolution of propeller
360
following conditions:
g-type skew and pitch distribution
Blade peak stress near the trailing edge greater than 85% of the maximum stress at the root was also avoided.
3.6 An example of propeller design
To see the usefulness of the criteria and also the practical
guidance described in 3.5, design of a propeller was conducted
and its characteristics were checked by model tests. A container ship propeller was chosen, since the guidance was
deduced from a systematic study of skewed propellers designed
for a full ship.
The principal specifications of the ship are shown in Table
7. Design conditions were as follows:
D =7.0m
Z = 5
A.= 26.0m2 (A./ Ad = 0.6756)
Design stress = 5.3 kg/mm2 g-type skew and pitch distribution
The principal specifications of the propeller which was
designed are shown in Table 8.
The relation between skew s' (%) and the blade area ratio Ile/Ad is plotted in Fig. 39. The propeller has the maximum skew applicable for the blade area ratio.
Fig. 40 shows the blade stress distribution at the design
15
10
Gauge point
cn 0.25 R Point of max. thickness C) 0.40R
0.50R 10% chord length
0.60R from trailing edge
0
0.70R *Compression 0 _ a-C)..r* cfoxf
0I,/ cf KTO =0.1730 if
a
rArs.' ®Relation between corrosion fatigue strength (108) and mean tensile_ strength
10 15 20
T (kg/mrn2)
Fig. 43 Mean and amplitude of blade stress
Fig. 44 Full-scale highly skewed propeller installed on the container ship
load. The maximum blade stress occurs at the root, and the peak value along the trailing edge near 0.6R was 80% of the
maximum value.
Strain gauges were put on the model propeller of the subject ship, the scale ratio of which was 1:28. Measurements were conducted in a simulated wake in the cavitation tunnel.
Table 7 Principal dimensions
of the container ship
Table 8 Principal
specifics-tions of the propeller
Ship Container ship Dl(m) 7.0
Hull Lpp 191.00m 0.9714 BMLO 32.20m Ad 0.6756 dB, 9.50m t/C) O., d/D 0.0406 0.1757 Eriine Diesel MR 18 890 Ps Rake (ang.) 3.0 93 rpm Skew (%) 50 5 Material NiAl Bz Max. 111 =t411 Ave. ©;C) Min. 0O88 1 2 1.0. 1.4 Kr/Kro
Fig. 42 Dynamic blade stresses in simulated wake
,--Dynamic blade stress was measured not only at design load Kro(= 0.173), but also at K/ K0 =0.8, 1.2, 1.4 to see the changes in dynamic blade stress caused by loading.
Fig. 41 shows the changes in blade stress during one
revolution of the propeller. In this case, the change in blade
stress at the 90% chord length point from the leading edge at 0.6R (gauge No. 5) is not so different from that near the
mid-chord point of the blade root (gauge No. 2). In Fig. 42, the
maximum and average values of blade stress are plotted
against the thrust coefficient. It can be seen that the maximum
blade stress near the trailing edge of the skewed propeller increased considerably with the increase in propeller loading.
The mean and amplitude of blade stress are plotted in Fig. 43. In this case, all the data points are lower than the limit line.
Thus, it can be said that this highly skewed propeller is safe from the point of view of fatigue strength and it has been installed on the ship and is now in operation (Fig. 44). 4. Conclusions
In order to ensure the reliable operation of ships, strength
design of marine propellers is one of the most important items
to be considered. Since a propeller operates in a non-uniform flow field, i.e., in the wake of a ship's hull, the blades suffer from periodical changes in dynamic load. For this reason,
corrosion fatigue strength is considered to be the key
mechani-cal characteristic of the propeller material. Thus, checking the dynamic blade stress of the propeller in the early stages of propeller design is important.
In these circumstances, a method of estimating the
dynamic blade stress of conventional propellers operating in the wake of a ship's hull was studied in the first part of this paper based on data obtained by full-scale measurements of a container ship. The important conclusions are as follows:A modified quasi-steady method, with the introduction of the idea of an averaged wake with weight function for estimating dynamic blade load, gives almost the same level of accuracy as existing unsteady propeller lifting surface
calculations for conventional propellers.
The most difficult part of the estimation method is to
estimate the ship's wake distribution or effective ship's wake distribution correctly.
Kume H., Fracture of Marine Propeller Blades, Proc. 2nd
Symp. Marine Propeller, SNAJ (1971)
Nippon Kaiji Kyokai, Kosen Kisoku Shyu, Part D, Chapter 7:
Propellers (1985)
Lloyd's Register of Shipping, Rules and Regulations for the Classification of Ships, Part 5 Main and Auxiliary Machinery, Chapter 7: Propellers (1985)
American Bureau of Shipping, Section 37, Propellers and Propulsion Shafting (1985)
Det Norske Veritas, Rules for Classification of Steel Ships, Part 3, Chapter 3: Hull Equipment and Appendages, Section 7:
Propellers (1985)
Bureau Veritas, Rules and Rugulations for Construction and Classification of Steel Vessels, Volume C: Machinery System, Section 17-7: Propellers (1982)
Keil H. et. al., Flugelblatsschvvingungen am Propeller eines Frachschiffes, JSTG, 64 Band (1970)
Chirila J.C, Dynamische Beanspruchung von Propellerflugeln auf den Motorschiff "PEKARI", SCHIFF und HAFEN Heft 3,
References
Full-scale measurements showed that the mean stress level
near the root is almost the same as that estimated in the
design stages. Ship motion increases mainly the mean stress
level whilst changes in amplitude are small.
Further accumulation of full-scale data is necessary, since
the data obtained here are limited.
Regarding the dynamic blade stress of highly skewed propellers, based on the examination of a series of highly
skewed propellers, criteria for designing highly skewed propel-lers were proposed as follows:
Any stress concentration with maximum stress on the blade near the trailing edge around the mid-radius area is to
be avoided.
Stress concentration patterns with a low stress level on the
blade near the trailing edge around the mid-radius area are
acceptable.
A practical guidance for selecting the amount of skew was
also derived from the criteria through systematic design
studies of highly skewed propellers.
Due to strong demand for the reduction of ship vibration,
highly skewed propellers will be increasingly used on all kinds of ships. However, fractures of highly skewed propellers have
recently been reported(58). Thus, the criteria and practical
guidance proposed here will be useful in designing highly
skewed propellers with reliable ship operation. The
accumula-tion of full-scale data on blade stress measurements of highly skewed propellers is also needed to check the criteria. Acknowledgement
The author would like to express his foremost apprecia-tion to Professor Emeritus T. Nishiyama of Tohoku Univer-sity, for his valuable advice, suggestions and continuous
encouragement.
He also would like to express his appreciation to Prof. H. Abe and Prof. T. Ohta of the Department of Mechanical Engineering, and Prof. R. Kobayashi of the Department of Mechanical Engineering II of Tohoku University for their valuable criticism of this paper.
Furthermore, the author would also like to express his sincere thanks to Professor Emeritus R. Yamazaki of Kyushu
University, for his valuable comments.
22 Jahrgang (1971)
Dashnaw F.J., Propeller Strain Measurements on the S.S. Michigan, Marine Technology Vol. 8 No. 4 (1971)
Meyne E., Statische und dynamiche Beanspruchung von
Schiffspropellerflugeln, JSTG, 64 Band (1970)
SR 126th Committee, Research on the Stress and Strength of Large-Sized Propellers, Report 74, SRAJ (1975)
Committee of Ship Structure, Symp. on Vibration and
Shipboard Noise and Countermeasures, SNAJ (1970) Cumming R.A., Morgan Wm., B. and Boswell R.J., Highly Skewed Propellers, Trans. SNAME Vol. 80 (1972)
Fujita T., On the Flow Measurement in High Wake Region at the Propeller Plane, Jour. SNAJ Vol. 145 (1979)
Lammers A. and Lauden J., Laser Doppler Velocimeter Flow Measurements, Proc. 16th ITTC, Leningrad (1981)
Sasajima 'H., Tanaka I. and Suzuki T., Wake Distribution of Full Ships, Jour. SNAJ Vol. 120 (1966)
Hoekstra M., Prediction of Full Scale Wake Characteristics Based on Model Wake Survey, Proc. Symp. on High Powered
