Tolerances in propeller design and manufacturing

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SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HØVIK OUTSIDE OSLO, MARCH 20. 25., 1917

"TOLERANCES IN PROPELLER DESIGN AND MANUFACTURING"

By W.W. Wiegant

Lips B.V. Propeller Works, Drunen, The Netherlands

SPONSOR: DET NORSKE VER ITAS

Lab. y. Scheepsbouwkindt

Technische Hog5school

Deift

3 S.

.\s6:i..

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The design geometry of a propeller is not uniquely defined as it ¡s sensitive to inaccuracy in the input parameters. The geometry of a finished propeller ¡s one specimen out of a set of geometries, deviating within tolerance from the design geometry.

In this paper first the input parameters and their reliability are summarized and discussed. After the presentation of a design computer program, results of calculations with this program are given to

assess the order of the variations in the geometry due to inaccuracy in the measured model wakefield and the way in which it ¡s

transformed, to simulate transition toa full scale wakefield. A manufacturing method ¡s described next and in particular an

electronic measuring apparatus. Results of an analysis of deviations of a large number of propellers from their design geometry are then presented. Finally a comparison ¡s made of the margins between which a design geometry may vary with the standard tolerances.

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1. Introduction

A propeller manufacturer has the objective to produce a metal body appropriate to propel a distinct ship at a desired speed while absorbing a specified power at a required number of revolutions with optimum efficiency causing the least possible amount of noise

and vibrations and staying intact for a period as lengthy as possible. To this end a design has to be made and the designed propeller has to be manufactured. Like in any other manufacturing process ¡t ¡s impossible to make the product exactly as it has been designed. Therefore tolerances on the final product are to be

accepted. It is obvious that the order of magnitude of these

tolerances should be such that the objective is achieved by any product deviating from the design within tolerance. However, the relation between this design and the objective is equally liable to uncertainties and inaccuracies. This paper is concerned with a study of the inaccuracies in both the design and the manufacturing stage in comparison with the currently accepted tolerances on the geometry of propellers.

The designing of a propeller is based on information, from the shpowner, the engine-manufacturer, the yard and a towing tank. This information is processed through a design procedure,

consisting of a mixture of experience, diagram reading and calculations, either by hand or by computer, based on the

application of hydrodynamic theories. This results in what may be called the software propeller i.e. the propeller of which the designer, to the best of his knowledge, confides to real ize the objective stated above, when exactly reproduced ¡n metal. In the factory then the mould is composed, the material cast and the cast

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is measured and finished. The finished propeller is hereafter called the hardware propeller, and is as close to the designed

propeller as possible. This sequence of the design and manufacturing activities ¡s represented in Table 1. In this table the

uncertainties of each stage are indicated symbolically. The

geometrical and metallurgical properties of both the software and the hardware propeller are Hable to a variety of influences, each of a specific sort, which affect the achieved result. This means that the result of each activity is not uniquely defined and has to be regarded upon as a random choice out of a set of other equally probable possibilities. In this paper an endeavour is undertaken to establish and compare the order of magnitude of AI, AM and AC (see Table i).

2. The design stage

2.1. Input

Before designing a propeller the designer must be provided with information originating from various sources. Table 2 presents a list of the sources and the information to be expected.

In most cases the data received from the shipyard are fixed. Sometimes the designer with his experience in the field of

sternarrangements ¡n relation to propeller performance may propose an improvement in the afterbody to favour the inflow into the propeller plane. After these preliminary discussions the data regarding the ships form and the draughts to be considered must be left unchanged. The mission profile of the ship, i.e. the rate of power as a function of time, expected for the ship to sail in,

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should be known in order to establish the condition for which the requirement of optimum efficiency has to be met. In addition, the mission profile is needed to assess an off-design condition of maximum propeller loading at which the strength criteria have to be

fulfilled. This is an important point, not always fully recognised, for there have been found shipowners operating their craft in

conditions considerably different from those in which it was meant

to sail , which proved not rarely detrimental to the propeller.

Regarding the engine characteristics, the designer has to consider the data he receives from the engine manufacturer as fixed. The advice of the engine manufacturer as to the power-rpm combination for which the propeller has to be designed will in general cause the propeller to be somewhat light in order to create the

necessary margin against the fouling of the hull and the changing properties of the engine. This applies of course only for newly built ships. In case a propeller has to be designed for a ship already in service for some time, there has to be a good insight in

the state of the ships hull and the engine, in order to be able to determine the proper design parameters as to power, revolutions and speed.

Nowadays, in a majority of cases information about the ships resistance and selfpropulsion characteristics is gathered ¡n an early stage with the aid of a towing tank. The results of a

selfpropulsion test carried out with a propeller out of the stock of the towing tank indicate to the propeller designer the mean

pitch to be applied for his design. In addition, when combined with the open water characteristics of this propeller, the mean

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design a propeller to absorb the right power with the required number of revolutions at a specific speed of advance. The

difficulty however, often lies ¡n the interpretation of the results of the tests. There is a remarkable variety in the methods used by

the various towing tanks to derive from the measurements the curves of their expectations. In particular the multitude of allowance factors, the reasons why and the extent to which, they are applied need elucidation. Even when several tests are performed on one ship, the results scatter considerably, as has been shown in Ref. [i]. it

is a weilknown fact that ¡f the prediction of the resistance of the ship is incorrect the propeller will consequently be designed for an incorrect number of revolutions. The margins between which, -this applies of course mainly for propellers with fixed pitch -, the number of revolutions has to lie, are usually from one to two percent, but in case the prime mover is a turbine the margin at the upper side is very small and sometimes even zero. The interpretation of the designer of the results of these tests forms an important source of uncertainties.

Another major influence on the indefiniteness of the ultimate result is the way ¡n which measured the wakefield is used. On the one hand there is a normal amount of measuring inaccuracy in the survey of the nominal wakefield in question and on the other hand a choice has to be made as to the kind of transformation to be applied on the measured values to obtain an effective wakefield.

The metallurgical laboratory provides the designer with information about the material of the propeller. This comprises data on the ultimate tensile strength, the proportionality limit, the

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way ¡n which these properties vary with the local dimensions of the propeller.

Finally the views of the designer himself on all of these matters, the experience he gathered in previous similar cases and his

knowledge of the way ¡n which the design procedure has to be used and its sensitivity to variations in the input data, determine greatly his expectations about the resulting propeller as is

illustrated ¡n Ref.[2].

2.2. Design procedure

The design procedure can be regarded as a transfer function. This function transfers also the uncertainties ¡n the input,

AI,

to the uncertainties AP of the result. The design procedure used here to

assess the dependence of the result on AI is a design program making use of a computer of both high speed and accuracy. A flow diagram of the design part of the procram is represented ¡n Figure

i and a more detailed description of the components ¡s given below.

2.2.1. Input to the design program

Beside the obvious input of the data described ¡n Section 2.1., the following features apply:

At least axial values of the wakefield over the complete propeller disc must be provided and if available tangential

val ues.

Either a radial distribution of pitch or of circulation must be given.

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must be provided.

4. At each radius the extent of backsheet cavitation must be stipulated and a margin against face cavitation prescribed.

2.2.2. Wakefield preparation

This part of the program is mainly concerned with the adaptation of the wakefield to the mean wake value at the propeller disc. There are still no ways to calculate a ships wake analytically and the methods to transform a nominal model wakefield into a full scale effective one of e.g. Sasajima

[3]

or Hoekstra [u], are not always applicable without restrictions. For the time being a simple way has been chosen to account for the difference between the mean wake fraction calculated from the wake field input (wN) and the mean effective wake fraction stipulated (wE). This is achieved either by multiplying all velocities by the quantity

1-w ), or by adding to

N

all velocities the quantity (wN_wE).VS, where V is the

shipspeed. The multiplicative method enlarges the variations ¡n inflow speed and consequently ¡n angle of attack whereas the additive method leaves these variations essentially invariant.

2.2.3. Power iteration

The power iteration comprises the determination of the mean pitch or the pitch at each radius by way of an iterative application of an adaptation to lifting I ¡ne theory, taking into account the mean

inflow velocities at each radius and the prescribed pitch or circulation distribution, respectively, in order to make the

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2.2.L. Strength calculation

Static bending moments according to [5] at a number of blade positions during a revolution for three radii are evaluated in order to establish the ratio between maximum bending moment and average bending moment during a revolution. Thus taking into account the dynamic stresses in a quasi-steady way. With this ratio and a Smith diagram of the material the allowable mean stress level is asses5ed and with the latter the minimum required thickness is calculated. This procedure is performed also for an off-design condition defined by the designer and if applicable the minimum measure of thickness required by a classification society is

determined, taking into account the increase in thickness due to a possibly specified iceclass. As a final result a radial thickness distribution of the form:

t = t .

ttt

. (l-x)+(l-x).(x-x ).(P+Q+(l-x)3)

X tip

_lXhb

hub

where x = nondimensional radial station t = maximum thickness at radius x

x

P and Q = coefficients to make the curve pass through the maximum thickness at two intermediate radii,

¡s calculated by sucFessive least squares approximations, to meet all requirements.

2.2.5. Cavitation calculation

n general it is the aim of a propeller design to avoid as far as

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-8-inevitable, be allowed but bubble cavitation on the back and face cavitation should preferably be completely absent. To this end the cavitation part of this design program determines at each radial station the minimum chordlength for which these conditions apply. This is achieved by evaluating cavitation buckets for several

chordlength-camber combinations, comparing them with the variations in angle of attack due to the wake fluctuations during a revolution and selecting the most favourable of them. The designer must define a percentage of each chord over which from the leading edge of the blade a cavity at the backside extends. If the designer expects that danger of face cavitation exists, e.g. when a controllable pitch propeller has to operate over a large range of its pitch

settings with constant engine speed, he may at each radius prescribe a margin against face cavitation in terms of an extra angle of

attack. Otherwise the profiles for which a backsheet is allowed will operate on the verge of face cavitation to keep the extent of the sheet at the back to a minimum. At the radial stations where no backsheet is allowed, shockfree entrance as far as possible is maintained for the mean inflow condition.

The blade shape originating from the established chordlengths, as

they are based on cavitation considerations

for

each

single

radius,

will

in general be rather irregular. It is therefore faired either with the use of a blade outline prescribed by the designer or by a

mathematical function of the form:

f(x) = a.x . (l-x)

to envelop all calculated minimum chordlengths. As a last step the camber of the profiles associated with the faired blade shape is

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established by calculating a set of cavitation buckets as a function of camber only and picking the most favourable value of camber to meet the cavitation criteria.

2.2.6. Results

The power, strength and cavitation calculations are performed in a repetitive sequence until the difference between the blade area ratio of two consecutive cycles is less than about two percent. The calculations so far have been of an almost purely two dimensional kind. Therefore the propeller data are corrected for lifting surface effects according to [6] with the use of a polonomial

approximation technique taken from [7]. The printed results consist of a comprehensive set of information. They comprise nondimensional propeller characteristics, nondimensional propeller geometry,

propeller geometry in meters, loading data, cavitation data for both mean load, maximum load and minimum load over a revolution per

radial station and strength data for the design condition and the defined off-design condition.

2.3 The software propeller

The parameters of the propeller resulting from the design procedure must be judged with respect to power absorption, cavitation and

strength. This judgement must imply also a consideration of the behaviour of the propeller over the complete range of its operation, ¡n particular in the case of a controllable pitch propeller. If in any of these aspects the judgement is not satisfactory the appropriate

input parameters must be modified. The design procedure is _then reiterated until the propeller complies with the views _{of the}

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designer. Nowadays in many cases the design ¡s tested on model scale by doing another selfpropulsion test, a cavitation test, and often measurement of pressure fluctuations, and generated noise, to check

the performance of the propeller.

The result of the testing of a design at a towing tank and a

cavitation tunnel are reliable to a certain extent and should only be regarded upon as an indication of what can be expected to occur behind the ships stern, for the following reasons:

- the prediction method appi ied by a towing tank may be subject

to ample discussion and depends on statistics in which no full insight exists.

- the cavitation phenomena observed at a cavitation test may vary

from tank to tank. This is illustrated in Figure 2 where the result of cavitation observations with one and the same propeller at the cavitation tunnels of Paris, Berlin and Wageningen are shown.

the correlation between the observed phenomena and the full scale behaviour ¡s often doubtful. See Ref. [8].

The conclusion ¡s that it requires skill and experience to interpret the results of such tests. This implies that again a source of

inaccuracy is introduceth

2.3.1. Sensitivity of the software propeller for inaccuracy in the input

To study the sensitivity of the software propeller for effects in the wakefield a series of calculations has been performed. Three examples

have been chosen, for the design of which a nominal axial wakefield had been measured. The design for these propellers had been tested before in a cavitation tunnel and proved to be satisfactory. The

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three examples have been used to ¡Ilustrate the effect of

inaccuracies ¡n the measured wakefield on the design. The procedure adopted was to transform the nominal model wakefield ¡n the

following way:

VA = (VA - VA).0 + VA

r4) r4)

where: _VA = the inflow speed at angle 4) and radial station r

VA = the overall mean inflow speed

VA = the local inflow speed after transformation

r4)

C = a factor taking the values 0.90, 0.95, 0.98,

1.00, 1.02, 1.05, 1.10, respectively.

This transformation is illustrated in Figure 3. The wakefield qiven in the left part is the original one. The curves of equal wake are left unchanged by the transformation but the values they represent are altered. Thus the transformation means a contraction of the field towards the curve of equal mean wake - in the illustration

the mean wake fraction ¡s assumed to be .3 - if the value of C ¡s less than 1.00 and an expansion from this curve if the value of C is

greater than 1.00. The mean wake value is invariant for any value of C. A deviation, caused by a systematic measuring inaccuracy, in the overall mean level of the wake will be corrected by the adaptation of the mean level to the stipulated effective full scale wake by the method described ¡n Section 2.2.2. In this case the additive method

is used because of the ¡mportance of the preservation of the variations in wake during a revolution. The transformation method described above has been chosen to try to simulate the effect of measuring inaccuracies on the variations ¡n wake during a revolution.

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In Tables 3, 14 _{and 5 some of the geometrical parameters of the}

propellers are shown in their dependence upon the measure of simulated inaccuracy in the wakefield. As could be expected the effect of such a transformation is mainly observable ¡n the change

in camber, as camber determines greatly the possibility to absorb the fluctuations ¡n the wakefield. Also the thickness ¡s influenced, as it is determined by dynamic stresses. This can, however, not be observed ¡n the cases B and C where the thicknesses, obtained from the rules of a classification society, exceed those established by the calculations incorporated in the design process, which takes into account the dynamic stresses. The blade area ratio remains fairly constant whereas the mean pitch undergoes a slight change, as a compensation for the changes ¡n camber.

In addition the three wakefields have been used to establish the order of magnitude of the changes caused by transformation of the nominal model wakefield to a full scale nominal wakefield. This has been done by applying the transformation method suggested by

Hoekstra, see Ref. [14]. This transformation consists mainly of three separate contractions viz, a concentric contraction, a contraction

towards the centerplane and a contraction towards a surface above the wakefield. The extent to which each of these contractions are to be applied is determined from three parameters derived from the harmonic content of the wakefield. In Figures 14, 5 and 6 the result of this transformation is shown. Wakefields A, B and C are the same as have been used to investigate the influence of measuring inaccuracies. Design calculations for the propeller in the transformed fields have been performed, the results of which are shown ¡n the column of Tables

3,

4'and .marked with TH. The last two columns of these

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tables contain the differences ¡n geometry caused by the simulated measuring inaccuracies ¡n the wakefield and the differences caused by a transition from nominal wakefield to nominal ship wakefield. Later on these results will be discussed further in their relation with the manufacturing tolerances.

3. The manufacturing stage

Although ¡t ¡s beyond the scope of this treatise to discuss the various aspects of manufacturing a propeller, fully defined ¡n a numerical form, a brief description of the main characteristics of the manufacturing method ¡s given ¡n order to bring to mind the sources of deviations that may occur.

3.1. The manufacturing method

The numerical data defining the software propeller are, with the aid of a computer program, brought into a suitable form to be used by

the people who shape the components of the casting mould from a mixture of cement and sand. This computer program duely accounts for

the geometrical deformations and the chemical processes occurring during the actual casting as there are: the shrinking of the

liquid

material, the sagging of the mould and the forming of the so-called casting skin in the contact area between the material of the mould and the liquid metal. The number of components needed depends of course upon the number of blades of the propeller. These components are obtained by shaping one of them and copying the others from ¡t. The components of the mould then are put together _{on the location} where the propeller ¡s to be cast. It will be clear that the highest degree of accuracy is vital in this stage of the procedure because

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the possibilities to introduce errors are very numerous. After the casting, the propeller is moved to the machining site where the forward face of the hub, which will be used as a plane of reference henceforth, and the shafthole are machined. This operation again requires a high degree of accuracy as for example a small deviation ¡n angle of the forward hub face with the centreline of the shaft causes different pitch deviations for different blades resulting ¡n a more pronounced fluctuation of thrust and torque and their eccen-tricities during a revolution. The propeller is now measured with the use of measuring equipment especially designed for this purpose, of which a description ¡n more detail will be given later. The points on the propeller surface where the measurements have to be taken are

predetermined and remain fixed during the entire manufacturing process. The measurements are recorded on papertape. By a computer program which compares the measured propeller with the software propeller it is established at each measured point, to what depth

the material has to be ground off to meet standard tolerances. This program contains an iterative procedure to obtain a smooth surface on both back and face of the propeller, which deviates within tolerance from the software propeller and lies underneath the measured surface. This is achieved by consecutive approximations, based on the deviations derived from the measurements, with a

polynomial _{in the radius r and the angular coordinate q, of a degree}

as low as possible but no higher than . The finally obtained

polynomial represents the deviations that will remain between the finished hardware propeller and the software propeller. At each measured point a hole is drilled to show to the grinder to what

depth the material has to be removed. The propeller is then finished, measured again and this time the measurements are processed by a computer program to provide finally a printed certificate to be

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presented at the acceptation by the purchaser.

For the purpose of this paper it is not important to discuss amply the sources of the possible errors Introduced during the operì1ions

resulting ¡n the final propeller. Only the way in which the finished propeller ¡s compared with the originally designed one deserves

interest, because there the accumulated effects of all deviations are established. In this comparison the measuring equipment is of decisive importance.

3.2. The measuring equipment

In Figure 7 a schematic representation is shown of the measuring equipment. The propeller to be measured is placed with the forward face of the hub upon a circular horizontal table which is rotatable about a vertical axis. The centreline of the shafthole must coincide with the axis of rotation of the table. At the circumference of the table a gear ring with 180 teeth ¡s mounted. The propeller may be

rotated, almost without friction by way of an air bearing, by means of a hand wheel, see Figure 8. The propeller ¡s locked into position by either one of two locking pins entering a tooth space. The distance between the two pins, synchronized by a rod mechanism,

¡s such that the propeller can be rotated over one degree of arc at a time.

The second part of the equipment consists of a horizontal guiding frame on which a vertical column can be moved. Along this vertical column two horizontal arms with an adjustable relative position, move up and down. At the end of each arm ¡s a measuring probe which operates a micro switch, when activated with a certain pressure, and

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an ink spray device.

The third part of the equipment is an electronic unit which controls the motion of the table, the column and the arms, collects the

measured values, punches them into papertape and calculates local thicknesses and local difference ¡n height between consecutive measured points on one side of the propeller.

Although the ISO recommendation R+814-1966 (Ref. [9]) states that the inaccuracy of a measuring apparatus is allowed to amount to half of the tolerance, it has been considered favourable by the designers of this very measuring equipment to try to increase the accuracy as far as possible and reasonable with respect to cost. In workshops

commonly a measuring inaccuracy of one tenth of the tolerated

deviation is applied. It has been tried to arrive at the same figure for this apparatus as well. In Table 6 the actual inaccuracy of the equipment is given and the tolerances according to the ISO

recommendation for classes S, I and II.

The inaccuracy of such a complex machine is composed of several distinct inaccuracies in the parts of which ¡t is constructed. For instance:

- vertical distance between upper and lower probe.

angle over which the table rotates.

coplanarity of the path described by the measuring probes, when moved, and the axis of rotation.

- parallellity of the line connecting the two probes and the axis

of rotation.

rectangularity of the table surface and the axis of rotation. - _{uniquity of the relation between the electronics and the actual}

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of the measuring probes.

- resistance against sliding of the probes on the sloped surface

of the propeller blade.

Part of these conditions have been adjusted in the construction stage and are to be checked from time to time and if necessary readjusted.

As for the remaining part of the conditions a set of gauging aids has been developed and a well defined calibrating procedure ¡s executed before a propeller is measured. The actual measuring is started at the outer radius. The first measuring point of the first blade is moved to a position perpendicularly under the upper measuring probe, the arms are lowered and when the micro switch is operated the face point ¡s marked with ink and the direction of motion of the arms reversed. After the backside point has been measured the propeller

¡s rotated over a predetermined angle. One blade at a fixed radial position can be measured automatically, provided that the angle over which the propeller has to be rotated after each pair of measurements has been entered into the memory of the electronic steering unit. After the completion of one blade the propeller ¡s rotated manually to the first measuring point of the next blade. When all blades have been measured successively the vertical column ¡s moved to the next

radius inward.

4. Certîfication

In the certification procedure the measured dimensions of the finished propeller are compared with the geometry of the software propeller. This ¡s achieved by the use of a computer program, especially designed for this purpose. As a first step the program

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replaces improbable or unreliable measurements by interpolation. They may occur at places on the propeller surface, for instance where a

lifting eye has been cast-on. It is also meant to rectify possible temporary failure of the electronics of the measuring equipment or of the papertape punch or measurements maimed otherwise. After this

the deviations in local thickness and pitch are calculated together with other information to be compared with ISO tolerances. Finally a comprehensive review, the certificate, is produced of this comparison with the tolerances ¡n order to enable the accepter to check the data minutely.

It ¡s important to have an impression of the amount to which a

hard-ware propeller deviates from a softhard-ware propeller ¡n comparison with the current tolerances in a more general way. To investigate this the records of a number of propellers have been analysed. The computer program usually applied to certify a single propeller was adapted to collect data about a number of propellers and ¡n the end produce the collected results. The propellers chosen had all been finished to satisfy ISO tolerance class I. In Table 7 the number of propellers is shown together with the number of measured points and radii. A division of the propellers with respect to blade number has been made to create the possibility to study whether there are systematic

differences between propellers with different blade numbers. In this paper only the deviations in local thickness and the deviation in pitch over a radius have been considered. In Figures 9, lO and 11 the results with respect to local thickness are given. Jt can be

concluded that about 10 percent of all measured points is outside the thickness tolerance. This seems a rather large amount. But taking into account the requirement of ISO, that a propeller blade be measured at a minimum of 5 radii with at each radius at least 3

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points and considering the mean values from Table 7 viz. 8.9 measured radii with 1L+.O measured points, it ¡s obvious that for each

propeller blade it is possible to choose five radii, reasonably well divided over the blade, with at least three points per radius within tolerance.

lt is clear from the figures that as the thickness decreases the

fraction of points outside tolerance increases. Relatively small thicknesses are found in the tip region and at the leading and trailing edges of a propeller blade. A further investigation into this phenomenon, using the measurements of the 50 four bladed propellers, showed that ¡f only the points on the blades at the radii below .8R are considered 7.7 percent of the measured thicknes-ses is outside tolerance. If on the other hand the points within

12.5 percent from either the leading or the trailing edge are disre-garded, 6.6 percent is outside tolerance. In the tip region the blade lengths are in general smaller than in the remaining area of the blade. Because the number of measuring points increases per unit of arc near the edges, a profile with a small chordlength is measured at relatively many edge points in comparison with a longer profile. Taking into consideration that part of the effect of the tip region is caused by the relatively high amount of edge points near the tip, the effect of the edge points itself must be the most important. lt appeared that the points at the edge, i.e. 39 percent of all points, account for 56 percent of the points outside tolerance. This

relatively high amount of deviations outside the thickness tolerance at the edges is mainly caused by the tolerance on chordlengths. As the edges of a blade are finished with the aid of templates, _{a small} deviation in chordlength while preserving the shape of the nose of the profile and the coordinates of the measuring point results in a

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strong deviation in thickness. See Figure 12.

A slight increase in the fraction of points outside tolerance with increasing number of blades can be observed. This is explained ¡n the following way. A mould for e.g. a six bladed propeller consists of more components than that of a four bladed propeller. The accumulated

inaccuracy of the mould is therefore greater for a six bladed propeller than for a four bladed one. This leads often to more difficulty to bring the pitch within tolerance. As giving the propeller the right pitch is considered to be more important than bringing the thickness within tolerance at any cost, part of the points are allowed to be outside thickness tolerance in order to

improve the pitch. In addition propellers with higher blade numbers have in general smaller chordlengths than four bladed propellers which causes a relatively high amount of edge points with their

inherent thickness deviations, as explained above.

The radial pitch of all propellers at each radius considered, appeared to be within tolerance. Therefore the amount to which the tolerance has been used was investigated. The results are shown in Figures 13, l and 1. It can be seen that even if the tolerances

were halved, still only about ten percent would be outside tolerance.

5.

Accuracy and tolerance

In Section 2.3.1. ¡t has been endeavoured to assess the extent to which variations ¡n the input affect the geometry of the designed propeller. That the variations ¡n the software propeller are of the same order as the tolerated deviations is shown in Table 8, where the calculated differences ¡n the geometry of a propeller caused by

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on the one hand a simulation of measuring inaccuracy ¡n the wakefield 3nd on the other hand a transformed wakefield, meant to approximate the full scale wakefield are given, together with the tolerances. The tolerances on camber are calculated by a composlon of the maximum

tolerance on local pitch and thickness.

The tolerances for manufacturing and finishing ship screw propellers, as they are ¡n common use now, are meant to serve two purposes. The

first is to enable anyone who owns a workshop to manufacture and finish propellers, and to establish, also with simple measuring means, whether his product is within or outside tolerance. To this end use has been made of knowledge of and experience with tolerances prevailing for products of similar size and material. The second is

to ensure that the performance of a ft.rll scale propeller does not

deviate unreasonably much from the performance expected from the software propeller. This has been achieved by estimating and accounting for Full scale effects and the effects of deformation which a finished propeller may undergo caused by e.g. transportation, temperature change and application of the full hydrodynamical loading when operating behind the ship.

In this paper material has been provided to show that the tolerances also allow for inaccuracy in the information used for the design of the propeller which affects the propeller geometry.

6. Conclusions and final remarks

1. _{From the results of the study conducted in this paper the}

indication can be derived that the inaccuracy in the geometry of a software propeller caused by inaccuracy of the input is of

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manufacturing and finishing of the hardware propeller.

The fact that results of tests performed by a towing tank imply inaccuracies originating from measuring and statistical

operations should be recognised to a larger extent. Rather than to state the results ¡n an apodictic way ¡t is desirable to accomplany them with the inaccuracy of the data. Predictions as they depend on statistics, should be given together with the way they are obtained and with information showing the degree of reliability e.g. in the form of confidence intervals.

The performance of a propeller is judged by its properties in full scale regarding power absorption, cavitation and strength. Tolerances for manufacturing and finishing should therefore be

formulated in those terms rather than ¡n purely geometrical terms.

References

NILLSON, G. and RESTAD, K. "Problems ¡n full scale propulsion from a shipbuilder's viewpoint'', Proceedings of Third Lips Propeller Symposium.

COX, G.G. "Propeller design methods and decisions'', Proceedings of 13th ITTC, 1972.

SASAJIMA, H. and TANAKA, _{I. "On the estimation of wake of}

ships", Proceedings of 11th ITTC, Tokyo.

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based on model wake survey", Proceedings of NSMB Symposium on: High powered propulsion of large ships. December l97i.

KEYSER, R. and ARNOLDUS, W. "Strength calculation of marine propellers", International Shipbuilding Progress. Vol. 6; No.53, 1959.

MORGAN, W.B., SILOVIC, V. and DENNY, S.B. "Propeller lifting surface corrections", Paper presented at annual meeting of SNAME. November 1968.

7 OOSSANEN, P. VAN "Calculation of performance and cavitation

characteristics of propellers, including effects of non-uniform flow and viscosity", Doctors thesis, Technical University, Delft, The Netherlands. June 1972.

VOOGD, A.A. "Some developments in the design of cavitation erosion free propellers", Proceedings of NSMB symposium on: High powered propulsion of large ships. December 197k.

ISO "Recommendation for manufacturing tolerances for casting and finishing ship screw propellers", ISO/Rk8k-1966 (E).

(26)

Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15

Flow diagram of design computer program.

Cavitation phenomena observed in three different ca-vitation tunnels with one propeller in one condition. Measured wakefield.

Wakefield with simulated measuring inaccuracies. Wakefield A. Wakefield A transformed. Wakefield B. Wakefield B transformed. Wakefield C. Wakefield C transformed.

Principle of measuring equipment. Photo of measuring equipment.

Number of measured points within or outside ISO class

I thickness tolerance, _{in percents, per thickness}

class, of 50 four bladed propellers.

Number of measured points within or outside ISO class I thickness tolerance, in percents, per thickness class, of 26 five bladed propellers.

Number of measured points within or outside ISO class

I _{thickness tolerance, in percents, per thickness}

class, of 15 six bladed propellers.

Illustration of thickness deviations due to tolerance on blade length.

Number of measured radii, divided into classes of the extent to which the ISO class I pitch tolerance over a radius is used, _{in percents, per class of height} difference, of 50 four bladed propellers.

Number of measured radii, divided into classes of the extent to which the ISO class I pitch tolerance over a radius is used, _{in percents, per class of height} difference, of 26 five bladed propellers.

Number of measured radii, divided into classes of the extent to which the ISO class I pitch tolerance over a radius is used, _{¡n percents, per class of}

height difference, of 15 six bladed propellers.

Figure 1 Figure 2 Figure 3(1) Figure 3(2) Figure 4(1) Figure 4(2) Figure i(i) Figure 5(2) Figure 6(1) Figure 6(2) Figure 7 Figure 8 Figure 9

(27)

Sequence of activities.

Sources of information to the designer.

Effect of simulated measuring inaccuracies and trans-formation of the wakefield on some parameters of the geometry of propeller A.

Effect of simulated measuring inaccuracies and trans-formation of the wakefield on some parameters of the geometry of propeller B.

Effect of simulated measuring inaccuracies and trans-formation of the wakefield on some parameters of the geometry of propeller C.

Comparison of inaccuracy of measuring equipment with tolerances.

Information about the propellers of which the certi-fication measurements were analysed.

Comparison of deviations from Tables 3, 14 _{and 5 and}

tolerances of ISO class I. Table i Table 2 Table 3 Table 14 Ta b i e 5 Table 6 Table 7 Table 8

(28)

Table 1. Sequence of activities. stage starting datum activity result 1. input [I + I] design

[o +

AD] software propeller = F (1,D)

AP(AI,AD)]

2. software propeller [P5] manufacturing [M + AM] hardware propeller h = Ph(P,M) +

APh(AP,M)]

3. hardware propeller certification [C + AC]

summary of deviations [0Ev

=

(29)

Table 2. Sources of information to the designer.

shipyard ship dimensions

draughts

prevailing sailing condition possible ice strengthening mission profile

expected shipspeed

engine manufacturer engine characteristics

advised design power-rpm combination

towing tank _{result of resistance test}

result of self-propulsion test expected sh i pspeed

open water diagram of propeller used wake survey

(30)

PROPELLER A

Table

3.

Effect of simulated measuring inaccuracies and

transformation of the wakefield on some parameters

of the geometry of propeller

A. VALUE OF C TH

A(.95,1.05)

A(1.00,TH)

.90

.95

.98

1.00

1.02

1.05

1.10

Blade area ratio

.532

.529

.530

.527

.529

.527

.551

.000

Mean pitch (mm) 4818 4829 4834 14839 4843 14849 4858 4836 20

Camber (mm) Radial station

1.0

6.2

6.14

6.3

6.7

6.9

7.1

7.5

6.9

0.7 .975

11.8

11.6

11.14 11.14

11.3

11.1

10.8

12.6 -0.5

.95

16.0

15.5

15.1 114.9

l'i.6

114.2

13.5

17.1

-1.3

.9

19.8

19.0

18.5

18.2

17.9

17.4

16.6

22.6 -1.6

.85

22.6

21.7

21.2

20.9

20.5

20.0

19.0

25.8 -1.7

.8

25.7

24.8

214.3

23.9

23.5

23.0

22.0

28.6 -1.8

.7

36.0

35.3

314.9

34.7

34.2

33.9

33.0

34.4

-1.14

- 0.3

.6

49.2

148.3 148.3 148.4 148.2 148.3

48.5

38.9

0.0 - 9.5

.5

56.0

54.7

55.3

55.9

56.1

56.8

58.8

45.8

2.1 -10.1

.4

59.0

60.8

61.9

62.8

63.3

64.5

67.8

63.6

3.7 .35

60.0

62.0

63.3

64.2

64.9

66.2

69.6

68.8

14.2

.3

57.9

60.1

61.5

62.5

63.3

64.7

67.9

70.2

4.6

hub

56.2

58.5

59.9

60.8

61.8

63.14

66.3

69.4

14.9

Thickness (mm) Radial station

1.0

18.0

18.1

18.0

.1

.975

20.8

20.9

21.0

21.3

21.0

.2

.95

23.9

214.0 214.0 214.1 214.1 214.3

24.8

24.4

.3

.9

31.1

31.3

31.5

31.8

32.8

32.2

.5

.85

39.14

39.7

39.8

140.0

40.1

40.5

41.8

141.2

.8

48.9

49.3

149.4

49.7

49.8

50.3

52.0

51.4

1.0 .7

70.9

71.6

71.8

72.2

72.3

72.9

75.0

75.1

1.3 .6

97.0

97.9

98.2

98.7

98.9

99.14

101.8

102.8

1.5 .5

127.9

128.9

129.14

130.0

130.3

130.6

133.0

135.7

1.7 .4

165.7

167.1

167.6

168.14

168.8

169.1

171.2

176.3

2.0

.35

188.6

190.0

190.7

191.5

192.0

192.14

194.2

201.1

2.4 .3

215.1

216.6

217.5

218.2

218.8

219.5

221.0

230.2

2.9

hub

224.9

226.4

227.4

228.0

228.7

229.5

230.9

241.9

3.1

(31)

PROPELLER B

rrect or simuiatea measuring inaccuracies and transtormation of the wakefield on some parameters

of the geometry of propeller B.

VALUE OF C TH A(.95,1.05) .90

.95

.98

1.00

1.02

1.05

1.10

Blade area ratio

.1469 .1450 .467

.468

.473

.474

.499

0.023

Mean pitch (mm) 21457 21458 21461 21461 21463 2464 2467 24142 6

1.0 14.2 14.2

3.6

3.8

3.14

3.7

7.9 - 0.5

.975

7.5

7.14

7.3

7.2

10.1

- 0.1

.95

10.2

10.0

10.2

10.1

10.2

10.1

9.8

12.0

0.1 .9

13.7

13.3

13.2

13.1

13.0

12.7

14.6 - 0.3

.85

16.14

15.8

15.9

15.8

15.7

15.5

15.3

16.9 - 0.3

.8

19.1

18.4

18.5

18.14

18.3

18.2

18.0

19.2 - 0.2

.7

24.2

23.6

23.8

23.7

23.6

23.4

23.3

0.0 .6

27.3

27.0

27.6

27.7

26.6

0.7 .5

29.14

29.4

30.3

30.14

30.5

30.8

31.2

29.2

1.14 .14

31.0

31.5

32.5

32.7

33.0

33.4

314.1 31.14

1.9 .35

31.9

32.6

33.5

33.8

34.1

3l4.7

35.6

32.5

2.1 .3

33.1

33.8

34.6

35.0

35.4

36.0

37.0

33.14

2.2

hub

33.3

34.3

35.0

35.1-i

35.8

36.4

37.5

33.8

2.1

1.0

9.0

0.0 .975

10.3

10.2

10.3

10.2

0.0 .95

11.7

11.6

11.7

11.14

0.0 .9

114.8 114.8

14.8

114.8

14.8

15.0

14.5

0.0 .85

18.4

18.5

18.7

18.0

0.1

.8

22.5

22.6

22.9

22.1

0.1

.7

32.1

32.0

32.1

32.2

32.3

32.6

31.8

0.3 .6

143.3

43.3

143.4 143.5 143.5 143.6

44.1

43.7

0.3 .5

56.5

56.6

56.7

56.8

57.0

57.6

57.7

0.5 .4

72.0

72.1

72.3

72.14

72.6

72.8

73.4

74.1

0.7 .35

80.8

81.1

81.3

81.5

81.6

81.8

82.5

83.4

0.7 .3

90.6

91.0

91.3

91.5

91.7

92.0

92.5

93.14

1.0

hub

94.3

94.8

95.1 95.14

95.5

95.9

96.4

97.2

1.1 L

rrr_

-r

i . . a

(32)

-PROPELLER C

Table 5.

Effect of simulated measuring inaccuracies and transformation of the wakefield on some parameters of the geometry of propeller C.

VALUE OF C TH (.95,1.o5) A(l.00,TH)

.90

.95

.98

1.00

1.02

1.05

1.10

Blade area ratio

.490

.486

.48'-I

.482

.485

.489

.531

-0.001

Mean pitch (mm) 3861 3869 3873 3876 3879 3883 3889 3851 14

Camber (mm) Radial Station

1.0

7.3

6.3

7.0

6.3

6.6

7.1

6.7

7.7

0.8 .975

12.2

11.8

11.7

11.5

11.0

12.4 - 0.3

.95

16.3

16.2

15.7

15.9

15.5

15.2

14.6

16.3 - 1.0

.9

22.0

21.5

21.2

20.9

20.7

20.4

19.8

21.7 - 1.1

.85

26.7

26.1

25.8

25.5

25.4

25.0

24.5

26.6 - 1.1

.8

31.2

30.5

30.1

29.9

29.7

29.4

28.9

31.2 - 1.1

.7

38.5

37.9

37.5

37.2

36.9

36.6

38.8 - 1.0

.6

43.4

43.1

42.9

42.8

43.0

43.2

44.6 - 0.1

.5

46.4

46.6

46.8

46.9

47.4

47.8

48.7

48.9

1.2 .4

48.2

49.0

49.6

50.1

50.8

51.5

53.0

52.3

1.5 .35

48.8

50.0

50.8

51.4

52.1

53.1

54.8

53.8

3.1 .3

49.3

50.9

51.9

52.6

53.3

54.4

56.2

55.3

3.5

hub

47.8

49.7

50.8

51.5

52.3

53.4

55.2

56.4

3.7

1.0

15.0

14.9

15.0

14.9

15.1

0.0 .975

17.2

17.0

0.0 - 0.2

.95

19.6

19.7

19.8

19.7

19.3

0.1 - 0.4

.9

25.3

25.4

25.5

25.6

25.5

24.7

0.2 - 0.8

.85

31.9

32.1

32.2

32.3

32.2

31.1

0.2 -.8

39.4

39.6

39.7

39.9

39.8

38.5

0.3 -.7

56.6

56.8

57.1

57.4

57.3

57.5

57.4

56.0

0.7 - 1.4

.6

76.5

76.9

77.3

77.6

77.7

77.9

78.0

76.9

1.0 - 0.7

.5

100.0

100.4

101.0

101.4

101.6

101.9

102.1

101.9

1.5 .4

129.5

130.0

130.5

131.0

131.2

131.6

131.9

132.7

1.6 .35

148.0

148.4

148.9

149.2

149.4

149.7

150.1

151.3

1.3 .3

170.2

170.3

170.6

170.8

170.9

171.1

171.3

172.8

0.8

hub

191.3

191.2

191.1 191.1 191.1 191.1

192.6 - 0.1

(33)

Table 6. Comparison of inaccuracy of measuring equipment with tolerances. Tolerances on inaccuracy S I II Local pitch, with a minimum of 0.2 °/ 1.5 ° 15 mm 2.0

°

20 mm 3.0 30 mm Tip radius,

withaminimumof

0.5 mm 0.25

2mm

0.5 °/ 3mm 0.5 3 mm Thickness, with a minimum of 0.25 0.25 mm 1 1 mm 1.5 °/ 1.5 mm 2 2 mm

(34)

Table 7.

Information about the propellers of which the certification

measurements were analysed.

Propeller type Number of measured propellers Number of measured points Number of measured radii

Average number of measured points per radius

Average

Four bladed Five bladed Six bladed

50 26 15 214512 16015 111406 1760 1130 828

13.9 li.2

13.8

Total 91 51933 3718 114.0

(35)

Table

8.

Comparison of deviations from Tables

3,

14

and

5

and tolerances of ISO class I.

A(.95.1.05)

A(1.00,TH) A

SOclass

IA(.95,1.05) A(1.00,TH) A

ISOclass

IA(.95,1.05)

A(1.00,TH) L ISOclass I

Blade area ratio

.000 .021

0.023

.031

-0.001

0.049

Mean Pitch (mm) 20

-3

-148.1+ 48.+ 6 -1

-21i.6

2L,.6 114

-25

-38.8

1.0

0.7

0.2 -1.3

1.8 -0.5

14.1

-1.3

1.8

0.8

1 '4

-1.2

.975

-0.5

1.2 -1.3

1.8 -0.1

2.8 -1.3

1.8 -0.3

0.7 -1.2

.95

-1.3

2.2 -1.3

1.8

0.1

1.9 -1.3

1.8 -1.0

0i

-1.3

.9

-1.6

11.1,

-1.3

1.8 -0.3

1 14

-1.3

1.8 -1.1

0.8 -1.3

.85

-1.7

".9

-1.3

1.8 -0.3

1.1

-1 1

1.9 -1.1

1.1

-1.3

.8

-1.8

4.7

-1 1'

1.9 -0.2

0.8

-1.14

1.9 -1.1

1.3

-1 14 .7

-1.4

- 0.3

-1.5

2.0

0.0 -0.4

-1.5

2.0 -1.0

1.6

-1.14

.6

13.0

- 9.5

-1.5

2.3

0.7 -1.0

-1.6

2.1 -0.1

1.8 -1.5

.5

2.1 -10.1

-1.9

2.8

1 1

-0.8

-1.7

2.2

1.2

2.0 -1.6

1

3.7

0.8 -2.3

3.5

1.9 -1.3

-1.9

2.14

1.5

2.2 -2.0

.35

1+.2 14.6

-2.5

3.9

2.1

-1.3

-1.9

2.1,

3.1

2.14

-2.2

.3

14.6

7.7 -2.8

4.14

2.2 -1.6

-2.0

2,5

3.5

2.7 -2.4

hub

4.9

8.6 -2.9

4.6

2.1 -1.6

-2.1

2.6

3.7

14.9

-2.6

1.0 0.1 0.0

-1.5

2.5

0.0

0.0 -1.5

2.5

0.0

0.2 -1.5

.975

0.2

0.1

-1.5

2.5

0.0

0.0 -1.5

2.5

0.0 -0.2

-1.5

.95

0.3

0.3 -1.5

2.5

0.0 -0.2

-1.5

2.5

0.1

-0.14

-1.5

.9

0.5

0.7 -1.5

2.5

0.0 -0.3

-1.5

2.5

0.2 -0.8

-1.5

.85

0.8

1.2 -1.5

2.5

0.1 -0.14

-1.5

2.5

0.2 -1.2

-1.5

.8

1.0

1.7 -1.5

2.5

0.1 -0.5

-1.5

2.5

0.3

-1.14

-1.5

.7

1.3

2.9 -1.5

2.5

0.3 -0.3

-1.5

2.5

0.7

-1.14

-1.5

.6

1.5

14.1

-1.5

3.0

0.3

0.2 -1.5

2.5

1.0 -0.7

-1.5

.5

1.7

5.7 -2.0

3.9

0.5

0.1 -1.5

2.5

1.5

0.5 -1.5

1

2.0

7.9 -2.5

5.1

0.7

1.7 -1.5

2.5

1.6

1.7 -2.0

.35

2.4

9.6 -2.9

5.7

0.7

1.9 -1.5

2.5

1.3

2.1 -2.2

.3

2.9

12.0 -3.3

6.5

1.0

1.9 -1.5

2.7

0.8

2.0 -2.6

hub

3.1

13.9 -3.9

6.8

1.1

1.8 -1.5

2.9 -0.1

1.5 -2.9

PROPELLER A PROPELLER B PROPELLER C

(36)

wake f ¡ e d p repa ra t i on power i terat ¡on strength calcul a t ¡ on cay i ta t i on

ca] cul a t ion

printing

resu] ts

Figure 1. Flow diagram of design computer program.

giving mean pitch

giving distribution of maximum thickness giving distribution of chordlength and camber

J

(37)

Cavitation tunnel I: Acceptable cavitation pattern at the back; _{Cavitation tunnel II: Unacceptable because of bubble cavitation} _{Cavitation tunnel III: Unacceptable,}

too heavy, unstable backsheet with bubble cavitation.

Fig&ire 2. CavItation phenomena

(38)

(39)

(40)

(41)

WAKEFIELD C

0.4

0.2

Vx

(42)

Y

GIRCU LAR

TABLE

L':

-MEASURI NG ARMS

Figure 7. Principle of measuring equipment.

VERTICAL

COLUMN

(43)

(44)

20

lo

o Nr.of points

,wì

yy4

FIg. 9. Niaber

of

_{measured points within or outside ISO class I thickness}

tolerance1 in percents, p.r thickness class,

_{of 50}

_{four bladed propellers.}

24512

0- 20-

40- 60-

80- _{100-120- 140-160- 180- 200- 220-240- 260-280-} ₃₀₀ _total

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Thickness class (me).

90

*

(45)

20

lo

Nr.

Sf

pOints 0- 20- 3.0- 60- 80- 100- 120-13.0- 160- 180-200- 220-23.0- 260- 28O-300 total 20 3.0 60 80 100 120 13.0 160 180 200 220 23.0 260 280 3O Thicnsss class ().

FIg. 10. Niab.r of ..asur.d points within or outside ISO class I thickness

tolerance, In percents, p.r thickness class, of 26 fIve bleded propellers.

90

(46)

90 * 20 lo o Nr. of points 0- 20- 40- 60- 80-100- 120- 140-160- 180- 200-220- 240260- 280- 3OO 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Thickness class ().

FIg. 11. Nia.b.r of measur.d points within or outside ISO class I thickness

toisrance, in percents, p.r thickness class of 15 sIx blad.d propellers.

11406

total

UPPFI'

D

within tol.rance

outside negativ. toI. outside positive tal.

4

(47)

(48)

90 80 70 60 50 40 -30 20 10 o Nr.of radi ¡

Height difference class over a radius

Fig. 13. Number of measured redil, divided Into classes of the extent to which the

ISO class I pitch tolerance over a radius is used, in percsnts, per class of height difference, of 50 four bladed propeller..

I

1760 total 36 212 180 220 164 244 236 276 84 64 32 4 100 200 300 400 500 600 700 800 ₉₀₀ 1000 1100 1200 200 350 450 510 610 710 850 910 1500 i f50 1210 1350

(49)

90 80 70 60

*

50 40 30 20 10 o

I

lII'ïPT

"I4III1I '

1130 total 165 50 20 50 20 15 50 30 90 700 850 800 900 1000 910 1 oSo 1110 1100 1210 1200 1300 lkOO 1310 1 klO 1550 >1500 Nr.of 5 25 100 125 130 lleO 115 rad i 0 100 200 300 kOO 500 600

ib

210 350

'ib

550 650 710

Height differ.nce class over a radius (ima).

Fig. 1k. Nber of measured radii, divided Into classes of the extent to which the

ISO class I pitch tolerance over a radius Is used, in percents, per class

(50)

90 80 70 60 * 50 eO 30 20 lo o Nr.of radii ₁₀₀ ₂₀₀ 300 400 500 600 700 800 900 1000 1100 1200

250 350 5o 550 CSo 750 BSO 950

i5oo i iSo

1250 1350

Height difference class over e radius (nvs).

FIg. 15. _{Number of measured radii, divided into class.s of the extent to which the}

ISO class I pitch tolerance ovsr a radius is used, in percents, p.r class

of height diff.renc., of 15 six bladed propel lars.

Deviation between ptc.and ptc.of

to-O - 25 lerance

25 - 50

50 - 75

75 -100