The Controllable Pitch Propeller as a Pitch-Govenor

Paper prepared for the

Third Ship Control Systems Symposium

26 - 28

September 1972

Bath, United Kingdom

ibliotheek van

-Onderafdelin5

ei-bsbouwkunde tiTsclie Hogeschoo DOCUMENTATIE

DATUM:

1DOCUMENTATIEI

THE CONTROLLABLE PITCH PROPELLER AS A PITCH -GOVERNOR

4-72ci

By

ei,4n4,/

C. Pronk

LIPS N.V. Propeller Works Technical Report No.

871-7224

-Table of contents

Page

Abstract ₃

introduction ₃

Rotating system ₅

Fluctuation of propeller torque 6

Response of the uncontrolled system

Pitch changing ₉ Discussion ₁₀ Conclusions ₁₀ List of symbols ₁₁ References ₁₃ Appendix 14 .. ... . . .

THE CONTROLLABLE PITCH PROPELLER AS A PITCH - GOVERNOR

Abstract

A brief description is given of the control systems nowadays applied to controllable pitch propellers. The potentialities of the control system in which the controllable pitch propeller is used as a pitch-governor in constant r.p.m. installations are inveStigated. The fluctuations in r.p.m. due to wave load and controlled by a pitch-governor can be described as a one mass-spring system excited by forces expressed in a spectrum. The damping forces, which are determined on a quasi-stationary basis, are significant. The conclusion is made that the rate of pitch change as well as the magnitude of the changes itselves which are needed to use the controllable pitch

propeller as a pitch-governor, can be coped with by present designs. The expected number of changes over the lifetime requires a reconsideration of the design of servo mechanism and blade suspension in view of wear.

Introduction

Considering the principle of control systems applied to ships equipped with

controllable pitch propellers, we can distinguish three types, which are in operation (see reference [l])

programmed control (P.R.C.). This type has been applied in the majority of running ships. The characteristic feature is that rotational speed and propeller pitcn are the two parameters controlled simultaneously.

It will be clear that for the P.R.C. type an additional overtorque protection is necessary.

load control (L.C.1). Presently, this appears to be the standard for gasturbine driven ships. Propeller pitch is maintained at a prescribed value, only the thermal load of the gasturbine - rotational speed of compressor - is varied when a speed alteration is required.

load control (L.C.2). The name of this type is misleading, since the parameters which are maintained at their desired values are rotational speed and propeller pitch. This second type of load control has been derived from the P.R.C. type by extending the overtorque protection to a "protection' of an arbitrary torque value. In figure 1 a L.C.2 control system is shown.

3

-In case of exceeding this controllable torque value the corrective action cnanges the desired pitch value. So in fact L.C.2 only controls the load temporarily. Nevertheless this appears to be the forerunner of the load control as mentioned in reference [2] : the control system which maintains

torque and rotational speed at their desired values.

In the case of the latter type of load control the conventional action of the governor

should be

adapted and the propeller pitch instead of the fuel rack is controlled by the governor. The expression pitch-governor which is often used in this connection originates from a variant of the P.R.C. system. This variant is planned on board of ships with alternators connected to the shaftline. In this case the rotational speed

is allowed to vary only within narrow limits. It is already known from ships equipped with fixed pitch propellers that the disturbances due to the environment can be such that the governor is unable to maintain the rotational speed within these

limits. Particularly, torque increase is limited and low r.p.m. values occur more easily than high values. When necessary the propeller pitch is adjusted to assist in keeping the rotational speed constant. Actually the pitch-governor acts with a rather wide dead band, in which only the engine-governor is used. So there are two control systems whereby the propeller pitch is used to keep the rotational speed constant.

In the load control system with pitch-governor pitch changes occur more often than in the P.R.C. system with pitch-governor. In this respect it is useful to realise that the propeller is originally a device to transform rotational energy in trans-lational energy. In reference [3] a review is given of the evolution of the purpose of the controllable pitch propeller and the relation to its construction. This review

shows an increase in the frequency of pitch changing. Except for the cases in which tne propeller acts as a pitch-governor, on board of ships where manoeuvring takes much of the lifetime, such as ferries, harbour tugs, dynamic positioned drilling ships,

pitch changing occurs most frequently. An average frequency of one change per minute over the lifetime of the installation is a realistic figure, and is incorporated in

present designs. The rate of pitch change will be high at ships with relatively low displacement or in ships like dynamic positioned drilling ships. A rate of pitch change of 20 degrees per second has been realised. When the controllable pitch

propeller should act as a pitch-governor, it is very well possible that the required number of changes per unit of time and the rate of pitch change as well as the

magnitude of the change of pitch with respect to adjusting forces lie beyond what can be obtained with present c.p.propeller designs.The reliability of the controllable

pitch propeller will be influenced by using this device in _{circumstances not considered} in the development of the standardized construction. Therefore _{an investigation in the} action of the controllable pitch propeller as a pitch-governor is desired. Although

the pitch-governor at the moment is applied _{to assist the engine-governor, the action} of the pitch-governor performing all the corrective _{action will be considered below.}

Rotating system

The rotation of the snaftline is caused and maintained by prime mover and propeller torque. The coupling with other motions of the system only occurs via the propeller torque. The rotational acceleration of a single shaftline can be described by the differential equation : d [in] 27 dt _Pm (n,F) . f - Qprop (n X.,t) in which = time [sec]

= rotational speed [revs.sec-1]

= moment of inertia of all connected parts reduced to propeller revolutions, included added inertia [kg.m2]

Pm = prime mover torque, in case of reduction gear multiplied by gear ratio [N.m]

= fuel consumption per unit time [m3 sec-1]

prop = propeller torque [N.m] = pitch angle at .7 Radius

Xi = ordinates and velocities of propeller relative to water [m] and [m sec-1]

= coefficient allowing for shaft friction (f = 0.97)

It _{is assumed that the fluctuations in rotational speed are reacted by the propeller}

only, so the fuel consumption is supposed to be constant. The propeller torque is fluctuating continuously due to waves, shipmotions, corrective action of pitch and

resulting changes of r.p.m.. Differentiating equation (1) will separate the torque fluctuations due to these various effects

d2 [Jn] f ()-pm dn

27

dt2 Dn dt

pQprop dn

Dn dt

+ DQprop cli ₊ , prop 1

dX.

+ prop

4

dt i )(i _dt

9 t

Assuming that for an average propeller the change in _{moment of inertia for limited} pitch changes will be _{restricted to a small fraction of the total}

inertia, the

5 prop

derivatives

of J

can be neglected and the equation gets the form

d2n

a + =

_{AQpitch +Q}

dt2 dt

in

which

a '=, 27rJ is the inertia term

3Q DQ

prop.

f Pm represents the damping 1

1

3n

M

A .

Qpitch

AQ'env

lh the appendix 4 short.discussion. is given on the magnitude of the inertia and damping terms in equation (2). From these, values can be derived that the propeller damping, is of high importance. Therefore. the response

of

_{the system will l'oe highly} determined by the propeller damping,

Fluctuation of propeller_torque

The frequency of pitch changing will be

in

the Same order of magnitude as the frequency of encounter with the waves. For this frequency range, lt, _{can be assumed} that quasi-steady considerations can be applied for the determination of the propeller torque. Then the torque alteration, per degree of pitch change can be obtained from the propeller open water diagram. In figure 2 an open water diagram of a tontr011abie pitch propeller is given. The partial derivative of the propeller'

torque is aK, prop p n2 I (). I

prop

dcp

rate of propeller torque alteration due to pltch changing

4

dt

IQ dX. alcI i

I

prop J

4. prop: _{rate of. torque fluctuation due to 'short}

i OXi dt _at

term disturbances from the environment

From the open water diagram can be noted that for moderate changes of pitchlthe derivative of KQ

tan be

assumed to be, constant. So the torque alteration AQ;

itch can be written as follows :

AQpitch -= (n) dt

where Cpis only a, function of rotational speed and independent of propeller pitch. The' torque fluctuations due to the environment AQenv are much more

difficui ,

to

determine, even if we limit ourselves to longcrested head and,

following

seas'

...(3)

Jue to waves the waterparticles are subject to. orbital motions and consequently tre intake velocity in the propeller disk will be a function of time- The orbital velocity is a function; of the position, in the wave, which again, IS a function of the ship motions. In addition the surging motion causes, high velocities, of the propeller relative to the water, while unfortunately these velocities can have a. phase, angle with respect to the orbital velocities such that they add to each

other. This has been described, in reference [4]. Pitching and heaving have a direct influence on the position of the propeller in the wave ,(arbitail velocities) and relative to the watersurface and inclined flow in the propeller disk is caused by pitching. Also wake, fluctuations. are caused by pitching motions, as is clear from

the well-known influence of trim on wake., in figure 5 a scheme of the relation

between torque and seaway is given. This relation is so complex that no satisfactory' computational Method exists at the moment. Experimental data on torque fluctuations

in regular waves have been published in references, [5] and [6]. Although theory does not predict so, in both references is stated that a linear relationship, exists between wave amplitude' and torque amplitude, for Sine form waves provided the propeller

immersion is sufficient. for nigher wave heights this condition no longer holds- Then! the torque, is, strongly influenced by air suction] and partial submergence, It is

doubtful if qtasi-steady considerations can still be applied in this case, and if a,

linear relation with wave height will be found. The occurrence of the resulting propeller racing can be predicted as

is,

done in reference [7].. Particularly

in

irregular seas the

influence of racing on propeller torque can only be approximated. Therefore the following considerations will be limited to fully submerged, propellers.

The experimental results of references [5] and [6] make it possible to represent the torque fluctuation, by a spectrum, of which the spectral density will be

SQQ.

Ca

in which is S spectral density of seaway

= / 2.

S Aw

a - cc e

Q.a. = amplitude of torque fluctuation in regular sine form waveS with length such that frequency' of encounter' is

Accordingly in equation (2) can be inserted

YCO

7

A(lehv

[

/ 2 SQQ (we) dwe , wecos (wet E)

10,

in which c is the randomly distributed phase angle..

2

=

Response of the uncontrolled system

Since the exciting torque of the rotational fluctuations can be represented by sine series it _{is worth considering linearisation of equation (2) by assuming that the} damping-coefficient is constant for limited deviations in rotational speed. _{Then the}

linear superposition principle can be applied for the uncontrolled system. The

response spectrum can be obtained in the same manner as for any similar case in ship motion theory Snn 'JO Snn (we) dwe < 0 2 SQQ

Computing _{significant fluctuations in rotational speed and computing the probability} of exceeding a prescribed limit can be done with the well-known methods usrig the Reyleigh distribution for the maximum values of rotational speed. An _{example is given}

in table 1. From this example it can be seen that, with a certain probability P no pitch changings are necessary to keep the r.p.m. fluctuations within the allowable deviation in r.p.m. Ana. When no pitch changing is _{necessary, the spectrum of r.p.m.} fluctuations must satisfy the relation:

Ana 2

2 In f1/(1-P)1

If sufficient data on transfer functions would be available, prediction of the necessity of pitch changing under various conditions can be done in this way. The probability of meeting these various conditions is treated in _{reference [8]. An}

important factor in the response of the system is the absence of a restoring term

na

in the equation. Especially in following _{seas the transfer function gets a much} higher value than it would get with the presence of a restoring term, for then the other terms in the transfer function are highly influenced by the low frequency of encounter. Nevertheless the significant value of the r.p.m. fluctuation in following seas is smaller than in head waves due to the narrow spectrum. For the example of table 1, _{the values corresponding to Beaufort scale 11 in following seas are:}

significant r.p.m. fluctuation is 2 r.p.m.

probability of deviating from the nominal r.p.m. by more than 4 revolutions is : 0.024

Except for the restoring term the equation describing the _{fluctuation of r.p.m. is} identical to the equation describing the rolling of the ship. The analogy can be further extended.

-[na

Controlling the rolling of the ship by a fin stabilizer and controlling the rotational speed of the shaftline by a pitch-governor are both based on rotating a lifting surface around an axis perpendicular to the axis of motion of the

system. The rolling of a ship and its control by active fin stabilizers has been extensively treated in reference [9].

Pitch changing

In the preceeding paragraph it has been shown that in a sea-state with a spectrum such that (CO An 2 a Snn dwe > 2 In l/(1-P)1 0

pitch changing is necessary to limit r.p.m. fluctuations to values smaller than Ana. For present controllable pitch propeller installations the change in pitch

CIT can be written as

ccib

(nact - ndes) = c An(I)

where

nact = actual number of revolutions ndes = desired number of revolutions

Inserting =

odes + An in equation (2) and using relations

(3)

and (4) we obtain act

DK

aAii + bA[.1 =

-

_{p(ndes +} An)2 D5 --s- . An +

Qai we.cos(a)e t

+)

Dqb

or

2ccAn3

aAri + bal + cAn + An 2 + =

al

XQ.w

_e. cos(we.t + c.)1 ndes ndes2 i 1 1 aK in which : c = cc/) p D5 --1:-1 n2des Dcp

Linearisation leads to the following equation :

aAN + bAn + cAn = _{Qai we.cos(we.t + c.)}

1 d t e -ai . des 5 )

The coefficient c in tnis equation is linear with the coefficient c the controller and for present installations the coefficient c can have a magnitude equal to that of

the coefficient b.

The solution of equation (5) is well-known. The fluctuation in rotational speed can be represented by a spectrum. Also the propeller pitch changing and the resulting pitch angle can be described by a spectrum. For the propeller pitch spectrum holds

S.

=AnAn

In which the magnitude of c, is determined by relation (4) and describes the controller characteristics. Once the value of c Has been selected the rate of change of the

45

propeller pitch is known. Some numerical results are given in table 2.

Discussion

Although the available experimental data on torque fluctuations in regular waves are very limited, calculations with the available data indicate that the significant value of pitch alteration is limited. This means that the rate of pitch change as it can be applied for present installations would be sufficient for using the propeller as a pitch-governor. _{In this respect it can be mentioned, that the maximum lift force for} active fin stabilizers is _{limited by cavitation but on the other hand cavitation}

problems for tne propeller in a seaway are influenced in a favourable sense when using the propeller as a pitch-governor. With regard to the number of pitch changes tie available data are insufficient to come to a founded conclusion. However, we feel that Sue number of required pitch changes on routes with a high frequency of bad weather will be such that a thorough analysis of the construction

of the

servo-mechanism and blade suspension in view of wear will be necessary.

Conclusions

, owadays the potentialities of the control able pitch propeller as a pitch-governor are only partially utilised.

Fluctuations in r.p.m. are strongly influenced by the damping of the propeller. ilodel experiments are needed to obtain necessary data on the torque fluctuations

in regular waves.

- The necessary rate of pitch _{change and the sin'ficant values of pitch change are}

limited and can be coped with by present designs.

w

of

-- It _{is expected that wear of a controllable pitch propeller used as a}

pitch-governor will be such tnat its present design must be reconsidered.

List of symbols

a _{coefficient representing moment of inertia [kg m2]}

coefficient representing damping [kg m2 sec-1]

coefficient representing spring constant [N in sec-1]

cnaracteristic of controller

coefficient allowing for mechanical shaft friction

-,

rotational speed

Lsec1

j

-1-n actual rotational speed [sec j

act

ndes desired rotational speed [sec-1]

deviation from desired rotational speed

_[sec]

allowable-1

allowable deviation in rotational speed

_[sec]

time [sec]

intake velocity in propeller disk

_{[m sec]}

gradient

gradient of propeller torque [N m]

diameter [m]

-1-fuel consumption [m3 sec 1]

moment of inertia [kg m2]

advance coefficient

An

V A

KT AN1/3

Qaai

Snn, SAnAn we torque coefficient tnrust coefficient

significant fluctuation in r.p.m. [sec-1]

probability

torque of prime mover [N m]

torque of propeller [N m]

-11

rate of torque alteration due to pitch change [N m

_sec]

AQ.env rate of torque fluctuation due to environment

[N m sec]

amplitude of torque fluctuation in sine form wave [N m]

spectral density of torque [N2 m2]

spectral density of wave

[m2]

spectral density of rotational speed deviation [sec-2]

position and velocities of propeller relative to the water

[m] and [m sec 1]

phase angle

amplitude of sine form wave [m]

specific density [kg m-3]

pitch angle

frequency of encounter [sec-1] Pm Qprop

AQptch

prop -QQ AnAn env a

References

Prank, C.: "Selection and Simulation of Marine Propulsion Control Systems", paper presented at Technical Presentation Day Lips

Propeller Works, September 1971, International Shipbuilding

//

_Z)

Progress 1972.

Schanz, F.: "Lieber die gemeinsame Steuerung von Schiffsdieselmotor

und Verstellpropeller", Schiffstechnik 1963, Heft

51/52.

_,f I

6

Wind, J.: "The Development of Controllable Pitch Propeller Systems", Diesel and Gas Turbine Progress, November-December _1971.

"Investigation into the seagoing qualities of the single-screw cargo ship Nissei Maru by actual and model ship experiments", Report of

the Shipbuilding Research Association of Japan No. 1, 1954.

Vedeler, B.: "A note on wave influence on propulsion systems", European Shipbuilding No.

6, 1970.

Van Sluys, M.F.: "Performance and Propeller Load Fluctuations of a

Ship in Waves", Netherlands Ship Research Centre TNO Report

No. 163 S,

1972.

Van den Berg, W.: "Aspecten van de voortstuwing van schepen in zeegang", Graduation Thesis Delft University of Technology, 1970.

Zubaly, R.B.: "Average Power Increase due to Waves for a Ship on a

Specific Trade Route", International Shipbuilding Progress 1970.

Conolly, J.E.: "Rolling and its Stabilisation by Active Fins",

Transactions of Royal _{Institution of Naval Architects, Volume 111, 1969.}

13

[2]

Appendix

Discussion on magnitude of inertia and damping

Inertia

For the inertia of the propeller a thumb rule exists which approximates the moment of inertia by WD2 = 15 D5. The added inertia is strongly depending on the pitch and the blade area ratio. For a propeller with a pitch diameter ratio of 1 and a blade area ratio of .55 an added moment of inertia is approximately 25% of the moment of inertia of the propeller itself. The moment of inertia of prime mover, gearbox and possible alternators is hard to relate to the moment of inertia of the propeller. An estimated value of the coefficient a will be a = 5 D5.

Damping

In figure 2 an open water diagram is shown of a propeller out of a systematic series. From tnis diagram the KQ gradient can be obtained and inserted in the formula

prop

- 2K pn

D5 Th

This leads for a velocity of 20 kn. and a diameter of 6 m to Q

p

VA Di4

The damping of the prime mover can be 40% of the propeller damping, but can have opposite signs for diesel engine and gasturbine.

Concluding one could state that the ratio between damping and inertia can vary witnin a wide interval, but an average value of 4 can be used.

t

TABLE 2 Influence of pitch control on r.p.m. fluctuation. Significant changes in pitch angle.

Beaufort scale Significant fluctuation in r.p.m. Probability of exceeding limit of 4 r.p.m. deviation 5

1.02

_.001 7

2.55

_.007

9

4.45

.20 11

5.70

_.38

Beaufort scale Significant r.p.m. - fluctuation AN1/3

uncontrolled

Significant r.p.m. - fluctuation AN1/3 controlled Significant pitch change Alp1/3 [degr] Apparent average period of pitch change [sec] ( C = 12 ) 5

1.02

0.72

.12

6.97

7

2.55

1.72

_.40

_7.29

9

4.45

2.93

.70 7.54 11

5.70

_3.75

_.91

_7.65

TABLE 1 Significant r.p.m. fluctuation and probability of exceeding the limit of 4 r.p.m. calculated for a freighter of appr. 16000 tons, Froude number

0.17

in longcrested head seas and sea-state

represented by Pierson-Moskowic spectrum.

A ST E RN I I I I PITCH SETTING 11 SPEED SETTING 11 11

PITCH CORRECTIVE SIGNAL

R.RM SIGNAL N

to

I 4444m

If

LOAD ADJUST

PROGRAMMED PNEUMATIC-HYDRAULIC REMOTE

CONTROL WITH IPLOT (load control) SYSTEM

figure 1

LOAD ADJUST KNOB

LOAD CONTROL BOX LOAD SENSOR LOAD CONTROL CYLINDER PNEUMATIC RECEIVER GOVERNER PNEUMATIC MICRO SWITCH

4 WAY VALVE

SERVO CYLINDER

FEED BACK BOX

RELIEF VALVE

BACK PRESSURE VALVE

HYDRAULIC PUMP SERVO VALVE PROPELLER OILTRANSFER UNIT R.P. M SENSOR

K

''

NM

EMIL

h

... 1 1 FIGURE. 2

Open water characteristics for propeller from Lips controllable pitch propeller

,

11LIIIIIIhl

Ne

mi,

systematic series, running ahad. Aumber of blades

4

Blade area ratio

4

0.545

Pitch diameter ratio

1 14

.

Hub diameter ratio

1 0.28

NNEEL

K.,.

...,-,,

41Wklillfilltki

-11) KQ .

1lA

liklib

+ 2.5

1%12. 5.

:\

\...

,

1141

1,/11/4W

11-'4NI

littei

1 o°

Ihk_

It.

L

. 1_

ft.. .'

. ba

___,

'NEIL

.'"4111111111111

-.1111111..

we -- '12.5° .

-1)° SI

-w44111

I.

hb,.

1111kh

.,

IMH"nilliL-1111111111h.___.

_ -22.

Ii

01

0.3 0.6

07

09

1,0 11 1.2 13

1.1

045

050

0_3

03

02

: : 5°

02

0,9

£17

05

03

0.1

propeller torque seaway

FIGURE 3 Relation between seaway and propeller torque. ship motions orbital velocity position of propeller in waves wake propeller velocity immersion intake velocity