A note on dynamometer system of jointed segmented ship model

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A Note on Dyriamometer System of Jointed Segmented Ship Model (Preliminary outline of the problem)

by

B. V. Korvin-Kroukovsky.

January 1, 1961.

In the now familiar analysis of ship motions and ship bending

moments the analyses are carried _{out on basis of the vertical (z)}

components of all forces arid the effect of the fore-and-aft (X)

components is neglected. This is _{justified since the net X component} for a ship Is very small in comparison _{to the vertical Z force,}

the center of buoyancy and. the center of gravity are not too widely separated in vertical direction, _{and the pitching moment of the}

hydrodynamic force abput C.. therefore _{is negligibly small. Irr} model tests the model is usually _{pivoted at C.(.}

The horizontal components of various forces, _{however, should} not be neglected in the dynamic _{analysis of an individual segment}

behavior, _{The unbalanced horizontal force in this case .is consideraWa,} and in the bow and stern sections is of the same order of magnitud.e

as the vertical force. Short length of a segment and _{often large} vertical distance between dynamometers _{and C.C.. (and C.B.) permit a} pronounced rotation of a segment and _{an appreciable horizontal}

displacement of C.G., leading to a complex three-mode motion.

The following formal statement of the _{problem is sketched on} the assumption of a _{pure heaving motion of the segment-supporting}

strongbaci4vith circular frequency (.Q . The same reasoning (but somewhat more complicated) will _{apply to the pitching motion and} to the motions in waves. _{The accompanying sketch show segment}

supported by three dynamometers (i),(ii) _{and (iii). The set of}

coupled equations 1,2 and 3 is written _{visualizing instantaneous} downward motion of the strongback _{and upwards directed (positive)}

inertial, buoyancy and hydrodynami c forces. Symbols:

rn, J _{mass and mass moment of inertia of}

a segment of a jointed ship model,

z

vertical displacement of the strongbacic, assumed to be infinetely rigid.

Z,X,M Total vertical and horizontal _{forces and pitching moment}

acting on a segment0

83 _{deflections of dynamometers I, II and III} k1, k2, k. _springconst, " ti It II

F _{Toral time-dependent force caused ty water pressures}

(exclusive of hydrostatic).

Phase lag angles with respect to the _strongback I oscillation e1t.

Contributed to the January 5,1961 meeting of the S-3 Panel

of the S.N.A.M.E. and. to the Committee Ofl Model Testing in Waves,I.S.S.C.

-I

2.

-

-

'-L: 1b

5)

P

(cJ

where B1 and B2 are model beams at two ends of the segment.

p-.-Coupled Equations of Motions;

u)

z = m

(

-

!ts)

7f-c55i

-s-r

-2 -

'

z) X

ma%LrA

_{-v? "-ç7}

- rs

c2

-

-

o

) n

"vi;

*/cpé

c/7/

*/ÇL

.=o

Equation (3) is written by taking moments about point of

intersection of axes of dynamometers II and III. M0 is the pure

moment caused by water pressure distribution, I.E. it is the pitching moment which exists when POG

Method of Solution:

In the usual form of solution the transient disturbances are

neglected and the established steady-state oscillations are

assumed. The solution is then efected by following substitutions

in equatïons 1,2 and 3:

i t s= ,

where ¡(ampl.of s

5 _iAt n I' 0 _{s e1} se , 63 ( s e-'

Fe

, F ¿ e e

t

_'i

e t , where e1 " M0 (ampi. of ;) e11(

Upon substitution of the foregoing expressions into Eqs.i,2,3 the factor e14)t is cancelled throughout, and. the resultant

alge-braie equations are solved to express the functional relationship

between two groups of variables: three values of s in one group and

F,I,f,

and M0in the other group. However several difficulties

are immediately evidnt, First, the terms containing terms in F

yield the factor e1 in second and third power. Piiysical1 this

appears to indicate the presence of the frequencies

2&and 3in

the s record.s0 Analyticall this appears to indicate that the solution is possible only alter an arbitrary assumption that the angle and the distance

E

are constants, although uknowi and different for each segment of the model. There are now three equations for four uknowns, and it is further necessary to assume

O. These assumptions appear to be reasonably valid for the central segments and at zero model speed. They become increasingly questionable for the end segments and with increasing model speed,

The solution of equations 1,2,3 becomes theoretically straight forward after making the foregoing assumptions, In practice it

may be complicated by the noise in the records which may make three

algebraic equations incompatible, Also, in the foregoing solution the stability of differential equations was not investigated. The

questions of compatibility and. stability of equations has not been critical in the experience with pitching and. heaving of complete ship models. They become more important and require investigation in case of individual segments because of the increase of the

degrees of freedom from 2 to 3 and because the damping in the

motions of individual segments may prove to be small because their

ends are not subjected to water pressure.

In the practice heretofore used. at the Colorado State University-the dynamometer III was not provided, and construction of University-the J dynamometers I and. II provided the necessary reacfion to the

longitudinal force X, and in effect made S3.O. This,however, does not eliminate the equation (2), but merely leaves the reaction k3s3

uknovm, The solution of the coupled set of equations 1,2,3 is thereby made impossible0 It was carried out by an expedient of

neglecting the cross coupling among three modes of motion and

by treating each dynamometer as an independent simple oscillator, The consideration of the coupled set of equations 1,2,3 is necessary in order to evaluate correctly the phase lag angles O_,,6' , The experience with the analysis of ship motions has

showii that phase angles are strongly affected by couplings.

4

The knowledge of the theoretical relationships leading to the

evaluation of the phases

,Yis

necessary for the final

evaluation pf tle phase angle

J

of the force P.

This phase angle

determines the resolution of the hydrodynamic force P -

PC

t)

into components connected with added mass and damping.

Suggestions for the design and analysis of experiments:

The foregoing material is a sketcIIpresentation of the problem,

but nevertheless it already points to the desired design of

experiments.

The available theory of ship motions indicates that

predominant part of the hydrodynamic force is related to the

displaced volume and reasonably can be assumed to act through i

the center of buoyancy of a segment.

The segment can be ballasted

o that its center of gravity coincides with its center of buoyancy.

The fact that this ballasting does not correspond to the prototype

ship is of no importance in this connection.

The dynamometers I

and II should be located in the segment at the level of the now

combined C.B.and C.G.

,

thus making hHO0 The design of dynamornetv,

as in Colorado case will provide longitudinal restraint, s= O,

By these actions the equation (2) will be uncoupled from () and (3),

The knowledge of the force component F s!n

and of the angler

will be unnecessary, and the solution will be carried out only for

the vertical force component PF cos.

The dynamic system will

consist of two coupled equations (i) and (3) to be solved for two

uknowns F and ¿ as functions of the measured

and

The dynamic system of two degrees of freedom wirl be more stable

than the original one of three degrees9 and less noise in the

records can be expected.

Proper evaluation of the added mass and damping forces rests

on the reliability of the observed phase lag anglesc(andin the

dynainometer records s1 and

₂

The use of electronic filtering to

reduce noise requires exbrerne

pi

_{caution to prevent changes in}

indicated phase relationships0

_{It appears to the author that more}

reliable results can be secured by harmonic analysis of the

records

and completing the analysis on basis of the amplitudes and phases

of the fundamental frequency.,

1-lowever, it may be worth while to

investigate the statistical approach, treating records

as random

time series and evaluating phase relationships by cross-spectral

analysis.

B. V. Korvin-Kroukovsky

Edst Rondolph, Vermont

February 11,1961.

SUPPLEfl'TT to a 'Note on Dynamometer system of Jointed Segnented Ship Model" of January 1, 196!.

In tue discussion at S-3 Panel meeting of _{January 5,1961, it} was pointed out that it is not necessary to bring the _{center of} gravity of a segment to its center _{of buoyancy. It is only}

necessary to install dynamometers at the level of the center of

gravity.

Dynamometer damping terms were inadvented.ly omitted in

equations of segment motions. _{If the dynamometers are installed}

at the level of C.G., it will be necessary to consider only the first and third equations. The _{terms to be added are:}

in (i) _{or approximately}

in (3)

)

where ) _{is a Jnas3 times the non-dimensional}

damping coefficient It is not possible to use _{(kappa) since the e,dded mass of water}

is not yet determined. _{is expected to he independent of frequency}

C) within the normal range of frequencies* . It may be affected by the amplitude of oscillation.

The question of sealing the _{gap between adjacent segments was} discussed at the panel meeting. _{The sealing is necessary, since}

the large segment end area and the uknoim water _pressure dJstri-hution in the gap would _{introduce large spurious readings}

of

dynamometers. The elasto-plastic _{material used for this purpose}

can be expected to be primarily _{responsible for the damping of} dynamometer system, particularly

_{if dynamometers consist of}

simple undamped springs. _{It should also be remembered}

that damping has a large effect on phase relationships. _{To avoid confusion, the} evident fact will be re-stated: _{the word damping is used in}

this

note in two connections: _{the damping as}

an out of phase vector of

the hydrodynamic force F, _{which is the object of the test,}

and

the damping characteristics _{of the dynamometer}

system which must

he determined in the _{calibration proceedure.}

Since the position of the damping force vector due to the sealing material is not _{known, it is impossible}

to correlate the damping in pitching oscillation with cLynamometer _{deflections s1 and} s2 _{The total damping can only be expressed}

by the E,S.Sorokin, _{On the Theory of the Internal Friction in}

Oscillations of Elastic _{Systemns,' (in Russian)}

,

2

coefficient related to the segment rotation _si

-2.

The damping coefficients can be evaluated by solving equations (1) and (3) of the original flote' for _{an oscillation experiment}

conducted in air, i.e. with FO, Since only two

_{equations are}

available at anyone frequency _{of the experiment, the soluion} can be carried out only for the lumped coefficients V3and

'4

In making the afore-mentioned oscillatory clfbration, _the

values of the spring constants k1 and _{k2 of necessity will be}

taken on basis of static calibraion _{It should be remembered,} however, that the sealing material will also contribute _{to some}

extent to dynamometer spring constunts.

_{The elasplastic}

properties of the material may make this _{contribution dependent} on the time history of the deflection, i.e. may make k1 _{and k2} in oscillatory motion different from that obtained in static calibration. An investigation of this effect can be made by conducting oscillation calibrution at two frequencies _while assuming the expected independence of _{and from frequency,}

The calibration at two (not too widely separatd) _frequencies will provide four equations for evaluation of , , k1,and

k2. It hardly will be practical to do this _{as a routine calibration,} but the proceedure is suggested for _{the preliminary investigation}