[MOORINGS] otc17789 - Predicting the Torsional Response of Large Mooring Chains.pdf

7/27/2019 [MOORINGS] otc17789 - Predicting the Torsional Response of Large Mooring Chains.pdf

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Copyright 2006, Offshore Technology Conference

This paper was prepared for presentation at the 2006 Offshore Technology Conference held inHouston, Texas, U.S.A., 14 May 2006.

This paper was selected for presentation by an OTC Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Offshore Technology Conference and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Offshore Technology Conference, its officers, or members. Papers presented atOTC are subject to publication review by Sponsor Society Committees of the OffshoreTechnology Conference. Electronic reproduction, distribution, or storage of any part of this

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AbstractThe extensive use of chain as an element in multi-component

moorings by the offshore industry has led to a requirement to

be able to predict the torsional response of chain under a

variety of service applications. Chain exhibits some interesting

behaviour in that when straight and subject to an axial load, it

does not twist or generate any torque. However, if chain istwisted while carrying axial load, or subjected to axial load

when in a pre-twisted condition, it behaves in a highly non-

linear manner, with the magnitude of the torque dependent

upon the level of twist and the axial load. Consequences of

this behaviour can include handling difficulties or even a loss

of integrity in the mooring system, and care must be taken toavoid problems for both the chain and any components to

which it is connected.

Clearly an understanding of the way in which chains may

behave and interact with other mooring components (such as

wire rope, which also exhibits coupling between axial load and

generated torque) when they are in service is essential. Evenwith knowledge of the potential problems, there will always be

occasions where, despite the utmost care, twist occurs. Thus it

is important to be able to determine the effects, but the sizes of

chain which are in use in offshore moorings (typical bar

diameters are 75 mm and greater) are too large to allow easy

testing at meaningful loads and there is virtually no predictiveinformation on the torsional response of chain available in the

literature.

This paper addresses the issues and considerations relevant

to torque in large mooring chains. The authors introduce a

frictionless theory which predicts the torques and end-shortening in the chain as non-dimensionalised functions of

the angle of twist. The theoretical model is compared with

finite element studies that include friction.

Experimental data is also presented in both constant twist

and constant load forms for stud-less and stud-link chains of

41 and 56 mm bar diameter.

Non-dimensionalised design curves are then given for typical

stud-less and stud-link chain geometries, curves which will

allow a designer to estimate the torque and end-shortening for

any bar diameter, axial load and twist angle combination.

1 IntroductionChain is widely used in mooring applications for offshore oil

platforms, both drilling and production, as well as general

marine purposes. It may be used as the sole component in a

mooring line, but is more usually employed as part of a system

combining chain and rope, be it fibre or wire. There are a

number of reasons why chain is a popular choice in a system:

It is rugged and less damage prone than wire or fibre ropewhen operating on deck hardware or seabed.

It is less prone to corrosion than wire rope.

Chain weight per unit length is higher than for wire ropefor a given strength. Hence the chain may be used mid-line

as a clump weight to alter the catenary shape, or as a

ground line so that a smaller anchor may be employed.

Chain is intrinsically torque balanced, in that an axialload does not generate twist or torsional moments in a

straight chain.

It is easier to handle and requires smaller deck tensionequipment than a wire rope.

So why is torsional stiffness, or induced torque, relevant inmooring chain? There are two reasons:

Firstly, because (as just stated) typical moorings includewire or fibre rope in series with chain, and while chain is

intrinsically torque balanced, the other elements may not

be, and will try to turn the chain when the combination issubject to axial load.

Secondly, it is easy to get a mooring twisted duringdeployment, or during service, often in ways that were not

foreseen at the design stage. A means of transferring large

amounts of twist into a chain during installation when

under nominally zero tension has previously been reported

by Chaplin1, 2

.

OTC 17789

Predicting the Torsional Response of Large Mooring ChainsI.M.L. Ridge, CASAR Drahtseilwerk Saar GmbH; R.E. Hobbs, Imperial College/Tension Technology Intl.; andJ. Fernandez, Labein Technological Centre


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It is noted that industry is becoming increasingly aware of

the problems which may be caused by allowing components to

twist during installation, or by connecting torsionally mis-

matched components, but even so, twist may be unavoidable,

and the engineer may need to understand the response of the

system to such effects.

1.1 Previous researchMany previous investigations into the behaviour of chain

have considered various aspects of the strength and fatigue

performance, but all in cases where the chain is not twisted3-14

.

Casey15

provides a very useful summary of the available

laboratory strength and fatigue test data. Other authors have

considered the effects of stresses and proof loading in chainwith the use of FEA packages

12, 16, 17.

By comparison, very little work has been reported which

considers the torsional response of chain. It has been

traditionally assumed that up to 3 turn per link (or

equivalently 3 turn per link to link interface) there is very

little resistance to the twisting of a chain, while after that it

rises rapidly. It is not clear what the source of this folk-information is, or indeed how accurate it is.

Hiroshima and Sawa18

have considered the effect on

strength of twist in a chain which is subject to an impact load.

Making use of both finite element (FE) and experimental data

their paper considers the loss of strength caused in small

chains (approx 14 mm) such as those used in chain hoists and

lifting tackle, although it does not discuss the torque in the

chain itself.

Turning to some prior work specifically on the torque-twist

relationship, Economides19

suggests that the level of 3 turnper link is associated with the rather modest initial frictional

torque between any two contacting links. At greater levels of

twist the contact area starts to increase significantly beforesplitting into two separate patches and geometric interaction of

the links then causes the torque to rise very much more

rapidly.Chaplin et al.

20present a series of constant twist tests - in

which the twist in the chain is held constant - and the torque

measured as a function of load. This work is for a 20.5 mm

stud-link chain. It not only shows how the induced torque is

highly non-linear for a range of applied levels of twist up to

26.7 turn per link, but it also highlights how different theresponse is from that of six strand wire and parallel laid fibre

ropes.

Economides19

also presents some experimental data

measuring the torque in a 13 mm stud-less chain for a series of

four constant load tests. However, limitations in his equipment

meant that he could not investigate very high levels of twist,

with his tests typically running up to 10 per contact although

at lower loads he did get up to 16 twist per contact.

1.2 Types of chain

There are two main types of chain: stud-less and studdedor stud-link, which are illustrated in Figure 1. The selection of

the type of chain will be influenced by the application. Stud-

link chain is commonly used for moorings which have to be

re-set often during their service life, e.g. those for a semi-

submersible drilling platform, as it is less prone to knotting

during handling; whilst stud-less chain is more commonly

used for permanent moorings, (e.g. those for FPSO, FPS,

Spars or buoys). Stud-link chain tends to be stronger for a

given size and grade of steel, but it weighs more (about 9%)

and is more expensive to produce. There are also issues

concerned with the stud working loose, initiating corrosion or

promoting poor fatigue performance. However, it should be

noted that manufacturers are constantly working to address the

strength issues and industry seems to be moving towards usinglarge stud-less chain.

Figure 1 - Typical nominal link geometries for stud-less (left) andstud-link chain (right)

21

Referring to Figure 1, can be seen that it is usual to define the

main dimensions of the link in terms of its bar stock diameter,

D. Stud-less links are essentially two hemi-toroids of diametertypically 3.35 D, with a parallel section in between, whilst the

studded link geometry is more complicated resulting in a

slightly wider link of typically 3.6 D, although the outer radius

at the link-to-link interface is smaller than 1.8 D, (see below).

The size of chain in use varies greatly, and is of course

dependent upon the application. Stud-less chain may start as

small as 4 mm with stud-link available from 16 mm becauseof the manufacturing complication of positioning the stud. At

the other end of the spectrum, a stud-link chain fabricated

using 182 mm bar has been employed by Petrobras22

, whilst

stud-less links formed from 178 mm (7 inch) bar have been

used offshore in the Terranova project23

. Such links are 641

mm wide, 1068 mm long and weigh approximately 650 kg

each21

.

In addition to the range of sizes, chain is also produced in a

number of strength grades, again depending upon the

applications requirements. However, for all sizes of chain, the

basic geometric similarities hold for the two types, and are

used below to define the chain in the analysis.

1.3 Current work

The review of previous work shows that very little

information is available about the behaviour of chain whensubject to twist. In addressing this problem, there are two

related issues which need to be considered:

the torsional moment needed to cause a given twist in anaxially preloaded chain (assuming the load stays constant);and,

the response (in the form of generated torque) of applyingan axial load to a pre-twisted chain (assuming the twist

stays constant).


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This paper presents experimental work and results for tests

undertaken on realistically sized stud-less and stud-link chain.

The tests have been performed in both constant load and

constant twist modes. In addition to the experimental work,

two analyses have been made, the first a purely geometric,

frictionless analysis of the twist of one link upon another,

where a link is modelled as two rigid half toroids joined by

straight bars. This model works by following the movement ofthe contact patches as the link turns, and using their positions

to calculate the torque generated by an axial load. In addition,

the development of the lift between the links is treated, and

non-dimensionlised results obtained which may be used to

predict the torsional response for chains of varying diameters.

The geometric frictionless analysis has the advantage thatit can be used fairly quickly at the development stage to

provide a good indication of the torques which will be

produced up to realistic levels of twist. An additional

advantage is that it does not require expensive computing or

test equipment. (The computer code is presented in an

appendix to this paper.)

The second analysis is an FE model, which includes theeffect of friction. In addition to the torque and lift, it also

considers the stress levels in the links.

2 Experimental Study2.1 Test equipment

The equipment used for the experimental measurements

reported here was the 3 MN/14 kNm tension-torsion machine

at the University of Reading. This machine (Figs. 2 and 3) has

a hydraulic actuator with stroke of 1000 mm and load capacityof 3 MN. A hydraulic motor is mounted at the rear of the

linear actuator which is capable of providing torques up to 14

kNm. The tensile actuator may be controlled in either load orstroke, and the rotary motor in either rotation or torque control

mode. Thus tests may be run in either load or stroke control in

combination with either rotation or torque control, whilstmonitoring all four parameters.

Figure 2 - 41 mm chain in the 3 MN/14 kNm tension-torsion testmachine.

Figure 3 - Schematic of the 3 MN/14 kNm tension-torsion machine at the University of Reading. The bed length is approx. 5 m. (Note that mainpower pack, accumulators, controller, hydraulic hoses, etc. are not shown.)

Hydraulic motorMain actuator Load cylinderTension-torsion load

cell


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2.2 Test samples

Two chain samples were used in the series of tests reported

here: one stud-less, and one stud-link. The main parameters of

the samples are listed in Table 1. It should be noted that

considerable difficulty was experienced in obtaining suitably

sized samples of appropriate length for this study. Thus the

samples tested were a compromise based on availability and

cost.

Parameter

Nominal chain size (mm) 41 56

Chain type Stud-less Stud-link

Chain finish natural natural

Average bar diameter, D* (mm) 43.1 56.97

Average link length* (mm) 254.7 330.9

Average link width, W* (mm) 141.0 203.17

Nominal W/D (-) 3.35 3.6

Average measured, W/D (-) 3.27 3.57

Effective W/D at end of link (-) 3.22 3.37Chain breaking load B (kN) 973 ca. 2000

Number of links in test sample (-) 19 23

* Average of 5 links

Table 1 - Test chain parameters.

2.3 Experimental procedure

As mentioned earlier, two types of test were of interest in

this study:

Constant load tests, in which the chain is tensioned to agiven load which is then maintained as the chain is twisted

by the hydraulic motor and the applied torque measured.

Constant twist tests, in which the chain is twisted underlow load to a series of levels of twist in turn (defined in per contact of two adjacent links). For each level of twist,

with the twist held constant, the axial load is then varied,

measuring generated torque as a function of load. For the

tests described here, the levels of twist used were 0, 1, 2, 3,

6, 9 up to a maximum of 24 per contact. In each case

the chain was loaded to a maximum of 40% of the nominalchain breaking load.

A full description of the test procedure may be found in

Ridge and Hobbs24

.

3 Modelling3.1 Geometrical frictionless theory

The analysis presented here in summary (fuller details are

given by Hobbs and Ridge25

) models the interaction between

two chain links in a very simple manner, neglecting friction

and any elastic or plastic response of the links at the contact

between the links or elsewhere. As noted earlier, it is purely

geometric in nature, following the changes seen at the contact

point between two adjacent links as one of the links rotates

about the axis of the preloaded chain, before using statics to

find the relationship between torque, turn, and axial load in a

non-dimensional form. Additionally, the theory predicts theend-shortening of the chain as it is twisted.

Figure 4 defines some dimensional parameters for the

hemi-toroidal (half donut) end of each studless link. The

radius and diameter of the parent bar stock used in making the

chain are taken as randD, respectively. The torus centre-line

radius is taken asR, and the link width Wis then simply 2(r+

R). Wis typically 3.35 D over a wide range ofD for studless

chain, encouraging the development of the non-

dimensionalised results presented later.

r

R r

W

D

Figure 4 - Model of the interaction between the two stud-lesschain links: definition of variables.

Initially, the links are at 90 to each other (Fig. 5(a)), and

the contact patch is nominally circular, although it is probably

significantly bigger than Hertzian contact stress theory would

predict for the given axial load because of proof loading

during manufacture. As the links turn relative to each other

(Fig. 5(b)), the patch initially becomes oval, and then separates

into two distinct patches. These patches move up the

shoulders of the links as turn continues to grow, and a gap

appears between the links at the initial contact point. This gap

is the source of the end-shortening in a twisted chain. As the

turn is further increased, the patches move further and further

around the links, and in principle a lock-up situation occurs

(with perhaps 30 turn between a pair of links), Fig. 5(c), with

contact on the straight parts of the links.

It is recognised that this discussion is not fully applicable

to studded links whose ovoid shape means that less than a fullsemi-circle is available at the ends of a link, and the stud will

also impede large twists. Additionally, for studless links with

an overall length of 6D as shown in Figure 1, contact will

occur between a given link and the back of the next link but

one shortly before the situation envisaged in Figure 5(c) canbe achieved.

As indicated above, Figure 5 shows a sequence of views

along the axis of the chain as the two half-links are twisted

relative to each other. In each case, the acute angle to a mid-

plane between the links is identified. The symmetries revealed

on this plane are central to the analysis. Figures 6 and 7


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OTC 17789 5

indicate the coordinate systems used, where Figure 6 shows a

Cartesian system X, Y, Z defined so that X and Z lie in the

plane of the link. The angles and define a (contact) point Pon the surface of the torus. Using standard procedures

25it is

easy to define the X, Y, Z coordinates of P in terms ofand ,

and then transform these coordinates into a second set x, y, z

defined with respect to the mid-plane between the links,

Figure 7.

(a) Initial position = 45

(b) Intermediate < 45

(c) Final lock up = L

Figure 5 - Sequence of views along the axis of the chain as thetwo half links are twisted relative to each other.

R

r

A

A

Z

XO

P

Section A-A

Figure 6 - Definition of the X, Y, Z co-ordinate system (Y intopage).

Figure 7 - Definition of x, y, z co-ordinate system and (y intopage).

The cross-hatched area in Figure 7 represents the plane y =

0, a plane that by symmetry must contain the contact point or

points between the links. For close to 45 (small twists), thearea is roughly elliptical, while as twist increases the shaded

area becomes kidney shaped as shown in Figure 7. The contact

points C are to be found at the lowest point or points of the

boundary of the shaded area. This fact allows and to be

found25

in terms of:

=

r

R

21 sincos (1)

and

=

sin

cossinsin 1

t

r(2)

where

cosrRt = (3)

Since cos cannot exceed 1, Equation (1) gives an upper

limit on at which the initial single central contact separates

into two contacts. Denoting this value as u, and rearranging

Equation (1) with cos= 1 gives:


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R

ru

1sin= (4)

There is also a lower limit on , the value L at lock-up

shown in Figure 5(c). From that figure

= Rr

L

1sin (5)

For any value of between these limits, the torque T is

then given in terms of the axial loadPby:

tantanPRT= (6)

while the end-shortening per link on one interface (Figure 7)is:

cos)( trR = (7)

Working between the limits on given by Equations (4)

and (5), Equations (6) and (7) have been used to generate the

theoretical results presented in comparison with experimental

and FE data below, and the non-dimensionalised design curves

that follow later. The simple Fortran program used for these

calculations is presented in the Appendix.

3.2 Finite element model

All finite element analyses were performed at the LABEIN

Technological Centre, Spain, with the nonlinear codeABAQUS 6.5 of Hibbitt, Karlsson and Sorensen

26.

Two finite element models have been developed, one for

41 mm stud-less and the other for 56 mm stud-link chains,based on the actual measured geometry of the links as defined

in Table 1. The FE models consider inter-link contacts, large

displacements and material non-linearities.Figure 8 shows the finite element meshes used in the

computations. In each case, the interaction between three links

has been modelled, the complete middle link being solid and

the adjoining (half) links rigid. The solid link is built up

from eight node linear brick elements with reduced

integration, while the adjoining links are meshed with rigid

shell elements. The mechanical contact between the links has

been defined with a friction coefficient of 0.3.

The rigid half-link 1 is fully restrained, while rigid half-

link 2 can displace along its longitudinal axis and rotatearound it.

The simulations consider a material with an elastic-plastic

behaviour, with the material properties slightly higher than the

minimum properties dictated for grade 3 material by DNV CN

2.627

. This specifies a yield stress of 410 MPa, tensile strength

of 690 MPa and a corresponding tensile strength strain of

10%. The minimum elongation required by the CertificationNotes is 17%.

A bilinear hardening material curve was used considering

the true values corresponding to the engineering values above.

However, for the low axial loads, the behaviour depends

predominantly on the geometry, with the material having little

influence, the whole stress field being under the yield stress.

Thus, the same results may be expected for grades 4 and grade

5 now emerging in the market.

The axial loadPand the torque Tare applied to rigid half

link 2 consecutively, that is the assembly is loaded and then

twisted incrementally.

Figure 8 - Studless and studlink chain model meshes.

4. ResultsThe results from the tests on the different chain samples are

presented in three different types of graphs:

Firstly, the constant load tests are plotted as a graph of the

non-dimensionalised torque (T/PD; where T is the measured

torque,Pthe axial load andD the chains parent bar diameter)

as a function of the link rotation parameter expressed in

degrees. As is the angle from the plane of the link to the mid

plane between two links, note that starts at 45 and tends

towards L (angle at lock) as the chain is twisted (See Fig. 5).

Thus = 45 /2, where is the twist per link. The value ofL

will vary depending upon the ratio W/D.Secondly, the lift or gap, 2, between links as a function

of twist is also of interest. Here, the non-dimensionalised lift

/D is plotted as a function of.

Thirdly, the constant twist data are presented as a series of

lines for different levels of twist (expressed in terms of

degrees per contact) either as the non-dimensionalised torque(T/BD) plotted as a function of load (now expressed as a

percentage of the chain breaking load, B), or as torque as a

function of load.

4.1 Stud-less chain

Constant load tests

The chain was loaded to 10 kN in these tests, (which it is

recognised is a very low load in terms of the chain MBL)

which was just enough to remove the sag from the sample.

Testing was undertaken in three stages, to 300 overall twist

and then to 500, and 526 twist. The constant load results are

presented in Figs. 9 and 10. Figure 9 shows the torsional

response of the stud-less chain as it is twisted under constant

load. The upper part of the curves are the twisting-up part of

loading and the lower the un-twisting. The three sets of

experimental results presented show that at relatively low

levels of twist, the behaviour is very consistent, whilst at

higher levels, such as in the second and third twistings, there ismore variation. The local spikes on the graph are attributable


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OTC 17789 7

to a stick-slip behaviour between the links. It can be seen that

upon reversal of the twist, i.e. un-twisting, the torque

immediately falls very sharply, and the un-twisting

relationship for all three curves is very similar. The dashed

line shows the non-dimensionalised torque as predicted by the

FE model, which is in good agreement with the experimental

data in both the loading and unloading processes. It was found

that variation in the friction parameter in the FE model hadsome effect on the results. As previously mentioned, in themodel a coefficient of friction of 0.3 was used, which gave a

good agreement with the experimental results. This value

might seem unrealistically high in real terms, but is a result

of the resolution of the mesh used to model the links at their

points of contact.Also presented in Fig. 9 is the theoretical non-

dimensionalised torque for W/D = 3.22 (derived from the

geometrical analysis). Previous work has shown that it is more

accurate to use the local geometry of the chain link rather than

that defined by the manufacturers catalogue24

. The theory

shows some agreement with the experimental data,

particularly for the unloading curves. However, the point atwhich there is a sharp increase in torque is found in practice to

be at a lower level of twist (higher value of of 30.4) than

predicted by the geometry-based frictionless theory, which

gives a value ofL = 26.7 forW/D = 3.22.

With reference to the un-twisting part of the curves

presented in Fig. 9, a comparison with the theoretical values

shows that all three are in very good agreement following the

initial sharp drop in torque found as the direction of the twist

is reversed. It is suggested that friction and the need to shorten

the chain to generate the lift between the links increases thetorque above the geometrical theoretical value during the

loading process. On unloading, the release of stored elastic

energy, and the reduction of the lift (perhaps momentarilyunloading individual contacts) are available to drive the

unloading curve closer to the theoretical line.

The non-dimensionalised lift per link has been plotted inFigure 10. The experimental data here are averages for each

link, derived from the actuator stroke at a given twist. It is

assumed that the links remain axial to the centre-line of the

machine as they separate. At low levels of twist this

assumption is acceptable, but as the higher levels, it is clearly

not. Owing to the geometrical imperfections in the links, and

influenced by friction, at higher levels of twist the links start to

tilt. The horizontal sections of the second and third loading

lines in Figure 10 are associated with the sharp increase in the

torsional response (c.f. Fig. 9). This would suggest that the

links are in the process of locking at this level of twist. The

lift predicted by the FE model and the geometrical theory have

also been plotted on this graph. They are in very good

agreement with each other and in good agreement with the

experimental data, although they consistently underestimate

the experimental level of lift. This offset may be associated

with the mutual indentation of the links from previous loadingconditions.

Constant twist tests

Figure 11 presents the results of the constant twist test.

Each line on the graph is for one of the set levels of twist

(defined in per link-link contact). In this graph the loading

and un-loading sections have been indicated by means of solid

and dashed lines respectively. Note that the twist values are in

unequal increments of: 0, 1, 2, 3, then 6, 9 and 12/contact, in

this way attention has been focussed on the low levels of twist.

The low level twist tests are of interest to compare with the

traditionally quoted accommodation of 3/link. Twelve

degrees per contact is equivalent to = 39 which is quite a

low level of twist in terms of this study, but the associatedtorques at approx. 45% chain MBL approached the capacity ofthe machine so it was not possible to go any further with this

size chain. Figure 11 has been plotted using the chain breaking

strength B to normalise the torque (T/BD). The results

presented in this figure show that the torsional response for a

given state of twist is broadly linear as might be expected.Doubling the axial load doubles the torque until the load gets

too big and the contacts dig in and/or elastic effects take over.

As with the constant load tests, there is considerable

hysteresis at the higher twist levels and the torque falls sharply

on reversal of the loading. The graph also shows that the chain

tested is not perfectly torque balanced in its untwisted state.

This is thought to be due to geometrical imperfections in thechain links.

4.2 Stud-link chain

Constant load tests

Constant load tests on the 56 mm stud-link chain were

undertaken for a range of loads between 10 kN and 500 kN

(approximately 0.5% - 25% of chain breaking load). Owing to

the magnitude of the torques required, the chain could only be

taken to high twist levels at the lower loads. Figure 12 shows

the results for this series of tests. The upper part of the curvesare the twisting up part of loading and the lower the un-

twisting. For the range of loads investigated, the non-

dimensional torque response is very similar for a given levelof twist. (Note that the constant load tests were performed at a

single load of 10 kN for the stud-less chain.)

During this series of tests the opportunity was also taken tocompare the effects of twisting the chain in different

directions. The two curves for the constant load of 10 kN show

a broadly similar behaviour, any differences being attributable

to geometrical inconsistencies and friction between the links.

Note that all tests were undertaken on the same length of chain

and thus after the first loading some damage/wear would have

been caused at the inter-link contact points which would have

had an effect on subsequent loading/twisting.

As with the stud-less chain (Fig. 9) there is a series of

stick-slip spikes on the loading part of the curves. In this case

the spikes are more numerous and pronounced in size and

were accompanied by considerable noise from the test sample.

Here it may be seen that as with the stud-less chain, the

geometrical model gives a good prediction of the torque

during untwisting where the friction effects do not dominate.

The finite element model for the 10 kN load predicts that the

chain locks up somewhat earlier than was found in practice.Two other lines are presented in Figure 12, both simulating

twist with an axial load of 50 kN. In one instance the FE

model was set so that no plasticity was allowed in the material,

and in the second, plasticity was allowed. It can be seen that

both models fit well with the experimental data obtained for

the 50 kN load during testing. The no plasticity model is


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8 OTC 17789

also in good agreement with the non-dimensionalised torque

found for the 10 kN data at higher levels of twist. This is

reasonable, since as stated earlier, the FE model determined

that the stresses in the 10 kN test would not reach the elastic

limit. The second 50 kN line on the graph shows what happens

at higher twist levels where the combination of axial load and

torsion cause the chain material to exceed its elastic limit.

Figure 13 plots the implied lift of each link as a function ofthe twist in the chain for the range of constant loads. Theseresults are very consistent, and in good agreement with the

theoretical results. As observed, with the stud-less chain, at the

higher twist levels the links tended to rotate rather than just

lift, so there is some source of error present. A further

limitation with stud-link chain is that the links will hit the studwhich will prevent further lift. Typical stud width is usually

just under D, which effectively limits the lift to a value of

approximately 0.25D.

Constant twist tests

Figure 14 below presents the constant twist results for the

56 mm stud-link chain. In an effort to be able to investigate

the higher twist range, the maximum load has been kept to 250

kN some 12.5% of the chains breaking load. As with the

stud-less chain the torsional response is broadly linear even at

higher levels of twist. The noise on the curves at higher twist

levels is due to the stick-slip behaviour of the chain.Hysteresis is quite marked at levels above 9 /link twist.

This data has not been non-dimensionalised note the

magnitude of the torque (approx. 12 kNm) at fairly low loads

but high levels of twist.

0

5

10

15

20

25

2527293133353739414345

(degrees)

Non-dimensio

nalisedtorque(T/PD)

1st loading 2nd loading 3rd loading FE model geometrical model W/D = 3.22

Figure 9 - Non-dimensionalised torque T/PD (-) vs. (degrees) for a constant load of 10 kN for 41 mm stud-less chain, twisting-up and un-twisting. Also presented are the results from the FE model (dashed line) and the geometrical model response forW/D = 3.22.


9/15

OTC 17789 9

0.0

0.1

0.2

0.3

0.4

0.5

0.6

2527293133353739414345

(degrees)

Non-dimensionalisedlinklift

(/D)

3rd loading 2nd loading 1st loading FE model geometrical model W/D = 3.22

Figure 10 - Non-dimensionalised lift /D (-) vs. (degrees) for constant load test (10 kN) for 41 mm stud-less chain. Also presented are theresults from the FE model (dashed line) and the geometrical model response forW/D = 3.22.

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0 10 20 30 40 50

Load (%B)

Non-dimensionalisedtorque(T/BD)

Twist (degrees per contact)

9

12

6

3

2

1

0

Figure 11 - Non-dimensionalised torque T/BD as a function of load (%B) for a series of constant twists (degrees per contact), loading (solidline) and un-loading (dashed line) for a nominal 41 mm stud-less chain.


10/15

10 OTC 17789

0

5

10

15

20

202530354045

(degrees)

Non-dimensionalisedtorqu

e

(T/PD)

load = 10 kN load = 10 kN opposite load = 50 kN

load = 250 kN load = 500 kN geometrical model W/D = 3.37

FE model 50 kN no plasticity FE model 10 kN elasto-plastic FE model 50 kN elasto-plastic

Figure 12 - Non-dimensionalised torque T/PD as a function of for a 56 mm stud-link chain for a series of constant loads twisting up (upperpart of curves) and un-twisting. Also included is the geometrical theoretical data forW/D = 3.37 and three predictions comparing the elasto-plastic and no plastic behaviour of the FE model.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

202530354045

(degrees)

No

n-dimensionalisedlift(

/D)

load = 10 kN load = 10 kN opposite load = 20 kN

load = 20 kN repeat load = 50 kN load = 100 kN

load = 250 kN load = 500 kN repeat geometrical model W/D = 3.37

FE model 10 kN elasto-plastic

Figure 13 - Implied lift /D as a function of in the constant load tests for a 56 mm stud-link chain. Also included is the geometrical theoretical

prediction and FE model for a chain under 10 kN load.


11/15

OTC 17789 11

-2000

0

2000

4000

6000

8000

10000

12000

0 50 100 150 200 250 300

Load (kN)

Torque(Nm)

Twist (degrees per contact)

24

9

6

3

0

12

15

18

21

Figure 14 - Torque as a function of load for a series of constant twists (degrees per contact) loading (solid line) and un-loading (dotted line)for a 56 mm stud-link chain.

4.3 Stress in the chain links

The finite element model allows an inspection of the

stresses to which the chain links are subject under differing

loading combinations of twist and axial load. It was noted atthe end of section 4.2 that the magnitude of torque in a twisted

chain was very large at fairly modest axial loads. Figure 15

shows the stress contour plot for a stud-less chain with very

low load (about 1% of its breaking load), but an extreme level

of twist (note the lift between the links). Similar levels of

maximum stress will be obtained for the same links underlower levels of twist but at higher axial load (Figure 16).

Figure 15 - Max principal stress. P = 10 kN and extreme twist = 28.8/link for studless chain

Figure 16 - Max principal stress. P = 200 kN and twist = 17/link for studless chain


12/15

12 OTC 17789

Figures 17 and 18 show the same effect for a stud-link

chain.

Figure 17: Max principal stress. P = 10 kN; and extreme twist

= 28 for stud chainFigure 18: Max principal stress. P = 250 kN; and extreme twist

= 13 for stud chain

The same FE model was used to predict the response for

the chains under higher (service) loads (Figure 19). Here it can

be seen that permanent plastic deformation occurs at fairly

modest levels of twist. As a result of this analysis it may be

seen that for values greater than 38 (i.e. inter link angle

lower than 14), that the T/PD curves obtained are

approximately coincident under all axial loads considered (as

would be expected). For this angle and load range the stress

field of the link remains under yield, after which plasticity

begins and sooner for the higher axial load cases.

0

5

10

15

20

25

202530354045

(degrees)

T/PD

load = 10 kN load = 50 kN load = 250 kN load = 500 kN load = 600 kN

Figure 19 - Showing FE model prediction of plastic deformation of 56 mm stud-link chain links under high load at low angles of twist.


13/15

OTC 17789 13

Using all the results obtained in the finite element simulations,

the following upper bound regression formulae have been

derived for the torque generated as twist increases under

constant axial load in studded and studless chains:

Studless chain:

04.00194.000196.00003.0 23 ++=

DP

T (8)

Studded chain:

04.00117.000054.000023.023 ++=

DP

T(9)

with

140


14/15

14 OTC 17789

6. Stiff, J.J., Smith D.W., and Casey, N.F.: Fatigue of mooringchain in air and water - Results and analysis , paper no. OTC8147 presented at the Offshore Technology Conference,

Houston, Texas, May 1996 pp.291-297.7. Van Helviort, L.C.: Static and fatigue tests on chain links and

chain connecting links, paper no. OTC 4179 presented at the

Offshore Technology Conference, Houston, Texas, May 1982,

pp165-171.8. Abolfathi, E., Modlen, G.F., Webster, P.J. and Mills, G.: The

effect of the manufacturing test load on the fatigue of hoistchains, Proc. IMechE Part B - Journal of Engineering

Manufacture 1995, 209, 2 133-139.

9. Tipton S.M. and Shoup, G.J.: The effect of proof loading on thefatigue behaviour of open link chain, Journal of EngineeringMaterials and Technology - Trans. ASME1992 114 1 27-33.

10. Berg, A. and Taraldsen, A.: Long-term mooring and anchoringof large structure and drilling units (Reliability and safety of

anchor chain systems), paper no. OTC 3813 presented at theOffshore Technology Conference, Houston, Texas, May 1980.

11. Dowdy, M.J. and Graham, D.J.: A method for evaluating andextending the useful life of in-service anchor chain, papernumber OTC 5719 presented at the 20 th Annual Offshore

Technology Conference, Houston, Texas, May 1988.12. Pacheco, P.M.C.L., Kenedi, P.P. and Jorge. J.C.F.:

Elastoplastic analysis of the residual stress in chain links,Proc. OMAE02 21st International Conference on OffshoreMechanics and Arctic Engineering, Oslo, Norway, June 2002,pp39 46.

13. Brown, M.G., Hall, T.D., Marr, D.G., English, M. and Snell,R.O.: Floating production mooring integrity JIP keyfindings, paper OTC 17499 presented at the 2005 OffshoreTechnology Conference, Houston Texas, May 2005.

14. Jean, P., Goessens, K. and LHostis, D.: Failure of chains bybending on deepwater mooring systems, paper OTC 17238presented at the 2005 Offshore Technology Conference,

Houston Texas, May 2005.

15. Casey, N.F.: A review of available laboratory test data onmooring chain applications, OTO 96 033 Health & SafetyExecutive, February 1998.

16. Nicol, D.: Case Study: Use of studless mooring chain forFPSO mooring at Texacos Captain field, Vicinay Cadenas,S.A., Bilbao, Spain 1996.

17. Canada, L, Vicinay, J, Sanz, A, and Lopez, E.: New mooringchain designs, paper OTC 8148 presented at the OffshoreTechnology Conference, Houston, Texas, May 1996 pp.299-

314.

18. Hiroshima, T. and Sawa, T.: Three-dimensional elastoplasticfinite-element analysis of link chains in chain hoist subjected tocombined loads of torsion and impact tension, Transactions ofthe Japan Society of Mechanical Engineers, Part A (November

1995) 61, 591, 2442-2449.

19. Economides, C.: Torsion in offshore mooring, and thetorsional response of mooring chain, Final year MEng report,Imperial College of Science, Technology and Medicine,

University of London, Department of Civil Engineering, 2002.20. Chaplin, C.R., Rebel, G. and Ridge, I.M.L.: Tension-torsion

interactions in multicomponent mooring lines, paper OTC12173 presented at the Offshore Technology Conference,

Houston, Texas, May 2000.21. Vicinay Cadenas SA: Supremacy by innovation, (Chain

manufactures sales brochure) Bilbao, Spain, 2002.

22. Anon: World record, Newslink No. 8, 2002, Vicinay CadenasSA, Bilbao, Spain.

23. Anon: Bringing to the present our desires for the future,Newslink No. 3, 1999, Vicinay Cadenas SA, Bilbao, Spain.

24. Ridge, I.M.L. and Hobbs, R.E.: Torque in Mooring Chain Part II Experimental investigation J. Strain Analysis 2005 40,

7, 715-728.

25. Hobbs, R.E. and Ridge, I.M.L.: Torque in Mooring Chain Part I Background and Theory, J. Strain Analysis 2005 40,7,703-713.

26. ABAQUS: ABAQUS version 6.5 suite of manuals, Hibbit,Karlsson & Sorensen, Inc. www.abaqus .com

27. DNV Certification: Notes No. 2.6. Certification of offshoremooring chain, August 1995.

Appendix

Computer program to evaluate torque and lift as functions of

PROGRAM CHAIN

OPEN(UNIT=6,FILE=Resultname)

DEG = 180.0/(4.0*ATAN(1.0))

READ*,D,DRATIO

WIDTH = D*DRATIO

! D is the chainmakers serial size, DRATIO is, e.g., 3.35 to give the overall link WIDTH

WRITE(6,200) D,DRATIO, WIDTH

200 FORMAT(10F10.2)

! R=D/2, RA is the toroid radius

R = 0.5*D

RA = 0.5*WIDTH R

RRATIO = RA/R

WRITE(6,200)R,RA,RRATIO

! G is used as a header for the various gamma values

GLOCK = ASIN(1.0/RRATIO)

GLODEG = GLOCK*DEG

GLIFT = ASIN(SQRT(1.0/RRATIO))GLIDEG = GLIFT*DEG

WRITE(6,200)GLIFT,GLIDEG,GLOCK,GLODEG


15/15

OTC 17789 15

DELG = (GLOCK-GLIFT)/100.0

G = GLIFT

GDEG = G*DEG

! Loop over the range of gamma between lift and lock

DO 100 I = 1,101

PHI = ACOS(RRATIO*SIN(G)*SIN(G))

PHIDEG = PHI*DEG

T = RA-R*COS(PHI)THETA = ASIN(R*SIN(PHI)*COS(G)/(T*SIN(G)))THDEG = THETA*DEG

DELTA = (RA-R)-T*COS(THETA)

DELTD = DELTA/D

TOVERP = RA*TAN(THETA)*TAN(PHI)

TOVERPD = TOVERP/DWRITE(6,200)GDEG,PHIDEG,THDEG,TOVERP,TOVERPD,DELTA,DELTD

G = GLIFT+DELG*FLOAT(I)

GDEG = G*DEG

100 CONTINUE

STOP

END

[MOORINGS] otc17789 - Predicting the Torsional Response of Large Mooring Chains.pdf

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[MOORINGS] otc17789 - Predicting the Torsional Response of Large Mooring Chains.pdf