structural reliability assessment of a winch drum for an offshore crane

Structural Reliability Assessment of a Winch Drum for an Offshore Crane

Leslie L Moyo

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Structural Reliability Assessment of a Hoist Drum for

an Offshore Crane

Leslie L Moyo

(061140947)

A Dissertation submitted in partial fulfilment for of the

requirements for the qualification of

MSc in Safety, Risk & Reliability Engineering

Supervisor: Dr Dimitry Val

School of the Built Environment, Heriot-Watt University

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DECLARATION

I Leslie L Moyo confirm that this work submitted for assessment is my own and is

expressed in my own words. Any uses made within it of the works of other authors in

any form (e.g. ideas, equations, figures, text, tables, programmes) are properly

acknowledged at the point of their use. A full list of the references employed has been

included.

Signed: …………………………….

Date: 28-Jul-09

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Table of Contents

Contents Table of Contents __________________________________________________iii List of Tables _____________________________________________________iv List of Figures _____________________________________________________iv Acknowledgements_________________________________________________ v Abstract __________________________________________________________vi Glossary of Terms_________________________________________________ vii Nomenclature ____________________________________________________viii Project Planning Documents__________________________________________ix Chapter 1 Introduction_____________________________________________ 1 Chapter 2 Literature review: Design Requirements for Offshore Hoist Drums _ 3 Chapter 3 Hoist Drum Structural Strength Requirements _________________ 23 Chapter 4 Case Study: Auxiliary Hoist Drum on Ruston Bucyrus Crane_____ 32 Chapter 5 Probability of Failure of Hoist Drum ________________________ 41 Chapter 6 Discussion of Results ____________________________________ 65 Chapter 7 Conclusions and Recommendations _________________________ 67 Chapter 8 Suggestions for future work _______________________________ 68 References_______________________________________________________ 71 Appendices ______________________________________________________ 73 Appendix A: MIPEG Rated Capacity Indicators _________________________ 74 Appendix B: MIPEG Data from Ruston Bucyrus Crane ___________________ 77 Appendix C: Project GANTT Chart ___________________________________ 86

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List of Tables

Table 1 Failure Mode & Effects Analysis___________________________________ 31 Table 2 Material Properties______________________________________________ 38 Table 3 FORM Results – Flange Failure ___________________________________ 58 Table 4 FORM Results – Fatigue Failure ___________________________________ 60 Table 5 MIPEG Data___________________________________________________ 85

List of Figures

Figure 1 Diagram showing rope forces on flange for Method 1 (3) ________________ 5 Figure 2 Diagram showing rope forces for Method 2 (3) ________________________ 6 Figure 3 Relationship between P & P΄ (3) ___________________________________ 7 Figure 4 Load Cell Positions on Drum Flange (2) _____________________________ 9 Figure 5 Flange Design Curves (2) ________________________________________ 10 Figure 6 Variation of Flange Force with Number of layers (3) __________________ 11 Figure 7 Asymmetric Deformation of Drum Flange (13)_______________________ 12 Figure 8 T-joint _______________________________________________________ 14 Figure 9 Hoist Drum Requirements according to API 2C (23) __________________ 19 Figure 10 Drum Forces _________________________________________________ 24 Figure 11 Drum Forces _________________________________________________ 25 Figure 12 Flange Loading (33) ___________________________________________ 28 Figure 13 Schematic of the Ruston Bucyrus Crane (34)________________________ 33 Figure 14 Failed Original Drum (34) ______________________________________ 34 Figure 15 Close-up of Failed Flange on Original Drum (34) ____________________ 35 Figure 16 Failed Replacement Drum (34) __________________________________ 36 Figure 17 Close-up of Failed Flange on Replacement Drum (34) ________________ 37 Figure 18 Schematic of Proposed Replacement Drum (34) _____________________ 38 Figure 19 Visual Basic Subroutine for the Monte Carlo Simulation of Flange Failure 63 Figure 20 Results of Monte Carlo Simulation for Flange Failure ________________ 63 Figure 21 Visual Basic Subroutine for the Monte Carlo Simulation of Fatigue Failure 64 Figure 22 Results of Monte Carlo Simulation of Fatigue Failure_________________ 64 Figure 23 Calculation of Flange Force using Roark (33) _______________________ 70

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Acknowledgements I wish to thank Dr Dimitry Val for his assistance and guidance during this project. I would also like to thank Dr Phil Clark for his kind assistance and guidance in selecting an appropriate project. I would also like to thank Lloyd's Register staff in Aberdeen, namely Mr Manoj Tripathi, Mr Peter Davies and Mr Rubik Allhaverdi for their assistance in researching some parts of this document. I am also grateful to Mr Ian Cumming of Specialist Maintenance Services for his assistance in obtaining information about the hoist drum failures considered in this project. I would like to dedicate this project to my darling Anna without whose support this project would never have been completed.

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Abstract Most hoist drums consist of a drum to wind the rope and where a number of layers are required, end plates (flanges) are fitted. Whilst the effects of rope pressure on the drum itself are well researched and understood, the effect of flange forces in hoist drums is constantly underestimated resulting in the catastrophic failure of the drum. In addition flanges are also sometimes subjected to forces from band brakes, clutches or both. These additional forces further complicate hoist drum design, and clear guidance on how the drum flange is to be designed is not readily available. The difficulty lies in determining the magnitude and pattern of loading of the drum flange. Once the flange force has been determined, the stresses can be evaluated. From the research undertaken during this project, it was found that the magnitude of the flange force varies significantly depending on various hoist characteristics such as rope type, drum grooving, rope tension, number of layers and the fleet angle. It was also found that despite significant research and experiments undertaken on the subject, the findings are yet to be incorporated into most design standards. It appears that even though hoist drum design is a complex subject, it is considered trivial by most design standards. Most design codes and standards do not even specify any requirements for the drum flange, leaving the designer to decide the best way to proceed based on their knowledge and experience. This project looks at the requirements for the design of hoist drums from various design codes and carries out a literature review on the subject. A case study is considered where the hoist drum flange failed twice due to poor design, and the reliability of the proposed replacement drum is evaluated. The reliability of the hoist drum is calculated based on the probability of failure of a proposed replacement drum using various methods.

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Glossary of Terms Fleet Angle Angle at which the rope approaches the drum to the drum centre

line

Lang’s Lay The rope is constructed such that the direction of twist of the

wires in the strand is in the same direction to that of the strands in

the rope.

LeBus Winding system on the drum

Ordinary Lay The rope is constructed such that the direction of twist of the

wires in the strand is opposite to that of the strands in the rope.

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Nomenclature DNV Det Norske Veritas

FC Fibre Core

FEM Federation Europeenne de la Manutention

IWRC Independent Wire Rope Core

OEM Original Equipment Manufacturer

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Project Planning Documents These are

1. Project Gantt chart.

2. Project method statement.

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Chapter 1 Introduction 1.1 General

Crane safety is of critical importance today, especially if the HSE are going to achieve

their target of reducing lifting equipment related accidents by 10% by 2012 in the North

Sea(BAE Systems, 2002). The integrity of individual crane elements therefore is critical

as it affects the overall crane safety. Crane design criteria will determine the likelihood

of crane failure and crane approval standards are central in determining the reliability of

the crane and by extension, its mechanisms. There are a number of Standards and

Design Rules for Offshore Cranes with differing requirements. In general, however,

they all leave the determination of the drum strength to good engineering practise.

Hoist drums are single line components whose failure will result in the failure of the

hoisting system. This project looks at the various methods used in industry to determine

hoist drum strength along with the design equations for each failure mode and where

possible the probability of failure associated with each method is calculated. A case

study of the failure of two auxiliary hoist drums of an MK35 AD Ruston Bucyrus

Pedestal Crane is used as an example.

1.2 Scope

A typical hoisting system consists of various components that include the mounting

frame, bolts, shafts, bearings, the drum, the hoist rope, the drive system that will include

a motor (usually hydraulic) and may include a gearing system and the braking system.

This research is limited to the hoist drum which is essentially a component of the

hoisting system.

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1.3 Aims

To assess the different methods used to determine the structural strength of a hoist drum

and establish how the effect of flange forces is considered in hoist drum design. Based

on a Case Study, the probability of failure associated with the effect of the flange forces

will then be determined using various methods. This is then used as an indicator of the

criticality of considering flange forces during hoist drum design.

1.4 Objectives

To achieve the above aims, the following objectives were set;

• Review of crane hoist design standards mainly FEM, BS2573, API2C, AS1418,

DNV and Lloyd’s Register Code of Lifting Appliances in a Marine

Environment.

• Literature review on hoist drum design.

• Outline of hoist drum design criteria in use.

• Strength analysis of hoist drum using a selected method.

• Determine the structural reliability of a hoist drum by calculating the design

probability of failure using various methods.

1.5 Method

A literature review on the subject of hoist drum flange forces is undertaken. The

requirements to design a hoist drum flange from various design codes available are then

outlined and a method selected from the most comprehensive design code. The hoist

drum strength is then assessed based on the selected code and MIPEG data for an

auxiliary hoist drum is then used to calculate the probability of failure of the drum

which is used as an indicator of the hoist drum reliability.

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Chapter 2 Literature review: Design Requirements for Offshore Hoist Drums Introduction

2.1 Hoist Drum Design

The drum is made up of a barrel to wind the rope and where it is not practicable to

accommodate all the rope in a single layer, a flange is fitted. Grooved sleeves are

optional, but where fitted aid in guiding the rope onto the drum. The flange is connected

to the drum through various means, with the most ideal being the barrel and flange cast

as a single unit. Other methods include welding the flange to the barrel or bolting it or a

combination of the above. Hoist drums have been in use for a long time on cranes and

winches, with the larger capacity drums being found in the mining industry. Even

though hoist drum failures are rare, when they do occur they have the potential to result

in significant damage to the environment and may also result in harm to personnel in the

vicinity. Hence, the strength of hoist drums has been the subject of many studies in the

past. It is accepted that hoist drums generally fail in two ways(Song, et al., 1979);

1. High rope tensions causing the internal compressive hoop stress in the drum

barrel to exceed the ultimate limit strength of the drum material.

2. The pressure on the wound rope on the drum flanges causes a high stress

concentration at the root or fillet of the flanges. This causes the flange to part

from the drum barrel.

As stated previously, the first mode of failure does not present a novel problem as the

methods for calculating the strength are well researched and understood. It is generally

accepted that the second mode of failure is not well understood. A number of studies

have found that hoist drums failed as a result of poorly designed drums due to a lack of

understanding of the effects of the rope pressure on the flange(Bellamy NW, 1969).

Additionally, as the drum and flange is a single unit, failure of the drum will in some

cases affect the flange as well. An instance has been recorded where the drum hoop

stress exceeded the yield stress at the centre of the drum causing the flanges to deflect

inwards. One of the flanges was geared and the deflection caused the gear teeth to

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disengage resulting in uncontrolled lowering of the load(IMCA, 2009). As a result the

reliability of the hoist drum will be based on an assessment of the strength of the flange.

The literature review looks at published material relating to the strength of drum flanges

as well as design standards that are currently in use. The most common design standards

are;

1. Federation Europeenne de la Manutention commonly referred to as FEM

2. BS2573

3. API2C

4. AS1418

5. Lloyd's Register Code of Lifting Appliances in a Marine Environment

6. DNV Rules for Certification of Lifting Appliances

2.2 Hoist Drum Flange Forces

The forces acting on the drum flange are poorly understood and numerous studies have

been undertaken to determine the size of the flange forces. In cases where the rope is

wound onto the drum in one layer, the flange is not really essential in this instance.

However, in instances where larger quantities of rope are required, it would be

impractical to have the rope in a single layer, and hence flanges are used to contain the

layers of rope. This then introduces the question of how thick the flange has to be. This

question is best answered by considering the magnitude of the forces exerted on the

flange by the rope. Numerous papers have been presented on the subject, with the

earliest being the paper presented by E. O. Waters in 1920.

Waters reported that flange thickness was a function of rope tension and the depth of the

winding. Using two methods, he derived formulae to calculate the total pressure acting

on the flange of a grooved drum with a given initial tension and depth. Two other

formulae were then deduced, which related total pressure to the flange thickness and the

maximum allowable tensile and shearing stress in the material. The second formula

presented by Waters took into account the effect of friction between adjacent layers of

rope and between the rope and drum, as well as the flattening of the rope coils which

relieves the rope of some of the tension and resulting in a reduction in the pressure

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against the flanges. Waters conducted a number of experiments to substantiate his

theory.

Waters First Method

Figure 1 Diagram showing rope forces on flange for Method 1(Waters, 1920)

The formula to calculate flange pressure is given below;

lb

Where;

N Total axial thrust

m No. of layers

P Rope tension

γ Angle as shown in the Figure above

He found this formula to give excessive values of the flange thrust as it did not take into

account rope friction, reduction in rope tension due to rope compression and the cross-

over of the rope.

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Waters Second Method

The second method he proposed took the above factors into account. A diagram

illustrating the forces taken into account is given below;

Figure 2 Diagram showing rope forces for Method 2(Waters, 1920)

This second formula is given below;

lb

Where;

N Total axial thrust

p No. of coils between a and b

μ coefficient of friction between rope layers

γ Angle as shown in the Figure above

P Rope tension in coil

P΄ Tension loss in coil

The relationship between P and P΄ is given in the table below;

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Figure 3 Relationship between P & P΄(Waters, 1920)

He found that the two equations gave significantly different results particularly for a

large number of layers. To simplify the formulae he derived, Waters made the following

assumptions;

• The shear at the surface of the flange is zero,

• The slope of the deflected flange is zero at the shoulder (i.e. a rigid connection

between the flange and the drum),

• The deflection of the flange at the edge is maximum,

• The flange is of constant thickness.

He then considered the flange as a short cantilever beam with a depth equal to the flange

thickness and a length equal to the circumference at the surface of the drum. The

cantilever is loaded with a uniformly distributed load N (Flange axial thrust). Other

loads, such as brake or clutch forces may also be included. The maximum radial stress

(tension or compression) which acts at the shoulder of the flange is then given by;

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lb/in2

Where and;

ri Drum outer radius

ro Outer rope layer radius

ti Flange thickness

N Flange thrust as calculated

The maximum shear stress is given by;

lb/in2

From the experiments he carried out, Waters found that flange pressure increased in

direct ratio to the number of layers (i.e. a straight line relationship), contrary to the

formulae he had presented. He accounted for this by pointing out that the formulae took

into account several variables that may not have been present in the experiment.

Hoist Drums in Mining

Hoist drums were widely used in the mining industry and in 1949; Crawford(Crawford,

1949) presented a series of papers discussing the strength of drums. In them, he

assumed that the supports deflect radially inwards when the shell is loaded. This is

similar to Waters assumption that the drum/flange connection is rigid. He also assumed

that the supported ends of the shell do not rotate.

In 1957, Dolan(Dolan, 1957) carried out experiments similar to those carried out by

Waters and he demonstrated that the approach proposed by Waters results in too thin a

shell. Dolan presented a second paper(Dolan, 1963) where he investigated various drum

failures and proposed formulae to be used to determine the strength of the drum for

design purposes. In 1958, Egawa & Taneda(Egawa, et al., 1958) also presented a paper

with experimental backing on the determination of flange forces. However, their work

as was the work of Dolan, Broughton(Broughton, 1928, Revised 1948) and

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Torrance(Torrance, 1965) was largely concerned with stresses in drum barrels and did

not present significant findings on flange forces.

In 1966, Atkinson & Taylor(Atkinson LTJ, 1966) also presented a series of papers on

the analysis and design of fabricated drums for mine winders. They found that a number

of drums designed using Waters approach had failed. They also found that some drums

which theoretically would have failed under Dolan’s criteria were still operational and

drums which were well below the design limit had failed. They presented a number of

formulae to determine the drum strength taking into account dynamic effects of the rope

under load(Atkinson LTJ, 1967).

Further Research

In 1968, Bellamy& Philips(Bellamy NW, 1969) also carried out a series of experiments

based on Waters experiments to investigate the forces acting on a winch drum during

multi-layered rope winding. They considered the effects of rope construction, rope

tension and the spooling arrangement. Four different types of rope were used and the

test drum was of welded construction made from mild steel and had load cells placed in

the flange to measure exact pressures. The load cells were positioned as shown below;

Figure 4 Load Cell Positions on Drum Flange(Bellamy NW, 1969)

For an identical rope tension, different types of rope constructions were found to exert

significantly different forces on the flange. For example, the force exerted by an 18 x 7

Fibre Core Lang’s lay rope was more than twice that of a 6 x 37 Independent Wire Rope

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Core rope with all other parameters constant. When the results were processed to give

graphs of average pressure exerted by rope on the flange, it was noted that the average

pressure on the flange became constant with an approximately uniform distribution after

a few layers. However, the 18 x 7 Fibre Core Lang’s lay rope had a higher flange

pressure. Ropes with an independent wire rope core were found to present lower flange

forces and fillet strains. From their findings, they presented a series of design curves as

shown below;

Figure 5 Flange Design Curves(Bellamy NW, 1969)

Where;

Rope A Type 6 x 37 Fibre Core, Lang’s Lay

Rope B Type 6 x 37 Independent Wire Rope Core, Lang’s Lay

Rope C Type 18 x 7 Fibre Core Ordinary Lay

Rope D Type 18 x 7 Fibre Core, Lang’s Lay

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They stated that they found it impossible to present an empirical formula for the failure

of drum flanges due to the diverse forms of flanges in existence. They also found that

flange forces were mainly dependent on three main variables;

a) Type of rope construction,

b) Rope tension,

c) Type of spooling.

Other factors they found to be important included rope size, rope lubrication, LeBus

spacing, drum grooving, settling time and variable rope tensions. The curves presented

in Figure 5 above are applicable for the rope constructions specified. To use the curves,

the rope winding stress is calculated from the rope tension and cross-section; then the

flange pressure is obtained for the particular type of rope construction and spooling. A

graph showing the variation of flange pressure with the number of layers is given

below;

Figure 6 Variation of Flange Force with Number of layers(Bellamy NW, 1969)

In 1979; Song, Rao & Childers(Song, et al., 1979) investigated winch drum design in

mooring applications offshore. The drums are generally larger than the hoist drum

found on cranes for instance, as mooring applications generally require ropes of larger

diameter (up to 89mm diameter rope was found, normal hoisting applications on

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average require diameters up to 20mm). They found that flange splitting was the most

common structural failure in the large wire rope mooring winch drums. One of the

reasons they gave for the failures was that designers were using formulae derived for

use with smaller hoist drums. Their study is of interest as it shows that hoist drum

design is a complex area that is affected by a number of variables.

Recent Research

The University of Clausthal in Germany has also done a significant amount of work

under the leadership of Dr Peter Dietz(Dietz, 1972), who presented the principle that

tension reduction occurs due to the flattening of the wire and the radial deflection of the

layer on which the successive layers are wrapped. In 2002, Otto, Mupende &

Dietz(Otto, et al., 2002) using experimental methods and Finite Element Analysis found

that LeBus spooling resulted in asymmetric pressure distribution over the flange.

Conventional methods for determining the strength of a drum flange have assumed a

symmetric load distribution. The effect of this is shown in the picture of a failed drum

shown below;

Figure 7 Asymmetric Deformation of Drum Flange(Otto, et al., 2002)

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2.3 The attachment of Flanges to Drum Barrel

Most researchers consider the drum flange region to be rigid. This would indicate that

the drum and flange are cast as a single unit or the attachment consists of a full

penetration weld. However, this is not the case in some circumstances, the flange is

often attached using partial penetration welds or even bolted to the drum. This is

therefore a critical area in hoist drum design and maybe the weakest area of the drum

unit. The section below considers welded and bolted joints in detail.

2.3.1 Bolting

It is essential that the loading on the flange is modelled correctly so that the required

strength of the bolts can be determined accurately. The maximum force that a bolt is

capable of supporting is basically given by the product of the bolt’s yield or ultimate

stress and the bolt’s stress area. The bolt’s stress area is dependent on the thread pitch

diameter. It is commonly accepted that a minimum Grade of 8.8 for the bolt according

to ISO 898/1 will be used for structural purposes. Black bolts (i.e. bolts of a Grade

below 8.8) are normally not accepted for structural purposes.

Where a bolt is supporting a flange, the point of application of the force is not normally

coincident with the location of the bolts. This is because the force on the flange due to

rope pressure is considered to be a uniformly distributed load as described by Waters,

and the bolts are usually fitted around the drum’s circumference. This will therefore

give rise to a moment that will tend pry the flange from the barrel.

Fatigue is also significant in this case as the loading will be cyclic i.e. the load will vary

as the rope is wound and unwound onto the drum.

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2.3.2 Welding

A welded drum-flange structure, however intricate its shape, is usually composed from

a number of fundamental joint types. Since in most circumstances, the flange and the

drum are at right angles to each other, they are normally joined using a T-joint as shown

below (Hicks, 1999);

Figure 8 T-joint

3.3.2.1 Weld Strength

The basic strength of a butt weld is normally taken as equal to that of the parent

material. A perfect butt weld joint, when subjected to an external force, provides a

distribution of stress throughout its volume which is not significantly greater than that

within the parent metal. This is achieved as long as the following features apply(Oberg,

2008):

• Welds should consist of solid metal throughout a cross section at least equal to

that of the parent metal.

• All parts of a weld should be fully fused to the parent metal.

• Welds should have smoothly blended surfaces.

If any of these requirements are not fulfilled then the weld is imperfect and the stress

distribution through the joint is disrupted.

According to BS2573-1(British Standards, 1983), a continuous partial-penetration weld

welded from one side only or from both sides can be used provided that it is not

subjected to a bending moment about the longitudinal axis of the weld other than that

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resulting from the eccentricity of the weld metal relative to the parts joined or from

secondary moments. A partial-penetration weld welded from one side only shall not be

subjected to any loading that would cause the root of the weld to be in tension if failure

due to such tension would be liable to be progressive and to lead to structural collapse

unless it can be demonstrated that proper attention has been paid to the detailed design

of the joint and testing and operational experience has shown this detail to be

satisfactory. Partial penetration welds have a weld root which acts as a stress

concentration point(Maddox, 1969). Based on this, full penetration welds are therefore

recommended for drum-flange joints.

The weld strength in the case of a partial penetration weld is given by the length of the

weld multiplied by the weld throat. The throat thickness of a partial-penetration butt

weld welded from one side only shall be taken as the depth of penetration and the

adverse effect of the eccentricity of the weld metal relative to the parts joined shall also

be allowed for when calculating the strength.

2.3.3 Fatigue Failure of Welded Joints

Fatigue is considered the most common cause of structural failure for in-service

structural items(Gagg, et al., 2009). It is clear that fatigue is critical in the reliability of

hoist drums as the structure is subjected to cyclic application of stress, the magnitude of

which would normally be insufficient to cause failure(Gagg, et al., 2009). Fatigue

involves the initiation and gradual growth of cracks until the remaining section of

material cannot support the applied service load.

Several methods have been proposed to mitigate the failure of welded members due to

fatigue. One such approach is ultrasonic peening(Jinu, et al., 2009), which was found to

increase fatigue life by up to 35% at 250 Mpa of applied stress.

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2.4 Design Standards

2.4.1 FEM(FEM, 1998)

This is a collection of internationally accepted guidelines for crane design. This code is

split into 9 booklets, each covering a separate element of the crane design. The first

edition of the code was published in 1962 and the second in 1970. The code requires

that only the element that is under unfavourable loading should be verified for strength.

Standard equipment which has been verified once and for all and is under normal

loading need not be verified. The purpose of the code is to determine the loads and

combinations of loads which must be taken into account and to establish the strength

and stability conditions to be observed for the various load combinations.

The code requires the end user to define two elements;

1. The class of utilisation.

2. The load spectrum

The code differentiates between an appliance, a mechanism and a component and

classes these separately based on the class of utilisation and the load spectrum (stress

spectrum in the case of components). The only specific requirement from the Code

relating to hoist drums is the minimum winding diameter which is given below.

Minimum Winding Diameter

The drum’s minimum diameter in FEM is determined by;

dHD ⋅≥

where

D - is drum diameter

H - is a coefficient dependant upon the mechanism group

D - is the nominal diameter of the rope.

The determination of the strength of the drum is left to the designer.

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2.4.2 BS2573(British Standards, 1980)

This is the British Standard for the design of cranes and mechanisms. The code is split

into two parts, BS2573-1:1983 covering the design of structural elements of the crane

and BS2573-2:1980 covering the design of mechanisms and components. As the hoist is

essentially a mechanism, the research is therefore mainly limited to BS2573-2:1983.

The classification of mechanisms in BS2573 is similar to that in FEM and is based on

class of utilisation and the state of loading. The standard only specifies the minimum

winding diameter which is given below. Determination of the strength of the hoist drum

is left to the designer.

Minimum Winding Diameter

The drum’s minimum diameter in BS2573-2 is determined in a similar way as in FEM;

dHD ⋅≥

where

D - is drum diameter

H - is a coefficient dependant upon the mechanism group

d - is the nominal diameter of the rope.

The minimum value of H is 16, which means that the drum diameter has to be at least

16 times the rope diameter.

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2.4.3 AS1418.1-2002(Australian Standards, 2002)

This is the Australian Standard for the design of cranes and associated components.

This code specifies the requirements for cranes, winches, hoists and their components. It

is regarded as one of the most comprehensive available. It states the design life of crane

mechanical components as 10 years unless otherwise specified. Crane mechanisms are

again classified according to the class of utilisation and the state of loading, in a similar

way as in BS2573-2 and FEM.

Basis of Design

The design of power operated mechanisms is based on the following;

1. Strength basis.

2. Life basis based on wear or fatigue (finite or infinite).

Details of the structural strength requirements according to AS1418 are covered in the

next section as they are quite detailed. The calculation of stresses is based on the

approach by Dr Helmut Ernst and Peter Dietz who published detailed papers on the

strength of crane hoist drums. The standard has comprehensive requirements for the

drum barrel but has limited requirements relating directly to the drum flange.

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2.4.4 API 2C(API, 2004)

This standard is produced by the American Petroleum Institute and covers the design of

offshore cranes. The standard also specifies the requirements for hoist drums. It does

not base strength requirements on utilisation or state of loading as does FEM and

BS2573-2.

Basis of Design

The drum is required to provide a minimum first layer rope pitch of 18 times the

nominal rope diameter. This is more onerous than the requirements of FEM and

BS2573-2 where the requirement is 16 times.

API 2C also requires that the flange extend a minimum distance of 2.5 times the wire

rope diameter over the top layer of the rope unless an additional means of keeping the

rope on the drum is provided e.g. keeper plates, rope guards or kicker rings. A minimum

of 5 wraps of the rope are also required to remain on the drum in the operating

condition. This would prevent the rope anchor failure as cases have been documented

where the rope has detached from the rope anchor(Piskoty, et al., 2009). The standard

does not specify particular requirements relating to the drum flange and leaves it to the

designer.

Figure 9 Hoist Drum Requirements according to API 2C(API, 2004)

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2.4.5 Lloyds Register Code of Lifting Appliances in a Marine Environment

(Lloyds Register, 2008)

The requirements for hoist drums are not stated explicitly in the code but the generally

accepted practise is described below. The design of rope drums is based on the BS5500

1982 Code where the hoist drum is regarded as a pressure vessel loaded externally. The

rope around the drum is considered to impart a uniform pressure on the drum and the

drum stresses are then calculated using formulae outlined in the next Chapter.

In addition, the maximum rope tension is considered taking into account dynamic

loading conditions, friction effects and any environmental effects as well as the stalling

force corresponding to the maximum line load attainable due to an overload condition

such as may occur in the event of snagging of the lifting hook or attached load.

The capacity of the drum should normally be designed to accommodate the rope on a

maximum of three layers of rope. Where a greater number of rope layers are required,

suitable spooling arrangements are to be provided. A single layer of rope is acceptable

provided the rope ends are adequately secured to anchor points. A minimum of three

complete turns of rope is to remain on the rope drum at all times during normal

operation. This is less than the API 2C requirement of a minimum of 5 turns of rope.

There are no specific requirements for the drum flange in the code.

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2.4.6 DNV Rules for Certification of Lifting Appliances(DNV, 2007)

The requirements from the Code are quite comprehensive and are outlined below. The

ratio of the drum diameter to hoist rope diameter is not to be less than 18, which is

similar to the requirement in API 2C. The number of rope layers on the drum is also

limited to 3 unless the hoist rope has an independent wire rope core and one of the

following conditions complied with;

• A spooling device is provided

• The drum is grooved

• The fleet angle is restricted to 2°

• A separate traction drum is fitted.

Special consideration will be given when the number of rope layers exceeds 7. The

distance between the top layer of the wire rope on the drum and the outer edge of the

drum flanges is to be at least 2.5 times the diameter of the wire rope, except in cases

where wire rope guards are fitted to prevent overspilling of the wire. This requirement is

also similar to that given in API 2C.

The drum barrel is to be designed to withstand the surface pressure acting on it due to

the maximum number of windings with the rope spooled under maximum uniform rope

tension. The DNV Code also requires that drums are checked with respect to their

overall equilibrium situation and beam action, with the maximum rope tension acting in

the most unfavourable position. The effect of the support forces, overall bending, shear

and torsion is to be considered at the maximum rope tension including any amplification

factors. However, if more unfavourable the situation with forces directly dependent on

motor or brake action is to be considered. The structural requirements for hoist drums

according to DNV are outlined in the next section. There is evidence that DNV Rules

are likely to be revised in future to include methods for estimating target

reliability(Ruud, et al., 2007). The code states that the pressure acting on the flange

varies linearly from zero at the outer layer to a maximum near the barrel surface. A

formula is given to determine the magnitude of the flange pressure.

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2.5 Conclusion

It is clear from the literature review that methods for determining drum barrel strength

are readily available and the mechanism of failure is well understood. Research also

indicates that flange failure is the most common mode of drum failure and as a result

the reliability of the hoist drum will be based on an assessment of the flange’s structural

strength.

It can be seen from the literature review that the most comprehensive standard is the

DNV Rules for Lifting Equipment when it comes to hoist drum design. The code

considers the effects of flange forces, and outlines formulae to be used. The evaluation

of the drum flange structural strength will therefore be based on the DNV approach.

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Chapter 3 Hoist Drum Structural Strength Requirements Introduction

There are various approaches to assessing the structural strength of a hoist drum. The

following chapter looks at the various methods of checking the hoist drum as presented

in the various codes or standards. The main drum components are the barrel, the flanges

and the attachment between the barrel and the flange. As has been determined, most

design standards do not specify particular approaches for determining the strength of

hoist drums but leave it to the user to determine which approach would be most suitable

based on sound engineering practise. It is therefore of critical importance to designers

and certifying authorities that the different approaches available are assessed to

determine the most reliable.

3.1 The Barrel

The barrel is subjected to bending, crushing and buckling stresses. The design

calculations therefore have to take all these factors into account. Most of the codes or

standards only specify requirements for some of these stresses and only the Australian

Standard AS1418 specifies requirements for all the stresses mentioned above. The

different approaches to hoist barrel design are outlined below.

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3.1.1 DNV Approach: Hoop stress

The drum hoop stress, which is the stress acting on the drum due to the squeezing effect

of the rope on the drum, is calculated using the formula below must not exceed 85% of

the material’s yield stress;

avhoop tp

SC⋅⋅

=σ

where;

C - amplification factor (1.75 for more than one layer).

S - rope tension under spooling

P - pitch of rope grooving

tav - average drum thickness

3.1.2 Lloyds Register Approach: Drum Barrel

The Lloyd's Register approach is based on the BS 5500:1982 code as previously

outlined. The approach assumes that the drum is a pressure vessel under external

pressure and calculates the minimum drum barrel thickness required to prevent

buckling. This method is very similar to that outlined in Omer W. Blodgett’s book, The

Design of Weldments, James F Lincoln Arc Welding Foundation (1963)(Blodgett,

1976). This method considers the rope to be applying an external pressure on the drum

due to the line tension as shown in the drawing below;

Figure 10 Drum Forces

The hoop stress is given by;

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trP

hoop⋅

=σ

where;

P - external pressure

r - radius of drum

t - drum shell thickness

The line tension F gives rise to the external pressure acting on the drum shell and can be

expressed as;

tbF hoop ⋅⋅= σ

where;

b - width

therefore;

tbF

hoop ⋅=σ

and therefore;

brFP⋅

=

Figure 11 Drum Forces

This method then assumes that each of the succeeding layers will add to the pressure

acting on the drum. However, the outside layers will tend to force the preceding layers

into a smaller diameter, reducing their tension and hence the pressure. Therefore, only

the effect of the outer two layers is considered;

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1++= nnT ppp

The minimum thickness of the drum that prevents failure due to buckling is then

determined using the formula below;

32

3

)1(4 rtEpcr ν−

⋅=

Where;

Pcr - Critical Pressure acting on barrel and resulting in buckling

E - Youngs Modulus for the material (Modulus of elasticity)

t - Barrel thickness

r - Barrel inner radius

ν - Poisson’s ratio

Therefore, to prevent buckling the minimum thickness will be;

332

min)1(4

ErP

t cr ν−=

This method calculates the minimum required drum barrel thickness to prevent drum

buckling. As outlined above it is similar to the Lloyds Register approach. The method is

sometimes used by manufacturers to determine the minimum barrel thickness even

though it only considers failure due to buckling only.

However, from analysis, it has been found that the minimum drum barrel thickness

determined using this method is inadequate to resist the hoop stress as calculated using

the DNV Hoop Stress formula and is much less than the minimum thickness calculated

using the approach presented in the Australian Standard AS1418. This approach is

therefore to be used with caution and its limitations must be fully understood by the

designer.

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3.1.3 AS1418: Drum Barrel

As previously mentioned, this method includes the calculation of drum barrel stresses

presented by Dr Helmut Ernst and Peter Dietz who published detailed papers on the

strength of crane hoist drums. AS1418 presents a method for working out the

recommended minimum thickness of the drum and also presents methods for

determining stresses in the drum barrel. The minimum theoretical thickness of the drum

barrel is determined from;

( )22min DCDCDBDB TTTTT +⋅+=

where;

TDB - is the minimum theoretical thickness of the drum shell allowing only for

the beam bending stresses given by;

bDMDB FD

MT⋅

= 21250

TDC - is the minimum theoretical thickness of the drum shell allowing only for

the compressive stresses given by;

c

RSRLDC Fp

PKT

⋅⋅

=1000

M - is the bending moment due to beam action of unfactored (static) rope

load (PRS)

Fb - is the permissible bending stress in MPa (67% of yield stress)

DDM - is the mean diameter of the drum shell in mm.(DDN-Tmin)

DDN - is the nominal diameter of the drum shell

KRL - is the rope layer factor and rigidity constant for the drum shell (1.6 for

more than three layers)

p - is the pitch of the rope coils

d - is the nominal diameter of the rope

Fc - is the permissible compressive stress in MPa.

PRS - is the maximum unfactored rope load in kN

It can be seen from the formulae presented above that the minimum theoretical

thickness as calculated will take into account the effect of bending, buckling and the

compressive stress.

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3.2 The Hoist Drum Flanges

Most of the codes do not present a way of assessing the strength of the hoist drum

flanges. Only DNV presents a method which is outlined below. The method assumes

that the flanges are under a direct pressure due to the wire rope ‘wedge’ effect. In

determining the strength of the flange this pressure is assumed to vary linearly from a

maximum near the drum barrel to zero at the outer layer. An average value of this

pressure is then taken and assumed to act at a point. The loading of the flange can be

represented as shown below;

Figure 12 Flange Loading(Young, et al., 2002)

In this case the following assumptions are made;

a) The flange is assumed to be loaded at a third of the height.

b) The plate is flat and of uniform thickness.

c) All forces/reactions are normal to the plane of the plate.

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3.2.1 DNV Approach: Flange

The pressure acting on the flange is assumed to be increasing linearly from zero at the

top layer to the value given by the formula below;

Dt

p hoopavf 3

2 σ⋅⋅=

where;

avhoop tp

SC⋅⋅

=σ

and;

D - outer diameter of barrel

p - wire rope pitch

C,S are defined in the previous section

then;

DpSCp f ⋅⋅

⋅⋅=

32

The maximum force on the flange is then given by the product of the pressure and the

area over which the force acts. This is the area of the flange covered by the rope layers

and is given by;

( )4

22 DDA Outerlayer

flange

−⋅=

π

therefore the force on the flange is given by; flangefflange ApF ⋅=

or simply; ( )

DpDDSC

F outerlayerflange ⋅⋅

−⋅⋅⋅=

6

22π

The force in the flange Fflange shall not be greater than the allowable force in the flange

as determined from the allowable stress multiplied by the area of the flange covered by

the rope layers.

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30

3.3 Hoist Failure Modes

There are several modes of failure associated with each particular element of the drum. It is apparent from the previous sections that design codes select which failure modes to specify requirements for, even though there are a number of modes of failure which are significant. A Failure Mode & Effects Analysis is carried out below to illustrate the modes of failure possible for the hoist drum. In this instance, failure of a single component of the hoist drum unit is considered as failure of the whole system. 3.3.1 The Barrel The barrel is likely to fail due to the modes outlined below;

• Buckling,

• Cracking,

• Fatigue.

3.3.2 The Flange The flange is likely to fail due to the modes outlined below;

• Elastic failure,

• Cracking,

• Fatigue.

3.3.3 Means of Attachment The means of attachment can be welding or bolting as outlined in the previous section. Bolts are likely to fail due to the modes outlined below;

• Elastic failure

Welds are likely to fail due to the modes outlined below;

• Elastic failure,

• Cracking,

• Fatigue.

The results of a Failure Mode and Effects Analysis are shown in the Table overleaf.


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31

Description of unit Description of failure Component Failure Mode Failure Mechanism

Effects of failure on System Function

Failure Rate

Severity Ranking

Risk Reducing Measures Comments

Drum Flange Elastic failure Bending Dropped load Collapse

High Inspection Design information, Crane history/records, NDE inspection records, End of life assessment

Drum Flange Excessive deflection Overload Damaged wire rope Dropped load

High Inspection Repair Replacement Maintenance

Fatigue failure in parent metal, weld or connection could result in a sudden failure leading to collapse and dropped load/jib.

Drum flange Plastic Collapse Bending Damaged wire rope Dropped load

High Inspection Replacement

Drum flange Brittle fracture Stress concentration Damaged wire rope Dropped load

High Inspection Repair

Drum Barrel Elastic failure Bending Damaged wire rope Dropped load


Drum Barrel Buckling Overload Damaged wire rope Dropped load


Drum weld Elastic failure Overload Damaged wire rope Dropped load


Drum weld Fatigue Cracking Damaged wire rope Dropped load


Drum weld Buckling Overload Damaged wire rope Dropped load


Drum weld Brittle fracture Stress concentration Damaged wire rope Dropped load


Bolts Elastic failure Shearing Damaged wire rope Dropped load


Table 1 Failure Mode & Effects Analysis

It is clear from the above analysis that a lot is left to the discretion of the designer. For instance, none of the design codes specify requirements relating to fatigue,

even though it is a significant mode of failure. In this instance, failure of a single component of the hoist drum unit is considered as failure of the whole system.


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Chapter 4 Case Study: Auxiliary Hoist Drum on Ruston Bucyrus Crane Introduction

The Ruston Bucyrus MK35 Crane experienced two hoist drum failures and is an ideal

example of how critical the strength of hoist drums is. The hoist drum originally

supplied with the crane failed due to cracking of the flange. A replacement hoist drum

with a bolted flange also failed during load testing due to failure of the means of

attachment without causing any significant damage. Another replacement drum was

then designed and forwarded to Lloyd’s Register to assess its structural strength. This

project will consider the design of the replacement hoist drum and assess its structural

strength using methods outlined in the previous section. The hoist drum’s probability of

failure will then be calculated based on historical loading records using various

methods.

4.1 Description of Crane

The Ruston Bucyrus MK35 Crane is a pedestal mounted, rope luffing offshore crane

located on the Rough Alpha Platform in the Southern North Sea. The auxiliary hoist is

powered by a closed loop hydraulic system and provides powered lifting and lowering

of the load. The hoist unit is mounted on the roof of the machinery house and operates

on single fall in an open sea environment up to Beaufort Sea State 6. It has a capacity of

4.5 Tonnes on the auxiliary hoist. A schematic of the crane is shown

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below; Figure 13 Schematic of the Ruston Bucyrus Crane(Specialist Maintenance Solutions, 2008)

The crane was supplied with the platform circa 1975. The crane is fitted with MIPEG

2000 (Sparrows Offshore) data instrument which monitors and records the loading data

over time (See Appendix A).

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4.2 Original Hoist Drum

The original drum consisted of a two piece casting, with a radial weld joining the two

pieces at the centre of the drum. The hoist drum was designed with an integrated wedge

and socket acting as the dead end rope anchor. It was supplied with the crane and was

at least 30 years old at the time of failure.

Figure 14 Failed Original Drum(Specialist Maintenance Solutions, 2008)

The flange failure is shown in the picture above, and other than the part of the flange that broke off, cracks were also observed on the flange.

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Figure 15 Close-up of Failed Flange on Original Drum(Specialist Maintenance Solutions, 2008)

The darker areas that can be observed from the picture above where the cracks would

have initiated. The mode of failure for the drum would therefore quite likely have been

fatigue, with the machined rope groove acting as a stress concentration point.

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4.3 Failed Replacement Drum

The replacement drum was made up of discrete units with the flange connected to the

drum unit using bolts as shown in the drawing below.

Figure 16 Failed Replacement Drum(Specialist Maintenance Solutions, 2008)

The drum flange can be observed to have parted from the drum at the top of the picture.

From the investigation, it was determined that failure occurred due to the flange bolts

shearing.

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Figure 17 Close-up of Failed Flange on Replacement Drum(Specialist Maintenance Solutions, 2008)

The parting of the flange from the drum resulted in significant damage to the wire rope

as can be observed from the picture above. Had the failure gone unnoticed, which is

possible as the hoist drum is positioned above the crane operator’s cabin, this may have

resulted in an uncontrolled lowering of the load.

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4.4 Proposed Replacement Drum

The proposed replacement drum consists of one piece drum welded to two flange plates.

The drum is similar in dimensions to the OEM drum except the drum length, measured

from flange face to flange face. This is one rope diameter shorter to accommodate a

rope anchor, which is placed outside the flange. The drum does not have grooves and

the wire rope diameter is 19mm. Based on the operating criteria, the minimum number

of layers required on the drum is 3 but it was designed for 5 layers.

Figure 18 Schematic of Proposed Replacement Drum(Specialist Maintenance Solutions, 2008)

The position of the hoist drum as well as the hoist drum specification is as shown

below;

Material

Properties used in making up drum are presented in Table below

Material Standard Min. Yield

(N/mm2)

UTS (N/mm2)

Plate BSEN 10025 345 490

Barrel API 5LX52 345 490

Table 2 Material Properties

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4.4 Structural Strength Assessment of Proposed Replacement Drum

The structural strength of the hoist drum is checked using the DNV method outlined in

the previous section.

4.4.1 The Barrel

The barrel strength is checked by calculating the hoop stress according to the DNV approach as outlined in the previous section.

avhoop tp

SC⋅⋅

=σ

Where C = 1.75, S = 45126N, p = 19 mm and the average thickness of the drum tav = 36mm. Therefore;

2/5.1153619

4512675.1 mmNhoop =⋅

⋅=σ

For the barrel to be acceptable, the hoop stress has to be less than 85% of the yield stress.

2/3.293345*85.0 mmNhoop ==σ The hoist drum is therefore acceptable. 4.4.2 The Flange

The flange’s strength is checked by using the DNV approach as well as outlined in the

previous section. The actual force acting on the flange is given by;

( )N

DpDDSC

F outerlayerflange 1047659

6

22

=⋅⋅

−⋅⋅⋅=

π

The maximum allowable force is given by;

weldyflangeAllowable AF ⋅= σ_

Where the yield stress is 345 N/mm2 and the weld area is 22368 mm2. Therefore;

NAF weldyflangeAllowable 771700822368*345_ ==⋅= σ

The flange and weld strength are therefore acceptable.

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4.4.3 The Means of Attachment

The flange is welded onto the barrel using a partial penetration butt weld. Its strength

has been checked in the preceding section using formulae developed by DNV and is of

sufficient strength. However, as described previously, the means of attachment is still

susceptible to failure through fatigue.

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s safe.

Assumptions

• All aspects of uncertainty associated with strength and loading characteristics

• racteristics have or are assumed to have Normal

• iables are independent.

Chapter 5 Probability of Failure of Hoist Drum

Introduction

The structural strength of the hoist drum replacement has been calculated using various

approaches in the previous section. It can be seen from the results that according to the

various code requirements, the hoist drum should be suitable for service. In this section,

the probability of failure of the hoist drum is calculated using the First Order Second

Moment Method (FOSM), the First Order Reliability Method (FORM) and the Monte

Carlo Method. The methods require a limit state function which is formulated in the

next section.

From the Case Study, it can be seen that the means of attaching the flange to the drum is

critical and this would be the area that is considered most likely to fail. The assessment

of the means of attachment also takes into consideration the strength of the barrel and

flange and the probability of failure of the means of attachment will be a good indicator

of barrel and flange strength.

5.1 The Limit State Function: General

The Limit State function is given by G(x) and is always defined such that when the

function is less than or equal to zero then failure has occurred. When G(x) is greater

than zero then the structure i

DemandCapabilityxG −=)(

can be assessed explicitly.

Strength and loading cha

Distributions.

All random var

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The Limit State function will also have a Normal Distribution with ;

DCG μμμ −= and 222DCG σσσ +=

where:

DCG ,,μ - Mean value of the function G(x), Capability and Demand

respectively.

DCG ,,σ - Standard deviation of G(x), Capability and Demand function

respectively.

and the probability of failure Pf is given by;

⎥⎦

⎤⎢⎣

⎡−=

G

GfP

σμφ

Where the value of ø is given in Normal Distribution Tables. G

G

σμ is also known as the

Safety or Reliability Index.

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5.2 Limit State Function: Flange Fillet

The weld fails if the force in the weld exceeds the maximum allowable force given by

the weld area multiplied by the material’s yield stress. The limit state function in this

case is then given by;

FlangeonactingForceStrengthWeldxG ____)( −=

Let;

Aweld weld area given by the product of weld throat(h) and weld length (lweld)

σy flange material yield stress

FAllowable allowable force in weld

The weld strength is given by the allowable force in the weld. The length of the weld is

given by the circumference of the barrel in this case and is equal to;

Dlweld ⋅= π

therefore;

yAllowable DhF σπ ⋅⋅⋅=

If the applied force in the weld area is F, then the limit state function can be stated as;

FDhxG y −⋅⋅⋅= σπ)(

Where F is the force acting on the flange and is dependent on the pressure due to the

rope force and is given by Fflange as defined in the previous section;

DpDDSC


−⋅⋅=

6)( 22π

Therefore the complete limit state function is given by;

DpDDSC

DhxG outerlayery ⋅⋅

−⋅⋅−⋅⋅⋅=

6)(

)(22π

σπ

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where;

C amplification factor (1.75 for more than one layer).

S rope tension under spooling

p pitch of rope grooving

D outer diameter of barrel

Each of these parameters is explained further in the following section.

MIPEG Load Data(Specialist Maintenance Solutions, 2008)

The hoist drum load data was recorded using the MIPEG system (See Appendix A) over

almost a 3 year period from August 2005 to March 2007. This is considered to be a

random variable which can be modelled and the variance and mean calculated. The

maximum safe working load is 4.5 Tonnes but it can be seen from the data that this was

often exceeded. The MIPEG load data recorded over the period has the following

parameters;

No. of cycles (n) 1074

Mean (μy) 21127N

Standard Deviation (σy) 8058N

However, the expected number of cycles for the life of the hoist drum (which is taken as

25 years) is approximately 25000 (based on 1000 cycles per year). The maximum load

distribution is assumed to be Extreme Value Distribution and will be approximated by a

normal distribution. Therefore, the mean and variance for the maximum loading

throughout the life of the hoist drum is then given by;

n 25 000

5.4)25000ln(2)ln(2 === nnα

And;

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45

962.35.4*2

)4ln()25000ln(ln(5.4)ln(22

)4ln())ln(ln()ln(2 =+

−=+

−=ππ

nnnun

The corresponding mean and variance of the Type I distribution are;

Nu yn

nyYn4.540868058*

5.4577216.0962.321127 =⎥⎦

⎤⎢⎣⎡ ++=⎥

⎦

⎤⎢⎣

⎡++= σ

αγμμ

Where γ is Euler’s number, and the variance is given by;

9.52744595.4*6

8058*6 2

22

2

222 ===

πασπ

σ yYn

n

n

Therefore, the standard deviation is given by;

NY 6.2296=σ

The rope tension distribution for the 25000 expected load cycles will be described as

below.

Rope Tension (S)

Parameter Mean (N) Standard Deviation (N)

S 54086.4 2296.6

Yield Stress (σy)

The yield stress depends on the material and in this case, steel to BSEN10025 with a

yield strength of 345 MPa was used. The yield strength is considered a random variable

with a Lognormal distribution.

Parameter Mean (N/mm2) Coefficient of Variation

σy 345 0.05

Where from Course Notes;

2

2

345ζλ

σμ+

== ey therefore 844.5)345ln(

2

==+ζλ2


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And;

22222 25.17

2

=−= + μσ ζλe

Therefore;

69.11)34525.17ln(22 222 =+=+ ζλ

Using the two equations obtained above, we get;

05.0=ζ and 842.5=λ

Outer Barrel Diameter (D)

This will vary with variations in material thickness, measurement error and so on. In

this case, the barrel dimension are taken as a constant.

Parameter Value (mm)

D 356

Pitch of rope Grooving (p)

This will vary with the rope grooving but in this case can be taken as a constant.


p 19

Outer Rope Layer Diameter (Douter layer)

The outer layer rope diameter will vary depending on the rope required to be stored on

the drum and also when the rope winds on/off the drum. In this case a sensitivity

analysis will be carried out for an outer layer diameter from 1 layer to 7 layers.


Douter layer1 394

Douter layer2 432

Douter layer3 470

Douter layer4 508

Douter layer5 546

Douter layer6 584

Douter layer7 622

Weld Throat (h)

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This will vary with material thickness and with welding errors. In this case however it

can be considered a random variable with a Normal distribution.

Parameter Mean (mm) Coefficient of Variation

h 20 0.05

Amplification Factor (C)

This is a random variable with a Beta distribution with a minimum value of 1 and a

maximum value of 2.

Parameter Mean Standard Deviation

C 1.75 0.363

π mathematical constant

The Limit State Function for Layer 1 is then given by;

CShDp

DDSCDhxG y

outerlayery 21.241.1118

6)(

)(22

−=⋅⋅

−⋅⋅−⋅⋅⋅= σ

πσπ

For Layer 2;

CShxG y 636.441.1118)( −= σ

For Layer 3;

CShxG y 289.741.1118)( −= σ

For Layer 4;

CShxG y 166.1041.1118)( −= σ

For Layer 5;

CShxG y 267.1341.1118)( −= σ

For Layer 6;

CShxG y 59.1641.1118)( −= σ

For Layer 7;

CShxG y 138.2041.1118)( −= σ

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5.3 Limit State Function: Weld Fatigue

The assessment of weld fatigue will be based on the JCSS Probabilistic Model Code

Part 3: Resistance Models (3rd draft/ November 2006). Using the S-N lines approach in

combination with Miner’s Damage Rule, the Limit State Function is given by(Joint

Committee of Structural Safety, 2006);

ncr DDxG −=)(

Where Dcr is Miners’ Damage Sum at Failure and;

⎥⎦⎤

⎢⎣⎡ Δ= )(1)( m

n SEA

nED

Where n is the expected number of cycles and A and m are the material parameters and

is the stress range. SΔ

The Limit State Function is then given by;

⎥⎦⎤

⎢⎣⎡ Δ−= )(1)()( m

cr SEA

nEDxG

The above parameters have the following characteristics [56];

Parameter Distribution Mean Coefficient of variation

Dcr Lognormal 1.0 0.3

A Lognormal 1.0E13 0.58

m 3

The expected number of cycles E(n) is 25000 as stated in the previous section. Since the

distributions are lognormal, the parameters to and s are calculated as below;

For Dcr;

[ ]959.0

3.01

1

122

=+

=

⎥⎦

⎤⎢⎣

⎡+

=

μσ

μot

Therefore;

042.0)ln( −=ot

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And;

294.0)3.01ln(1ln 22

=+=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

μσs

For A;

[ ]1265.8

58.01

130.1

122

EEto =+

=

⎥⎦

⎤⎢⎣

⎡+

=

μσ

μ

Therefore;

79.29)ln( =ot

And;

539.0)58.01ln(1ln 22

=+=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

μσs

Stress Range SΔ

Assuming the flange does not bend, the weld is primarily under a direct stress due to the

drum flange force. This stress has a minimum of zero when there is no force acting on

the flange and the maximum stress in the weld is given by;

AreaWeldFflange

_max =σ

The weld area is given by the weld throat multiplied by the length of the weld. These

parameters were detailed in the previous section. Therefore;

214.22368 mmDhAweld == π

The flange force (with 5 rope layers) is given by;

DpDDSC


−⋅⋅=

6)( 22π

Therefore;

22

22

max /6

)(mmN

hDpDDSC outerlayer

⋅⋅⋅−⋅

=σ

The stress varies from zero (when there is no loading) to the maximum value given by

the formula. The expected value [ ]mSE Δ is obtained using Appendix B of the JCSS

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Document (Joint Committee of Structural Safety, 2006), which requires an evaluation of

the standard deviation. The standard deviation is evaluated below;

Differentiating the function with respect to each variable;

1.326

)(2

22

max =⋅⋅⋅−

=∂∂

hDpDDS

Couterlayerσ

001.06

)(2

22

max =⋅⋅⋅−⋅

=∂∂

hDpDDC

Souterlayerσ

8.27.11222max −=−=

∂∂

hhσ

The variance is then given by;

22222222

1

max2 1*)8.2(6.2296*001.0363.0*1.32])[(max

−++=−⎥⎦

⎤⎢⎣

⎡∂

∂= ∑

=ii

n

i i

xEx

μσσσ

Therefore; 2/2.12

maxmmN=σσ

Assuming a Rayleigh Distribution and a Gaussian stress spectrum which is narrow

banded according to the JCSS document, then;

[ ] ⎟⎠⎞

⎜⎝⎛Γ=Δ

2)22(

max

mSE mmσσ where m = 3 as described above, then;

[ ]2

*)2*2.12*2( 33 π=ΔSE where

223 π

=⎟⎠⎞

⎜⎝⎛Γ

Therefore; [ ] 6.365283 =ΔSE

The Limit State Function is therefore;

AEDSE

AnEDxG cr

mcr

081.9)(1)()( −=⎥⎦⎤

⎢⎣⎡ Δ−=

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5.4 First Order Second Moment Method (FOSM)

The FOSM is a Level I method based on the limit state function. According to the

Structural Reliability Course Notes (Heriot Watt University), this was one of the first

structural reliability methods to be used. This method gives exact answers to certain

types of structural problems but will suffer from the ‘lack of invariance’ problem. This

is because this method assumes that the limit state function is linear. However, in some

cases the limit state function is not linear and the FOSM approach is considered to give

only an approximate answer.

A summary of how the method is applied is given below;

1. The Limit State function for a particular problem is generated.

2. The Mean Value of the Limit state function is then calculated using the means of

the variables.

3. The Limit State Function is then differentiated with respect to all the variables in

turn.

4. The variance for the Limit State Function is the calculated using the formula

below;

])[()( 22

1

2ii

n

i iG xE

xxG μσ −⎥

⎦

⎤⎢⎣

⎡∂

∂= ∑

=

5. The Safety or Reliability Index is then calculated from G

G

σμ .

6. The probability of failure is then obtained from Normal Distribution Tables.

In this case, the limit state function and the variables have been defined in the preceding

section. The calculation steps continue below with the evaluation of the mean value of

the limit state function.

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Flange Fillet Failure

The limit state function is given by;

DpDDSC


−⋅⋅−⋅⋅⋅=

6)(

)(22π

σπ

The values for the variables are given in the table below;

Parameter Mean Value Standard Deviation

σy 345 17.25

C 1.75 0.363

S 54086.4 2296.6

h 20 1

The values for the constants are given below;

Constant Value

π 3.14

D 356

Douter layer 546

p 19

The mean value is then given by;

DpDDSC

DhG outerlayeryG ⋅⋅

−⋅⋅−⋅⋅⋅==

6)(

)(22π

σπμμ

Therefore;

5.6461321=Gμ

Next, differentiating the Limit State function with respect to each variable;

14.22368)(==

∂∂ hDxG

y

πσ

and;

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22.236

)()( 22

=−

=∂

∂pD

DDCSxG outerlayerπ

4.385850)(==

∂∂

yDhxG σπ

And;

2.7175356

)()( 22

=−

=∂

∂pD

DDSC

xG outerlayerπ


2^1*2^4.385850363.0*2.7175356.2296*22.2325.17*22368])[()( 22222222

2 +++=−⎥⎦

⎤⎢⎣

⎡∂

∂= ∑

=ii

n

iG xE

xxG μσ

1i

G

Therefore;

2.604654=σ

The Safety or Reliability index is then given by;

7.103.4685785.6461321

=== G

σ G

μβ

and the probability of failure from Normal Distribution Tables is given by;

2709.5)( −=−= Ep f βφ

The hoist drum flange fillet therefore has a very low chance of failure with 5 layers

according to the FOSM method.

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Weld Fatigue Failure

The Limit State Function is given by;

AEDSE

AnEDxG cr

mcr

081.9)(1)()( −=⎥⎦⎤

⎢⎣⎡ Δ−=

Therefore, the mean value is then given by;

9999.0130.1081.91)( =−==

EEGG μμ

Therefore; 9999.0=Gμ

Next, differentiating the Limit State function with respect to each variable;

1)(=

∂∂

DxG

cr and; 2

081.9)(AE

AxG

=∂

∂


22

2222

2

1

2 128.5*131

081.93.0*1])[()( EE

ExEx

xGii

n

i iG ⎥⎦

⎤⎢⎣⎡+=−⎥

⎦

⎤⎢⎣

⎡∂

∂= ∑

=

μσ

Therefore; 3.0=Gσ

The Safety or Reliability index is then given by;

333.33.0

9999.0===

G

G

σμβ

and the probability of failure from Normal Distribution Tables is given by;

00043.0)( =−= βφfp

The hoist drum therefore has 0.043% chance of failure with 5 layers from weld fatigue

according to the FOSM method.

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5.5 First Order Reliability Method (FORM)

The FORM Method is a Level II Method that is considered to give a reasonable

approximation of the failure probability. According to the Structural Safety Module

Course Notes (Heriot Watt University), this method overcomes the ‘lack of invariance’

problem. This is done by expanding the Taylor series around the failure point and

converting the expansion from basic variable space to standard Normal space. The

Safety Index, in this case referred to as the Hasofer and Lind Reliability index is then

expressed as the distance from the origin in standard Normal space to the closest point

on the failure surface where G(x)=0. The Hasofer and Lind Reliability Index is then

estimated through iteration. A summary of the method is given below;

1. The Limit State Function for the problem is generated.

2. The Limit State Function is expressed in the form of standardised normal

variates, i.e.

i

iii

xxσ

μ−='

Any variable that is not normally distributed must be converted to the equivalent

Normal variable using the Normal Tail Approximation.

3. The starting values of the standardised normal variates are selected as 0, i.e. the

origin in the standard Normal space.

4. The partial derivatives of the limit state function G(x) at the current value of

are calculated.

'x

5. The direction cosines αi are then calculated using the formula below;

∑=

⎥⎦

⎤⎢⎣

⎡∂

∂

⎥⎦

⎤⎢⎣

⎡∂

∂

=

ni xi

xii

xxG

xxG

,1

2

'

'

'*

'*

)(

)(

α

6. The value of l is calculated from;

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∑=

⎥⎦

⎤⎢⎣

⎡∂

∂=

ni xixxGl

,1

2

'

'

'*

)(

7. The limit state function is then evaluated.

8. The first estimation of the Hasofer and Lind Reliability Index β is then estimated

from;

∑=

−=ni

ix,1

'*αβ

9. New values of are then computed using the equation below; 'x

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−=+ l

xGx mxm

mmm

')(

)( )(

)()('

)1( βα

10. Steps 4 through to 9 are then repeated until convergence is achieved or G(x) is

equal to or close to zero.

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57


As the Limit State Function has been generated in the previous section, this is then

expressed in terms of the standardised normal variates below;

DpDDSC


−⋅⋅−⋅⋅⋅=

6)(

)(22π

σπ

CShxG y 3.134.1118)( −=

Where the variables are σy and S. This can be simplified to;

σ

And the standardised normal variates are;

y

yyy

σ

σ

σμσ

σ−

=' , C

CCσ

C μ−=' ,

h

hhhσ

μ−='

and

S

SSSσ

μ−='

34525.17 ' += yy σσ 363.075.1 ' += C 20' += hh 6.22964. ' += SS

)'363.0746.22964.54086(3.13)'20)(25.17)( ''' CShxG y ++−++= σ

Therefore;

And;

And the partial derivatives are;

And;

*6.22964.54086(*363.0*3.13)('

'

CxG

+−=∂

∂

20(*25.17*4.1118)('

'xG

y

=∂

∂σ

)25.17345(4.1118'

)( ''

yhxG σ+=

∂∂

345(4.1118

, C , and 54086

)'h+

)'75.1(*6.)('

'

CSxG

+−=∂

∂

,

2296*3.13

)'S

.1)(

363.0


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58

As stated the starting point is chosen as the origin where the variables equal zero. The iterative calculations are then computed in an Excel

spreadsheet inserted below;

Variable Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 Iteration 6 Iteration 7 Iteration 8 Iteration 9

y_1 (Sig_y) 0.0000 -6.7666 -6.8635 -6.3465 -6.3960 -6.3966 -6.3971 -6.3970 -6.3970

y_2 (h) 0.0000 -6.7665 -6.8634 -6.3464 -6.3959 -6.3965 -6.3970 -6.3969 -6.3969

y_3 (C) 0.0000 4.5677 7.2801 7.2956 7.2245 7.2251 7.2241 7.2244 7.2243

y_4 (S) 0.0000 0.9350 2.7914 3.3514 3.2539 3.2468 3.2474 3.2472 3.2472

(dg(y)/dy_1) 385851.4500 255307.5271 253439.5807 263412.2840 262457.6213 262446.0075 262437.2333 262439.1574 262438.5978

(dg(y)/dy_2) 385848.0000 255304.0771 253435.5253 263407.9695 262453.2535 262441.6072 262432.8175 262434.7343 262434.1713

(dg(y)/dy_3) -260465.0312 -270806.3305 -291337.8303 -297531.3130 -296452.0163 -296374.3976 -296380.5063 -296377.9960 -296378.7261

(dg(y)/dy_4) -53318.5259 -103836.5551 -133834.9628 -134006.0374 -133219.8133 -133227.0906 -133215.3940 -133218.4711 -133217.5731

l 606996.6378 463120.0752 480885.3452 495229.5327 493352.8452 493295.7990 493286.9660 493288.3322 493287.9311

alpha_1 0.6357 0.5513 0.5270 0.5319 0.5320 0.5320 0.5320 0.5320 0.5320

alpha_2 0.6357 0.5513 0.5270 0.5319 0.5320 0.5320 0.5320 0.5320 0.5320

alpha_3 -0.4291 -0.5847 -0.6058 -0.6008 -0.6009 -0.6008 -0.6008 -0.6008 -0.6008

alpha_4 -0.0878 -0.2242 -0.2783 -0.2706 -0.2700 -0.2701 -0.2701 -0.2701 -0.2701

beta 0.0000 10.6448 12.4501 12.0422 12.0249 12.0240 12.0240 12.0240 12.0240

g(y) 6461343.5878 836078.7710 -196171.1257 -8553.5341 -424.4711 -0.9624 -0.0283 -0.0019 -0.0003

Probability of failure 5.000E-01 9.221E-27 6.984E-36 1.067E-33 1.315E-33 1.329E-33 1.329E-33 1.329E-33 1.329E-33

Table 3 FORM Results – Flange Failure

The probability of failure is therefore taken when the value of G(x`) approaches zero. The probability of failure with 5 rope layers according to the FORM method is therefore very low.


Leslie L Moyo

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As the Limit State Function has been generated in the previous section, this is then

expressed in terms of the standardised normal variates below;

AEDSE

AnEDxG cr

mcr

081.9)(1)()( −=⎥⎦⎤

⎢⎣⎡ Δ−=

Where the variables are σy and S. This can be simplified to;

AEDxG cr

081.9)( −=

And the standardised normal variates are;

y

yyy

σ

σ

σμσ

σ−

=' and A

AAAσ

μ−='

Therefore;

13.0 ' += crcr DD and 131128.5 ' EAEA +=

And;

131128.5081.913.0)( '

''

EAEEDxG cr +

−+=

And the partial derivatives are;

3.0)('

'

=∂

∂D

xGcr

and 2''

'

)131128.5(213.5)(

EAEE

AxG

+=

∂∂

As stated the starting point is chosen as the origin where the variables equal zero. The

iterative calculations are then computed in an Excel spreadsheet inserted below;

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Variable Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 y_1 (Dcr) 0.0000 -3.3330 -3.3330 -3.3330 -3.3330 y_2 (A) 0.0000 -0.0006 -0.0006 -0.0006 -0.0006 (dg(y)/dy_1) 0.3000 0.3000 0.3000 0.3000 0.3000 (dg(y)/dy_2) 0.0001 0.0001 0.0001 0.0001 0.0001 l 0.3000 0.3000 0.3000 0.3000 0.3000 alpha_1 1.0000 1.0000 1.0000 1.0000 1.0000 alpha_2 0.0002 0.0002 0.0002 0.0002 0.0002 beta 0.0000 3.3330 3.3330 3.3330 3.3330 g(y) 0.9999 0.0000 0.0000 0.0000 0.0000 Probability of failure 5.000E-01 4.295E-04 4.295E-04 4.295E-04 4.295E-04 Table 4 FORM Results – Fatigue Failure

The probability of failure is therefore taken when the value of G(x`) approaches zero.

The probability of failure with 5 rope layers according to the FORM method is therefore

0.043%.

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5.6 The Monte Carlo Method

The Monte Carlo Method is considered a Level III Method that can, in principle,

provide exact solutions for the probability of failure [Ref Course Notes]. It also has the

advantage that there is no need to transfer the variables into the standard Normal space,

as with Level II Methods, e.g. the FORM Method which was considered in the previous

section.

The Monte Carlo Method of determining the probability is conducted as follows;

1. Once the mean and standard deviation as well as the type of distribution of the

parameters have been determined, the initial values to be used in the analysis are

determined as follows;

For a Normal distribution;

)2cos()ln(2 211 uux xx πσμ −+=

And;

)2sin()ln(2 212 uux xx πσμ −+=

For a Lognormal distribution;

))2cos()ln(2)exp(ln( 211 uustx o π−+=

And;

))2sin()ln(2)exp(ln( 212 uustx o π−+=

For a Beta distribution;

Where u1 and u2 are the generated random numbers.

Since the Extreme Value Distribution is used for the rope tension, the initial

value is calculated from the Asymptotic distribution;

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62

))ln(ln(11 uxn

x −−=nx

−α

μσ

μ

2. The generated values are then substituted into the Limit State Function G(x) and

the value calculated.

3. The number of trials nf for which G(x) ≤ 0 are then counted. The estimate of the

probability of failure is then given by;

Nn

p ff =


Leslie L Moyo

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Due to the large number of trials that have to be carried out, a Visual Basic program is

developed in Excel and the calculations carried out. The subroutine for the simulation

solution for the flange fillet for Layer 5 is shown below; Private Sub CommandButton1_Click() ' Simulation solution for Flange Fillet mean_C = 1.75 sig_C = 0.363 Var_C = sig_C ^ 2 alpha = (mean_C - 1) * ((mean_C - 1) * (2 - mean_C) / Var_C - 1) beta = (2 - mean_C) * ((mean_C - 1) * (2 - mean_C) / Var_C - 1) u_1 = Rnd Numfails = 0 Ntrials = 100000 Numfails = 0 Ntrials = 100000 Randomize For x = 1 To Ntrials Sy = exp(5.842+0.05*Sqr(-2*log(Rnd))*cos(6.284*Rnd)) h = 20 + Sqr(-2 * Log(Rnd)) * Sin(6.284 * Rnd) C = Application.WorksheetFunction.BetaInv(u_1, alpha, beta, 1, 2) S = 8058 * (3.962 - (Log(-Log(Rnd))) / 4.5) + 21127 Gx = 1118.41 * Sy * h – 13.3 * C * S If Gx < 0! Then Numfails = Numfails + 1 End If Next x Pf = Numfails / Ntrials COV_Pf = Sqr((1# - Pf) / (Ntrials - 1) / Pf) Range("C8").Value = Ntrials Range("C10").Value = Numfails Range("C12").Value = Pf Range("C14").Value = COV_Pf End Sub Figure 19 Visual Basic Subroutine for the Monte Carlo Simulation of Flange Failure

The results of the simulation are shown below;

Number of simulation trials 100000

Number of times G(x) < 0 0

Probability of failure 0

COV_Pf

Monte Carlo SimulationFlange Fillet

Start simulation

Figure 20 Results of Monte Carlo Simulation for Flange Failure

The probability of failure of the flange fillet according to the Monte Carlo Method is

0% with 5 layers of rope.

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The subroutine for the simulation solution for weld fatigue is shown below; Private Sub CommandButton1_Click() ' Simulation solution for Weld Fatigue Numfails = 0 Ntrials = 1000000 Randomize For x = 1 To Ntrials Dcr = exp(-0.042+0.294*Sqr(-2*Log(Rnd))*sin(6.284*Rnd)) A = exp(29.79+0.539*Sqr(-2*Log(Rnd))*sin(6.284*Rnd)) Gx = Dcr-9.1E08/A If Gx < 0! Then Numfails = Numfails + 1 End If Next x Pf = Numfails / Ntrials COV_Pf = Sqr((1# - Pf) / (Ntrials - 1) / Pf) Range("C8").Value = Ntrials Range("C10").Value = Numfails Range("C12").Value = Pf Range("C14").Value = COV_Pf End Sub Figure 21 Visual Basic Subroutine for the Monte Carlo Simulation of Fatigue Failure

The results of the simulation are shown below;

Number of simulation cycles 1000000

Number of times G(X) < 0 0

Probability of failure 0

COV_Pf

Monte Carlo SimulationWeld Fatigue

Start simulation

Figure 22 Results of Monte Carlo Simulation of Fatigue Failure

The probability of failure due to weld fatigue according to the Monte Carlo Method is

0% with 5 layers of rope.

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Chapter 6 Discussion of Results The results obtained from the previous are summarised in the Table below; For the flange fillet failure with 5 layers of rope;

Method Probability of Failure

FOSM 5.09E-27 FORM 1.33E-33 Monte Carlo 0

For the weld fatigue failure with 5 layers of rope;

Method Probability of Failure (%)

FOSM 0.043 FORM 0.043 Monte Carlo 0

The results indicate that the probability of failure of the hoist drum flange is very low,

which implies a very high reliability of the hoist drum. However, the probability of

failure of the hoist drum is higher for the fatigue limit state using FOSM and FORM but

the Monte Carlo Simulation did not indicate any failures for weld fatigue failure, even

after the number of trials was increased to 1million.

It is possible that the hoist drum has been over designed since the probability of failure

is quite low. However, the previous failures of the drum indicate that failure is possible

and it is therefore quite possible that the formulae used do not model the flange loading

accurately. It is quite clear from the research that the drum flange forces are critical to

the reliability of the hoist drum, given the failures reported by Song & Rao which

further reinforces the possibility that the formulae used in determining the strength of

the drum flange do not give a true indication of the drum flange loading model.

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Unfortunately, there is no clear guidance on how the flange forces are to be evaluated,

and it appears that most design standards consider the issue of hoist drum design to be

trivial. Further work will need to be done to develop formulae that will model the drum

flange loading accurately.

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Chapter 7 Conclusions and Recommendations

The reliability of a hoist drum is subject to many factors and the results only give an

indicator of the probability of failure of the hoist drum assuming all other variables are

acceptable. Due to the large number of failures associated with the drum flange, the

flange strength has been selected as the most critical in this instance. However, the

results obtained seem to indicate that the failure of the hoist drum flange is unlikely in

this instance. It would have been worthwhile to apply the same approach to the failed

hoist drums with a view of verifying the accuracy of the formulae. The results therefore

are not conclusive, but indicate that further work needs to be done to come up with

substantive conclusions.

The differences in the pattern of loading are also quite significant. Waters suggests a

uniform loading of the flange, whereas DNV propose that the flange force increases

linearly from zero at the outer layer to a maximum near the barrel surface. Song & Rao

found that the flange thrust increased with the number of layers and Bellamy & Phillips

found that the flange force increased linearly with the number of layers but observed

non-linearity for one type of rope. Bellamy & Philips also observed that LeBus spooling

only had an effect on flange force for certain types of ropes, whilst the effect was

negligible for others.

Unfortunately, it appears as if none of the design standards have taken the work and

findings of the researched authors into account. It is accepted that the results from the

experiments carried out may now be out of date as the stiffness of steel wire ropes has

changed significantly(Lange, 2007) over the years. However, the research can be used

as a basis for future study on the subject.

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Chapter 8 Suggestions for future work

A similar study can be undertaken taking into consideration the failed drums to verify

the accuracy of the design code formulae. The magnitude of the flange forces as

calculated using approaches can also be compared. The project outlined the challenge

facing the hoist drum designer. Whilst the drum barrel can be designed based on clear

procedures and guidelines, the same is not true for the drum flange. The difficulty lies in

determining the magnitude and pattern of loading of the drum flange. Once the flange

force has been determined, the evaluation of the flange stresses is relatively straight

forward.

The approach proposed by Waters, the graphs presented by Bellamy and the DNV

formula can be compared to come up with a clear, verified procedure for determining

drum flange forces. Song & Rao also found significant variations in the flange forces

for small drums compared to large drums and it would be helpful to clarify these

variations. A common design code covering the design of winch drums can then be

developed. A considerable amount of research has been carried out on the subject of

drum flange forces, but unfortunately it does not appear as if any of the work has been

used in any of the design standards reviewed.

The University of Clausthal in Germany has also carried out a number of experiments to

determine the strength of drums in recent years. Unfortunately the papers they have

published are in German and the author did not have the resources to translate the

documents. It would be useful in future if the work was translated to English and the

findings combined with other research findings.

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8.1 Fleet Angle

The effects of rope fleet angle do not appear to have been considered in past

experiments. Industry practise normally limits the fleet angle to 2 degrees for grooved

drums and 1.5 degrees for smooth drums(Shapiro, et al., 1991). It is not clear what

effects larger fleet angles will have and the significance of the fleet angle may be

underestimated as a result. Dynamic effects due to braking(Perry, et al., 1932) and

dynamic loading due to the rope snatching also need to be considered(Imanishi, et al.,

2009).

8.2 Calculation of Stresses

Once the pattern and magnitude of the flange forces have been determined, the

determination of flange stresses is relatively straightforward. A way of calculating the

flange stresses is presented below. This would require the flange to be considered as an

annular ring as in Roark(Young, et al., 2002). This magnitude and pattern of loading

will need to be determined, in this instance the flange force is considered to be a point

load acting at a distance that is 1/3 of the distance from the outermost layer to the drum

surface, measured from the drum surface. Going forward, this approach could be

adopted into the design codes. An excel spreadsheet for the calculation is included

overleaf;

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Force per unit of circumferential length w = 956.5 N/mm

Outer radius a = 700 mm

Inner radius of annular plate b = 293.5 mm

Plate thickness t = 40 mm

Radial location of unit line loading r0 = 384.2 mm

Poisson's ratio υ = 0.3

Young's Modulus E = 210000 N/mm2

Plate Constants D = 1.2E+09

C2 = 0.12965

C3 = 0.02073

C5 = 0.4121

C6 = 0.09583

C8 = 0.71153

C9 = 0.29736

L3 = 0.01124

L6 = 0.06876

L9 = 0.28114

Therefore;

Reaction Mrb = -101739

Qb = 1252.09

ya = -1.0112

θ a = -0.0023

Then the stress is given by;σ = -381.52

Yield Stress = 355 N/mm2

Allowable Stress = 237.85

Utilisation Factor = 1.60405

= (E * t3) / (12 * [1 - υ2]) [Eqn. 1]

= 0.25 * (1 - [b / a]2 * [1 + 2 * ln{a / b}]) [Eqn. 2]

= (b / [4 * a]) * ([{b / a}2 + 1] * ln[a / b] + [b / a]2 - 1) [Eqn. 3]

= 0.5 * (1 - [b / a]2) [Eqn. 4]

= (b / [4 * a]) * ([b / a]2 - 1 + 2 * ln[a / b]) [Eqn. 5]

= 0.5 * (1 + υ + [1 - υ] * [b / a]2) [Eqn. 6]

= (b / a) * (0.5 * [1 + υ] * ln[a / b] + 0.25 * [1 - υ] * [1 - {b / a}2]) [Eqn. 7]

= (r0 / [4 * a]) * ([{r0 / a}2 + 1] * ln[a / r0] + [r0 / a]2 - 1) [Eqn. 8]

= (r0 / [4 * a]) * ([r0 / a]2 - 1 + 2 * ln[a / r0]) [Eqn. 9]

= (r0 / a) * (0.5 * [1 + υ] * ln[a / r0] + 0.25 * [1 - υ] * [1 - {r0 / a}2]) [Eqn. 10]

= - (w * a) / C8 * ([r0 * C9] / b - L9) [Eqn. 11]

= (w * r0) / b [Eqn. 12]

= - (w * a3) / D * ([C2 / C8] * [r0 * C9 / b - L9] - [r0 * C3 / b] + L3) [Eqn. 13]

= - (w * a2 / D) * ([C5 / C8] * [r0 * C9 / b - L9] - [r0 * C6 / b] + L6) [Eqn. 14]

N/mm2 = 6 * Mrb / t2 [Eqn. 15]

N/mm2 = 0.67 * Yield Stress [Eqn. 16]

= σ / Allowable Stress [Eqn. 17] Figure 23 Calculation of Flange Force using Roark(Young, et al., 2002)

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References API Specification for Offshore Pedestal Mounted Cranes [Book]. - Washington : API, 2004. - API 2C. Atkinson LTJ Taylor GL The Analysis and Design of Fabricated Steel Cylindrical Drums for Mine Winding Engines [Article] // Colliery Engineering. - January - August 1967. - pp. 44-45,32,79,115,201,236,315. Atkinson LTJ Taylor GL The Analysis and Design of Fabricated Steel Cylindrical Drums for Mine Winding Engines [Article] // Colliery Engineering. - December 1966. - pp. 43,524. Australian Standards Cranes, Hoists and Winches [Book]. - Sydney : Standards Australia, 2002. - AS1418-1. BAE Systems Beyond Lifetime Criteria of Offshore Cranes [Report]. - Norwich : HSE Books, 2002. Bellamy NW Phillips BDA An Investigation into Flange Forces in Winch Drums [Journal] // IMechE. - 1969. - Vol. 183 Pt 1 No. 27. - pp. 579-590. Blodgett Omer W. Design of Weldments [Book]. - Cleveland : James F. Lincoln Arc Foundation, 1976. British Standards Rules for the Design of Cranes - Part 1 [Book]. - [s.l.] : British Standards, 1983. - BS2573-1. British Standards Rules for the Design of Cranes - Part 2 [Book]. - 1980. - BS2573-2. Broughton H. H. Electric Winders - A Manual on the Design, Construction, Application and Operation of Winding Engines and Mine Hoists [Book]. - London : Spon, 1928, Revised 1948. Crawford WR Design of Colliery Machinery and Equipment [Article] // Colliery Engineering. - July & September 1949. - pp. 261, 319. Dietz Peter A Method for Calculating a Single & Multi-Layered Winch Drum [Journal]. - [s.l.] : Journal of the Societyof German Engineers, July 1972. - 13 : Vol. 12. - pp. 34-344. DNV Rules for Lifting Appliances [Book]. - Hovik : Det Norske Veritas, 2007. Dolan J Winding Drums, Shell Loading due to Successive Layers of Stressed ropes [Journal]. - [s.l.] : South African Institute of Mechanical Engineers, 1957. Dolan John Winder Drum Tread Design Investigation [Article] // The South African Mechanical Engineer. - 1963. Egawa T and Taneda M External Pressure produced by Multi-Layers of rope wound about a Hoisting Drum [Journal]. - [s.l.] : Japanese Society of Mechanical Engineers, 1958. - Vol. 1. - p. 133. FEM FEM Booklet 1 & 2 [Book]. - London : European Handling Federation, 1998. - Vol. 1 : 9. Gagg Colin R and Lewis Peter R In-service Fatigue Failure of Engineered Products and Structures - Case Study Review [Article] // Engineering Failure Analysis. - 2009. - pp. 1775-1793. Hicks John Welded Joint Design [Book]. - New York : Industrial Press, 1999. Imanishi Estujiro, Nanjo Takao and Kobayashi Takahiro Dynamic Simulation of Wire Rope with Contact [Journal] // Journal of Mechanical Science and Technology. - 2009. - pp. 1083-1088.

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IMCA Winch Drum Failure - Deep Water Operations [Article] // IMCA Safety Flash. - February 2009. Jinu GR, Ravichandran G and Rathinam A Investigation of the Fatigue Behaviour of Butt-Welded Joint treated by Ultrasonic Peening Process and compared with Fatigue Life Assessment Standards [Journal] // Int J Adv Manuf Technol. - 2009. - Vol. 40. - pp. 74 - 83. Joint Committee of Structural Safety JCSS Probabilistic Model Code Part3: Resistance Models; Part 3.12 Fatigue Models for Metallic Structures [Book] = JCSS. - 2006. - Third Draft. Lange Walter Design of Hoist Winches with Multi-Layer Spooling. - [s.l.] : Liebherr Cranes, 2007. - Presentation. Lloyds Register Code for Lifting Appliances in a Marine Environment [Book]. - London : Lloyds Register, 2008. Maddox SJ Fatigue Strength of Welded Structures [Book]. - Cambridge : Woodhead Publishing Ltd, 1969. Oberg Erik Machinery Handbook [Book]. - New York : Industrial Press, 2008. Otto S, Mupende I and Dietz P Influence of the Hoisting Drum Winding System on the End Plate Loads [Conference] // International Design Conference. - Dubrovnik : International Design Conference, 2002. Perry John F and Smith D M Mechanical Braking and its Influence on Winding Equipment [Journal]. - [s.l.] : Institute of Mechanical Engineers, 1932. - pp. 537-620. Piskoty G [et al.] Structural Failures of Rope Based Systems [Journal] // Engineering Failure Analysis. - 2009. - pp. 1929-1939. Ruud Stian and Mikkelsen Age Risk Based Rules for Crane Safety Systems [Journal] // Reliability Engineering and System Safety. - 2007. - pp. 1369-1376. Shapiro Howard, Shapiro Jay and Shapiro Lawrence Cranes and Derricks [Book]. - New York : Mcgraw-Hill, 1991. Song KK, Rao GP and Childers Mark A Large Wire Rope Mooring Winch Drum Analysis and Design Criteria [Conference] // Proceedings of the Annual Offshore Technology Conference. - Houston, Texas : Offshore Technology Conference, 1979. - pp. 2737-2746. Sparrows Offshore MIPEG Systems [Online]. - 24 September 2008. - http://www.sparrowsoffshore.com/MIPEG_Load_Monitoring_Systems.html. Specialist Maintenance Solutions Design Review for MK35 Whip Hoist Welded Drum / compl. Cumming Ian. - 2008. Torrance B. M. The Design of Winding Drums [Journal]. - [s.l.] : South African Society of Mechanical Engineers, 1965. - Vol. 15. - p. 123. Waters Everett O. Rational Design of Hoisting Drums [Journal] // ASME. - 1920. - pp. 463-473. Young Warren C and Budynas Richard G Roark's Formulas for Stress and Strain [Book]. - New York : Mcgraw-Hill, 2002.

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Appendices

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Appendix A: MIPEG Rated Capacity Indicators

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MIPEG has been a world wide market leader for decades. The MIPEG 2000 crane

monitoring system brings not only enhanced standards of safety to crane operation, but

also records historical lift information to support more cost efficient crane maintenance

planning and slewing replacement deferral.

Load sensors at the boom tip measure both the static load and the peak load during each

lift and pass the information to the central computer. Both main and auxiliary hoists

have load sensors fitted so that lift information is recorded regardless of which hook is

used.

The moment sensor on the A-frame measures the crane over turning moment - the

stresses on the bearing and the pedestal - with this parameter also being passed to the

central computer. Simultaneously, the Inclinometer at the boom foot measures boom

angle and translates this into operating radius before feeding this data to the computer.

This allows the computer to constantly monitor the safe working load (SWL) at any

given radius.

Figure A.1

Outputs from the computer are fed directly to the in-cab display and audio warnings.

The operator's display can also be mounted remotely from the crane where no cab

exists. The outputs can interface fully to the crane's gross overload protection system,

activating cut outs as required, typically boom out inhibit.

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All this data, which is used in real time to protect the crane, its operator and all those

within the vicinity of the lifting operation, can be recorded for subsequent download to

a standard laptop. These records provide complete analysis (for each individual lift and

cumulatively over the life of the crane) of the dynamic and static hook loads, over

turning moments, radius, number of rope falls set, sea condition, lift duration and many

other parameters. This information is invaluable in planning cost effective crane

maintenance, based on actual crane utilisation and also in gathering information to

guide upgrade or replacement strategies later in the crane's life.

The MIPEG range also includes a rope speed indicator (RSI) which assists the operator

when making 'blind lifts'. The unit displays rope speed visually, with a bar graph, and

audibly, using a buzzer, and has a reset button for zeroing height/depth display. The unit

can also be configured such that outputs can control rope paid out and anti two block

position.

Source: http://www.sparrowsoffshore.com/MIPEG_Load_Monitoring_Systems.html

Date: 24/09/08

Figure A.2

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Appendix B: MIPEG Data from Ruston Bucyrus Crane

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Table 5 MIPEG Data

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ID Task Name Duration Start Finish Predecessors

1 Dissertation 86 days Mon 15/09/08 Mon 01/12/082 Formulate Thesis (Aims, Objectives) 2 days Mon 15/09/08 Tue 16/09/083 Draft proposal 1 day Wed 17/09/08 Wed 17/09/08 24 Literature Review 45 days Thu 18/09/08 Tue 28/10/08 35 FEM 6 days Thu 18/09/08 Tue 23/09/086 AS1418 6 days Tue 23/09/08 Sun 28/09/08 57 API2C 6 days Sun 28/09/08 Sat 04/10/08 68 BS2573 6 days Sat 04/10/08 Thu 09/10/08 79 Lloyds Code 6 days Thu 09/10/08 Tue 14/10/08 810 DNV Code 6 days Wed 15/10/08 Mon 20/10/08 911 Completion of Draft Literature Review 3 days Mon 20/10/08 Thu 23/10/08 1012 Review of Historical Changes 6 days Thu 23/10/08 Tue 28/10/08 1113 Field Work 21 days Tue 28/10/08 Sun 16/11/08 1214 Accident data collection 15 days Tue 28/10/08 Mon 10/11/0815 Root cause analysis 5 days Tue 11/11/08 Sat 15/11/08 1416 Code requirement 1 day Sat 15/11/08 Sun 16/11/08 1517 Analysis of data/Survey results 3 days Sun 16/11/08 Wed 19/11/08 1618 Conclusions/Implications 5 days Wed 19/11/08 Sun 23/11/08 1719 Formulate Abstract 1 day Sun 23/11/08 Mon 24/11/08 1820 Draft Introduction and Executive Summary 1 day Mon 24/11/08 Tue 25/11/08 1921 Submit draft dissertation to supervisor 1 day Tue 25/11/08 Wed 26/11/08 2022 Final Draft (PDF) 6 days Wed 26/11/08 Mon 01/12/08 2123 Interview 1 day Mon 15/09/08 Mon 15/09/08

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