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Thesis Report On

ANALYSIS AND IMPROVEMENT OF JACKING SYSTEMS FOR JACK-UP RIG

Submitted by

NG JUN JIE U048851X

Department of Mechanical Engineering

In partial fulfillment of the requirements for the Degree of

Bachelor of Engineering National University of Singapore

Session 2007/2008

i

SUMMARY

As the need for energy increases globally, explorers have went out deeper

and deeper into the ocean for oil and gas which forms the world’s main

energy source. Jack-up rigs, which is one of the offshore structures that is

used in today’s extraction of oil from the seabed, is being analyzed.

This paper attempts to provide an insight to improving the fatigue life of the

lifting mechanism which comprises of the rack and pinion of a jack-up rig

by reducing the mean stress.

A practical model of a rack and pinion in a jack-up rig is modeled using

CAD and simulations are run on the model using finite element method

programs. The strength of the structure would be evaluated according to the

analysis results.

A study of the optimum fillet radius for the contact stress between the rack

and pinion is proposed which helps in reducing the fatigue failures by cyclic

loading of jack-ups.

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Acknowledgement

The author wishes to express his sincere gratitude to his guide, A/P Mr. H.P Lee, for his

valuable guidance, proper advice and constant encouragement during the course or his

work on this project.

The author also feel very much obliged to his co-supervisor, Dr. X.M Tan, Research

Scientist at Institute of High Performance Computing for his encouragement and

inspiration for execution of the project work.

The author is deeply indebted to his parents for their inspiration and ever encouraging

moral support, which enabled him to pursue his studies.

The author is also very thankful to the entire faculty and staff members of Mechanical

Engineering Department for their direct–indirect help and cooperation.

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TABLE OF CO"TE"TS

Title Page "umber

Summary ................................................................................ i

Acknowledgement ................................................................. ii

Table of Contents ................................................................. iii

List of Figures ........................................................................ v

List of Tables ...................................................................... viii

1. Introduction ....................................................................... 1

1.1 Thesis Outline ........................................................... 2

2. Literature Review .............................................................. 2

2.1 Jack-up Rigs ............................................................. 2

2.2 Types of Jack-up Units ............................................. 3

2.3 Types of Leggings..................................................... 4

2.4 Modes of Operations in a Jack-up ............................. 5

2.4.1 Afloat Transit Mode ..................................... 6

2.4.2 Preload Mode ............................................... 7

2.4.3 Elevated Mode ............................................. 8

2.5 Lifting Mechanism – Rack and Pinion ...................... 8

2.6 Failures of Jack-up Rigs ............................................ 9

2.6.1 Failure of Jack-up Rigs by Fatigue ............. 10

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2.6.2 Stress Reduction by Use of Fillets ............... 12

3. Problem Definition .......................................................... 13

3.1 Implementation ....................................................... 14

4. Numerical Investigation ................................................... 14

4.1Mesh sensitivity ....................................................... 14

4.1.1 Results ........................................................ 15

4.2 FEM model ............................................................. 16

4.3 Boundary Conditions .............................................. 21

4.3.1 Displacement .............................................. 22

4.3.2 Pressure ....................................................... 23

4.3.3 Contact ........................................................ 24

4.4 Material .................................................................. 25

5. Results ............................................................................. 26

5.1 Stress against Fillet Radius ..................................... 26

5.2 Plastic Strain against Fillet Radius ........................... 32

5.3 Displacement against Fillet Radius .......................... 38

6. Conclusion ....................................................................... 44

7. Recommendations ........................................................... 45

8. References ....................................................................... 46

v

List of Figures

1. Different working depths of offshore units.

2. Photograph of an offshore Jack-up in operation.

3. Top plane diagrams of (a) 4-legged jack-ups (b) 3-legged jack-ups.

4. Photographs of (a) cylindrical legs (b) truss legs.

5. Photograph of (a) Jack-up with legs retracted. (b) Jack-up under tow

(c) Jack-up on a loading vessel, accompanied by supporting towboats.

6. Photograph of a Jack-up Rig under preload conditions.

7. Diagram of a Jack-up Rig under transition.

8. Photograph of a Rack and Pinion system.

9. Case Histories classified according to causes of failures.

10. Causes of Jack-up Rigs During period of 1979 to 1988.

11. Schematic diagram of contact of pinion and rack with varying fillet radius.

12. Diagram of the changes in mesh sensitivity (a) Mesh = 0.015 (b) Mesh

=0.075 (c) Mesh =0.025 (d) Mesh =0.00125.

13. Table and Graph of Stress against Mesh Size.

14. Different views of rack model.

15. Different views of pinion model.

16. Different views of Rack and Pinion Configuration.

17. Comparison of Model with and without Fillets.

18. The pinion is constrained in all the three directions.

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19. The rack’s top and bottom is constrained in the x and y directions.

20. The rack’s side is constrained in the x direction.

21. Bottom elements are given pressure.

22. (a) Slave nodes of the rack (b) Master nodes of the pinion.

23. Overview of contact surface of the model.

24. Stress Variation in Rack and Pinion when fillet radius, r = 0mm.

25. Stress Variation in Rack and Pinion when fillet radius, r = 2.5mm.









34. Graph of Stress Against Fillet Radius.

35. Plastic Strain Variation in Rack and Pinion when fillet radius, r = 0mm.

36. Plastic Strain Variation in Rack and Pinion when fillet radius, r = 2.5mm.



39. Plastic Strain Variation in Rack and Pinion when fillet radius, r =

6.875mm.

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42. Plastic Strain Variation in Rack and Pinion when fillet radius, r =

8.125mm.



45. Graph of Plastic Strain against Fillet Radius.

46. Displacement Variation when fillet radius, r= 0mm.

47. Displacement Variation when fillet radius, r= 2.5mm.









56. Graph of Displacement Against Fillet Radius.

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List of Tables

1. Results of mesh element size and corresponding highest stress.

2. Table of property of steel

3. Table of Results of Fillet radius and Stress

4. Table of Results of Fillet radius and Strain

5. Table of Results of Fillet radius and Displacement

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1. Introduction The continuously rising oil price has been driving oil companies to put increasingly more

efforts in exploring and producing oil from the sea. The demand for oil has pushed

explorers to venture deeper and deeper into the ocean. There are now a lot of facilities

used for the extraction of oil from the seabed. They vary from Jack-ups to drill ships.

They are used in different environments and they are used for different sea depths. Figure

1 illustrates further on the different working depths of the mobile offshore units.

Fig 1: Different working depths of offshore units

Jack-up rigs are capable of working in sea depths up to 400ft (121m). For

semisubmersible rigs, they usually work up to a depth of 3280ft (1000m) [9]. Lastly,

drillships are usually used in very deep waters to extract oil from the seabed.

Jack-up rigs are mobile and they would be towed from one place to another after the

original oil site has either low production and cannot meet the demand or it is no longer

commercially profiteering to produce from that well. The legs of the jack-up would

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retract and extended during the transition. The upwards and downwards linear motion of

the lifting mechanism- the rack and pinion, would be experiencing stress repeatedly. It is

then proposed through the chamfering of the rack edges, to reduce the maximum contact

stress and thus increasing its fatigue life.

The purpose of this project is to conduct a parametric study of the relationship between

highest contact stress and the fillet radius of the rack edge.

1.1. Thesis Outline

Chapter 2 provides an introduction to the jack-up rig and some of the causes of failures

that offshore mobile units undergo. The chapter also goes through some of the past

statistics of jack-up rigs failures and its causes. Chapter 3 presents the problem of the

prevailing jack-up rigs and the numerical approach to solve for the optimum solution.

Chapter 4 shows the lifting mechanism which the rack and pinion is being developed into

a CAD model. It also presents the boundary conditions used in the simulation of real

environmental loads as well as the material properties. Chapter 5 presents the findings of

the simulations. Chapter 6 gives the conclusion of the study done. Lists of

recommendations are made in Chapter 7.

2. Literature Review

2.1 Jack-ups Rigs

Jack-up rigs are used in the exploration of oil since the 1950’s. They have been used for

exploration drilling, tender assisted drilling, production, accommodation, and work or

maintenance platforms. [1]

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A Jack-up rig is an offshore structure composed of a hull, legs and a lifting system that

allows it to be towed to a site, lower its legs into the seabed and elevate its hull to provide

a stable work deck capable of withstanding the environmental loads.

Jack-up rigs are used because they can be towed to another oil well after the well

production no longer can produce the required demand. A fixed platform would be

similar to a jack-up rig just that it is only built at that particular worksite and cannot be

moved. Jack-up rigs are thus more expensive to build than a fixed platform.

Fig 2: Photograph of an offshore Jack-up in operation

2.2 Types of Jack-up Units

There are typically 3-legged and 4-legged jack-ups in the world today. However the

majority of the jack-ups that are produced are 3 legged. [1]

The advantages of 4-legged jack-ups are that they have more work space as they require

no preload tankage and they are usually stiffer in the elevated mode because of the extra

leg. It is also because of the extra leg that the jack-up would experience additional wind,

(a) (b)

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current and wave conditions. In the afloat transit mode, the jack-up would also have a

greater draught due to the weight of the additional leg.

The 3-legged jack-ups on the other hand weighs lesser for a given hull size and can carry

more load. They also eliminate the construction of an additional leg, thus reducing the

number of lifting mechanism (racks, pinions, etc). This helps to reduce the power and

maintenance requirements. However unlike 4-legged jack-ups they require preload tanks

onboard which take up usable space.

Fig 3: Top plane diagrams of (a) 4-legged jack-ups (b) 3-legged jack-ups

2.3 Types of Leggings

There are two main types of leggings: cylindrical and trussed.

Cylindrical Legs are made up of hollow steel tubes. They may be fitted with rack and

pinions or holes in the shell to allow jacking up or down of the hull. They belong to an

older class of jack-ups rigs and they are used in water depths less than 300 ft. The main

advantage of using cylindrical legs is that it is smaller in cross-section and takes up less

deck space.

The newer jack-up units are equipped with truss legs as they are lighter and use less

material whilst providing the same resistance to the environmental loads. For the truss

(a) (b)

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legs to be able to match the strength of the cylindrical legs, one must carefully consider

its flexural and axial strength of the trusses’ chords and braces.

Fig 4: Photographs of (a) cylindrical legs (b) truss legs

2.4 Modes of Operations of a Jack-up

There are basically 3 types of modes a jack-up would experience when transiting from an

work site to another. They are the afloat transit mode, preload mode and the elevated

mode.

2.4.1 Afloat Transit Mode

When the hull of a jack-up is lowered from its elevated mode, the legs are retracted and

they leave the seabed. It is not necessary to full retract the legs as long as they have

enough clearance from the seabed. This would increase stability of the jack-up and

reduces the risk of wind overturning. The jack-up floats on the sea on its own hull and it

(a) (b)

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is towed by several towboats to the location. In some other cases, the jack-up unit is

brought up onto the deck of another vessel. In this case, the legs of the jack-up unit must

be retracted to the maximum before loading onto the loading vessel.

Fig 5: Photograph of (a) Jack-up with legs retracted. (b) Jack-up under tow

(c) Jack-up on a loading vessel, accompanied by supporting towboats.

2.4.2 Preload Mode

The jack-up unit has to be preloaded to simulate operating conditions. In this mode, the

hull is jacked up slowly to a height no more than 5 feet above the sea level. By pumping

in seawater from the surroundings to the onboard preload tanks, the hull carries extra

weight apart from its own weight. In this mode, there are chances that a leg shift or soil

failure might occur. If that happens, the jack-up would lose its balance, dropping its hull

(c)

(b) (a)

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into the water. The consequences are kept to a minimal as the hull is near the water, thus

reducing the wave impact.

For the 4-legged jack-up rigs, there is little or no preload water. It is usually done by

preloading 2 of its diagonally opposite legs by the weight of the hull itself. After settling

occurs, the 2 legs are lifted slightly to bring the other 2 legs to its preload period. After

the 4 legs are settled, the hull is then brought up to its operating height.

Fig 6: Photograph of a Jack-up Rig under preload conditions

2.4.3 Elevated Mode

Once the hull is in the operating height, the brakes are set and its weight lies fully on the

strength of the legs. The jack-up rig is ready to begin operations. Figure 7 illustrates the

various modes of operation from arriving at the oil site to operational mode.

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Fig 7: Diagram of a Jack-up Rig under transition

2.5 Lifting Mechanism – Rack and Pinion

All Jack-ups have mechanisms for lifting and lowering the hull. Majority of Jack-ups are

equipped with a Rack and Pinion system for continuous jacking operations. The power

sources used for jacking include both electric and hydraulic. Figure 8 shows a typical

rack and pinion system found on a jack-up rig.

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Fig 8: Photograph of a Rack and Pinion system

One point to take note is that the cross-sectional thickness of the pinion is usually larger

than the thickness of the rack. This is to prevent slipping of the rack off the pinion.

2.6 Failure of Jack-up Rigs

According to a report by MSL Engineering Ltd prepared for Health and Safety Executive

in 2004, 53% of the failures that jack-up rigs experiences is due to punch through of the

legs. Other causes include uneven seabed, volcanic activities, unexpected penetration of

the legs, sliding of mat foundation and mudslide.

10

Fig 9: Case Histories classified according to causes of failures

2.6.1 Failure of Jack-up Rigs by Fatigue

In high cycle fatigue situations, materials performance is normally characterized by the

S-N curve. The graph depicts of a cyclical stress(S) against cycles to failures (N). Failure

due to repeated loading is called fatigue.

Fatigue failures are often caused by the degradation of metal surface. A rough surface

finish, a scratch or oxidation will provide an initial crack. Cracks will propagate after

cyclical loading and eventually lead to fatigue failure.

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The factor that determines fatigue failure is mean stress. As the mean stress decreases, the

fatigue life increases. The defects on the contact surface will cause a decrease in the life

of a material. As such, sharp corners which stresses concentrate on will probably be the

first where cracks will occur and propagate.

In another paper by B. P. M. Sharpies, W. T. Bennett, Jr and J. C. Trickey, it spoke of the

failures that jack-up rigs experience due to a certain factor during the period 1979 to 1988.

Fatigue was one of the factors with 13 accidents out of the 226 accidents that occurred

during this period.

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Fig 10: Causes of Jack-up Rigs During period of 1979 to 1988

2.6.2 Stress Reduction by Use of Fillets

Gears develop high stress concentration at the gear tooth root stress and the contact point.

It is usually at these areas where there is a higher chance of fatigue failure. In normal

operations the contact point shifts along the profile of the tooth and a surface fatigue

failure is likely. In the normal jack up operation, the rack and pinion is held in place after

the hull is at its operational height. In this case, the contact point between the rack and

pinion will stay in one place for an extended period of time. This is when the relief

features are needed to reduce the highest stress at the contact point. Fatigue life will be

increased if fillets are introduced at the contact point.

Vasilios [21] introduces another method to find the minimum fillet stress using BEM and

further verification has been done using 2D photoelasticity. Math [20] proposes an

approach to determine the geometry of the spur gear tooth fillet. Equations have been set

up for the tangency of the involute curve and root fillet.

13

3. Problem Definition

The hull is supported by the Jack-up’s lifting mechanism; the consequences would be

catastrophic if the rack and pinion were to fail by fatigue. In recurring instances of

jacking up and down the legs due to its mobile nature, the rack and pinion experiences

repeated contact stress at sharp corners, especially at the edges of the rack. The cyclic

nature of loading and unloading the hull causes the rack to fail possibly by fatigue.

Therefore, it is paramount that the rack and pinion has relief features in areas where the

highest stress occurs. Presently there are no studies on this aspect of study. This is a new

area of study to look into. It could have possible tremendous positive impacts if this were

to be put into practice in the offshore industry. The relief fillet causes a lower distributed

stress at the edges. The chamfering of the edges of the rack at the contact surface gives

the rack a longer fatigue life. It is then proposed to investigate the relationship between

the fillet radius and its corresponding stress level at the point of contact to find an

optimum fillet radius for the rack.

Fig 11: Schematic diagram of contact of pinion and rack with varying fillet radius

The highest stress is found at the sharp corners of the rack. The rationale of the

simulation is that by chamfering the edges, the highest stress is reduced by distributing

Highest

stress Highest

stress

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the stress around the fillet radius. However with larger fillet radius, the area of contact of

the rack with the pinion is reduced. There is a point where the highest stress will start to

increase with larger fillet radius. The aim of this simulation is to find out the optimum

fillet radius.

3.1. Implementation

Software used: -

Modeling using Solidworks 2005, transferring of coordinates to MSC Patran 2005r3 and

analysis is done using Abaqus Version 6.41.

4. "umerical Investigation

4.1 Mesh Sensitivity

A study of varying element size on the rack surface has been done for convergence

purposes. This study is done on the purpose that the computational result does not deviate

too much from the actual stress. The convergence test is done on a single model.

Table 1: Results of mesh element size and corresponding highest stress

Mesh size (mm) HighestStress (Pa)

0.00125 7.55E+08

0.0025 7.53E+08

0.0075 7.36E+08

0.015 7.10E+08

15

\

Fig 12: Diagram of the changes in mesh sensitivity (a) Mesh = 0.015 (b) Mesh =0.075

(c) Mesh =0.025 (d) Mesh =0.00125

4.1.1 Results

The results of convergence are shown in the form of a table and graph shown below.

(a) (b)

(c) (d)

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Graph of Stress against Mesh Size

5.00E+08

5.50E+08

6.00E+08

6.50E+08

7.00E+08

7.50E+08

8.00E+08

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Mesh Size (mm)

Str

ess,

σ (

Pa))

Fig 13: Table and Graph of Stress against Mesh Size

The graph above shows the variation of element size and its corresponding stress. It

shows that even after the element size has been halved to 0.00125, the stress deviate from

the previous stress by less than 1%. Thus it would be more computationally expensive to

use element size of 0.00125 and below. It would be fairly accurate to use element size of

0.0025 in area of analysis.

4.2 FEM model

The model is based on a practical Rack and Pinion that is in a commercial Jack-up. The

original Rack and Pinion has been cut into half since it is symmetrical about its central

plane.

The rack is modeled and meshed as shown in Figure 15. Similarly the pinion can be

found in Figure 16. The final rack and pinion configuration is shown in Figure 17.

Finally, a contrast is shown between a rack with and without fillets in Figure 18.

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The FEM model is made up of all solid tetrahedral elements.

18

Fig 14: Different views of rack model

19

Fig 15: Different views of pinion model

20

21

Fig 16: Different views of Rack and Pinion Configuration

Fig 17: Comparison of Model with and without Fillets

4.3 Boundary Conditions

The model has boundary conditions like displacement, pressure and contact.

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4.3.1 Displacement

Firstly the pinion is given the boundary condition that the inner bore is constrained in all

the 3 directions. Figure 19 shows the boundary condition given to the pinion.

Fig 18: The pinion is constrained in all the three directions

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Fig 19: The rack’s top and bottom is constrained in the x and y directions

Fig 20: The rack’s side is constrained in the x direction

4.3.2 Pressure

The rack is given an upwards pressure of 1 kipf/sq in (6.89 MPa) and is applied at the

bottom surfaces of bottom elements.

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Fig 21: Bottom elements are given pressure

4.3.3 Contact

The surface of the rack has slave nodes and the surface of the pinion has master nodes in

defining the contact. A friction coefficient of 0.1 is being applied here.

Fig 22: (a) Slave nodes of the rack (b) Master nodes of the pinion

(a) (b)

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Fig 23: Overview of contact surface of the model

4.4 Material

All the models are given the property of steel. The properties of steel are presented in a

form of graph below.

Table 2: Table of property of steel

Properties of Steel

Elastic Modulus 2e11 Pa

Poisson Ratio 0.3

Density 7850 kg/m3

Yield Stress 7.24e8 Pa

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5. Results

The results of the simulations can be summarized into the following: Stress variation

against fillet radius, plastic strain against fillet radius and displacement against fillet

radius.

5.1 Stress Variation against Fillet radius

The following results are presented in the form of pictures shown below.

Fig 24: Stress Variation in Rack and Pinion when fillet radius, r = 0mm

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Fig 25: Stress Variation in Rack and Pinion when fillet radius, r = 2.5mm


28



29



30



31


Fillet radius r, mm Stress x108 , Pa

0.000 7.53

2.500 7.20

5.000 7.10

6.250 6.98

6.875 6.95

7.200 6.99

7.500 7.01

8.125 7.06

8.750 7.11

10.000 7.19

Table 3: Table of Results of Fillet radius and Stress

The highest stress from the diagrams is presented in a form of graph shown below.

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Stress Against Fillet Radius

6.9

7

7.1

7.2

7.3

7.4

7.5

7.6

0 2 4 6 8 10 12

Fillet Radius, r (mm)

Str

ess, σ

(P

a) x10

8

Fig 34: Graph of Stress Against Fillet Radius

5.2 Plastic Strain against Fillet Radius

The following pictures depict the plastic strains that are found by the edges of the rack.

Fig 35: Plastic Strain Variation in Rack and Pinion when fillet radius, r = 0mm

33

Fig 36: Plastic Strain Variation in Rack and Pinion when fillet radius, r = 2.5mm


34



35



36



37


Table 4: Table of Results of Fillet radius and Strain

Fillet radius r, mm Plastic Strain x10-2

0.000 6.92

2.500 5.00

5.000 4.66

6.250 4.21

6.875 4.13

7.200 4.17

7.500 4.23

8.125 4.43

8.750 4.68

10.000 4.98

38

Plastic Strain Against Fillet Radius

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12


Pla

sti

c S

train

x10

-2

Fig 45: Graph of Plastic Strain against Fillet Radius

5.3 Displacement against Fillet Radius

This simulation serves as a preliminary study of displacement. The following shows the

results of varying fillet radius against displacement. Figure 54 shows the graph of the

displacement and fillet radius.

39

Fig 46: Displacement Variation when fillet radius, r= 0mm

Fig 47: Displacement Variation when fillet radius, r= 2.5mm

40



41



42



43



44

Fillet radius r, mm Displacement x10-3 , mm

0.000 1.89

2.500 1.71

5.000 1.69

6.250 1.55

6.875 1.55

7.200 1.56

7.500 1.58

8.125 1.59

8.750 1.60

10.000 2.00

Table 5: Table of Results of Fillet radius and Displacement

Displacement Against Fillet Radius

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12


Dis

pla

cem

ent (m

m) x10

-3

Fig 56: Graph of Displacement Against Fillet Radius

6. Conclusion

From this study, we have found out an optimum fillet for the edges of the rack. It can be

concluded from the studies that a fillet radius of 6.875mm is the optimum radius. It

shows that with fillet radius of 6.875mm would yield the lowest stress of 6.95e8 Pa. It

means there is a reduction of about 7.7% in contact stress compared with the rack that is

45

without the fillets. The plastic strains are also the lowest when the fillet radius is

6.875mm. The maximum displacements are near the applied pressure and they are found

at the places where there is the least deformation. At fillet radius of 6.875mm and

6.25mm, the rack and pinion exhibits the least displacement.

All of the results that are exhibited are static stresses produced from constant loads. In

actual operation, the rack and pinion experiences dynamic loads variations. However the

dynamic loads will be small as the rotational speed of the pinion will be slow when

elevating the hull. For actual determination of the stresses, programs that are able to

calculate dynamic loads are suggested, for instance LS-DYNA.

7. Recommendations

In practical offshore industry, there is no record of filleting the edges of the rack.

However from this study, it shows that by chamfering the edges of the rack, one is able to

reduce the maximum contact stress, thus reducing mean stress. From there, the chances of

fatigue failure can be reduced too.

One recommendation is that instead of chamfering special fillet radius of 6.875mm which

requires precise machining, one can opt for common fillet radius like 6mm or even an

odd number 7mm which is close to the optimum fillet radius to reduce chances of fatigue

failure.

Another recommendation is that designers of jack-up rigs can indicate that in the

manufacture of the rack; to save cost, chamfer only the operational range. That is to say

only chamfer the range where the hull is in elevated mode. There is no need to chamfer

the whole rack as at full operational height of the hull would experience more cycles to

failure with real environment loads in times of storms.

46

8. References

1) Bennett and Associates, L.L.C and Offshore Technology Development Inc (July

1, 2005). “Jack up units: A technical primer for the offshore industry

professional.” Retrieved 23 Sep 2007, from

http://www.bbengr.com/jack_up_primer.pdf

2) B. P. M. Sharpies, W. T. Bennett, Jr and J. C. Trickey (1989), “Risk analysis of

Jackup Rigs.” Marine Structures, Vol. 2, pp. 281-303.

3) Chien-Hsing Li, Hong-Shun Chiou, Chinghua Hung, Yun-Yuan Chang and

Cheng-Chung Yen (2002), “Integration of Finite Element Analysis and Optimum

Design on Gear Systems”, Finite Elements in Analysis and Design, Vol. 38, pp.

179-192.

4) D.P. Stewart and I.M.S. Finnie (2001), “Spudcan-Footprint Interaction During

Jack-Up Workovers.”, Proceedings of the Eleventh International Offshore and

Polar Engineering Conference.

5) Dudley, D.W (1954), “Practical Gear Design”, McGraw-Hill, New York.

6) Fredette L. and Brown M. (1997), “Gear Stress Reduction Using Internal Stress

Relief Features”, Journal of Mechanical Design, Vol. 119, pp. 518-521.

7) Fumitaka Higuchi, Shuuichi Gofuku (2007), “Approximation of involute curves

for CAD-system processing.” Engineering with Computers, Vol 23, pp.207-214.

8) John J. Coy Dennis P. Townsend and Erwin V. Zaretsky (1985). “Gearing.”

NASA reference publication.

9) Keppel Fels (2008) Retrieved 23 Feb 2008, from

http://www.keppelfels.com.sg/products

47

10) Litvin, F.L (1996), “Application of Finite Element Analysis for Determination of

Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis,”

Journal of Mechanical Design, Transactions of the American Society of

Mechanical Engineers, Vol. 118, No. 4, pp. 561–567.

11) Litvin, F.L. (1994), Gear Geometry and Applied Theory, Prentice Hall,

Englewood Cliffs, NJ.

12) Litvin, F.L., and Hsiao, C.-L. (1993), “Computerized Simulation of Meshing and

Contact of Enveloping Gear Tooth Surfaces,” Computer Methods in Applied

Mechanics and Engineering, Vol. 102, pp. 337–366.

13) Moriwaki, I., Fukuda, T., Watabe, Y., Saito, K (1993), “Global Local Finite

Element Method (GLFEM) in Gear Tooth Stress Analysis”, Journal of

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