in the name of allah, most merciful, most gracious

3 downloads 6 Views 7MB Size Report
Figure 2: Rotating Bending Fatigue Testing Machine of the Cantilever Type ...... National Heat Transfer Conference, Niagara Falls, New York, ASME Heat ...... carried out using a plain hotwire in conjunction with a standard bridge (55M10).

IN THE NAME OF ALLAH, MOST MERCIFUL, MOST GRACIOUS

Proceedings of the Seventh Saudi Engineering Conference Riyadh 2-5, December 2007

  Volume V Research and development to serve the industry and upgrade its services Mechanical Engineering Industrial Engineering

PREFACE The Seventh Saudi Engineering Conference comes to complement the series of Saudi engineering conferences which started in 1402H and have been hosted successively by different colleges of engineering of the Saudi universities. The College of Engineering at King Saud University is honored to host the conference for the second time. These conferences have greatly contributed to the resettlement of technology, the dissemination and exchange of experiences between engineering professionals, and have helped to promote the scientific research besides advancing innovation and excellence. At a time of the advanced technology and the availability of information in various ways, nations have become closer and the world is turning into a small village, the economy has become the prime engine of the world. It is necessary for all nations to work hard to cope with this technical progress and benefit from it, and moreover create appropriate conditions to deal with this tremendous development and competition as much as possible. It is incumbent upon all professionals in general and engineers in particular to work hard to provide the proper environment in such circumstances. As a consequence, The Seventh Saudi Engineering Conference discusses an important and vital theme for researchers, engineers and industrialists. The theme is to provide an Engineering Environment to merge in a Competitive Global Economy in an open and boundary-less economy and profession. This conference is trying to answer this question through well-formulated seven topics. Conference topics discuss multiple issues related to engineering profession and engineering firm, engineering environment through education and labor market requirements, engineering rehabilitation, preservation of the environment, rationalization of resource consumption, Saudi construction code, development of the engineering sector to diversify sources of national income, and research and development to service the industry and upgrade its services.

PREFACE

The conference proceedings contain 168 refereed scientific research papers which are distributed into a number of volumes, and each volume contains one or more topic. A separate volume for paper abstract is also published in addition to electronic proceedings that includes all papers accepted in the conference. These proceedings will be a scientific reference for engineers in the Kingdom and the worldwide. Finally, thanks to Almighty God for his help in completing of this work and deep thanks for all members of the Conference Committees for their efforts, and special thanks to members of the Scientific Committee for their efforts to have this documentation of the huge scientific research, which is an important reference for researchers and engineers. Thanks also for authors and experts who have contributed their ideas, their research to the success of the conference.

Thanks Chair of organizing committee Prof. Abdulaziz A. Alhamid

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

VI

INTRODUCTION Under the high patronage of his Royal Highness the Prince Sultan Ibn Abdulaziz the crown prince and minister of defense, aviation and inspector general, the College of engineering at the King Saud university hosted the Seventh Saudi Engineering Conference during the period 22 to 25 Dhu Alqeeda 1428 corresponding to 2-5 December 2007. The theme issue of the conference is “Towards An Engineering Environment Competitive to the Economics of Globalization”. The response to contribute in the conference has been most encouraging. A large number of abstracts were received. After a thorough peer-review process for evaluating the submitted papers, the scientific committee has selected a total of 168 papers, presented by 300 researchers. The conference has drawn participants from the different kingdom universities, colleges, institutes and technical education establishments as well as governmental and national companies. The conference has also attracted international participation from universities and institutes of United Arab Emirates, Egypt, Sudan, Algeria, Tunisia, Malaysia, India, Great Britain, Germany, France, Deutschland, Canada, Japan and United States of America. One of the main objectives of the conference was to contribute to the review and development of important aspects of the engineering sector both public and private. The topics of the conference were chosen to tackle the challenges that engineering education and its outputs are facing. In addition, the themes also emphasized on the contribution of the engineers to the development of the country. The conference themes were as follows: • • • •

Engineering qualification and its role in the strategy of Saudization Engineering specialties as viewed from the educational establishments and the job market requirements Engineering sector contribution to resources conservation Engineering and environmental protection

VII Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

INTRODUCTION

• • •

The Saudi building code Development of the engineering sector for diversification of income resources Research and development in the service of industry and for the improvement of services

In addition to the specialized scientific papers that covered the above mentioned themes the conference also hosted a number of plenary lectures and discussion forums that attracted the participation of key policy makers as well as academics and economic parties. The selected abstracts and papers have been documented in the proceedings which comprise of six volumes in accordance with the conference themes. The papers are also documented in CDs. Before concluding I would like to express my gratitude to all members of the Scientific Committee for their efforts and active participation to the success of the conference. Thanks are also due to the referees who have been of great help in selecting high quality papers for the conference. The support provided by the secretarial and technical staff of the college of engineering is also thankfully acknowledged. Finally on my own behalf and behalf of the Scientific Committee I would like to record our appreciation and sincere thanks to His Excellency the rector of the King Saud University and the Dean of College of engineering, the chairman of the organizing committee for their continued support and valuable guidance, We are all hopeful that this scientific conference will be of a support for recruiting engineering specialties on a larger scale and contribute to the growth and prosperity of our country. May Allah Almighty accept our sincere efforts.

Chairman of the Scientific Committee Prof. Khalid Ibrahem Alhumaizi

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

VIII

Contents

Page No.

Topic 7 Research and development to serve the industry and upgrade its services • Mechanical Engineering FRACTURE SURFACE EXAMINATION OF STAINLESS STEEL 304 SPECIMEN UNDER CUMULATIVE FATIGUE DAMAGE INFLUENCE

1

3

Abdullah Mohammad AL-Garni , Ahmed K. AbdEl latif , Mostafa A. Hamed

NATURAL CONVECTION HEAT HORIZONTAL TRIANGULAR DUCTS

TRANSFER

FROM

17

DYNAMIC PERFORMANCE OF A WIND GENERATION SYSTEM WITH THYRISTOR CONTROLLED CAPACITOR COMPENSATION

33

Mohamed E. Ali and Hany Al-Ansary

M. F. Kandlawala, A. H. M. A .Rahim and M.Ahsanul Alam

SUPERSONIC MINIMUM LENGTH NOZZLE DESIGN AT HIGH TEMPERATURE

47

Toufik Zebbiche

NUMERICAL STUDY OF NATRUAL CONVECTION FROM A UNIFORMLY HEATED HORIZONTAL TRIANGULAR DUCT

69

H. Alansary , O. Zeitoun and Mohamed Ali

ACTIVE CONTROL OF THE FLOW FIELD AROUND A BARCHAN SAND DUNE MODEL

83

A. M. Shibl , M. F. Zedan , K. A. Al-Saif

AN EXPERIMENRAL RADIATIVE COOLING

INVESTIGATION

ON

NIGHT

99

H. Bassindowa, S. Al-Faidi, M.A. Bahafzallah, M.M. Al-Edini, A.Al-Ayiashi, O.M. Al-Rabghi and M. Akyurt

THE EFFECT OF TIH2 PARTICLE SIZES ON THE MORPHOLOGY OF AL-FOAM PRODUCED BY THE POWDER COMPACT MELTING PROCESS (PM) A.Ibrahim , K.Koerner , R.Singer

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

111

< 0, near the slit at small Reynolds number. It is also noticed that, these distributions are Reynolds number dependent near the slit however, away from the slit they are Re independent where the self-similar region is dominated. Therefore, in order to segregate between the two regions; a 0.5

5% increase or decrease has been taken from the values of C fx Re x at Re ≥ 1000 where the self-similar region is dominated. Therefore, the solid line connected the circle symbols presents the locus of these points. Hence, the region on the lift of the figure presents the effect of the near the slit characteristics where the full governing equations must be used however, the self-similar region is dominated on the right where the boundary layer assumptions are valid.

300 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Suhil Kiwan and Mohamed E. Ali

CONCLUSIONS The Finite volume method is used to solve the full governing equations of motion due to a linearly stretching surface with suction or injection at the isothermal surface in a porous media. Two distinct regions are characterized; non similar at upstream and similar region downstream. The region very close to the slit is Reynolds number dependent while the similar region is independent of Reynolds number since it reaches an asymptotic value corresponding to the parameter investigated. It also observed that, near the slit the injection cause the flow to overshoot at small Reynolds number however reverse flow are obtained when suction is on. For the range of parameters studied, the results show that the velocity profiles become similar and collapse on one curve and similar trends are obtained for the thermal characteristics. Furthermore, suction at the surface enhances the heat transfer coefficient while injection reduces it. On the other hand, the skin friction coefficient changes sign near the slit when moving from suction to injection before the profiles reach the asymptotic behavior at the self-similar region. It also noticed that, as Darcy resistance decreases the heat transfer coefficient decreases whereas the skin friction coefficient increases. Finally, two critical Reynolds numbers are obtained to distinguish the non similar from the similar regions for the different parameters used in this study. One critical Reynolds number corresponding to the heat transfer part and the second is for the flow part of the problem.

REFERENCES [1]

M.E. Ali, Heat transfer characteristics of a continuous stretching surface, Warme Stoubertrag. 29 (1994) 227–234.

[2]

M.E. Ali, On the thermal boundary layer on power low stretched surface with suction or injection, Int. J. Heat and Fluid Flow 16 (1995) 289-290.

[3]

E.M.A. Elbashbeshy, Heat transfer over a stretching surface with variable heat flux, J. Phys. D: Appl. Phys. 31 (1998) 1951–1955.

[4]

E.M.A. Elbashbeshy , M.A.A. Bazid, The effect of temperature-dependent viscosity on heat transfer over a continuous moving surface, J. Phys. D: Appl. Phys. 33 (2000) 2716–2721.

[5]

M.E. Ali, F. Al-Yousef, Laminar mixed convection boundary layer induced by a linearly stretching permeable surface, Int. J. Heat and Mass Trans. 45 (2002) 4241-4250.

[6]

E.M.A. Elbashbeshy, M.A.A. Bazid, Heat transfer over an unsteady stretching surface with, internal heat generation, Appl. Math. Comput. 138 (3) (2003) 239–245 301

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

FLOW AND HEAT TRANSFER CHARACTERISTICS INDUCED BY A STRETCHING SURFACE

[7]

S. Al-Sanea and M. Ali, The effect of extrusion slit on the flow and heattransfer characteristics from a continuously moving material with suction or injection, International Journal of Heat and Fluid Flow 21 (2000) 84-91

[8]

E.M.A. Elbashbeshy, M.A.A. Bazid, Heat transfer over a continuously moving plate embedded in a non-Darcian porous medium, Int. J. Heat Mass Transfer 43 (2000) 3087–3092.

[9]

E.M.A. Elbashbeshy, M.A.A. Bazid, heat transfer in a porous medium over a stretching surface with internal heat generation and suction and blowing. Appl. Math. Computation. 158 (2004) 799–807

[10] P.V. Subhas, Visco-elastic fluid flow and heat transfer in porous medium over a stretching sheet, Int. J. Non-Linear Mech. 33 (3) (1998) 531–540. [11] S. Kiwan, Laminar mixed convection heat transfer induced by a stretching flat plate in a porous medium, Int. J. Heat and Technology, Vol. 24 (2) (2006) . [12] R. Cortell, Flow and heat transfer of a fluid through a porous medium over a stretchingsurf ace with internal heat generation/absorption and suction/blowing, Fluid Dynamics Research 37 (2005) 231–245.

Figure 1. Schematic diagram for the problem under-consideration showing the applied boundary conditions.

302 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Suhil Kiwan and Mohamed E. Ali

1.2

(a)

1

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

U

*

0.8

0.6

0.4

0.2

0 0

0.005

0.01

0.015

Y

2

0

-2 U

*

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

-4

-6

-8 0

0.001

0.002

0.003 Y

(b)

0.004

0.005

10

(c)

8

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

U

*

6

4

2

0 0

0.001

0.002

0.003

0.004

Y

Figure 2. Velocity profiles for k1 = 1 at selected Re and fw (a) fw = 0, (b) fw = 0.3, and (c) fw = -0.3. 303 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

FLOW AND HEAT TRANSFER CHARACTERISTICS INDUCED BY A STRETCHING SURFACE

1.2

(a)

1

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

θ

0.8

0.6 (Re=1000-3000) 0.4

0.2

0 0

0.01

0.02

0.03

0.04

Y

1.2

(b)

1

θ

0.8

0.6

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

0.4

0.2

0 0

0.01

0.02

0.03

0.04

Y

1.2

(c)

1

θ

0.8

Re=1 Re=10 Re=100 Re=1000 Re=2000 Re=3000

0.6 (Re=1000-3000) 0.4

0.2

0 0

0.01

0.02

0.03

0.04

Y

Figure 3. Temperature profiles at selected Re and fw for k1=1(a) fw = 0, (b) fw = 0.3, and (c) fw = - 0.3.

304 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Suhil Kiwan and Mohamed E. Ali

2 K1=0 K1=0.002 K1=0.02 K1=0.2 K1=2 K1=3

Nu Re

x

-(1/2)

1.5

x

1

0.5

0 10

100 Re

1000

x

Figure 4. Variation of Nusselt parameter with Re at different k1 at fw = -0.1

5

fw=-0.5 fw=-0.3 fw=0. fw=0.3 fw=0.5

x

3

x

Nu Re

(-1/2)

4

2

1

0 10

100

1000

Re

x

Figure 5. Variation of Nusselt parameter with Re at different fw when k1 = 1

305 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

FLOW AND HEAT TRANSFER CHARACTERISTICS INDUCED BY A STRETCHING SURFACE

-2 k1=3 k1=2 k1=0.2 k1=0.02 k1=0.002 k1=0.

-1

x

1 2

x

Cf Re

(1/2)

0

3 4 5 6 1

10

100

1000

Re

x

Figure 6. Variation of skin friction coefficient with Re for selected values of k1 for fw = -0.1.

4 3 fw=-0.5 fw=-0.3 fw=0 fw=0.3 fw=0.5

2

0

fx

C Re

x

(1/2)

1

-1 -2 -3 -4 10

100

1000

Rex

Figure 7. Skin friction coefficient variation with Re at selected values of fw (k1 = 1)

306 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL AND TRIBOLOGICAL BEHAVIOR OF GREY CAST IRON A. Es. Nassef, A. Abo El-Nas, , G. E. Y. I. Abou Raya 1,3: Department of Production Engineering and Mechanical Design, Faculty of Engineering, Suez Canal University, Port Said, EGYPT : 2 Department of Production Engineering and Mechanical Design, Faculty of Engineering, Menoufiya University, Shebin El-Kom, EGYPT

ABSTRACT Grey cast iron containing different copper additions ranging from 0.0 to 4.0 wt.% were cast using sand mold in foundry. The alloys were melted by induction furnace unit and poured in the form of stepped bars. These procedures were performed in order to study the effect of both the copper additions and the cooling rate on the alloy microstructure, hardness, and wear resistance. Wear resistance of the alloys were investigated via friction tests by rubbing specimens against rotating steel disc using pin-on-disc apparatus. Mass loss has been estimated in terms of wear time for different copper additions and cooling rates. The experimental results of this work show that the copper additions have a significant effect on graphite morphology in terms of their aspect ratio. Highest hardness is obtained nearly at 2.5 wt.% Cu and higher cooling rate due to the increase of pearlite phase, and roundness of the graphite flake edges. It is suggested that copper is more effective in pearlite hardening and the increased pearlite hardening effect of copper is related to a finer interlamellar spacing. It is obtained that cast iron containing 2.0 wt.% Cu and 3.5 wt.% Cu are the higher wear resistant than the other alloys and the higher the cooling rate the higher the wear resistance.

KEYWORDS Copper Additions, Cooling Rate, Wear Resistance, Hardness, Grey Cast Iron

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

1. INTRODUCTION Cast irons are well known multicomponent ferrous alloys. Because its higher carbon content, the structure of cast iron exhibits a rich carbon phase. Depending primarily on composition, cooling rate and melt treatment, cast iron can solidify according to the thermodynamically metastable Fe-Fe3C system or the stable Fe-Gr system. Cast irons may often be used in place of steel at considerable cost savings [1,2]. The design and production advantages of cast iron include: low tooling and production cost, good machinability without burring, ability to cast into complex shapes, excellent wear resistance and high hardness and high inherent damping capabilities [3]. The properties of the cast iron are affected by the chemical composition of the iron, cooling rate of the casting in the mold, and type of graphite formed [2]. There are many known benefits to be gained by adding Cu to cast iron such as increased strength, toughness and corrosion resistance [4]. In conventional grey irons, it may improve graphitization and refine the structure. Cast irons make excellent casting alloys, have a wide range of strengths and hardness, and in most cases are easy to machine. This widespread use is primarily the result of their comparatively low cost and versatile engineering properties. In spite of vigorous competition from new materials, cast irons have proven to be the most economical and suitable materials for thousands of engineering applications. They are alloyed to produce superior wear, abrasion, and corrosion resistance [5]. It is well established that graphite morphology is the most significant factor that affects the mechanical and physical properties of cast irons. A wide spectrum of graphite morphology can be achieved by using different processing during and after the cast production [2]. The graphite in the microstructure of the cast iron increases the desirable properties such as wear resistance, hardness, corrosion resistance, thermal conductivity, damping capacity, and machinability [6]. The most likely used alloying elements in cast iron are Cr, Mn, Mo, Cu, V and Ti. These elements (except for Ti) inhabit the formation of ferrite and make pearlite more dispres [4,5]. Fairly little amount of research work have been made to examine the effect of copper additions on wear resistance, tensile and compression strength, toughness behavior, and corrosion behavior of the grey cast iron [4,5,7,8]. The microstructure of cast iron consists primarily of ferrite, pearlite or a combination of the two phases, and graphite. These constituents largely determine the mechanical properties of the grey cast iron. Minor amounts of harder phases including carbides and nitrides may be present, but, because of their small volumes, they are more difficult to detect than the major phases [9].

308 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

A. Es. Nassef, et al

As has been mentioned, the properties of grey cast iron components are controlled by the microstructure of the material, which consequentially are determined by the chemistry and processing technique of cast iron [2]. The mechanical and physical properties and wear resistance of as cast grey iron can be controlled by varing the amounts of ferrite, graphite and pearlite in the structure. Where the graphite is most flake-like and interconnected such physical properties are optimized-in a grey iron [5]. The change of the graphite shape and amount of ferrite/pearlite ratio formed can be influenced by either casting composition or by cooling rate. Since grey irons usually contain greater than 1 to 3.5 wt.% Si, which acts as a graphitizer and also promotes ferrite, control of the ferrite/pearlite ratio is usually accomplished with additions of elements that promote pearlite formation [8,9]. These elements increase pearlite formation by enhancing eutectic and eutectoid carbide formation (Cr, Mn) or decreasing the rate of carbon diffusion (Cu, Sn) in austenite. Manganese (Mn) is the most common element used to promote pearlite in grey and ductile cast irons, although Cu and tin (Sn) is also used extensively. The influence of Cu on the solidification and mechanical properties of grey iron has been comprehensively reviewed by Rooney et al [2]. Cooling rate influences both the temperature at which austenite transformation and the pearlite/ferrite ratio results from this transformation. The addition of Cu to grey cast iron may increase the tensile strength, hardness, and corrosion resistance [10-12]. The present work aims primarily at investigating the effect of Cu additions on the graphite morphology and mechanical behavior of the grey cast iron. Particular attention is given to investigate the effect of cooling rate and Cu additions on the wear behavior of these alloys. 2. EXPERIMENTAL PROCEDURES 2.1 Materials and Test Specimens The alloys used in this investigation were prepared by melting of 25 kg charges from amounts of high purity pig iron and foundry-grade ferroalloys and graphite. The chemical composition was adjusted through the addition of 75 wt.% FeSi and 80 wt.% FeMn. Melting was made in magnesia-lined induction furnace unit (3000-KHz) in the Foundry workshop in Faculty of Engineering, Port Said, and Suez Canal University. First, the ferrous charge was melted, the required ferroalloys were added and the melt was then superheated up to 1400 oC. Then, Cu powder was added to the molten iron in the furnace. The melt was stirred thoroughly to ensure complete mixing the solution and reaction of the Cu with the molten iron just before pouring. Different Cu additions were obtained ranging from 0.0 to 4.0 wt.%. The molten were then poured at 1350 oC into linseed oil bonded sand mould in form of stepped shaft with different diameters of 25, 50, and 75 mm, and length of 300 mm. The foundry Lab checks metal chemistry to insure that the iron alloys meets the standard specifications. After solidification, the cast ingots were extracted from the moulds at room temperature. The chemical compositions of the obtained alloys are shown in Table 1. Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

309

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

Table 1 Chemical analyses (wt.%) of the cast iron with different Cu additions. Alloy No.

Cu%

C%

Si%

Mn%

S%

P%

Fe%

1 2 3 4 5 6 7

0.00 0.50 1.25 2.00 2.50 3.25 4.00

2.79 2.78 2.75 2.77 2.78 2.82 2.85

1.95 1.98 1.96 1.97 1.98 1.95 1.93

0.8 7 0.90 0.82 0.89 0.88 0.87 0.85

< 0.05 < 0.05 < 0.05 < 0.05 < 0.05 < 0.05 < 0.05

< 0.045 < 0.045 < 0.045 < 0.045 < 0.045 < 0.045 < 0.045

Balance Balance Balance Balance Balance Balance Balance

The test specimens were machined from the center portion of the ingots in order to avoid problems associated with the outer layers of the cast materials. For the purpose of metallographic investigation, extensive microstructure examinations were made using optical microscopy (OM) in order to gain more understanding of the role played by the Cu additions in determining the graphite morphology. Six sets of cast iron specimens were chosen having different Cu additions ranging from 0.0 wt.% to 4.0 wt.% with higher cooling rate, d=25 mm. Samples were cut from the as-cast bars and were metallographically prepared by mechanical polishing and etching using a solution of 4.0% Nital for about 10 sec. Then, the metallographic examinations were made by using the OM. 2.2 Hardness Examinations Hardness is the most commonly determined property of metals and alloys. It is a simple test and many of the mechanical properties of metals and alloys are directly related to their hardness characteristics. The Brinell hardness test is used here because the Brinell test impression is large enough to average the hardness of the constituents in the microstructure. Specifying the hardness at a designated place on each cast is an excellent method for establishing consistency of castings in production quantities where the type of iron being used has been established as satisfactory for the application. Brinell hardness number (HBN) is measured using 10 mm ball diameter at 3000 Kg applied load for 60 sec. The HBN of each specimen was determined in different five locations along the specimen diameters.

310 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

A. Es. Nassef, et al

2.3 Wear Tests Dry sliding wear tests were carried out using a designed pin-on-disc wear test apparatus. Cylindrical specimens of 10 mm diameter and 25 mm in length is slid against a rotating steel disc (a hardened St-76, HV450) at a constant speed of 300 rpm and constant applied load of 10 N. Different wear times were applied to all specimens containing various Cu additions and cooling rates. Mass loss is measured in grams by the weight loss method with a precision of fourth decimal place by using a high accuracy digital balance (Mettler Balance), of 150 gm capacity. At least three specimens of each alloy were tested in order to verify the repeatability of the wear data.

3. RESLUTS AND DISCUSSIONS 3.1 Metallography Fig. 1 shows typical optical metallugraphs of grey cast iron specimens in the case of as-cast with different Cu additions. The micrographs show the actual changes of graphite size, and their distribution related to different Cu additions. As shown, grey cast iron is generally considered as a composite material consisting of precipitated graphite particles in a solid metal matrix. From the perspective of metallugraphs, the α-graphite flakes are uniformly distributed, randomly oriented and represent type 4A (according AFS and ASTM chart) distribution of graphite flaks [10,12]. The graphite flakes, in case of 0.0 wt.% Cu (Fig. 1.a), are not sharp and well identified. Large flakes randomly distributed originate when the nucleation rate is low, since there is small time for diffusion and graphization readily occurs. Small flakes are encouraged by rapid nucleation due to moderate under cooling conditions where there is still enough time for diffusion and graphitization. It can be seen from the micrographs, in Figs. 1.b–1.e, that as Cu percentage increases, number of the α-graphite flakes increases with finer shape and round ends. Sharper graphite flakes are generally observed as the Cu additions increased. It is also observed in Fig. 1.f that thicker graphite flakes with random distribution are obtained. It shown in Fig. 2, where the aspect ratio, l/d, is plotted against the Cu additions, that the aspect ratio of the α-graphite flakes decreased with increasing the Cu addition. The aspect ratio is an indication of extend of changes in graphite morphology. It also plays a principle role in determining the mechanical properties of the cast iron. This in turn means that not only the size of the graphite flakes has decreased with increasing the Cu contents but also roundness of edges the graphite flakes is obtained.

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

311

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

(e )

(f

Fig. 1 Optical metallugraphs showing the graphite morphology due to the addition of Cu to the grey iron (x100) and cooling rate, d=25 mm; a) Fe-0.0 wt.% Cu, b) Fe-0.5 wt.% Cu, c) Fe-1.25 wt.% Cu, d) Fe-2.0 wt.% Cu, e) Fe-2.5 wt.% Cu, f) Fe-4 wt.% Cu. 3.2 Hardness Behavior Hardness of the present grey cast iron alloys has been measured by Brinell hardness test. This particular measurement, which is a macroscopic measurement, is influenced by the properties of each microconstitunent (ferrite/pearlite) as well as the relative amount and hardness of each microconstituent. It is generally found that, hardness of the cast irons has appeared to be an important parameter affecting wear losses [13,14]. The effect of Cu additions and cooling rates on the Brinell hardness number (HBN) of the cast iron specimens are presented in Fig. 3. It is obvious from the figure that the hardness behavior is improved by increasing Cu content and the cooling rate. It is clear from Fig. 3 that, increasing Cu contents from 0.5 to 2.5 wt.% has increased the hardness of the specimens for all the cooling rates, after which a hardness decreasing is noticed for all the cooling rates.

312 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

A. Es. Nassef, et al

25

Aspect Ratio, (l/d)

20

15

10

5 0.0

1.0

2.0

3.0

4.0

5.0

Cu Additions (wt.%) Fig. 2 The aspect ratio of the graphite flake against the copper additions. Hardness peaks are obtained nearly at 2.5 wt.% Cu for each cooling rate. This behavior may be attributed to the increase of pearlite phase, and the roundness of edges of the graphite flakes as well as a complete dissolving the Cu in the alloy by formation the α-solid solution phase. The hardness after which is decreased with increasing the Cu additions over such amount where small amounts of Cu solvent decreased and graphite content tended to increases. It is also observed in Fig. 3, the hardness of the alloys containing various amounts of Cu increased as cooling rate increased. Cu is known an austenite stabilizer and acts to delay the start of transformation to pearlite. It refines the interlameller spacing in pearlite, and hardens ferrite by solution in the solid state [2]. The highest hardness has occurred at small size section (d=25 mm) where the cooling rate was the highest. A multiple regression analysis was conducted to relate the effect of Cu additions with the hardness. A relationship was obtained between Brinell hardness (HBN) and weight percentage of copper and described as following: HBN = A + B (WCu) – C (WCu)2

(1)

Where A, B, and C are constants obtained from the fitting of the experimental data, WCu is the weight percentage of copper. The values of the constants for different cooling rates, A, B, and C, are listed, in Table 2, as appeared from the curve fitting of the data in Fig. 3. Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

313

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

Table 2 Values of the constants A, B, and C in Eq. 1 Constants

d1= 25 mm

D2= 50 mm

D3= 75 mm

A B C

190.51 72.97 13.38 90.87%

175.95 49.11 7.94 (91.75%)

161.13 32.29 5.02 (93.70%)

Correlation factor, R2

300

BHN

250

200

Fe-(x)wt.% Cu 150

d1=25mm d2=50mm d3=75mm

100 0

1

2

3

4

Copper Content, wt. % Fig. 3 Brinell hardness number (HBN) of grey cast iron against copper additions, in weight percentage, under three different cooling rates.

314 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

5

A. Es. Nassef, et al

3.3 Wear Behavior The results of wear tests of the effect of Cu additions to the grey cast iron show an increasing in wear resistance as result of increasing the Cu content. Figs. 4.a–4.f shows the wear behavior of the grey cast iron specimens as a function of the testing time with Cu additions, ranging from 0.0 to 4.0 wt.%, at constant applied load and constant rotational speed (rpm). These wear data in these figures represent the results of three different cooling rates. It is generally observed that, the alloys with Cu additions, in Fig. 4.b-4.f, exhibited lower wear rate than that with no Cu addition, Fig. 4.a. It is also observed for all the wear data that the mass loss increases with increasing the wear time and decreases with increasing the cooling rate. As shown in Figs. 4.a–4.f, the wear resistance increased with increasing the Cu addition. Meanwhile, the wear results exhibited higher wear resistance for alloys having 2.0 wt.% Cu and 3.25 wt.% Cu, and higher cooling rate. These results are in contrast with that obtained in Fig. 3, where the maximum hardness is obtained for the alloys that have 2.0 wt.% Cu. The microstructure of these particular alloys consists of randomly distributed graphite with fine flakes. The combination of this microstructure and this graphite flaks arrangement is believed to exhibit better wear and friction among cast iron with Cu alloys. The experimental results indicate that the entire wear behavior consists mainly of four superimposed mechanisms which contribute to generation of wear particles: turncation, adhesion, delamination and ploughing [7,8,13]. Although these results appeared, in general, to be consistent with those obtained by other researchers, further work should be made in order to find a close relationship between the graphite morphology and the mechanical properties of grey cast iron.

4. CONCLUSIONS Grey cast iron containing different amount of copper ranging from 0.0 to 4.0 wt.% were cast using sand mold in foundry. Hardness and wear characteristics along with metallographic investigations were performed for the fabricated alloys. Based on the experimental results obtained and associated discussions, the following conclusions can be drawn: 1. Cu additions have a significant effect on graphite morphology including; graphite size, aspect ratio, and their distribution. It is also found that the graphite increases in fineness as result of increasing the cooling rate. 2. The hardness increased with increasing the Cu additions and cooling rate. It is obvious from the results that alloys contain 2.5% Cu recorded for the maximum hardness. The major contribution to the observed hardness improvement with higher cooling rate stems from the microstructural scale observed, it being much finer at higher copper addition than at lower copper. Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

315

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

3. Additions of Cu to grey cast iron resulted in better wear resistance and the highest the cooling rate the lowest the wear loss. The wear results exhibited a higher wear resistance for alloys having 2.0 wt.% Cu and 3.25 wt.% Cu, and higher cooling rate. It is generally found that the mass losses of the alloys are inversely proportional to the hardness and the size of graphite flakes.

REFERENCES 1. Li, H., and Griffin, R.D., 2003, "Evaluating Cast Iron Microstructures using Density Measurements", AFS Transactions, Vol. 111, No. 87, pp. 703-714. 2. Rooney, T.C., Wang, C.C., Rosenthal, P.C., Loper, C.R., and Heine, R.W., 1971, "Tin and Cu in Gary Cast Iron", AFS Transaction, Vol. 71, pp. 189. 3. Moore, D.J., Parolini, J.R., Rundman, K.B., 2003, "On the Kinetics of Austempered Grey Cast Iron", AFS Transactions, vol. 111, pp. 03-110 4. Abu El-Aini, H.M., Abd El-Mageed, A.M., and Abdel-Rahman, M., 1999, "Mechanical Properties and Corrosion Behavior of Grey Cast Iron With Cu Additions", 2nd Int. Conf. on Mech. Eng. Advanced Tech. For Indus. Prod., Assuit Uni., Assuit, Egypt, March 2-4, 1999, pp. 67-77. 5. Abdou, S.M.I., and El Nasser, G.A., March 2003,"The Tribological Behavior of Grey Cast Iron at Different Additions of Cu", PSERJ, Faculty of Engineering Port Said, Suez Canal University, Vol. 7, No. (1), pp 44-54. 6. Li, H., Griffin, R.D., Bates, C.E., 2005, "Grey Iron Property Measurements Using Ultrasonic Techniques, AFS Trans.© American Foundry Society, Schaumburg, IL USA Paper 05-122(05), pp. 1–11 7. Terheci, M., Manory, R.R., and Hensler, J.H., 1995, "The Friction and Wear of Automotive Grey Cast Iron under Dry Sliding Conditions, - Part 1- Relationships Between Wear Loss and Testing Parameters", Wear, Vol. 180, pp73-78. 8. Terheci, M., Manory, R.R., and Hensler, J.H., 1995, "The Friction and Wear of Automotive Grey Cast Iron under Dry Sliding Conditions, - Part 2- Friction and Wear- particle Generation Mechanisms and their Progress with Time", Wear, Vol. 185, pp119-124. 9. Xu, W., Ferry, M., Wang, Y., 2005, "Influence of Alloying Elements on as-Cast Microstructure and Strength of Gray Iron", Mater. Sci. Eng. A, Vol. 390, Issues 1-2, pp. 326-333. 316 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

A. Es. Nassef, et al

10. Shea, M.M., 1978, "Influence of Cooling rate and Manganese and Cu Content on Hardness of As-Cast Ductile Iron", AFS Trans., Jan. 1978, pp. 7-12. 11. Rundman, K.B., Parolini, J.R., Moore, D.J., 2005, "Relationship between Tensile Properties and Matrix Microstructure in Austempered Grey Iron", Paper 05-145(05), pdf, AFS Trans., American Foundry Society, Schaumburg, IL, USA, pp. 1-15 12. Abbasi, H.R., Bazdar, M., Halvaee, A., 2007, "Effect of Phosphorus as an Alloying Element on Microstructure and Mechanical Properties of Pearlitic Gray Cast Iron", Mater. Sci. Eng.: A, Vol. 444, Issues 1-2, 25, pp. 314-317 13. Prasad, B.K., 2007, "Sliding Wear Response of Cast Iron as Influenced By Microstructural Features and Test Condition", Mater. Sci. and Eng.: A, Available online, pp. 8-16. 14. Ramadan, M., Takita, M., Nomura, H., 2006, "Effect of Semi-Solid Processing on Solidification Microstructure and Mechanical Properties of Gray Cast Iron", Mater. Sci. Eng.: A, Volume 417, Issues 1-2, 15, pp. 166-173

ACKNOWLEDGMENTS The authors Yard-Port Said, for are extended to the Mechanical Design Port-Said, Egypt.

would like to acknowledge the Suez Canal Authority, Ship chemical analysis of the investigated specimens. Many thanks Staff and Laboratory members of Production Engineering and Department, Faculty of Engineering, Suez Canal University,

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

317

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

100

Fe-0.0 wt.%Cu d1=25 mm d2=50

Mass Loss, mg

80 60 40 20 0

0

10

20 30 40 50 Wear Time, min

100

Fe-0.5 wt.% Cu d1=25m m

Mass Loss, mg

80

d2=50m m d3=75m m

60

40

20

(b) 0 0

10

20

30

40

50

Wear Time, min

Fig. 4 Mass loss of grey cast iron specimens against wear time for different copper additions and each figure has three different cooling rates; (a) Fe-0.0 wt.% Cu, (b) Fe-0.5 wt.% Cu, (c) Fe-2.0 wt.% Cu, (d) Fe-2.5 wt.% Cu, (e) Fe3.25 wt.% Cu, and (f) Fe-4.0 wt.% Cu . 318 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

A. Es. Nassef, et al

100

Fe-2.0 wt.%Cu d1=25mm

80

Mass Loss, mg

d2=50mm d3=75mm

60 40 20

(c) 0 0

10

20

30

40

50

Wear Time, min 100

Fe-2.5 wt.% Cu d1=25m m

Mass Loss, mg

80

d2=50m m d3=75m m

60 40 20

(d) 0 0

10

20

30

40

50

Wear Time, min Fig. 4 Mass loss of grey cast iron specimens against wear time for different copper additions and each figure has three different cooling rates; (a) Fe-0.0 wt.% Cu, (b) Fe-0.5 wt.% Cu, (c) Fe-2.0 wt.% Cu, (d) Fe-2.5 wt.% Cu, (e) Fe3.25 wt.% Cu, and (f) Fe-4.0 wt.% Cu .

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

319

INFLUENCE OF COPPER ADDITIONS AND COOLING RATE ON MECHANICAL

100

Fe-4.0 wt.%Cu d1=25mm

Wear Loss, mg

80

d2=50mm d3=75mm

60

40

20

(f) 0 0

10

20

30

40

50

Wear Time, min

100 Fe-3.25 wt.%Cu

80

Mass Loss, mg

60

d1=25mm d2=50mm d3=75mm

40 20 0 0

10

20

30

40

50

Wear Time, min

Figure 4 : (cont.) cases f,e.

320 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL GROWTH IN SOLIDIFICATION

Faruk Yigit Department of Mechanical Engineering King Saud University P.O. Box 800, Riyadh 11421, Saudi Arabia [email protected]

ABSTRACT The role of the grooved mold surface topography on gap nucleation in pure metal solidification is investigated. The mold is assumed to be finite and deformable, and has a sinusoidal surface micro-geometry. Unlike previous models, the model developed herein assumes that the mold material has a non-negligible thermal capacitance. The present work also assumes that the thermal and mechanical problems in the mold-shell interface are uncoupled. It is shown that the inclusion of the thermal capacitance of the mold material, together with thermal capacitance of the shell and the mold distortion, may be sufficient to predict a critical wavelength beyond which no gap nucleation occurs at the troughs. Gap nucleation times, associated mean shell thicknesses, and critical wavelengths are calculated for pure copper and pure iron molds under identical process conditions. It is found that a copper mold leads to faster gap nucleation compared to an iron mold. The associated critical wavelengths of iron molds are shown to be larger than those of copper.

Key Words Solidification, Shell, Growth, Perturbation

INTRODUCTION During solidification of metals, the solidification front often exhibits nonuniformities known as cellular undulations. These macroscopic undulations represent a growth instability where certain regions of the solidification front grow faster than others. The result is significant thickness variation in the casting which can have a detrimental effect on the quality of the final cast product and the casting process itself [1]. Nonuniform growth can be accompanied by air gap nucleation which leads to a loss of heat transfer and separation of metallurgical constituents Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

which promotes surface cracking during subsequent process-intensive metalworking operations [2-4]. A detailed understanding of cellular undulations in metal casting is therefore of practical importance. In previous studies, it has been common practice to assume that the mold material has negligible thermal capacitance to focus on the effects of the solidified shell material on the growth instability. This assumption may be reasonable when the mold is very thin or its thermal diffusivity is infinitely large (in these cases, temperature variation in the mold can be assumed to be linear). Otherwise, the thermal capacitance of the mold needs to be considered when a more accurate prediction of gap nucleation and associated growth instability are desired. The only prior work on the interaction of the mold thermal capacity and the mold distortion is due to Yigit [6] who extended his earlier formulation [5] for a planar mold of finite thickness and a finite thermal capacity. Yigit [6] examined only the perturbation quantities resulting from a spatially nonuniform cooling profile along a planar mold surface, and hence he did not examine the evolution of total contact pressure at the mold-shell interface. It is therefore not possible to draw any definitive conclusion from his work about gap nucleation at the mold-shell interface and how the mold wavelength affects gap nucleation time and location. The main goal of the present work is to determine the origin of the critical wavelengths proposed by Hector et al. [7]. Do critical wavelengths only result when the theoretical analysis includes interface coupling and a deformable mold with finite thickness? This is the major question to be answered in the present work with the hope of revealing the theoretical origin of critical wavelengths within the constraints of the present theoretical formulation. Hence, the model we shall present is a simplification of that presented by Yigit and Hector [8, 9] in that we decoupled the thermal and mechanical fields at the mold/shell interface.

THERMAL MODEL The system modeled is shown in Figure 1. Heat is withdrawn from the bottom of a thermo-elastic mold of mean thickness h0 . Both the upper surface of the mold, which is in contact with the shell along

y = 0 , and the lower surface at

y = −h0 have sinusoidal surface topographies of wavelength λ . Molten metal, which is initially at its melting temperature, Tm , perfectly wets the upper surface of the mold at t = 0 . The location of the freezing front is denoted by s( x,t ) . All material properties are assumed to be constant and independent of temperature.

322 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

c

The temperature field in the solidified shell, T ( x , y ,t ) , and that in the d

mold, T ( x, y,t ) , are governed by the heat conduction equations which are subject to the following imposed initial and boundary conditions:

∇ 2T c ( x , y ,t ) =

Kc

1 ∂T c 1 ∂T d 2 d ; T ( x , y , t ) ∇ = k c ∂t k d ∂t s( x ,0 ) = lε 1cos( mx )

(2)

T c ( x , s ,t ) = Tm

(3)

∂s ∂T c ( x , s ,t ) = Lc ρ c ( x ,t ) ∂t ∂y

(4)

d ∂T c d ∂T K ( x, y1 ,t ) = K ( x, y1 ,t ) ∂y ∂y

y1 = lε1cos( mx )

(5)

∂T d 1 ( x, y2 ,t ) = ⎡⎣T c ( x, y1 ,t ) − T d ( x, y1 ,t )⎤⎦ ∂y R

(6)

c

Q( x,t ) = K d

(1)

y2 = −( h0 + lε 2 cos( mx )) ; Lc is the latent heat of fusion of the solidified material and R is the thermal contact resistance at the mold/solid interface. where

We define

ε 1 = a1 l ; ε 2 = a 2 l

(8)

as the upper and the lower mold surface aspect ratios, respectively, where l = λ 2π = 1 m and a1 , a 2 are, respectively, the amplitudes of the upper and lower

sinusoidal mold surfaces.

323 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

Figure 1: Geometry of the problem

To determine the temperature fields, we will follow the procedure developed in [10], noting, however, that in that case, the idealization of infinitely large mold thermal diffusivity (i.e., assumption of zero heat capacity of the mold) made the closed form solution possible for the temperature distribution in the mold as defined by Eqs. (64) and (65) of [10]. Whereas in the present problem, the zeroth and the first order temperature fields in the shell and the mold will be determined by the numerical solution of following equations with the associated boundary conditions. The Zeroth-order equations:

∂ 2T0c ∂ 2T0d 1 ∂T0c 1 ∂T0d ( y,t ) = ( y,t ) ( y,t ) = ( y,t ) ; ∂y 2 k c ∂t ∂y 2 k d ∂t

Kc

(9)

T0c ( s0 ,t ) = Tm

(10)

∂T0c ds ( t ) ( s0 ,t ) = Lc ρ c 0 ∂y dt

(11)

324 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

d ∂T0c d ∂T0 K ( 0 ,t ) = K ( 0 ,t ) ∂y ∂y c

Kc

(12)

∂T0c 1 ( 0 ,t ) = ⎡⎣T0c ( 0 ,t ) − T0d ( 0 ,t )⎤⎦ ∂y R Kd

(13)

∂T0d ( −h0 ,t ) = Q ∂y

(12)

The First-Order Equations:

∂ 2T1c 1 ∂T1c 2 c ( y,t ) − m T ( y,t ) = ( y,t ) ; 1 ∂y 2 k c ∂t ∂ 2T1d 1 ∂T1d 2 d ( y,t ) − m T ( y,t ) = ( y,t ) 1 ∂y 2 k d ∂t

(14)

s1( t )

∂T0c ( s0 ,t ) + T1c ( s0 ,t ) = 0 ∂y

(15)

Lc ρ c

⎡ ∂T c ( s ,t ) ∂ 2T c ( s ,t ) ⎤ ds1( t ) = K c ⎢ 1 0 + s1( t ) 1 2 0 ⎥ ∂y ∂y dt ⎣ ⎦

(16)

⎧ ∂ 2T c ⎧ ∂ 2T d ⎫ ⎫ ∂T c ∂T d K c ⎨ 20 ( 0,t )lε1 + 1 ( 0,t )⎬ = K d ⎨ 20 ( 0,t )lε1 + 1 ( 0,t )⎬ ∂y ∂y ⎭ ⎭ ⎩ ∂y ⎩ ∂y

(17)

∂T0c ∂T d ( 0 ,t ) + T1c ( 0 ,t ) = 0 ( 0 ,t )lε1 + T1d ( 0 ,t ) ∂y ∂y

(18)

∂ 2T0d ∂T1d ( −h0 ,t ) = lε 2 ( −h0 ,t ) ∂y ∂y 2

(19)

325 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

STRESS FIELD We shall follow the approach outlined in Ref. [11] for prediction of the stress field. Based upon the form of the temperature field, we assume that the total stress field in the shell and the resulting contact pressure at the mold-shell interface have the following forms:

σ iji ( x, y,t ) = σ iji 0 ( y,t ) + σ iji 1( y,t ) ; i = c,d

(20)

P( x,t ) = P0 ( t ) + P( 1 t )cos( mx )

(21)

c c P0 ( t ) = −σ yy 0 ( y1 ,t ) ; P( 1 t )cos( mx ) = −σ yy1 ( y1 ,t ) ; y1 = lε1cos( mx )

(22) where P0 ( t ) is the mean pressure from the molten metal. As discussed by Li and Barber [12], the total stress distribution in the solid shell and in the mold can be expressed as a linear combination of a particular solution, corresponds to the thermal field, an isothermal solution,

σ ijh , which

σ ijp , that

is allowed

to vary in time so as to satisfy time-varying terms in the boundary conditions, and a residual stress,

σ ijr , which is the stress that remains in the solid shell even

after it is cooled to a uniform temperature and relieved of all boundary tractions. In general,

σ ijr may be subsumed under σ ijh . Once the stress field is determined,

then P( 1 t ) is obtained from Eq. (25b). The present theory assumes that the shell retains contact with the mold surface and hence goes only so far as to monitor P( 1 t ) prior to air gap nucleation. The mechanical boundary conditions for frictionless contact at the mold surface are

σ nc1t1 = 0 ; σ nd1t1 = 0 ; y = y1 = lε1cos( mx ) u&nc1 = u&nd1 ; y = y1 = lε1cos( mx ) where

σ

c n1t1 ,

σ

d n1t 1 are

(23) (24)

the shear stresses in the ( n1 ,t1 ) coordinate system that c

d

rides along the mold surface (see Fig. 1) and u&n1 , u&n1 are the normal velocities of the casting and the mold, respectively. Solidification at the freezing front is assumed to occur in a state of hydrostatic stress 326 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

σ xxc = − p ; σ yyc = − p ; σ xyc = 0 ; y = s( x,t )

(25)

where p is the molten liquid pressure. The normal stresses between the solidified shell and the mold are continuous, and the mold rests on a smooth rigid foundation

σ nc1 = σ nd1 ; y = y1 = lε1cos( mx )

(26)

σ nd2t 2 = 0 ; u&nd2 ( x, y2 ,t ) = 0 ; y = y2 = −( h0 +lε 2 cos( mx ))

(27)

The stress field corresponding to the particular solution can be derived from the thermoelastic displacement potential, ϕ , through

where

2µ i u i = ∇ϕ i ; i = c,d

ϕ satisfies

∇ϕ i =

(28)

2µ iα i ( 1 + ν i ) i Ei i T ; µ = ; i = c,d 1 −ν i 2( 1 + ν i )

(29)

The superscript i refers to either the shell or mold materials. The stress and displacement fields corresponding to the particular solution are then derived from ∂ϕ ∂ 2ϕ i ; ∂ 2ϕ i ; i p 1 ∂ ⎡ ∂ϕ i ⎤ ; ( σ iyy ) p = − 2 ; ( σ xyi ) p = ( u& )y1 = ⎢ ⎥ 2 ∂x ∂x∂y ∂y 2 µ i ∂t ⎣ ∂y ⎦ 2

( σ xxi ) p =

i

i = c,d

(30)

The first-order stress field corresponding to the homogeneous solution can be derived from

( σ xxi )h =

∂ 2Φ i ∂ 2Φ i ∂ 2Φ i i h i h = − = ; ( σ ) ; ( σ ) ; i = c,d xy yy ∂y 2 ∂x 2 ∂x∂y

(31)

where Φ is the Airy stress function which satisfies the following compatibility relation: i

∂ 4 i ∇ Φ = 0 ; i = c,d ∂t

(32)

327 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

Derivation of the zeroth and the first order stress solutions is readily available in Refs. [6], [13], and [14]. Therefore, they are not repeated here and the reader is referred to these references for more details. Determination of the conditions for gap nucleation can be achieved through tr

examination of P , which is the ratio of the total (dimensional) contact pressure at the lowest points of the troughs to the mean pressure at the mold surface troughs [10]. Gap nucleation at the troughs will indicate the possibility of irregular growth of the shell since contact will simultaneously increase at the crests. Beyond gap nucleation time, the present model is no longer valid since it cannot account for continued growth of the gaps and the shell.

MATERIAL PROPERTIES AND PROCESS PARAMETERS tr

We shall examine the evolution of P (defined by Eq. (67) of Ref. [10]) for systems where the mold and the shell materials are combinations of pure aluminum, iron, and copper. The material properties used in the calculations are listed in Table 2. Note that the properties for pure aluminum are taken from Richmond et al. [5], and pertinent references to Fe and Cu are reported in [13]. The symbols Tm , K , ρ , L , E , α , ν , and k denote melting temperature, thermal conductivity, density, latent heat of fusion, Young's modulus, thermal expansion coefficient, Poisson's ratio, and thermal diffusivity, respectively. Although it is assumed that each property is a temperature-independent constant, most of the reported values were measured close to the melting temperature of each material. Unless otherwise specified, the process parameters are chosen to be h0 =50mm (mean mold thickness), Q =106 J/m2s (heat flux at the mold-shell interface), interface),

R =10-5 m2 sec oC/J (thermal contact resistance at the mold-shell P0 =10000Pa (mean contact pressure), and a =1.0 µ m (amplitude of

the upper and lower sinusoidal mold surfaces) in order to be able to compare the results to those reported in [11] and [10].

328 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

Table1:Material properties for pure aluminum, iron and copper at the melting temperature

Aluminum o

Iron

Copper

Tm ( C)

660

1536

1086

K (W/moC)

229.4

36.2

345.4

ρ (kg/m )

2650

7265

7938

L (105 J/kg)

3.9

2.7

2.0

E (1010 Pa)

6.0

14.4

6.4

37.8

23.4

26

ν

0.33

0.33

0.37

k (10-5 m2/s)

8.2

1.16

10.2

3

α (10

-6 o

-1

C )

Each of the following figures is generated through numerical solution of differential equations (54) and (56) of Ref. [10] under the assumption that thermal capacity of the mold is non-negligible. The results from these calculations are used to calculate the contact pressure perturbation, P( 1 t ) , using Eq. (55) of Ref. [10], tr and then the evolution of P is generated for variety of process conditions and mold-shell material combinations.

RESULTS AND DISCUSSIONS tr

Figure 2 examines the variation of P versus t for solidification of a pure aluminum shell on a pure copper mold. Note that the nominal contact pressure has P been increased to 0 =2MPa. Seven curves corresponding to wavelengths of 2mm, 2.22mm, 2.3mm, 2.8mm, 3.5mm, 5mm, and 8mm are shown.

329 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

1 λ = 8mm

0.8 λ = 5mm

0.6 Ptr 0.4 λ = 3.5mm

0.2 0 0

λ = 2.8mm λ R = 2.22mm λ = 2.3mm

λ = 2mm

2

4

6

8

10

t (sec)

Figure 2:

P tr versus t variation for aluminum-copper shell-mold system showing the critical wavelength at

λR =2.22 mm.

The wavelength λ =2.22mm meets the critical wavelength criteria defined in gap Eq. (1) of [15], and denoted by λR . Gap nucleation occurs at t =3.18sec. Wavelengths less than λR lead to gap nucleation. For example, gap nucleation occurs at 2.30sec for λ =2mm. However, wavelengths that are larger than λR never tr lead to gap nucleation over the time of interest since P defined in Eq. (67) of [10] tr never touches the time axis. As explained in [13], P increases at the lowest points of the upper mold surface troughs, while simultaneously decreasing at the highest points of the upper mold surface crests for these larger wavelengths. In an earlier work due to Yigit [10], such a critical wavelength was not observed in any case considered. Addition of the mold thermal capacity into the model presented in [10] further increases the stabilizing effect of thermal capacity of the solidified shell material and leads to a critical mold surface wavelength in the present model. tr

Figure 3 shows the evolution of P versus t for solidification of a pure aluminum shell on a pure iron mold. Seven curves corresponding to wavelengths of 3mm, 3.58mm, 3.6mm, 4mm, 5mm, 7mm, and 9mm are shown. In this case, the wavelength λ =3.58mm meets the critical wavelength criteria, and the corresponding gap gap nucleation time is t =4.99sec. Wavelengths in excess of λR =3.58mm never lead to gap nucleation. However, wavelengths, which are less than λR lead to gap nucleation. Note that the curves corresponding to λ =2.3mm and λ =3.6mm (which are very close to the critical wavelengths) for aluminum-copper and aluminum-iron shell-mold systems, respectively are provided to establish the uniqueness of λR in both cases. 330 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

1 λ = 9mm

0.8 0.6

λ = 5mm

tr

P

λ = 7mm

0.4 λ = 4mm λ = 3mm

0.2

λ = 3.6mm λ R = 3.58mm

0

0

2

4

6 8 10 t (sec) tr Figure 3: P versus t variation for aluminum-iron shell-mold system showing the critical wavelength at λR =3.58 mm.

Figure 4: Critical wavelength effect on position of gap nucleation along the mold shell interface. 331 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

Figure 4 summarizes the critical wavelength concept introduced in Figs 2 and 3. Figure 4(a) shows the mold-shell system prior to gap nucleation after the formation of a thin metal shell but prior to gap nucleation. Figures 4(b) and (c) show the two locations where gap nucleation can occur along the upper mold surface at later times in the process. Note that we represent each gap with a slight separation between the shell and the mold in each of these figures. This is for the purpose of illustration only, since the present theory is valid only to the point where the contact pressure falls to zero. Fig. 4(b) shows the case where gaps nucleate at the highest points of the upper mold crests. The wavelengths that lead to this situation are restricted to λ > λR . The anticipated growth of the shell freezing front in Fig. 4(c) is planar. This is the more desirable situation from a metallurgical standpoint. Figure 4(c) shows the case where gaps nucleate at the lowest points of the troughs in the upper mold surface. The wavelengths that lead to this situation are restricted to λ ≤ λR . The shell freezing front is likely to exhibit an undulatory morphology which is greatly in excess of the dendritic morphology. This situation should be avoided by careful choice of the process parameters.

CONCLUSIONS The interaction of solidifying shell and the mold thermal capacities with the mold deformation on gap nucleation in pure metal solidification processes was studied by the assumption that a metal shell solidified on a deformable mold having sinusoidal surfaces of equivalent wavelengths. For this purpose, the mold thermal capacity effect was incorporated into an earlier model to establish a definitive conclusion about the existence of the critical mold surface wavelength in the absence of coupling between the thermal and mechanical fields at the mold-shell interface. It is found that inclusion of the mold thermal capacity in the theory of Yigit [10] further increased the stabilizing effect of thermal capacity of the solidified shell material and led to a critical mold surface wavelength. In other words, thermal capacity of the mold, when combined with the mold distortion and the solidifying shell thermal capacitance effects, leads to a critical mold surface wavelength that serves as a cutoff between those wavelengths that lead to gap nucleation in the troughs and those that lead to gap nucleation in the crests.

332 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Faruk Yigit

REFERENCES [1]

Wray, P.J., 1977, “Nonuniform Growth of a Plate Solidifying on a Chilled Surface”, presentation Notes, Proceedings of the AIME Conference, Atlanta, GA.

[2]

Nishida, Y., Droste, W., Engler, S., 1986, “The Air-Gap Formation Process at the Casting-Mold Interface and the Heat Transfer Mechanism through the Gap”, Metall. Trans. B, Vol. 17, 833-844.

[3]

Cisse, J., Cole, G., and Bolling, G., 1971,”Freezing Front Asymmetry During Ingot Solidification of Aluminum and its Alloys”, AFS Cast Metals. Res. J., Vol. 7, 158-161.

[4]

Collins, D.W.L., 1967,” A New Explanation of the Surface Structure of DC Ingots”, Metallurgica, Vol. 76, 137-144.

[5]

Richmond, O., Hector Jr., L.G., and Fridy, J.M., 1990,” Growth Instability During Non-Uniform Directional Solidification of Pure Metals”, ASME J. Appl. Mech., Vol. 57, 529-536.

[6]

Yigit, F., 1999, “Growth Instability During Planar Solidification with a Mold of Finite Thermal Capacity”, J. Thermal Stresses, Vol. 22, 757-779.

[7]

Yigit, F., 1998, “Effect of Mold Properties on Thermoelastic Instability in Unidirectional Planar Solidification”, J. Thermal Stresses, Vol. 21, 55-81.

[8]

Yigit F. and L.G. Hector, Jr., 2000, “Critical Wavelengths for Gap Nucleation in Solidification. Part 1: Theoretical Methodology”, ASME J. Applied Mechanics, Vol. 67, 66-76.

[9]

Yigit F. and Hector, Jr., L.G., 2000, “Critical Wavelengths for Gap Nucleation in Solidification. Part 2. Results for Selected Mold-Shell Material Combinations”, ASME J. Applied Mechanics, Vol. 67, 77-86.

[10]

Yigit, F., 2005, “Combined Effects of Mold Deformation and Shell Thermal Capacity on Growth Instability During Unidirectional Solidification of Pure Metals”, J. Thermal Stresses, Vol. 28, 1199-1226.

333 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

IMPACT OF GROOVED MOLD SURFACE TOPOGRAPHY ON UNDULATORY SHELL

[11]

Yigit, F., Hector, L.G. Jr., and Richmond O., 2002, “A Theoretical Investigation of Pure Metal Solidification on a Deformable Mold in the Absence of Interfacial Coupling”, J. of Thermal Stresses, Vol. 25, 773-809.

[12]

Li, N.-Y. and Barber, J.R., 1991, “Thermoelastic Instability in Planar Solidification”, Int. J. Mech. Sci., Vol. 33, 945-959.

[13]

Yigit, F. and Hector, L.G. Jr., 2002, “Solidification of a Pure Metal with Finite Thermal Capacitance on a Sinusoidal Mold Surface”, J. of Thermal Stresses, Vol. 25, 663-690.

[14]

Yigit, F., 2004, “Existence of Critical Wavelength for Gap Nucleation in Solidification on a Rigid Mold”, ASME J. Applied Mechanics, Vol. 71, 96108.

334 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS IN ADVERSE WIND ENVIRONMENT M. Mahmood Mechanical Engineering Department King Fahd University of Petroleum & Minerals Dhahran 31261, Saudi Arabia email: [email protected]

ABSTRACT It is now well established fact that large suction pressures develop along the leading edges of the building due to the formation of corner vortices when the wind is incident at oblique angles. The information about these pressures is considered essential for the design of roofs, particularly for the buildings of low height when these pressures are often the largest. These heavy suction pressures are very important, especially in adverse wind environment, because of the heavy damage they can cause. In this paper, a study of pressure distribution, level of turbulence on some critical locations as well as some results from flow visualization obtained using 1:100 scale models of Texas Tech University (TTU) test building are discussed. High precision Betz-type water manometers utilized to record pressures. The hot wire measurements were carried out to record wind flow and roof turbulence characteristic using a plain hot wire DISA Type 55P11. Some of the flow visualization studies were carried out using smoke-wire technique and laser light sheet illumination technique. The results from experiments show that a separation and recirculation region exists on roof top at normal incidence, and corner vortices form at oblique incidence. There is enormous effect of rounding of roof edges on the flow, pressure, and turbulence characteristics. The mean pressure and turbulence levels on roof top reduce drastically when round-edge models were used in place of sharp edge. Different magnitude of rounding is influencing th pressures differently with reasonable reduction in turbulence level.

KEYWORDS Scale models, corner vortices, roofs, flow conditions, rounding.

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

INTRODUCTION Several investigations have been carried out in the past to study pressures on the roofs of low-rise buildings under normal and oblique incidences The low rise buildings have height usually less than 20 m. It is now well-known that the large suction pressures develop along the leading edges because of the formation of corner vortices. The pioneering work was done on scale models by Jensen and Frank [1]. This study tried to combine the field measurements with the results from wind tunnel experiments. The study carried out by Kind [2] has shown worst suction pressure experienced by roofs at oblique angles. With the advent of research facility at Texas Tech University [3, 4], a number of detailed studies have been carried on roof pressures of low-rise buildings. Mehta, et al. [5] conducted a study of roof corner pressures on Texas Tech University (TTU) test building and produced a reliable pressure data. Even peak suction pressures were measured at some locations. Bogusz, et al. [6] have conducted investigations on 1:25 scale TTU test building models focusing attention on windward corner region of the roof. Their study includes range of wind directions and different parapet heights, also noticed formation of corner vortices. Cochran and Cermak [7] have collected extensive pressure data on 1:100 and 1:50 scale models on a simulated boundary layer flow. This study claims that at the corner and edges the laboratory results agree well with the mean data from the field measurements. They also claim existence of heavy suction pressures at the leading edges. Letchford [8] has carried out simultaneous flow visualization and pressure measurement studies with particular reference to pressure under corner vortices. There have also been some wind load reduction studies by changing the roof design. These studies like [9, 10, etc.] aim at displacing the vortices position or destroying them altogether with some success. Though considerable work has been reported on the pressures on the roof top, it appears most of them employed only a limited number of pressure taps, in spite of roof being the most important part of the building, especially under adverse wind environment. The present work attempts a detailed study of the flow about a 1:100 scale models of TTU test building, like measuring pressures, turbulence levels, and some flow visualization studies.

EXPERIMENTAL RESULTS The experiments were conducted in the Research Wind Tunnel of King Fahd University of Petroleum & Minerals (KFUPM), which is open-return type and has a working test section of 1.1 m × 0.8 m × 4.0 m. The models were fabricated to 1:100 scales in plexiglass. Different types of flow conditions chosen include smooth flow turbulence less than 0.1%), nominal boundary 336 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

layer turbulent flow generated using 4% turbulence grid, and no roughness generating elements on the ground, and boundary layer turbulent flow generated using roughness elements. The velocity and turbulence intensity profile for different types of flows at the test section are given in Figure 1. The model was placed in the wind tunnel as shown in Figure 2-a and its surfaces were provided with a total of 108 pressure holes of 0.8 mm diameter (Figure٢b). High precision Betz-type manometers are used to record the pressure levels. Laser light sheet illumination and smoke-wire techniques were used to observe the flow past building models. The hot wire measurements were carried out using a plain hot wire of the DISA Type ٥٥P11. This was calibrated during many runs to ensure reliable data acquisition. The top edge radii of the models varied from R = 0 (sharp edge) to R = 5 mm, 8 mm, and ١٠mm (round edges) to study the effect on the flow characteristics due to rounding and arrive at some optimum values where pressure and turbulence reduces to a minimum. Uncertainty Analysis To determine the uncertainty in the experimental measurements two effects may be combined together, i.e., bias and precision uncertainties [11]

[1] where u is the total uncertainty, B and P are the bias and precision uncertainties, respectively. The sources of the measurement error are due to equipment and data acquisition system. The turbulence measurements were carried out using a plain hotwire in conjunction with a standard bridge (55M10) and RMS unit (55D35). Table 1 gives the summary of uncertainty analysis for turbulence measurements. The total uncertainty determined from the above equation using Table 1 is about 4%. This was obtained when the uncertainty value was divided with a voltage (velocity) of about ٨٠٠mV. The uncertainty determined for pressure measurements using Table 2 is about 3%. This value resulted when the uncertainty measurement was normalized with a dynamic pressure value of about 7.0 mm of water.

337 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

Table 1: Bias and Precision Levels for Turbulence Measurements .

Table 2: Bias and Precision Levels for Pressure Measurements.

RESULTS AND DISCUSSION The results in this section are presented for oblique incidence of 45°. Flow Visualization The flow was made visible on the top surface of the model at different locations using laser light illumination technique. Figure 3 shows a section of the flow near the leading edge corner when the wind is incident at . = 45°. This figure clearly shows two concentrated vortices springing from both the leading edges for a sharp edge model but for round edge model with R = 5 mm, the flow pattern is different. Since the region near the leading edge corner is considered critical. Maximum mean and peak suction pressures were recorded at hole # 50205, smoke wire technique was utilized to observe the flow past this region. This technique was successfully applied in studying the separation of flow past flat plates at various angles by Mahmood [12]. Figure 4 shows the separation of vortex sheets from leading edges when the wind is incident at oblique angle of 45°. The smoke streaks incident on the side wall at a distance of about 15% to 20% of the length of the side wall goes up and separated to form large separation bubble (bump) on the top surface of the sharp edge model as evident from Figure 4-a. The remaining flow moved down resulting in recirculation of the flow. With rounding of roof edges to R = 5 mm the height of the bump becomes smaller (Figure 4-b). For R = 10 mm, there was no flow separation near leading edge corner but at about 75% of the length there was mild separation and probably a loose vortex formation observed similar to that observed in Ref. [13]. 338 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Pressure Measurements Figures 5, 6, and 7, show the mean pressure distribution on the top surface of sharp edge and round edge models for incidence of . = 45°. The coefficient of pressure, Cp,was evaluated on the model surfaces using the following relationship

(1) where P = local static pressure recorded on model surface P∞ = free stream static pressure in the wind tunnel v∞ = wind velocity at model height ρ= density of air The existence of severe suctions near the edges of the model for both the smooth and turbulent flows and reduction in suction is visible while moving away from the leading edge corner in the x-direction. These peaks in the suction pressure are visible near the edges due to corner vortex formation. Other researchers [7, 8] have also noted such a trend for different models. For the model with sharp edge the maximum suction pressure was noted near leading edge corner on a hole located at a distance of about 12% of the longer leading edge in y-direction corresponding to hole # 50205 in TTU test building. But little less suction was recorded on almost an equivalent hole on the shorter side of the model and corresponding to hole # 50501. The reduced suction pressure may be attributed to its distance from the center of the vortex and possibly due to the effect of the shorter side. Here the vortex formed does not stay to a longer length and probably not able to induce higher suction pressure, a finding similar to that noted in Ref. [5]. It is evident from pressure plots as shown in Figures 5,6 and 7, that for models with rounding to a radius of R = 5.0 mm, there is about %٤٠reduction for severe suction recording holes (# 50205 and 50501) on longer and shorter sides, respectively. But the pressures recorded on model with radius R = 8.00 mm, a reduction of about 60% in the severe suctions. When the rounding was further increased to R = 10.0 mm, still higher change of about 80% in suction pressure was noted. This pressure pattern is different from sharp edge model as little change in pressure is evident away from both the leading edges in x- and y-directions probably indicating a change in the flow structure, thus establishing a maximum limit of rounding and a reasonable rounding radius. Probably no vortex is formed or if there is one, may be of loose or burst nature not causing the desired suction. This confirms the observations made in the 339 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

flow visualization where vortex sheets do not separate in the immediate vicinity of the leading edge corner. Upon close observations, it can be noted from the figures that suction peak is closer to the leading edge at least to a distance of 30%, whereas at around 50% distance from leading edge corner, the highest suction are shifted bit away to a point located at x/w = 0.25. This behavior shows that vortex axis is not straight. A similar observation was noted in Ref. [7]. Figure 7 shows the pressure pattern in highly turbulent boundary layer flow. In this type of flow also there are regions of low pressure adjacent to the leading edges but severe suctions noted here was comparatively less than that was noted in other flow conditions. The effect of rounding of roof edges is dominant in this type of flow also at about 15% of the model edge length. Whereas rounding of model edges to R = 10 mm shows a severe suction by about 80% (Figure 7). The pressure pattern is similar to all other flow conditions at all the stations except at y/L = 0.026, where the pressure behavior is different again, because of highly turbulent flow and because of not completely developed one. Hot-wire Measurements With the measurement of mean pressure on the model top surface a picture of the pressure variation and areas of low pressure become evident due to the presence of two corner vortices. Hole # 50205 and 50501 recorded the highest mean suction pressure at wind incidence angle of 45°. Since the highest mean pressure recorded was being affected due to rounding of roof edges, it was thought to scan the turbulence intensity close to model top surface. The rms velocity fluctuations and turbulence intensity should have a possible influence on suction pressure fluctuation characteristics as well. The intensity of turbulence Iu was evaluated using the relationship as follows

(2) where: Iu = intensity of turbulence r u = fluctuating part of the longitudinal velocity UB = mean velocity near measuring spot

340 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Figures 8-a, and -b- show that when hot-wire was placed close to the top surface of sharp edge model on the hole corresponding to # 50205 (place of severe suction) highest turbulence intensities were recorded in all the flow conditions as can be noted from above-mentioned figures. The rounding of roof edges results in the decrease in turbulence intensity for all the flow conditions. For the case of smooth flow rounding to a radius of R = 5 mm, the turbulence intensity dropped by about 40%. For the case of turbulent boundary layer flow (Figure 8-b) it can be noted that the turbulence intensity very close to the model surface was the highest of about 26% for a sharp edge model. There was a drop in turbulence intensity to 19% when round edge model with R = 5 mm was placed in the same. When the rounding was increased further to flow 10 mm radius the turbulence intensity dropped by about 35% showing the influence of increase in rounding radius on turbulence intensity and fluctuating pressures.

CONCLUSIONS It is noted that rounding of roof edges influence positively the pressures recorded on the highest suction recording holes, which show a big change in pressures. But some holes which are well inside away from the leading edge, show an opposite effect of rounding at some stations as seen in Figures 5, 6, and 7. But even with the opposite effect the overall effect is positive and more dominant than negative effect. The different magnitudes of rounding are influencing the pressure differently. The model edge radius of 10 mm gives maximum reduction of 80% and shows a change in pressure behavior. The flow visualization revealed formation of corner vortices for all the flow conditions. The rounding of roof edges is influencing the shear layer separation very much in the immediate vicinity of leading edge corner. There is a reasonable agreement and correlation between the flow visualization and pressure measurements. The rms velocity fluctuations and turbulence intensity measurements carried out at sensitive locations indicated that rounding of roof edges highly influenced the turbulence level in the immediate vicinity of the top surface and close to the leading edge and also away from them resulting in an effect on the fluctuating pressures also

341 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

. ACKNOWLEDGEMENTS The author acknowledges the support provided by King Fahd University of Petroleum Minerals, Dhahran, Saudi Arabia, and the University of Sydney, Australia.

REFERENCES [1]

Jensen, M., and N. Franck, 1965, Model Scale Tests in Turbulent Wind, The Danish Technical Press, Copenhagen.

[2]

Kind, R. J., 1986, “Worst Suctions near the Edges of Flat Roofs on Low-rise Buildings,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 25، pp.31-47.

[3]

Leviton, M. L., and K. C. Mehta, 1992, “Texas Tech Field Experiments for Wind Loads: Part I, Building Pressure Measuring System,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 41-44, pp.1565-1576.

[4]

Leviton, M. L., and K. C. Mehta, 1992, “Texas Tech Field Experiments for Wind Loads: Part II, Meteorological Instrumentation and Terrain Parameters”، Journal of Wind Engineering & Industrial Aerodynamics, Vol. 41-44، pp.1577-1588.

[5]

Mehta, K. C., M. L. Leviton, R. E. Iverson, and J. R. McDonald, 1992, “Roof Corner Pressures Measured in the Field on Low-building,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 41-44, pp.181-192.

[6]

Bienkiewicz, B., and Y. Sun, 1992, “Local Wind Loading on the Roof of Low-rise Buildings,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 45, pp.11-24.

[7]

Cochran, L. S., and J. E. Cermak, 1992, “Full and Model Scale Cladding Pressures on the Texas Tech University Experimental Building,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 41-44, pp.1189-1600.

342 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

[8]

Letchford, C. W., 1995, “Simultaneous Flow Visualization and Pressure Measurements on Texas Tech Building,” 9th International Conference on Wind Engineering, New Delhi, India, pp.524-535.

[9]

Surry, D., and J. X. Lin, 1993, “the Effect of Surroundings on Roof Corner Geometries Modifications on Roof Pressures on Low-rise Buildings,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 58, pp.113-138.

[10]

Cochran, L. S., J. E. Cermack, and E. C. English, 1995, “Load Reduction by Modifying Roof Corner Vortex,” 9th International Conference on Wind Engineering Proceedings, 1995, New Delhi, India, pp.1091-1111.

[11]

Coleman, H. W., and W. G. Steele, 1989, Experimentation and Uncertainty for Engineers, John Wiley, New York.

[12]

Mahmood, M., 1984, Low-speed Experiments on a Flat Square Plate at High Angles of Attack, M. S. Dissertation, King Fahd University of Petroleum& Minerals, Dhahran, Saudi Arabia

[13]

Stahl, W. H., M. Mahmood, and A. Asghar, 1994, “Experimental Investigations of the Vortex Flow on Delta Wings at High Incidence”، American Institute of Aeronautics and Astronautics Journal, Vol. 30(4،( pp.1027-1032.

[14]

Kawai, H., and G. Nishimura, 1996, “Characteristics of Fluctuating Suction and Conical Vortices on a Flat Roof in Oblique Flow,” Journal of Wind Engineering & Industrial Aerodynamics, Vol. 60, pp.211-228.

343 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

Figure 1. Velocity and turbulence intensity profiles in the wind tunnel test section for different flow conditions.

344 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Figure 2.a. Placement of model in the wind tunnel.

Figure 2. Distribution of 0.8 mm diameter holes on the top surface of model, and some of the locations selected for hot-wire measurements ( • ). Dimensions in mm.

345 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

Figure 3. Flow visualization, using laser light sheet illumination, . = 45°, smooth flow top surface.

346 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Figure 4. Flow visualization using smoke wire technique, . = 45°, smooth flow.

347 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

Figure 5. Measured mean pressure distribution on model top surface, . = 45°، smooth flow.

348 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Figure 6. Measured pressure distribution on model top surface, . = 45°, nominal boundary turbulent flow, 4% turbulence.

349 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

Figure 7. Measured mean pressure distribution on model top surface, . = 45°، turbulent boundary layer flow.

350 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

M. Mahmood

Figure 8. Turbulent intensity on the top surface of the model, corresponding to hole # 50205 at TTU building, . = 45°.

351 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

WIND PRESSURES AND TURBULENCE MEASUREMENTS ON BUILDING ROOFS

352 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Topic 7 Research and development to serve the industry and upgrade its services • Industrial Engineering

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL ON THE STRESSES DEVELOPED IN ARTIFACIAL KNEE

S. M. Darwish1, A. Al-Samhan2, 1 Professor, Industrial Engineering Department, King Saud University, POB 800, Riyadh 11421, KSA, [email protected] 2 Associate Professor, Industrial Engineering Department, King Saud University, POB 800, Riyadh 11421, KSA, [email protected], ABSTRACT A wide range of materials may be used in manufacturing tibia trays of artificial knee replacements. The Young's modulus of the prosthesis is a critical design variable, since it largely determines how the load is transferred, via the cement to the bone. The current investigation deals with the effect of Young's modulus of the prosthesis and cement and on the stresses developed in the constituents and surrounding bones of artificial knee. Two practical tibia tray materials of diversified Young's modulus were considered in the present work. These showed that increasing the Young's modulus of the prosthesis resulted in weakening the cement layer, while its effect on other constituents is insignificant. A 50% increase in cement Young's modulus resulted in strengthening both the polyethylene and cement layers.

KEYWORDS:

Finite-element model - Artificial knee design.

1.

INTRODUCTION

The human knee is like a hinge joint that moves in a complex arc and allows the human body to twist and move sideways. Normal knee joints consist of a set of bones, called the femur (upper part), patella and tibia (lower pat). For a knee to function normally, the quality of smoothness where each bone moves upon the other becomes important in the function of the knee joint [1-8].

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

Artificial knee replacement is a surgical operation in which the defective knee joint surfaces are replaced completely with an artificial joint. Total knee replacement (TKR), also referred to as total knee arthroplasty (TKA), is a surgical procedure where worn, diseased, or damaged surfaces of a knee joint are removed and replaced with artificial surfaces. Materials used for resurfacing the joint are not only strong and durable but also optimal for joint function as they produce as little friction as possible. The general goal of total knee replacement is designed to provide painless and unlimited standing, sitting, walking, and other normal activities of daily living. With proper care individuals who have had a total knee replacement can expect many years of faithful function. The major reason why artificial joints may eventually fail is because of loosening where the metal or cement meets the bone, as well as the wear of the polyethylene layer. There have been great advances in extending how long an artificial joint will last, but loosening is a possibility that may require a revision. A prosthesis is usually used with a cement layer to interlock the prosthesis into the bone. Reinforcement of the cement has been proposed to increase its strength and toughness; this will result in increased cement Young's modulus [12]. In order to support the reinforcement approach, its effect on the strength on the cement layer, surrounding bones and other prosthesis constituents should be predicted. The current investigation deals with one of the most important parameters in controlling the life span of artificial knees, which is the stiffness of tibia tray and the cement layer. Where the finite element technique has been adopted to model the prosthesis and its surroundings throughout the evaluation process.

2.

FINITE ELEMENT MODELING AND BOUNDARY CONDITIONS:

The current research was conducted on the cruciate retaining Sigma knee design used in Saudi hospitals [10 ]. The GID software [9] general- purpose structural finite element program with preprocessing and post-processing was used. Fig.1 shows the configuration and dimensions of the considered model. The selected cement thicknesses and properties were as used in actual surgery in the King Khaled University Hospital, Saudi Arabia [10]. The finite element model considered along with constraints and loading conditions is shown in Figs.2 and 3, while Fig 4 shows full solid and sub-solid models for the knee joint model. The material properties of the different materials involved are shown in Table 1.

356 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

S. M. Darwish , A. Al-Samhan

Fig.1 The configuration and dimensions of the model considered.

Z Y

X

Fig. 2 The configuration and outer dimensions (mm) of the artificial knee joint

357 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

Table 1 Material properties considered in finite-element model. Table 1 Material properties of involved materials [11]

Material Cancellous bone Polyethylene Titanium alloy Plan adhesive (cement) Sttiffied adhesive (I) Sttiffied adhesive (II) Cortical Bone Nickel -chrome alloy

Young Modulus Mpa 5.20E+02 3.20E+04 1.10E+05 2.50E+03 3.75E+03 5.00E+03 3.00E+04 2.00E+05

Poisson's ratio 0.29 0.2 0.36 0.38 0.38 0.38 0.29 0.3

Loading conditions: Normal load (pressure)

Polyethylene

Loading condition: Torsion Loading

Titanium alloy Adhesive (Cement)

Cortical Bone Constraint conditions along 3-axis

Fig. 3 Assigned material, loading and boundary conditions of FE

358 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

S. M. Darwish , A. Al-Samhan

Cement Model

Cancellous

Full Solid Model

Tibia Tray Model

Cortical Bone

Polyethylene

Fig 4 Full solid and sub-solid models for knee joint model.

359 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

Figure 3, shows that the lower part of the model is constrained in all directions. The applied load was normally distributed on the bearing area of the polyethylene layer. A load of 500 N was applied on each bearing area of the polyethylene layer (this is equivalent to the weight of a 50 kg person standing on one foot), coupled with a small torque of 1 Nm. The following assumption and boundary conditions were assumed throughout the idealization process: 1. 2. 3.

The problem is three dimensional All materials are isotropic, i.e. the properties of the materials are the same in each direction. The stress and strain applied on each material are in the elastic zone.

Since the stiffness of the tibia tray and cement is the most influencing constituent of the joint, the present work concentrated on the effect of the strength variation of these materials. The main objective was to increase the strength of these constituents, so that the joint could last with the patient as much as possible before replacement. To achieve this, two finite element models were built and used. It is worth mentioning that these models were selected after several careful mesh refinement investigations. The first model has a titanium tibia tray, which matches the currently available design used at K.K.U.H. The other model had a nickel –chrome tibia tray. The two models mesh had 1548 nodes and 7711 elements. A four element linear tetrahedron was used. It is worth noting that each model was run three times to account for different stiffness allocated to the cement material.

3.

STRENGTH PREDICTION OF ARTIFICIAL KNEE JOINT

The finite element mesh was generated using the GID preprocessing program [9]. To improve accuracy, a fine mesh was used in zones where rapid variation in stress was anticipated, rather than in the zones of constant stresses. The FE computation was carried out using the Calsef FE program. [9], which is an integral module inside the GID program.

360 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

S. M. Darwish , A. Al-Samhan

MPa

MPa

MPa

Fig. 5 Mesh generation and principle stress contours for FE model 1.(Titanium tibia tray).

361 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

GID [9 ] is widely used for preprocessing FE meshes and FE results visualization in a number of linear and non- linear problems in structural engineering, using the finite element method. The predicted normal stresses and shear stresses were converted into their equivalent principal stresses. Those nodes having maximum and minimum principal stress have been identified, for each material. Fig. 5 shows the principal stresses associated with model 1.

4.

MATERIAL ANALYSIS

Based on the principal stresses, the maximum developed Von Mises stresses in each constituents of the artificial knee (Titanium and nickel chrome tibia trays) were listed in Table 3 and Fig.6. From figure 6, it can be concluded that increasing the stiffness of the tibia tray resulted in weakening the cement layer. A 38% reduction in stresses was developed in the cement layer was achieved with tibia tray having the lowest Young's modulus (Titanium alloy tibia tray). This is may be explained by the fact that the higher the stiffness of the tibia tray material, the lower the displacement it undergoes and the higher the stresses it transfers to the cement material.

Table 3 The maximum compressive stress level achieved with different prosthesis materials (MPa). Constituent Polyethylene Tibia tray Cancellous Bone Cortical Bone Cement material

Model 1 Nickel-Chrome tray

Model 2 Titanium alloy

0.4516 0.2295 0.1855 0.428 0.321

0.4578 0.225 0.1892 0.432 0.233

362 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

% improvement

-0.01 0.02 -0.02 -0.01 27

S. M. Darwish , A. Al-Samhan

0.5 0.4578 0.45159

0.45

0.432

0.428

0.4

Von-Misses Stress MPa

0.35 0.321 Ti-alloy Tiabia Ni-Chrom alloy Tiabia

0.3 0.25

0.225

0.2295

0.233

0.2 0.1892

0.1855

0.15 0.1 0.05 0 Polyethylene

FE Results for 8mm polyethylene layer

Metal Tibia

Cement

Cancellous Bone

Cortical Bone

Fig.6 Effect of tibia tray material on Von Mises stresses.

5. EFFECT OF CEMENT STIFFNESS ON THE DEVELOPED STRESS LEVELS The addition of fibers to a polymer to form a composite causes improvement in the strength of the polymer since the fibers themselves become stressed and therefore take away some stress from the polymer. Fig. 7 and Fig. 8 show the effect of cement stiffness on other constituents of artificial knee both in titanium and nickel-chrome tibia trays. From the figures it can be observed that increasing the cement stiffness from 2 .5 MPa to 3.75 MPa (50% increase) resulted in strengthening mostly all constituents of artificial knee including the surrounding bones. However this trend is altered when the cement modulus was increased from 2.5 to 5 MPa (100% increase). So, it is recommended to increase the stiffness of the cement up to 50%. It can be also observed from the figures that the effect of increasing the cement stiffness on almost all constituents of artificial knee is identical whatever the tibia tray material is. The most pronounced effect of stiffening the cement is reducing the stress level in the polyethylene layer by 11%. Since both titanium alloy and nickel-chrome tibia trays act similarly, it

is recommended to use titanium tibia trays due to its lighter weight. 363 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

0.7 Cement-1

0.606 0.547 0.579

0.6

Cement-2 Cement-3 0.497

0.468

0.483

Von-Misses Stress MPa

0.5

0.4 0.332 0.297

0.295 0.269 0.284

0.315

0.3 0.232 0.214

0.223

0.2

0.1

0 Polyethylene

Metal Tibia

Cement

Cancellous Bone

Cortical Bone

Fig.7 Effect of cement stiffness on different constituents (titanium alloy tibia tray).

0.7 Cement-1

0.606

0.6

0.547 0.579

Cement-2 Cement-3 0.496

0.467

0.482

Von-Misses Stress MPa

0.5

0.4 0.327 0.297

0.291 0.269 0.284

0.3

0.311 0.232 0.214

0.224

0.2

0.1

0 Polyethylene

Metal Tibia

Cement

Cancellous Bone

Cortical Bone

Fig.8 Effect of cement stiffness on different constituents (nickel- chrome tibia tray).

364 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

S. M. Darwish , A. Al-Samhan

6. CONCLUSIONS 1- Increasing the Young's modulus of the prosthesis resulted in weakening the cement layer, while its effect on other constituents is negligible. 2- Stiffening the cement material resulted in lowering the stress level in the polyethylene. 3- It is recommended to increase the cement stiffness by maximum of 50%. 4- Since both titanium alloy and nickel -chrome tibia trays respond similarly, it is recommended to use titanium tibia trays due to its lighter weight.

REFERENCES

1. Villa,T.; Migliavacca,F.; Gastaldi,D.; Colombo M.; Pietrabissa, R., (2004), " Contact stresses and fatigue life in a knee prosthesis: comparison between in vitro measurements and computational simulations" J. of Biomechanics, vol.37, pp 45-53.

2. Lesaka,K.; Tsumura, H.; Sonoda, H.; Sawatari,T., Takasita, T.; Torisu, T., (2002), " The effects of tibia component inclination on bone stress after unicompartmental knee arthoplasty", J. of Biomechanics, vol.35, pp 969-974.

3. Giddinia,L.V. ; Kurtz, S.M.; Edidin, A.A., (2001), " Total knee replacement polyethylene stresses during loading in a case simulator", Trans. ASME J of Tribology,vol.123, pp 842-847.

4. DesJardins, D.J.; Walker, P. S.; Haider,H., Perry,J., (2000), "The use of a force-controlled knee simulator to quantify the mechanical performance of total knee replacement design during functional activity", J. of Biomechanics, vol.33, pp 1231-1242.

5. Jilani A., Shirazi-Adl, A.; Bendjaballah,M.Z., (1997), "Biomechanics of human tibia-femoral joint in axial rotation", The Knee, vol.4, pp 203-213.

6. Bendjaballah,M.Z.; Shirazi-Adl, A.; Zukor,D.J., (1997), " Finite element analysis of human knee joint in varus- valgus", Clinical Biomechanics, vol.3, pp. 139-148.

365 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

THE EFFECT OF CEMENT STIFFNESS AND TIBIA TRAY MATERIAL

7. Bendjaballah,M.Z.; Shirazi-Adl, A.; Zukor,D.J., (1995), "Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis", The Knee, vol.2, pp 69-79.

8. Donahue, T. L. ; Hull, M.L.; Rashid, M. M.; Jacobs, C.R., (2002), " A finite element model of the human knee joint for the study of tibia-femoral contact", J of Biomechanical Engineering, vol. 124, pp 273-280.

9. GID and Calsef software's are copy writes of International Center for Numerical Methods in Engineering (CIMNE)-Edificio C-1, Campus Norte UPC, 08034 Barcelona, Spain.

10. P. F. C. Sigma Knee System; Technical Monograph, "DePuy a Johnson & Johnson company", Leeds, U.K.

11. H.F. El-Sheikh, B. J. MacDonald, M.S. Hashmi, (2002), " Material selection in the design of the femoral component of cemented total hip replacement, j. of materials processing technology, vol. 122, pp 309-317.

12. Al-Samhan, S. M. Darwish, H. Al-Khawashki, M.M. Zamzam (2006), "Optimization of polyethylene layer thickness of artificial knee", UMTIK Conference, Turkey, vol.2, pp 703-712.

366 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACEQUENCHED SABIC STRUCTURAL STEEL Mahmoud S. Soliman1, Abdul-Rahman M. Al-Ahmari2, and Saied M. Darwish3 1. Professor, Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, [email protected] 2. Associate Professor, 3. Professor, Industrial Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421 ABSTRACT SABIC Hadeed Company in Saudi Arabia has introduced a new technology (bar quenching) to its rolling mills in Jubail, for the manufacture of superior quality concrete reinforcing bars. This technology uses the state of the art process involving high pressure surface quenching followed by self-tempering. As the bars emerge from the last rolling stand, the surface temperature is rapidly reduced by highpressure water jets. This action causes change in the structure, making it harder and stronger. The production of this type of bars is so large that it has been decided to market it for some other purposes such as machining. Since no or little machining data are available for cutting SABIC structural steel, a machining database for SABIC structural steel is to be established. Also, the machining parameters of SABIC structural steels are to be optimized to enhance machinability. KEYWORDS SABIC structural steel, Machinability, Surface roughness, Cutting force, Hardness 1- INTRODUCTION The optimization of machining operations has been and continues to be a topic of interest to many practitioners in the metal cutting industry. As a result, countless system metrics and indices have been developed in an attempt to offer very much needed insight about the materials, cutting conditions and system attributes selected for an operation [1-7]. Machinability ratings are often descriptive system metrics. These ratings, sometimes called indices, attempt to quantitatively denote the relative ease with which a material (usually a metal) can be machined when using standard tooling and cutting conditions. Various criteria are used to evaluate machinability, some of which include the following: tool life, cutting forces and power requirements, surface finish, dimensional control, metal removal rate and chip control. Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

Low-carbon steel or mild steel are often used to indicate carbon content of less than 0.25%. The structure of these steels is composed of ferrite and pearlite. Cold working can strengthen low carbon steel, but minor strengthening is possible by heat treatment. Such steels are used primarily in structural applications (bridges and buildings) and hence the term structural steel such as A36 was given according to ASTM standards. The chemical composition of these steels is in the range: 0.180.25% C, 0.6-1.25% Mn, 0.035% P, 0.04% S and 0.15-0.35% Si. Although moderate in yield strength and tensile strength, these steels have proper combination of strength, ductility, toughness and weldability to perform satisfactorily in structural application. Typical values for yield strength, tensile strength and ductility in A36 steel are 310, 450 MPa and 28% (in 50 mm gage length), respectively. The Vickers hardness HV for this steel can be estimated using the relationship between Vickers hardness HV and tensile strengthσu, which is usually expressed as [8]

HV = 3σ u

(1)

where HV is in MPa ( divide by 9.825 to convert to conventional hardness units kg/mm2). The calculated value for HV is 137, agrees very well with the tabulated value of hardness for hot rolled structural steels. The structural steels produced by SABIC in the form of reinforced bars, are usually quenched in water after hot deformation in the austenite region. Because of low hardenability (low carbon content ≤ 0.25) minor hardening is taking place; small fraction of austenite is transformed to martensite plus fine structure of ferrite and pearlite. Since no or little machining data are available for cutting SABIC structural steel, so the aim of the present work is to optimize the machining parameters of SABIC structural steels in order to enhance its machinability 2. EXPERIMENTAL WORK 2.1 Microstructure of SABIC Structural Steel The microstructures of the reinforced rods are shown in Figures 1 and 2. These figures suggest that the microstructure consists of ferrite and pearlite. It is possible that some martensite is formed on the surface of the specimens. In addition, the microstructure on the surface is finer than that in the center of the rod (Figure 2a). This microstructure reflects the high strength observed in reinforced bars produced by SABIC Hadeed Company.

368 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Mahmoud S. Soliman, et al

2.2 Mechanical properties measurements Vickers hardness and tensile strength were measured for two bars of 12-mm and 16-mm diameters. The Vickers hardness was measured using diamond pyramid as indenter at 10 or 20 kg load, taking the average of the two diagonals for the indentation and reading the corresponding value of the hardness from the tables. The tensile strength was measured using an Instron machine operating at constant cross-head speed of 10 mm/min.

Figure 1. Microstructure of ferrite and pearlite in 12mm diameter rod.

(a)

(b)

Figure 2. Microstructure of ferrite and pearlite; (a) in the center of 16mm diameter rod, (b) in the periphery of 14mm diameter rod. 369 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

The load-displacement curve was monitored using strip chart recorder. The load was measured using 100 kN-load cell. The average cross-section area, A was determined by weighing a specified length of the rods and finding the volume using the tabulated value for the density of structural steel (7.86x103 kg/m3). The calculations are given in Table1. The measured value for ultimate load Pu is also, included in the Table 1. Table1. Dimensions of Tested Specimens (12mm-diam. rod) and their ultimate strength Sample Length, m Weight, Volume, A, m2 Pu, kN σu, 3 kg m MPa 1 0.299 0.257 3.3x10-5 1.1x10-4 76.5 695 -5 2 0.199 0.165 2.1x10 1.1x10-4 78.2 711 The ductility (elongation percent) determined for specimen 2 is 26% in 100 mm. This value is comparable to that determined for A36 structural steel in specimens with 50 mm gage length. SABIC Structural steel has the advantage of high strength with moderate ductility as compared to ASTM standard steels. The ductility measurements require further investigation. The mechanical properties, HV and σu are listed in Table 2. The data for 12mm bar is satisfying the relationship represented by Eq. 1, i.e., when the value of HV (MPa) in the center is divided by σu, gives a value of 2.9. Therefore, the ultimate strength in 16-mm bar was estimated using Eq. (1). Table 2. Mechanical properties of reinforced bars Rod diameter., HV(Surface) HV(Center) σu, MPa mm kg/mm2 kg/mm2 12 291 207 703 16 263 179 586* * estimated using the relation between HV andσu. 3. MACHINING SET-UP OF THE PRESENT WORK The experimental set-up used throughout the present work includes the following: 1- A 3-component Kistler dynamometer model (9257 B). 2- Multi channel Kistler amplifier model (5019 B). 3- Data acquisition card set-up (DAS 1602/12). 4- Dynoware software set-up (version 2825 A-12). 370 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Mahmoud S. Soliman, et al

3.1 Work piece Materials The material used throughout this work was a SABIC structural steel (0.25% C, 0.6-1.25% Mn, 0.035% P, 0.04% S and 0.15-0.35% Si. The work pieces were in the form of cylinders 12 and 16 mm in diameter and 150 mm in length. 3.2 Tool material The cutting inserts used throughout the present work were carbide (triangular and diamond shape) tool bit inserts. In order to eliminate the effect of tool angles on the test results, a fresh identical cutting insert was used to conduct each cutting test condition. 3.3 Cutting force measurements A three-component 9257A Kistler dynamometer with special tool holder, connected to a 5001 three channel Kistler charge amplifier was used for measuring the cutting force components of the present work. It is worth noting that before running the cutting test, the Kistler dynamometer was calibrated on an Instron testing machine using a dummy tool, where the gain of the amplifier was adjusted at one volt for each one kN. 3.4 Surface roughness measurements The surface roughness was measured using the portable Suntronic-10 surface roughness meter. The center line average, Ra was taken to represent the particular test combination, and a cut-off value of 0.8 mm was used. Each cutting test was repeated four times. The average of the four readings was taken to represent the surface roughness of the particular test condition. It is worth mentioning that the work piece was not removed while measuring the surface roughness (in order to avoid the effect of different clamping on the test results) until all the cutting tests concerning a specific insert have been conducted. 3.5 Tool Flank Wear Measurements A Sptizenhope Carl – Ziess tool maker microscope was used for measuring the tool flank wear. Each cutting test was repeated four times, where the build-up of the tool flank wear was taken to represent the particular test condition. The workpiece was not removed until all the cutting tests concerning the specific insert have been conducted (in order to avoid the effect of different clamping on the test results). 4 CUTTING TEST PROCEDURE The process utilized was a turning operation, performed on a 10 kW SSSR (Russian made) engine lathe model 16K25. Cutting tests were conducted using carbide (triangular and diamond shape) identical tool bit inserts. Each test bar was placed between three jaws chuck and the tail stock of the lathe. The test bar was not 371 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

removed until all different cutting tests concerning the specific tool bit insert have been conducted (in order to avoid the effect of different clamping on the test results). Table 3 shows the cutting conditions used.

Table 3. The cutting conditions tested. High Level

Low Level

(+)

(-)

Velocity, v (m/min)

50.9

20.6

Feed Rate, f (mm/rev)

0.08

0.04

Depth of cut, d (mm)

1.5

0.6

Work piece Hardness, h

232

200

Level Factor

5. FACTORIAL DESIGN AND DESIGN MATRIX Full factorial design consists of all possible combinations of the factors and their levels. In the present work a 2k factorial design is adopted, where each factor in the experiment is studied at only two levels. There are several reasons for emphasizing the 2k design, such as relatively few runs are required, the design is easy to use in sequential experimentation and the data can be processed using graphical methods. Also, when a large number of factors are studied, the fractions of 2k designs can be used to keep the experiment at reasonable size [9-11]. Table 4 contains a list of the test combinations of these factors. 6. STATISTICAL ANALYSIS OF RESULTS The design of experiments (DOE) capabilities are used to provide simultaneously an investigation of the effect of multiple variables of cutting process (depth of cut, feed, speed and material hardness) on the output variables (responses). Four types of experiments [9-11] are supposed to be carried out in this paper for cutting force, surface roughness, tool wear, and tool life. These types of experiments are called factorial experiments, because each machining conditions of major concern to the experimenter. The value of the factors (machining conditions) in these experiments is called levels. Thus we deal with models in which the four machining conditions (v, f, d, h) are studied within two levels of each factor. Experiments are carried out to investigate the effect of the four machining conditions on cutting force, tool wear and surface roughness. The data collected is shown in Table 4. 372 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Mahmoud S. Soliman, et al

6.1 Postulation of the surface roughness and force models In this experiment, the four factors (v, f, d, h) are considered using factorial design to investigate their effect on the output (F and Ra). These experiments aim to study the general behavior of SABIC structural steel in machining. It is well known from the literature that the cuttings force, F and surface roughness, Ra is experimentally related by the cutting conditions as follows:

F = C F v n1 f n2 d n3 h n4 Ra = C R v c1 f c2 d c3 h c4

(2) (3)

where CF and CR are constants depending on the cutting parameters. The above relationships can generally be expressed in a logarithmic form as follows: Ln F= ln CF + n1 ln v + n2 lnf + n3ln d+ n4lnh

(4)

Ln Ra= ln CR + c1 ln v + c2ln f + c3 ln d + c4 lnh

(5)

In the present preliminary experiments, each machining variables is given two levels coded (- and +), which represent low level and high level of the variable. 16 experiments were conducted during which the response variables (surface roughness and cutting force) were measured. The obtained results from the regression analysis are shown in Table 4 for Ra and Force, respectively. From the above results of regression analysis the equations of force and surface roughness can be written as follows:

F = 3.62 × 10 5 v 0.001 f 0.738 d 0.638 h −0.929

(6)

Ra = 9.85 × 10 −3 v −0.181 f 0.969 d 0.555 h1.53

(7)

A sample of residual graphs is shown in Fig. 3.

373 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

6.2 analyses of the results The models are fitted to the data and graphs are generated to evaluate the effects of machining conditions on cutting forces and surface roughness. The results obtained from the fitted models and graphs are used to analyze which are important for reading the value of cutting force and surface roughness. In this section the Minitab results and illustrations provided by the software, to visualize the effects of machining conditions, are plotted and analyzed. Table 4. The implemented design matrix Factors Test No.

Cutting

Feed, f

Speed, v

Depth of cut, d

Cutting force Hardness h

Ra (µm)

Fs

Ff

Fr

F

1

-

-

-

-

56.99

10.04

117.37 130.86

٢٫٢

2

+

-

-

-

137.14

18.78

131.51 190.93

١٫٤

3

-

+

-

-

107.97

27.32

190.96 221.06

٤٫١

4

+

+

-

-

152.9

46.88

191.25 249.30

٣٫٣

5

-

-

+

-

93.05

57.66

232.97 257.40

٣٫٥

6

+

-

+

-

113.68

72.41

134.41 190.35

٤٫٦

7

-

+

+

-

191.9

147.91 463.54 523.04

٧٫٣

8

+

+

+

-

226.21 137.57

317.5

413.40

٣٫٥

9

-

-

-

+

36.41

33.42

121.97 131.60

٢٫١

10

+

-

-

+

45.55

43.5

123.68 138.79

٢٫٥

11

-

+

-

+

83.97

54.61

170.56 197.80

٤٫٨

12

+

+

-

+

92.41

65.36

157.57 194.01

٤٫٨

13

-

-

+

+

85.82

79.67

202.76 234.15

٤٫٧

14

+

-

+

+

93.01

93.78

209.1

247.32

٤٫٢

15

-

+

+

+

124.31 164.94

366.3

420.52

٦٫٠

16

+

+

+

+

142.04 156.36

402.95

5

374 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Mahmoud S. Soliman, et al

Fig. 4 shows the effect of factors levels on cutting force, F. It is clear from the figure that, high cutting speeds generate less cutting forces than at low levels. This may be explained by the fact that, higher cutting speeds generates higher temperatures which soften the material and reduces its shear strength, so less cutting force is required to shear the material. The feed rate and depth of cut showed an opposite effect on cutting force. Increasing feed rate and depth of cut produce higher cutting forces than those at low levels of these factors. It can be observed from the figure that, the low level of material hardness generates higher cutting forces when compared with the high hardness level. This can be explained by the fact that low hardness allows more chance to the work piece material to adhere to the tool which calls for higher cutting force to overcome it. Since the interaction in these experiments is significant, the interaction plot is generated as shown in Fig. 5. The interaction between every two factors is shown in the figure. It is clear from the plots that there is interaction between all factors except between depth of cut and hardness.

Residual Plots for lnforce Residuals Versus the Fitted Values 0.30

90

0.15 Residual

Percent

Normal Probability Plot of the Residuals 99

50 10

-0.15 -0.30

1 -0.4

-0.2

0.0 Residual

0.2

0.4

5.00

Histogram of the Residuals

0.30

4.5

0.15

3.0 1.5 0.0

5.25 5.50 5.75 Fitted Value

6.00

Residuals Versus the Order of the Data

6.0 Residual

Frequency

0.00

0.00 -0.15 -0.30

-0.3

-0.2

-0.1

0.0 0.1 Residual

0.2

0.3

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16

Observation Order

Figure 3. The force residual graphs

375 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

M ain Effe cts P lot (fitte d me a ns ) for F or ce v

350

f

300

Mean of Force

250 200 22

51

0 .0 4

0 .0 8

d

350

hd

300 250 200 0 .6

1 .5

263

291

Figure 4. Main effects plot (cutting force)

Inter action P lot (fitted means) for F orce 0.04

0.08

0.6

1.5

263

291 400 300

v

v 22 51

200

400 300

f

f 0.04 0.08

200 400 300

d

200

hd

Figure 5.Interaction between factors (cutting force)

376 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

d 0.6 1.5

Mahmoud S. Soliman, et al

Fig. 6 shows the effect on factors levels on the surface roughness of the machined work pieces. It is clear from the figures that, high cutting speeds generate less surface roughness than at low levels of speed. The feed rate shows the same trend as the cutting force although the depth of cut shows an opposite effect on surface roughness. The high feed rate and high depth of cut produce higher surface roughness than at low levels of these factors. The low level of material hardness generates higher roughness when compared with the high hardness level.

Main Effects Plot (fitted means) for Ra v

5.0

f

4.5 4.0

Mean of Ra

3.5 3.0 22

51

0.04

d

5.0

0.08 hd

4.5 4.0 3.5 3.0 0.6

1.5

263

291

Figure 6. Main effects plot (surface roughness condition) Other analysis is given to illustrate more details about the effects of the considered factors in Figs 7 and 8. These figures show the plots of normal probability and pareto charts of the effects for both responses surface roughness, Ra and cutting force, F.

377 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

6.3 Surface Analysis After determining the models and the effects, surface plots of surface roughness and cutting forces can be generated vs. two of the variables. In present case there are four variables, therefore, six surface plots are generated for each response, as shown in Figs 9-12. N o r m a l P r o b a b i l i ty P l o t o f the E f f e c ts (r e s p o n s e is R a , A lp h a = .0 5 ) 99

E ffec t T y p e N o t S ig n ific an t S ig n ific an t

C

95 90

F a cto r A B C D

B

Percent

80 70 60 50 40 30

N am e v f d hd

20 10 5 1

- 1 .0

- 0 .5

0 .0

0 .5 Effe c t

1 .0

1 .5

2 .0

Le n th's P S E = 0 .5 6 2 5

Figure 7. Normal probability plot of the effects.

P a r e t o C h a r t o f t h e E f f e c ts ( r e s p o n s e is R a , A lp h a = .0 5 ) 1 .4 4 6 F a c to r A B C D

C B A AB BC

Term

A BC D A BC D AD A BD A C BC AC

C D D D

BD

0 .0

0 .5

1 .0 Ef f e c t

1 .5

L e n th 's P S E = 0 .5 6 2 5

Figure 8. Pareto chart of the effects 378 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

2 .0

N am e v f d hd

Mahmoud S. Soliman, et al

S ur f a c e P l o t o f R a v s d ; v H o ld V alu es f 0.04 hd 263

4 Ra

3 2 1 .5 1 20

1 .0 30 v

40

50

d

0.5

Figure 9. Surface plot for surface roughness

S ur fa ce P lot of R a v s hd; v H o ld V a lu e s f 0 .0 4 d 0.6

2 .5

Ra

2 .0

1 .5

290 280 20

270

30 v

40

50

hd

260

Figure10. Surface plot for surface roughness

379 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

S ur fa c e P lo t o f F o r c e v s d; f H o ld V a lu e s v 22 h d 263

500 400 F or ce

300 200

1 .5 1 .0

0 .0 4 f

0 .0 6

0 .0 8

d

0 .5

Figure11. Force surface plot

S ur f a c e P lo t o f F o r c e v s d; v H o ld V alu es f 0.04 hd 263

250

F o r ce

200

150

1.5 20

1 .0 30 v

40

50

d

0 .5

Figure12. Force surface plot

380 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Mahmoud S. Soliman, et al

7. CONCLUSIONS •

• • • • • •

SABIC is producing two levels of structural steel with respect to material hardness. The harder material demonstrated higher machinability characteristics (demonstrated in lower cutting forces and surface roughness). At present experiments, the speed has very little effect on both cutting force and surface roughness. The cutting force is inversely proportional to hardness. Higher surface quality is associated with higher cutting speeds and material hardness. Feed rate and depth of cut are the most factors affecting surface roughness. It is advisable to SABIC company to change the flow rate of quenching, in accordance with diameter of quenched bar to obtain the higher level of hardness despite changing the bars diameters. The equations of surface roughness and cutting force are useful in predicting, the appropriate machining parameters for certain conditions.

• 8. ACKNOWLEDGEMENTS This work was supported by SABIC company (grant number 28/423) through the Research Center, College of Engineering, King Saud University. This support is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5. 6.

Shaw, M.C., Vyas, A. (1993)، "Chip Formation in The Machining of Hardened Steel ،"Annals of CIRP, vol. 42, No. 1, pp. 29-33. Narutaki, N., Yamne, Y.، ،(١٩٩٣) "High-Speed Machining of Inconel 718 With Ceramic Tools ،"Annals of CIRP, vol. 42, No. 1, pp 100-105. Hodgson, T.; Trendler, P. (1981)"،Turning Hardened Tool Steel With Cubic Boron Nitride ،"Annals of the CIRP, vol. 30, pp 63. Koning, et al (1984), "Machining of Hard Materials ،"Annals of the CIRP, vol. 32, No. 2, pp 417-427. Daniel, E.H., (1982)"،Now: Turn Hardened Steel and Tough Super-alloys as Easily as Mild Steels ،"Machining of Hard Materials, ASM. Farag, M.M., (1989),"Selection of Materials and Manufacturing Processes for Engineering Design ،"Prentice Hall, New York. 381

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

MACHINING CONDITIONS OF HIGH PRESSURE SURFACE- QUENCHED SABIC STRUCTURAL STEEL

7.

Darwish, S. and Davies, R., (1989)"،Investigation of Heat Flow Through Bonded and Brazed Metal Cutting Tools ،"Int. J. Mach. Tools & Manufacture., vol. 29, No. 2, pp. 229-237. 8. Ashby, M. F. and Jones, D. R. H., (1998) “Materials Engineering” 2nd edition, Butterworth-Heinemann, Oxford. 9. Janc, D.Y.; Choi, Y.; Kim, H.; Hsiano, A., (1996),"Study of The Correlation Between Surface Roughness and Cutting Vibrations to Develop on-line Measuring Technique in Hard Turning ،"Int. J. Mach. Tools Manufacture., vol. 36, No. 5, pp. 453-464. 10. Ronald, D.M.; Thomas, W.; Lloyd, P.P., (1991)"،Improving Quality Through Planned Experimentation ،"McGraw-Hill, New York. 11. Montgomery, D.C., (1996), "Design and Analysis of Experiments”, 4th edition, John Wiley & Sons, U.S.A.

382 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA 1

2

N.M. Al-Abbadi , M.A. El-Kady 1: King Abdulaziz City for Science and Technology, [email protected] 2: King Saud University, Riyadh, Saudi Arabia, [email protected]

ABSTRACT Worker’s and public safety issues are always top on the business agenda of industrial companies. However, too conservative designs, because of lack of accurate assessment, could be too expensive. In industrial premises, public and worker’s safety represents a priority item in all electrical installations, devices and equipment. Almost all design, planning and operation aspects of industrial factories, electric power utility stations and commercial buildings adopt strict electrical safety measures to ensure the security and safety of both workers and the public. Nevertheless, incidents of electrocution fatalities, explosions in electrical equipment and electrically initiated fires are frequently heard of from time to time. With the help of advanced, state-of-the-art computer simulation software and site measurements, investigations pertaining to electrical safety, electrocution hazards and associated risk assessment could be conducted. The aim of this paper is to present a modern practical approach for assessing public and worker's safety at electrical industrial installations. The paper also presents an implementation outline and practical applications which involve assessment of grounding schemes employed by the industrial company as well as adequacy of fault current and protection levels at the supplier side (the electricity company).

KEY WORDS Public and worker safety, electrocution hazards, step and touch potentials, safety assessment, risk analysis.

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

1. INTRODUCTION Safe, yet cost effective designs and efficient, low maintenance operation schemes are key requirements for survival in today’s industrial establishments. Worker’s and public safety issues are always top on the business agenda of industrial companies. However, too conservative designs, because of lack of accurate assessment, could be too expensive [1,2]. Risks, which were qualitatively accepted a few years ago, must now be quantified so that appropriate decisions can be made. As is well known, there is no device or technology that is absolutely safe! In industrial premises, public and worker’s safety represents a priority item in all electrical installations, devices and equipment. Almost all design, planning and operation aspects of industrial factories, electric power utility stations and commercial buildings adopt strict electrical safety measures to ensure the security and safety of both workers and the public [3-5]. Nevertheless, incidents of electrocution fatalities, explosions in electrical equipment and electrically initiated fires are frequently heard of from time to time. With the help of advanced, state-of-the-art computer simulation software and site measurements, investigations pertaining to electrical safety, electrocution hazards and associated risk assessment could be conducted. With such advanced capabilities, research and development teams at national institutions can fulfill an important mandate towards the society and industry across the Kingdom of Saudi Arabia. The aim of this paper is to present a modern practical approach for assessing public and worker's safety at electrical industrial installations. The approach combines site measurements and computer simulation techniques in order to analyze, evaluate and assess the risk levels associated with electrocution hazards to personnel at industrial sites owned and operated by major industrial companies in the Kingdom of Saudi Arabia. The paper also presents an implementation outline and practical applications which involve assessment of grounding schemes employed by the industrial company as well as adequacy of fault current and protection levels at the supplier side (the electricity company). The contributions and results of this paper are believed to serve two main objectives, namely: 1) Demonstration of how modern advanced simulation software tools can be used in conjunction of site measurements to evaluate the electrocution hazard risk levels, as they currently exist, and compare these levels with the international norms, and 2) Investigation of potential opportunities for improving electrical safety within industrial establishments at minimum added costs.

384 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

N.M. Al-Abbadi , M.A. El-Kady

2. THRESHOLD ELECTROCUTION CURRENTS 2.1 Background As the standard of living advances, safety requirements in practically every aspect of human activity are being reviewed and updated. Thus the questions associated with defining acceptable risk levels for particular activities and evaluating the costs necessary to obtain certain levels of safety must be answered. One of the ways to quantify risk is to calculate the Fatal Accident Frequency Rate (FAFR). The FAFR is the number of fatal accidents per 1000 persons in a working lifetime (100 million man-hours). Another way to describe the risks involved in various activities is to calculate the probability of a fatality per person per year. The risk associated with grounding hazards near high voltage power equipment and transmission line structures during system ground faults is presently of interest to utility designers and operators in view of increasing fault current levels and public usage of rights-of-way. The work of this paper is devoted mainly to the two main concerns of human safety in the vicinity of high voltage structures at the time of a system ground fault, namely the so-called "step potential" and "touch potential". A particular attention will be given to the analysis aspect of the step and touch potentials as well as the advanced methodology used to evaluate the associated risk to human lives.

2.2 Step and Touch Potentials Equipment protection is only part of the reason that power system premises including, for example, transmission line corridors and substations are so well grounded. Personnel protection is a major consideration as well. A continuous current through the trunk part of the body of about 0.15 A is almost always fatal. Electric shock death usually occurs from ventricular fibrillation, where the electrical signals that drive the heart contractions lose their harmony causing very rapid, but ineffectual, heart contractions to occur. The trunk of the body can withstand higher currents, but only for short times, and any current in the trunk over 0.1 A is dangerous. The Institute of Electrical and Electronic Engineers (IEEE) has set a standard for non-fatal body current at 201 mA for 0.33 second for a 50 kg (110 lb) person for the general public. Therefore, for the public, we could use the following empirical formula (Dalziel's empirical electrocution equation [6])

Imax-P = 0.116 / √t

(1)

where I is the threshold current for ventricular fibrillation in amperes, and t represents the shock duration in seconds and is assumed to be in the range of 0.03 to 3 s. For workmen inside a substation, the limit is 272 mA, for 0.33 second, for a 70 kg (110 lb) person. This leads to the following empirical formula 385 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

Imax-W = 0.157 / √t

(2)

These currents could be reached in a person only under unusually poor circumstances, such as when being wet from a rain or standing on wet ground with wet shoes. The body current is limited around a substation, or any other electrical power structure such as a transmission tower, by reducing the ground impedance to such a degree that any easily touchable point will not develop enough voltage to cause a fatality during a ground fault. The assumed body resistance for such calculations is 1000 Ω, much less than the normal total body resistance. In this respect, two safety related voltages are defined, namely the touch potential and the step potential. 2.2.1 Touch Potential Touch potential is defined as the maximum voltage allowed on any structure from any point within reach from the ground, standing 3 feet from the structure, because of ground fault current. The maximum touch voltage is 653 V inside a substation, where only competent workers in proper clothing should be allowed, and 207 V on the substation fence. The magnitude of fault current that would produce the maximum touch voltage would be very large. Figure 1 [7] illustrates the touch voltage. According to recognized international standards, the average tolerable touch potential, Vtouch, which is the voltage between any point on the ground, where a person may stand, and a point that can be touched simultaneously by either hand is given by

Vtouch

= (0.116 Rb + 0.5 Rg) / √t

(3)

where Rb is the resistance of the human body in Ω, Rg is the foot-to-ground resistance in Ω, and t is the duration of exposure in seconds. A standard conventional assumption, in applying the above formula, is that the average body resistance = 1400 Ω and Rg = 0.5 ρs, where ρs is the soil resistivity in Ω.m. This yields the following familiar expression for the tolerable touch potential

Vtouch

= (165 + 0.25 ρs) / √t

386 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

(4)

N.M. Al-Abbadi , M.A. El-Kady

In some other applications, a value of Rg = 3 ρs was suggested when a homogeneous surface layer is present for a depth of at least 0.5 m. Also, a value of Rb = 1000 Ω is sometimes suggested.

Fig. 1 Touch potential: (a) Definition, (b) Minimized by grounding [7]

2.2.2 Step Potential Step potential is defined as the maximum voltage that can flow, inside the human body, from foot to foot as one is walking during a fault condition, as shown in Figure 2. According to recognized international standards, the average tolerable step potential, Vstep, which is the voltage between any two points on the ground surface that can be touched simultaneously by the feet, is given by

Vstep

= (0.116 Rb + 2 Rg) / √t

(5)

where, again, Rb is the resistance of the human body in Ω, Rg is the foot-toground resistance in Ω, and t is the duration of exposure in seconds. A standard conventional assumption, in applying the above formula, is that the average body resistance = 1400 Ω and Rg = 0.5 ρs, where ρs is the soil resistivity in Ω.m. This yields the following familiar expression for the tolerable step potential

Vstep

= (165 + ρs) / √t

(6)

387 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

In practical power systems, all substations have a ground mat. Every piece of equipment and every support structure in the substation is connected to the ground mat, as is the substation fence. In generation substation, the generator is also grounded. The purpose of the ground mat is to ensure personnel safety by keeping both the touch and step voltages low during ground faults, and to prevent induced voltages on equipment and structures during normal operation. The same equipment and support structure grounding system is used even with delta and ungrounded wye systems that have no neutral return. The bulk of the resistance associated with a grounding system is in the contact between the Earth and the ground conductors. If a good contact is established between the conductor and the deep sub-soil, the Earth resistance is very small.

Fig. 2 Step potential: (a) Definition, (b) Occurrence of high step voltage [7]

3. ELECTROCUTION RISK ASSESSMENT METHODOLOGY Excessive step and touch potentials near high voltage structures, such as transmission line towers and substation equipment, due to severe ground faults present a hazard to anyone in proximity to a structure when a fault occurs. A proper probabilistic analysis is required to assess the risk posed to personnel due to step and touch potentials in the vicinity of high-voltage power equipment and structures. 3.1 Risk Assessment Methodology The classical formulation based on the probabilistic convolution of stress (applied) and strength (withstand) distributions is used to assess the risk of human fatality due to step and touch potentials. Specific statistical representations of both the step and touch potentials which stress the human body and the corresponding strength (or capability) of the body to withstand shocks due to such potentials are used in the overall risk assessment methodology.

388 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

N.M. Al-Abbadi , M.A. El-Kady

When the probability distributions of both the applied (stress) and the withstand (strength) potentials are available, the probability that the applied potential exceeds the withstand potential of the body can be evaluated. This so-called "failure probability" together with the probability of a person being exposed to the applied potentials are multiplied to produce the overall step and touch risk. 3.2 Applied Step and Touch Potential Distributions The computational procedure for evaluating the probability distributions of applied (stress) step and touch potentials starts with the probabilistic evaluation of the electrical equipment potential rise using any conventional probabilistic fault analysis program. Practical probabilistic fault analysis programs often use a Monte Carlo simulation method to calculate the probability distributions of fault currents and voltages at the vicinity of the electrical installation under study and subject to random variations in system supply and equipment operating conditions as well as random variations in fault time, location and type [8]. The random fault conditions are biased, using statistical event data, to simulate the actual electrical installation and system supply history. The output of the probabilistic fault analysis program is the first step in the analysis which includes calculation of the probability distribution of the ground potential rise and subsequently the step and touch potential distributions. 3.3 Withstand Step and Touch Potential Distributions The probability distributions of applied step and touch potentials discussed in the previous sub-section provide statistical information concerning the levels of these potentials expected in the operation of the power network. Nevertheless, the ultimate goal in the present analysis is to evaluate the fatality probability associated with the excessive levels of such stress potentials. This requires the evaluation of the corresponding withstand step and touch potentials which represent the capability of the human body to resist stress voltages. The standard assumption of heart fibrillation being the cause of the fatal electrical accidents is accepted in this analysis. The withstand potential is, therefore, a function of various parameters affecting the initiation of heart fibrillation. These parameters include the current through the body, its path and duration, the skin condition, the internal body impedance, etc. In reality, all of these parameters are statistical and can be associated with probability distributions which eventually define a probability distribution of withstand potentials. A number of approaches have been developed in the literature to define the formulas and/or the probability distributions of the withstand step and touch potentials. The approach adopted in the present study is based on the previously stated equations (3) and (5) for withstand step potential Vws and touch potential Vwt. The variable Rg is the foot-to-ground resistance in Ω, which is proportional to the soil resistivity ρs in Ω.m. 389 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

Although the foregoing equations and assumptions have been adopted in conformance with the existing international standards, it is worth noting that some recent research and development efforts have indicated that some of these procedures and assumptions might have to be reassessed and modified. The total impedance of the human body includes the skin and internal impedances. It is a function of the current path, contact area, body weight and other physical conditions. For voltages above 200 V, however, the skin impedance and condition (temperature, moisture, etc.) and the contact area are less important than the internal body impedance. The value of 1000 Ω for the total body impedance suggested by some international standards could be high for accidents associated with voltages above a few hundred volts. However, the hand and shoe contact resistances are assumed negligible, indicating a conservative assumption regarding the resulting step and touch potentials. In the formulas (3) and (5), which define the withstand step and touch potentials, the parameters t, Rb and Rg are statistical parameters. For example, Rg can be determined by the probability distribution of the soil electrical resistivity and t can be determined by the fault clearing time distribution of the associated equipment protection device. When the probability distributions associated with these parameters are known, the probability distributions of the withstand step and touch potentials can be calculated which represent single-valued analytic and monotonic functions V ws = V step and V wt = V touch in terms of the three parameters. 3.4 Calculation of Failure Probability In the previous two sub-sections, the techniques for evaluating the probability distributions of both the applied (stress) and withstand (strength) step and touch potentials were discussed. As mentioned before, both distributions are needed to evaluate the failure probability, illustrated in Figure 3, which denotes the probability that the applied potential exceeds the withstand potential. Denoting by p a(V a) and p w (V w ) the probability density function of the applied and withstand potentials, respectively, the probability of the applied potential being between Va and Va-dV a , for an infinitesimal dVa , is p a (V a ).dV a . The probability of the withstand potential being less than V a is given by integrating the density function pw (V w) over the range from zero to V a . Since the applied and withstand functions are statistically independent, the probability of the applied potential being between V a and (Va-dV a) and the withstand potential being less than V a is simply the product of the above two probabilities.

390 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

N.M. Al-Abbadi , M.A. El-Kady

Fig. 3 Failure probability evaluation Therefore, for all possible values of the applied potential Va, the failure probability Pf is given by integrating this product over the range of Va, that is

Pf =

∞ Va ∫ p(Va) [ ∫ p(Vw) dVw] dVa 0

(7)

0

Note that the applied potential Va can be either an applied step potential Vas or an applied touch potential Vat. Similarly, the withstand potential Vw can be either a withstand step potential Vws or a withstand touch potential Vwt. The failure probability Pf of (7) should be calculated individually for the step and the touch potentials. In order to evaluate the integral (7) for non-standard probability distributions p(Va) and p(Vw) obtained by the probabilistic fault analysis and the withstand potential formulas, a complementary software package is often used, which contains sub-programs for analytical evaluation of Pf for arbitrary stress and strength distributions. A separate routine is also available for evaluating the failure probability of (7) using the Monte Carlo simulation method. 3.5 Overall Risk Evaluation In terms of the risk associated with exposure to step and touch potentials, the event that the applied (stress) potential exceeds the withstand potential denotes a fatal accident. In this respect, the failure probability Pf given by equation (7) represents the probability of a fatal accident due to a step (touch) potential given that a ground fault occurs in the equipment or installation vicinity, and given that a person is present at the time of fault. Therefore, in order to calculate the overall risk, one more quantity needs 391 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

to be evaluated, namely, the probability of presence at the time of fault (Pe). Formulas for calculating the probability of presence are normally based on the assumed time spent by the person in the dangerous zone. Knowing the failure probability and the probability of presence at the time of fault, the overall risk can be evaluated by simply multiplying the two probabilities. That is,

Rt = Pf * Pe

(8)

where Rt is the electrocution risk, which measures the probability of fatal accident per year, in the fault-assigned area, due to either step or touch potentials, which arise as a result of system ground faults in the area.

4. PRACTICAL APPLICATION This section describes briefly some of the results of a recent application to an industrial site in the Kingdom. In this application, the design features of an industrial distribution substation are studied in regard to electrocution risk to public and personnel. While hundreds of design scenarios were analyzed as part of this study, only two scenarios are presented here for illustration. It should be noted that the scenarios presented in this section are illustrative scenarios, which are considered for demonstration purposes only. The following program screen and Figure 4(a) show key data and output calculated results for the base-case safety grounding scenario under consideration. Figure 4(b) shows the output calculated results for the same previous base-case scenario, but with incorporating artificial means to lower soil resistivity in the industrial plant. It is noted that the grounding design in this case is safe in regard to both step and touch potentials.

392 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

N.M. Al-Abbadi , M.A. El-Kady

ELECTROCUTION HAZARDS RISK ASSESSMENT OF G-SCHEME {Summary Report} Study: Industrial Substation Electrocution Risk Study {Test Case} ------------------------------------------------------------------------- {M-3σ}-VALUE {M+3σ}VALUE {MEAN}-VALUE -----------------------------------------------------------Grid Ground Resistance {ohm} 6.7 11.1 8.9 Total Body Resistance {ohm} 398.1 1486.9 942.5 Exposure Time ........ {sec} 0.031 0.073 0.052 Applied Step Voltage ... 1676.6 938.9 Withstand Step Voltage . 1416.8 1189.1

{V}

201.2

{V}

961.4

Applied Touch Voltage .. {V} 167.7 1508.9 838.3 Withstand Touch Voltage {V} 722.6 1091.0 906.8 .......................................................... ................. Probability of Step-V Electrocution = 0.330 Probability of Touch-V Electrocution = 0.449 Expected Number of Fatalities per 1000000 PersonExposures = 389.444

393 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

T.Design Costs...{MSR} = 0.16

Tot. Death /1000 Pe.Ex =

{Grid: Nx = 10 , Ny = 5}

{Grid: Dx =2.0 , Dy =1.0}

Under-Grid Soil{ohm.m} = 200.0

Under-Grid S.Depth {m} =

Above-Grid Soil{ohm.m} = 200.0

Above-Grid S.Depth {m} =

#Ft=449

T.Design Costs...{MSR} = 0.16

Tot. Death /1000 Pe.Ex =

{Grid: Nx = 10 , Ny = 5}

{Grid: Dx =2.0 , Dy =1.0}

0.5

Under-Grid Soil{ohm.m} = 200.0

Under-Grid S.Depth {m} =

0.5

0.5

Above-Grid Soil{ohm.m} = 200.0

Above-Grid S.Depth {m} =

0.5

390

#Fs=330

#Ft=0

{erzs}: GRAPHICAL ASSESSMENT OF ELECTORCUTION RISK

(a) Results for base-case scenario scenario

0

#Fs=0

{erzs}: GRAPHICAL ASSESSMENT OF ELECTORCUTION RISK

(b)

Results

for

low

resistivity

Fig. 4 Illustrative application results

6. CONCLUSIONS The risk associated with grounding hazards near high voltage power equipment and electrical installations was the main focus of the present paper. An efficient and effective procedure for calculating the overall risk associated with hazardous step and touch potentials at the electrical installation of interest was described in the paper. The procedure comprises the evaluation of the probability distributions of both the applied and the withstand potentials as well as the probability of exposure to these potentials. The accuracy of the final result is determined by the accuracy of the model and availability of the historical operation records for fault occurrence and exposures to step and touch potentials. The overall accuracy can be improved by calculating the risk for individual structures or groups of structures having specific withstand and exposure characteristics rather than by employing average parameter values for the whole installation. The results of the application presented show the significant impact of lowering the soil resistivity around the installation on the calculated electrocution risk. It is important to note that the material presented in this paper has not been intended to discuss acceptable levels of risk. It rather describes a complete computational procedure to evaluate the risk for a region around an electrical installation where random faults and random exposure to step and touch potentials occur. The selection of acceptable risk levels depends on comparable risks, cost benefit factors, and other considerations beyond the 394 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

N.M. Al-Abbadi , M.A. El-Kady

scope of this paper. The advanced simulation software used in the work of this paper offers several powerful capabilities, where the failure probabilities for both step and the touch potentials are evaluated using highly accurate convolution procedures within the Monte Carlo simulation method.

REFERENCES [1]

Bridges, J.E., 1981, "An investigation on low-impedance low-voltage shocks", IEEE Transaction on Power Apparatus and Systems, Vol. PAS100, pp. 1529-1537.

[2] El-Kady, M.A., Hotte, P.W. and Vainberg, M.Y., 1983, "Probabilistic assessment of step and touch potentials near transmission line structures", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, pp. 640-645. [3]

Bielgelmeier, G. and Lee, W.R., 1980, "New considerations on the threshold of ventricular fibrillation for ac shocks at 50-60 Hz", Proceeding of IEE, Vol. 127, pp. 103-110.

[4]

Bielgelmeier, G. and Mirsch, J., 1980, "Effect of the skin on the body impedance of humans", Electrotechnik and Maschinenbau, Vol. 97, No. 9, pp. 369-378.

[5]

Franklin, J.B., Parker, D. and Cosby, L., 1999, “Testing electrical power systems for safety and reliability”, Proceeding of the IEEE Annual Textile, Fiber and Film Industry Technical Conference, p. 7.

[6]

Dalziel, C.F. and Lee, W.R., 1968, "Re-evaluation of lethal electric currents", IEEE Transactions on Industry Applications, Vol. IA-4, pp. 467476.

[7]

Faulkenberry, L.M. and Coffer, W., 1996, Electrical Power Distribution and Transmission, Prentice-Hall, UK.

[8]

El-Kady, M.A. and Ford, G.L., 1983, "An advanced probabilistic short-circuit program", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, pp. 1240-1248.

395 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ADVANCED ASSESSMENT OF PUBLIC AND WORKER'S SAFETY AT INDUSTRIAL INSTALLATIONS IN KSA

396 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ON RELIABILITY-COST CHARACTERIZATION OF A PARTIALLY REDUNDANT SYSTEM Ali Muhammad Rushdi and Abdulaziz Efaien Alsolami King Abdulaziz University, Department of Electrical and Computer Engineering, Faculty of Engineering, P.O. Box 80204, Jeddah 21589, Saudi Arabia [email protected], [email protected]

ABSTRACT Simple reliability-cost metrics (such as reliability per cost or life expectancy per cost) can be used to guide the selection of a system from among several systems that are candidates for providing the same performance in a given mission. Other more elaborate metrics (such as the cost elasticity of reliability ∈R,C or cost elasticity of life expectancy ∈T,C ) can be used to assess the cost-benefit aspect of adding redundancy to a system with the purpose of enhancing its reliability. We study the ∈R,C and ∈T,C metrics analytically and numerically for the partially redundant or k-out-of-n:G(F) system (or k-out-of-n system, for short). We believe the ∈T,C metric is a more tangible and a more cumulative measure than the ∈R,C metric. The expression of ∈R,C is dependent on component reliability or failure rate, and is highly susceptible to round-off errors to the extent that catastrophic cancellations take place. By contrast, our expression for ∈T,C is independent of component characteristics and is really insensitive to round-off errors since it is a purely additive formula. We provide charts for ∈T,C that a reliability engineer can use to assess the cost incurred in achieving a certain life expectancy for a partially redundant system. These charts are also applicable to any coherent system, since the life expectancy for a coherent system can be approximated by that of a partially redundant system. KEY WORDS Cost, Reliability, Life expectancy (Mean time to failure), Partially redundant or k-out-of-n:G(F) system.

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

ON RELIABILITY-COST CHARACTERIZATION OF A PARTIALLY REDUNDANT SYSTEM

I. INTRODUCTION The reliability R(t) of a system is the probability that the system will adequately perform its specified purpose for a specified period of time (0, t] under specified environmental conditions [1]. Suppose that a certain engineering job or function can be equally done or performed over the time period (0, t] by several candidate systems. If system i has reliability Ri(t) and cost Ci, then classical reliability-cost considerations makes it imperative to choose the system that has the maximum reliability per cost, i.e., the one that satisfies

maximum

R i (t)/C i .

i

(1)

If the time span for operating the system is not known in advance, then a more prudent choice can be based not on the reliability of the system but rather on its life expectancy or Mean Time To Failure (MTTF) Ti. Hence, the preferred candidate system is the one having the maximum life expectancy per cost, i.e., the one satisfying

maximum i

Ti /Ci .

(2)

Beside the simple metrics in (1) and (2), which guide the selection of a system from among several candidate systems of equivalent performance, there are more elaborate metrics that can be used to assess the cost-benefit aspect of adding redundancy to a system with the purpose of enhancing its reliability. Notable among these are two metrics: (a) the cost elasticity of reliability

∈R,C

[2, 3], and (b) the cost elasticity of life expectancy or MTTF





[3]. We study the R,C and T,C metrics analytically and numerically for the partially redundant or k-out-of-n:G(F) system (or k-out-of-n system, for short), which is a system of n components that functions (fails) if at least k out of its n components function (fail). Situations in which this system serves as a useful model are frequently encountered in practice [4]. The k-out-of-n system plays a central role for the general class of coherent systems, as it can be used to approximate the reliability of such systems [5]. While virtually all nontrivial network reliability problems are known to be NP-hard for general networks [6], the regular structure of the k-out-of-n system allows the existence of efficient algorithms for its reliability analysis that are of quadratic-time linearspace complexity in the worst case [4, 7-10]. The k-out-of-n:G system covers many interesting systems as special cases. These include the perfectly reliable system (k=0), the parallel system (k=1), the voting or N-modular redundancy (NMR) system( k

= ⎡(n + 1) / 2⎤ ), the fail-safe system (k=n-1), the series

398 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

Ali Muhammad Rushdi and Abdulaziz Efaien Alsolami

system (k=n), and the totally unreliable system (k=n+1). We use the terms kout-of-n system and partially redundant system as synonymous, though some authors [11, 12] restrict their equivalence to the case 1 ((n + 1) / k ) R 0 , i.e., unless R0 < k /(n + 1) . Figures 2 and 3 present a cost-reliability characterization ( ∈R,C versus n) for a 20-out-of-n:G system with component reliabilities R0 = 0.8 and R0 = 0.99, respectively. Formula (15) for the cost elasticity of reliability ∈R,C gives satisfactory results up to R0 = 0.8 (Fig. 2) and then starts to exhibit some unacceptable negative values (values of -0 rather than +0), i.e. it exhibits erratic behavior for very small or negligible values of ∈R,C (Fig. 3). We must stress that the erratic behavior obtained is solely due to aggravated cumulative round-off error and is definitely not a result of some error in formulation or programming. Formula (15) gives acceptable and verifiable results for a wide range of values of k, n, and R0. However, it fails to assess ∈R,C properly for systems having good components (i.e., for systems of practical interest). Anyhow, for such systems ∈R,C diminishes and becomes indistinguishable from zero.

Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

403

ON RELIABILITY-COST CHARACTERIZATION OF A PARTIALLY REDUNDANT SYSTEM

Fig. 2. Cost-reliability characterization of a 20-out-of-n:G system with component reliabilities R0 = 0.8 .

Fig. 3. Cost-reliability characterization of a 20-out-of-n:G system with component reliabilities R0 = 0.99 .

IV. COST ELASTICITY OF LIFE EXPECTANCY From cost considerations, life expectancy seems to be a more tangible and cumulative measure than reliability itself. Therefore, we introduced in an earlier paper [3] the concept of the cost elasticity of life expectancy or MTTF, which we defined as

∈T,C =

(∆T / T ) (∆T / T ) = , (∆C / C ) (∆n / n)

(16)

For a k-out-of-n:G system, if we let the number of components n change to (n + ∆n) in (8), then the Life Expectancy changes to (T+ ∆T) given by

T + ∆T =

1

λ

n + ∆n



m=k

1 . m

404 Proceedings of the 7th Saudi Engineering Conference, KSU, Riyadh, 2007

(17)

Ali Muhammad Rushdi and Abdulaziz Efaien Alsolami

From (8) and (17), we can express the change ∆T in T due to a unit change ∆n = 1 in the number of components as

( ∆ T ) ∆ n =1 =

1

1 , λ n +1

(18)

and hence, we can express ∈T,C as

n 1 1 n n n +1 . ∈T,C = λ n n+ 1 = nn + 1 = 1 1 1 1 1 1 1 + + .... + + ∑ ∑ k k +1 n −1 n λ m=k m m=k m

(19)

The cost elasticity ∈T,C of the life expectancy of a k-out-of-n:G system is a function of n and k only and is independent of the component reliability R0 and the component failure rate λ. Noting that the sum S = n 1 satisfies the following inequalities for k >1

∑m

m=k

n +1

S>

∫ k

dx ⎛ n + 1⎞ = ln ⎜ ⎟, x ⎝ k ⎠ n +1

S

Suggest Documents