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• Miltos Boboulos

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• Motor de combustión interna
• Motor diésel
• Avería eléctrica
• Combustión
• Gasolina

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Abstract This publication aims at covering subjects related to mechanisms and machines in general, such as design theory and methodology, kinematics of mechanisms, computational kinematics, multibody dynamics, dynamics of machinery, gearing and transmissions, and transportation machinery. Internal combustion engines have been analyzed in Chapter 1 while modern nondismountable steel shell spark plugs are examined in the second chapter. Progressive technological methods implemented in production, high mechanization and automation were examined in the third chapter., Gear mechanisms used as summing (subtraction) mechanisms, mechanisms for co-ordination of two movements, mechanisms for compensating for the difference in angular speeds of independent movements, have been described in detail in the fourth Chapter. Suitable pressure vessel designs for minimum masses of transporting and storing compressed air were examined in the last chapter. The vessels were to carry an internal pressure, contain an internal volume and be made from material for ease of storage and transportation. Discussion of relevant decisions and applicability selection has been based on the design of thin shells depending primarily on the magnitude of the general system of membrane stresses. Attention has been also given to the effect of local bending stresses at regions of discontinuity in the shell. Chapter 6 analyzes handling mechanisms and namely, manual winches. Most of them are designed for industrial applications to handle heavy loads. Finally in the seventh chapter a bench drilling machine is designed and developed, intended to fill the market niche providing construction and functionality. By drilling small diameter holes in semi-finished products and materials is constantly the bench drill is required in large and small-scale industrial production, maintenance and repair activities, in subcontractor workshops, and at home. The size range of these holes makes the use of large size drill presses inefficient.

TABLE OF CONTENTS

CHAPTER 1: Internal Combustion Systems ___________________________ 1 1.1

Car Engines ____________________________________________________ 1

1.2. Carburetor type engine fuel _______________________________________ 4 1.3. Diesel engines fuels _____________________________________________ 5 References__________________________________________________________ 6

CHAPTER 2: Spark Plug Material Selection & Manufacturing ____________ 8 2.1

Electric spark ignition of combustion mixture ________________________ 8 2.1.1 Spark plug breakdown voltage__________________________________ 8 2.1.2 Moment of applying the spark __________________________________ 9 2.1.3 Spark plug arrangement______________________________________ 10 2.1.4 Electrodes ________________________________________________ 12 2.1.5 Insulator __________________________________________________ 12 2.1.6 Shell _____________________________________________________ 13 2.1.7 Shield ____________________________________________________ 13

2.2

Spark Plug Thermal Characteristics _______________________________ 13

2.3

Manufacture ___________________________________________________ 14 2.3.1 Body shell manufacture ______________________________________ 14 2.3.2 Selecting materials and manufacturing spark plug insulator __________ 15 References_________________________________________________________ 16

CHAPTER 3: High Energy Rate (Her) Forming ________________________ 18 3.1

Explosives and physical nature of explosions _______________________ 19

3.2

Characteristics & Technological Features Of Hydro-Explosive Deformation___________________________________________________ 21

References_________________________________________________________ 24

CHAPTER 4: Gear Drive Assembly _________________________________ 25 4.1 Explanatory ___________________________________________________ 25 4.2 Operation principle _____________________________________________ 25 4.3 Design calculations _____________________________________________ 26 4.4 Description of the Mechanism ____________________________________ 29 4.5 Mechanism specification& design _________________________________ 30 References_________________________________________________________ 45

CHAPTER 5: Local Bending Stresses in Axi-Symmetrical Thin Shells for Storing Pressure Vessels ______________________________________ 47 5.1

Introduction ___________________________________________________ 47

5.2

Aluminium Small Capacity, Highly Pressurized Shell _________________ 47 5.2.1. Material selection ___________________________________________ 47 5.2.2. Thin-wall cylinder theory: Strength calculations & dimensioning _______ 48 5.2.3. Safety factor selection and allowable stress determination. __________ 49 5.2.4. Stressed state and strength requirements ________________________ 49 5.2.5. Dimensioning ______________________________________________ 50 5.2.6. Strength and deformation calculations using the Finite Element Method (FEM) _____________________________________________ 52

5.3

HSS Large Capacity, Low Pressure Loading Tank ____________________ 56

5.4

Discussion ____________________________________________________ 63 5.4.1. Aluminium small capacity, highly pressurized shell: finite element calculation results___________________________________________ 63 5.4.2. HSS large capacity, low pressure loading tank: finite element calculation results___________________________________________ 67

5.5. Selecting Acid-Resistant Materials ________________________________ 70 5.5.1 Introduction _______________________________________________ 70 5.5.2 Anodic passivation __________________________________________ 71 5.5.3 Mechanics of anodic passivation _______________________________ 71 5.5.4 Experimental studies – anodic protection of mild steel in sulphuric acid solution _______________________________________________ 72 5.5.5 Selecting materials for the tank ________________________________ 74 5.5.6 Factors influencing the efficiency of the tank and its usage___________ 76 5.5.7 Using the tank for storage of 10% hydrochloric acid.________________ 77 5.6 Additional Tank Protection Techniques ____________________________ 77 5.7. Selecting the Metal Material for Making Another Storage Tank for 10% Sulphuric Acid_________________________________________________ 79 5.7.1 For a cost limit of 3 Pounds per kilogram _________________________ 79 5.7.2 For a cost limit of 1 Pound per kilogram__________________________ 80 5.7.3 Selecting the steel for designing the storage tank __________________ 81 5.7.4 Anodic protection ___________________________________________ 82 5.7.5 Cathode protection__________________________________________ 82 5.7.6 Protection by using additives (inhibitors) _________________________ 83 5.7.7 Factors affecting tank efficiency and usage _______________________ 83 5.7.8 Using the tank for the storage of 10% hydrochloric acid _____________ 84 References ________________________________________________________ 84

CHAPTER 6: A Manual Winch Design _______________________________ 86 6.1

Introduction ___________________________________________________ 86

6.2

Design Requirements ___________________________________________ 86

6.3

Conceptualisation & Design Creativity _____________________________ 87

6.4

The Design Concept ____________________________________________ 88

6.5

Development Stages____________________________________________ 89

6.6

Market Research _______________________________________________ 90

6.7

Initial Parameters Determination__________________________________ 90

6.8

Mechanical Diagram Selection ___________________________________ 91

6.9

Calculations & Assemblies & Components Selection_________________ 91

6.10 Marketing criteria. End-user & market requirements. _________________ 96 6.11 Product Functionality, End Use & Performance Specification__________ 98 References________________________________________________________ 105

CHAPTER 7: A Bench Drilling Machine _____________________________ 106 7.1

Introduction __________________________________________________ 106

7.2

Available Product Types ________________________________________ 106

7.3

Design Development Of The Bench Drilling Machine ________________ 110

7.4

Determining the Rotation Speed & Power of The Electrical Motor ______ 111

7.5

Kinematical Calculations for the Belt Drive ________________________ 112

7.6

Bearings Calculations __________________________________________ 115

7.7

Calculating the Feed Gear Drive__________________________________ 116

7.8

Design Conceptualisation of THE Work Table Moving Mechanism _____ 117

7.9

Support Base of the Bench-Drilling Machine (Figure 16)______________ 118

7.10 Ergonomic & Aesthetic Appearance Machine Conceptualisation ______ 118 7.11 Operation of the Machine _______________________________________ 119 7.12 Conclusions __________________________________________________ 120 References________________________________________________________ 136

CHAPTER 1 Internal Combustion Systems

1.1

Car Engines

Modern car industry uses mainly internal combustion engines. The reason for calling them this is fuel combustion taking place in the engine cylinder. The car industry meets the 21st century with a wide variety of design solutions for the internal combustion engines. This diversification could be classified on the basis of some basic principles listed underneath: Based on the type of fuel used engines could be [1]: •

petrol type

•

diesel fuel type (Fig.1)

•

liquid gas type engines;

•

There are some internal combustion engines using other types of fuel but they are not found so often. These are some special purpose cars (like sports cars, for example) that are uniquely manufactured.

Based on operation principle [2]: • Four-stroke engines. The characteristic feature for them is that their operation cycle involves four strokes (Fig.2). First stroke (admission) – the air-fuel mixture enters the cylinder. Second stroke (compression) – the piston compresses the air-fuel mixture through its motion. Third stroke (combustion) – the air-fuel mixture ignites and combusts thus moving the piston and this is the only stroke in the cycle performing work. Fourth stroke (release) - the exhaust gas is released [2].

Fig.1

• Two-stroke engines (Fig.3) [3]. First stroke – admission of fresh gas into the cylinder from carburetor and simultaneous compression of the gas mixture in the area above the piston. Second stroke - precompression of fresh gas in the crankcase and combustion of gas mixture in the cylinder. Exhaust gases are released and fresh gas enters the combustion section from the crankcase through overflow ducts [3].

1

Fig. 2 The two-stroke type of engine with its gasdistribution mechanism is cheaper to produce and easier to maintain compared to the four-stroke type. Engine lubrication is very simplified and still reliable as oil is mixed with the fuel. This saves power and additional fuel consumption needed to drive supplementary systems – lubrication and gas-distribution mechanisms. Besides, the two-stroke type features more uniform torque as a combustion stroke is performed for each turn of the crankshaft [3]. The disadvantages of the two-stroke type of engine are the inevitable losses of scavenging leading to power reduction and higher fuel consumption. Incomplete Fig. 3 combustion results in higher harmful emissions in exhaust gases. This type of engines have higher average temperature in the cylinder due to the higher number of combustion strokes. The two-stroke type of engine is incapable of providing efficiencies similar to those of the four-stroke one as the latter has time available for one complete piston stroke during cylinder charging and discharging, which helps achieve better completeness of the two processes [3]. Based on the number of cylinders used the engines are 1, 2, 3, 4, 6, 8 and 12-cylinder type. Based on cylinders:

the

location

of

the

• In-line engines – cylinders are vertically positioned in a line (Fig. 4,I); • Box engines – cylinders are horizontally positioned one against the other (Fig. 4,II); • V-type engines – cylinders are positioned at an angle and

Fig. 4

2

mounted on a common crankshaft (Fig. 4, III). Based on the piston movement in the cylinder engines are [4]: • Reciprocating piston engines (Fig. 5); • Rotary piston engines – Vankel engines (Fig. 6);

Fig. 5

Fig. 6

The following classification could be made from thermodynamics point of view: • Constant volume internal combustion engine v = const. This is known in practice as a carburetor type of engine (or Otto’s engine) [5]. Combustion is instantaneous and has explosive nature when v = const.; • Constant pressure p = const. internal combustion engine. This is the engine of R.Diesel. Combustion is performed under relatively constant pressure and a portion of fuel is constantly admitted until the end of this stroke under high pressure [6]; • Constant volume and constant pressure internal combustion engine (v = const. and p = const.). Efficiency is the parameter featuring the effectiveness of engine energy transformation. When considering internal combustion engines as heat machines, the thermal efficiency best characterizes the differences between various engine types from thermodynamics point of view. The thermal efficiency (ηt) of an internal combustion engine at v = const. (carburetor type engine) is as follows [6]: 1 ηt = 1 − κ − 1 , where ε ε - is the extent of compression, cp κ = is adiabatic parameter, cv cp = volume specific heat capacity at p = const, cv = volume specific heat capacity at v = const. It could be seen from the above formula that efficiency increases with the increase of the extent of combustion. The thermal efficiency (ηt) of an internal combustion engine at p = const. (diesel type of engine) is as follows: 3

ηt = 1 − ρ - is the degree of pre-expansion.

ρκ − 1

κε κ − 1(ρ − 1)

, where:

When we analyse this formula we could see that efficiency increases when the extent of compression increases or when the degree of pre-expansion decreases. So far, we have only considered thermal efficiency but we should point out that the overall efficiency of an internal combustion engine is the product of its thermal efficiency and mechanical efficiency (considering friction losses) [6]:

η = ηt . ηmech . The following advantages of the diesel type of engines could be pointed out when comparing them to the carburetor type [7]: -

Lower fuel consumption determined by the higher degree of compression;

-

Diesel engines have higher efficiency;

-

Diesel fuel is cheaper than petrol;

-

The risk of fire is lower due to the higher ignition temperature of the diesel fuel;

-

Exhaust gases of diesel engines are less toxic compared to those of carburetor engines;

and the following disadvantages: -

Diesel engines are heavier than carburetor ones. Their components are larger due to the high forces involved;

-

The cost of production and repair of diesel engines is higher due to the complicated and precise combustion mechanism;

-

Diesel engines are noisier.

To give a better idea of the advantages and disadvantages of both types of engines I would like to consider the types of fuel they use.

1.2. Carburetor type engine fuel In order for a certain fuel to be suitable for carburetor engines it is necessary that it has such steam pressure (good evaporation characteristics, low boiling temperature) that it completely evaporates in the volume of air provided for combustion even at the lowest operation environment temperature. The basic part of fuels suitable for carburetor type of engines is produced from petroleum by means of direct distillation of respective light fractions or by cracking heavier and less deficient fractions. The formation of double bonds in the cracking process follows a certain regularity, which depends on the depth of hydrocarbon braking. Along with this, some reactions take place, which transform unsaturated hydrocarbons into other more stable cyclic compounds [7]. CH2 CH2 CH3

CH2

CH2

CH2

CH = CH2

CH2 CH2 CH2

-3H2

CH CH CH CH CH

4

Thus, some valuable for petrol composition compounds are produced – naphthenic and aromatic hydrocarbons. The liquid products from the cracking process are subjected to fraction distillation to extract petrol. The residue containing heavier hydrocarbons, resins, etc, compounds is usually burned out or added to heavy diesel fuel. The petrol fractions practically contain no resins and the acid and sulphur content in them is relatively low. Catalytic cracking and reforming processes could produce even purer petrol fractions [8].

1.3. Diesel engines fuels The diesel fuel is ignited in the chamber by the air heated in the compression so of major importance here is its lowest ignition temperature (self-ignition temperature). Low-boiling point fuels like petrol and kerosene are not suitable for this purpose. Gas oil fractions proved to be the most suitable fuel for diesel engines [8]. Actually, diesel engines have been developed working on heavier petroleum fractions – even with tail fractions. From all fuel properties surface resistance and especially viscosity are the most important for the degree of dispersion. The speed of combustion in diesel engines and from this, the degree of combustion could be increased by means of additives. Known as positive catalysts are naphthenates of some metals – barium, copper (Cu). It should be noted here that the presence of water and hard impurities in diesel fuel results in more intensive wear in the combustion system [8]. Considering all said above we should mention some ecological aspects of petrol and diesel fuel usage. The share of contamination caused by car engines where fuel combustion is incomplete in the global ecological problem is fairly large. Various toxic substances are concentrated in the exhaust gases of internal combustion engines and these could be classified into the following sequence depending on the degree of their harmful effect on human health [9]: Carbon oxide (CO), hydrocarbons, nitrogen oxides, cancerous substances, soot, lead compounds and sulphur dioxide (SO2). While petrol engines produce highly poisonous carbon oxide, diesel engines are significantly better as they operate on excessive air and burn our fuel in a more perfect way. Carbon oxide could cause lasting damages even when in insignificant quantities (0.5% by volume) and in larger concentrations could even cause death. Soot is mainly produced from diesel engines with malfunctioning spraying systems [9]. Sulphur compounds are also produced as a result of diesel fuel combustion. Lead compounds are released in environment with the exhaust gases of some carburetor type fuels the octane number of which has been increased using ethylization with lead tetraethyl [9]. The operational performance of the engine significantly affects the toxic content of the exhaust gases. Design imperfections result in incomplete combustion and hence, increased harmful emissions. It is impossible to counteract to all harmful substances in exhaust gases to an adequate degree but still, a number of efficient methods have been developed to significantly reduce mainly carbon oxide and hydrocarbon additions content in air [9]. In pursuit of eliminating harmful emissions in exhaust gases resulted in the wide usage of unleaded petrol and catalysts. The four-stroke engines taking over the two-stroke ones also resulted in improved environmental parameters. The car industry nowadays is paying more attention to ecological aspects both in the production process and the products themselves. Their constructions, technologies and 5

selected materials are making better use of the principles of modern design considering ecological requirements, recycling possibilities, etc. The basic parameters of internal combustion engines are engine stroke (displacement) capacity, degree of compression, engine power and the type of fuel used [10]. An important feature of an engine is its so-called stroke (displacement) capacity [11]. This is equal to the product of the piston area, its stroke and the number of cylinders. The degree of compression is another parameter that characterizes the engine. This is determined by dividing the overall cylinder volume by the volume of combustion chamber [12]. Engine power is the work the engine performs per unit time. Car design engineers have always tried to get the highest possible efficiency from an engine [12]. This determines the variety of technical and technological solutions being searched for in the following basic areas [13]:

• Increasing the degree of compression – this is the most often used parameter to influence engine efficiency; • Reducing the degree of pre-expansion – used to influence efficiency of diesel engines; • Improvement of intake during the admission stroke – this is influenced using the following factors: -

low cylinder temperature;

-

good cooling;

-

low mixture temperature ensuring intake of larger quantities (mass) of it;

-

low rarification (vacuum) in the intake stroke (absence of throttling);

-

low residual exhaust gases pressure [14].

• Special design of the combustion chamber – a wide variety of shape exists; • M-process by MAN - in diesel engines engineers are considering not the classical uniform fuel distribution (which along with heat and pressure is a reason for transforming part of the fuel into soot), but spraying that forms a thin layer along the spherical combustion chamber in the piston [14].

References 1. C.D. Rakopoulos, E.G. Giakoumis, Second-law analyses applied to internal combustion engines operation. Progress in Energy and Combustion Science, Volume 32, Issue 1, 2006, Pages 2-47. 2. Sebastian Verhelst, Thomas Wallner, Hydrogen-fueled internal combustion engines. Progress in Energy and Combustion Science, Volume 35, Issue 6, December 2009, Pages 490-527. 3. O.K. Kwon, H.S. Kong, C.H. Kim, P.K. Oh, Condition monitoring techniques for an internal combustion engine. Tribology International, Volume 20, Issue 3, June 1987, 6

Pages 153-159. 4. G. De Nicolao, C. Rossi, R. Scattolini, M. Suffritti, Identification and idle speed control of internal combustion engines. Control Engineering Practice, Volume 7, Issue 9, September 1999, Pages 1061-1069. 5. F. Payri, J.M. Luján, J. Martín, A. Abbad, Digital signal processing of in-cylinder pressure for combustion diagnosis of internal combustion engines. Mechanical Systems and Signal Processing, Volume 24, Issue 6, August 2010, Pages 1767-1784. 6. A.K. Sen, G. Litak, C.E.A. Finney, C.S. Daw, R.M. Wagner, Analysis of heat release dynamics in an internal combustion engine using multifractals and wavelets. Applied Energy, Volume 87, Issue 5, May 2010, Pages 1736-1743. 7. Zhichao Tan, Rolf D. Reitz, An ignition and combustion model based on the level-set method for spark ignition engine multidimensional modelling. Combustion and Flame, Volume 145, Issues 1-2, April 2006, Pages 1-15. 8. J. I. Ramos, Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines. Applied Mathematical Modelling, Volume 10, Issue 6, December 1986, Pages 409-422. 9. Alex M.K.P. Taylor, Science review of internal combustion engines. Energy Policy, Volume 36, Issue 12, December 2008, Pages 4657-4667. 10. V. S. S. Chan, J. T. Turner, Velocity measurement inside a motored internal combustion engine using three-component laser Doppler anemometry. Optics & Laser Technology, Volume 32, Issues 7-8, October 2000, Pages 557-566. 11. F. Payri, J. Benajes, F. V. Tinaut, A phenomenological combustion model for directinjection, compression-ignition engines. Applied Mathematical Modelling, Volume 12, Issue 3, June 1988, Pages 293-304. 12. Zissimos P. Mourelatos, A crankshaft system model for structural dynamic analysis of internal combustion engines. Computers & Structures, Volume 79, Issues 20-21, August 2001, Pages 2009-2027. 13. S. Richard, O. Colin, O. Vermorel, A. Benkenida, C. Angelberger, D. Veynante, Towards large eddy simulation of combustion in spark ignition engines. Proceedings of the Combustion Institute, Volume 31, Issue 2, January 2007, Pages 3059-3066. 14. Ugur Kesgin, Study on the design of inlet and exhaust system of a stationary internal combustion engine. Energy Conversion and Management, Volume 46, Issues 13-14, August 2005, Pages 2258-2287.

7

CHAPTER 2 Spark Plug Material Selection & Manufacturing

2.1

Electric spark ignition of combustion mixture

2.1.1 Spark plug breakdown voltage An electrical spark past the spark plug electrodes ignites the combustion mixture in the cylinders of carburettor and gas engines and petrol-injection engines. When voltage is applied to the plug electrodes a negative ion and electron flow directed towards the negative electrode is being created in the gas and combustion vapours area between the electrodes. The so-called “glow discharge” occurs between the electrodes of the spark plug [1]. When the applied voltage is increased this increases the speed of moving ions and electrons. Under certain voltage the speed of ions and electrons and their kinetic energy reaches such high values that when they hit neutral molecules they break them [1]. The result is collision ionization. Collision ionization builds up as an avalanche and a breakdown of the gas gap occurs – the spark plug electrodes are connected by a continuous ion and electron flow. The result is the occurrence of so-called spark discharge between plug electrodes. Heat is emitted when ions and electrons hit neutral molecules. The gaseous shell of the ion and electron flow heats up and expands abruptly thus causing light and sound effects [1]. The voltage causing a sparkle to pass between the plug electrodes is called breakdown voltage. The breakdown voltage depends on the spark gap, the temperature and pressure of the combustion mixture in the cylinder, on the shape, polarity, material and temperature of electrodes and also on engine characteristics and operation conditions [2]. There is an almost linear relation between breakdown voltage and spark gap. The influence of electrode polarity over breakdown voltage is as high as is the difference in shape between electrodes and their temperature. The breakdown voltage could be 10 to 15% higher for a positive polarity of the central electrode than for a negative polarity [2]. To reduce breakdown voltage the spark plug electrodes should be made sharp but they easily burn at such shape. So the most suitable shape for electrodes is the cylindrical shape with flat ends, as these would burn significantly less [2]. -

When the temperature of the central electrode of a spark plug is increased the breakdown voltage decreases.

-

When the temperature of the gas between plugs electrodes is increased the ionisation increases and the breakdown voltage decreases.

-

The pressure in the cylinder has the opposite effect. When pressure is increased the gas density is also increased and breakdown voltage increases.

When the engine is initially started the walls of the cylinder and spark plugs are cold. The combustion mixture has low temperature, too. So the breakdown voltage would be higher when the engine is initially started.

8

As engine speed increases the breakdown voltage is reduced as the mixture temperature and the temperature of the central plug electrode increase with the increase of rotation frequency. The wider the throttle valve is opened the larger the quantity of fresh combustion mixture is and the higher the pressure at compression end would be. The breakdown voltage is higher [3]. But as the quantity of fresh combustion mixture increases the pressure increases, too as is the temperature of the mixture and of spark plug electrodes. The influence of temperature in some engines is so significant that breakdown voltage for some speed conditions is higher for a fully open throttle valve than it is for a partially open throttle valve [3]. The breakdown voltage increases when the mixture is being concatenated or enriched. Engines work efficiently with lean mixtures. Lean mixtures are harder to ignite. To ensure their ignition the spark gap of the spark plug should be increased from 0.6 - 0.7 mm to 0.8 – 0.9 mm. This additionally increases the breakdown voltage [4]. The lowest necessary voltage that should be applied by the ignition system to spark plug electrodes is equal to the highest breakdown voltage. Table 1 shows the voltage for which the strikes of the ignition system should be calculated for a spark gap of 1mm [4]. Engine parameters Degree of compression

7 - 7,5 8 – 8,5

Max. rotation frequency

4000- 4500 5000

Breakdown voltage In operation mode n = 1000 – 1500

12000 – 14000 13000 – 15000

In start mode n = 150 – 200

16000 – 18000 18000 – 20000

With a spark gap of the spark plug of 0.6 – 0.7mm and a moderate degree of compression the minimum voltage necessary would be 11000 - 12000 V. With normally operating warmed up engines the mixture temperature at the moment of applying the spark would be close to the self-ignition temperature. This is why only a negligible amount of electrical spark energy (1 – 5 MJ) would be sufficient to ignite the mixture. The ignition system of modern engines provides sparks of significantly higher energy (15- 50) mJ [4].

2.1.2 Moment of applying the spark The combustion mixture in engine cylinders does not burn immediately but takes some time (several milliseconds). An engine would have the highest power and saving when the mixture burns out at the smallest possible volume, i.e. when the piston is close to the top dead centre This is achieved by igniting the combustion mixture earlier, before the piston moves to the top dead centre the burning out of the mixture starts before the top dead centre and ends after the top dead centre, i.e. this is performed at the smallest possible volume and lowest possible heat loss, respectively [4]. The moment of ignition is determined by the angle between the position of the engine crankshaft at the moment of applying the spark between the spark plug electrodes and the position of the same crankshaft when the piston is in the top dead centre. This angle is called angle of advance ignition. Depending on the design, fuel and combustion mixture quality and operating conditions each individual engine has an optimum angle of advance of ignition when the engine is capable of providing the highest power. 9

When the ignition is too short the mixture burns out mainly during the expansion and could sometimes continue even during the release cycle. Due to the fact that the mixture burns in a larger volume, i.e. with a larger available cooling surface, heat losses are significant. The engine is less powerful and overheats [5]. When the ignition is too early the mixture burns out mainly before the top dead centre the pressure in the cylinder reaches its maximum before the piston is in its top dead centre– thus the piston is subjected to strong counter impacts and large negative work is performed. The engine overheats and is less powerful. External signs for too early ignition are the characteristic metal knocking due to the counter impacts and engine overheating. The optimum advance angle of ignition depends on a number of factors [5]: A. Rotation frequency of the engine. As rotation frequency of the engine increases the turbulence of the combustion mixture becomes more intensive and burning is speeded up but the increased burning speed could not compensate for the reduced time during which the piston moves close to the top dead centre. The higher the rotation frequency is the earlier should the spark be applied so burning is performed close to the top dead centre in the smallest possible volume, i.e. with minimum loss. It is necessary to maintain the angle of advance of ignition with respect to the engine rotation frequency. A special regulator, usually a centrifugal type, ensures this. B. Engine load. As the load on the engine increases the throttle valve opens wider, the quantity of combustion mixture increases and the mixture temperature and pressure increase in the end of compression. When the quantity of combustion mixture is higher its contamination with burnt gases is lower. The higher the temperature and pressure at the moment of ignition and the purer the mixture is, the higher would the burning speed be and the smaller the optimum angle of advance of ignition. It is necessary to have the angle of advance ignition to correspond to the load of the engine. A vacuum regulator accomplishes this. C. Detonation. Detonation is burning the mixture at abnormally high speed. The occurrence of detonation is determined by fuel and combustion mixture quality, temperature, pressure and the duration of temperature and pressure applied to the combustion mixture. A measure of the anti-detonation resistance of fuel is its octane number. At larger angle of advance of ignition the mixture burns out at increasing temperature and pressure in the cylinder and this creates favourable conditions for detonation. A limit angle of advance of ignition exists for each individual engine operation condition and certain time (octane number) and when this limit is exceeded detonation results [6]. The signs for detonation during engine operation are the metallic hammering, overheating, black smoke, reduction in power and saving. It is not recommended to run an engine with detonation for a long time [6]. Detonation could be avoided by reducing the angle of advance of ignition. A special device called octane corrector accomplishes this.

2.1.3 Spark plug arrangement Modern spark plugs are non-dismountable. They comprise a steel shell, washers, insulator, stem, central electrode and side electrode [7]. The steel shell 1 is threaded in its bottom end to allow screwing to a cylinder head. A bended side electrode 6 is attached to the shell. The insulator 3 is positioned within the shell. Two copper washers 2 are positioned between the insulator and the shell to seal the assembly. A 10

steel stem 4 is positioned in the insulator and the stem is threaded in its upper end to match the terminal nut and ends in the central electrode in its bottom end. The high voltage wire from the rectifier is connected by means of the terminal nut to the stem [7]. The high voltage is transmitted via the stem to the central electrode and if it is sufficient to break down the spark gap a spark is passed between the electrodes, which ignites the combustion mixture in the cylinder. The dismountable spark plug is only different in that the insulator is fastened to the shell by means of a nut. When the nut is unscrewed the insulator could be removed from the shell to be cleaned or exchanged when damaged [7]. The spark plug is subjected to extremely heavy conditions during engine operation. It is subjected to mechanical, heat and electrical load and chemically active substances. The bottom end of the spark plug contacts gases of various temperatures depending on the process taking place in the cylinder. During filling the temperature of the combustion mixture is 323-353 K and at the end of combustion gas temperature reaches 2500 K and more. The spark plug possesses certain heat inertia and its bottom end temperature could not be varied with the variation in gases temperature in the cylinder for one cycle. As the average temperature of the gases in the cylinder for one operation cycle is significant the spark plug heats up considerably and a certain average temperature is maintained in each point. The larger portion of heat transmitted by the gasses in the cylinder to the insulator is discharged via the copper washers to the shell and from there, to the cylinder head and cooling medium and the remaining heat – via the insulator and shell into the environment. Fig. 1 shows heat flows through the spark plug (temperatures are in °C) [7]. The bottom end temperature of the insulator depends on a number of factors: temperature of gases in the cylinder; frequency of operation Fig. 1 cycles; design of cylinder head and the position of the spark plug; the surface area of the bottom shell of the insulator, the design and number of side electrodes; the heat conductivity of individual components; cooling conditions of the spark plug, etc. Insulator bottom end temperature and central electrode temperature reach 773-1073 K. The side electrode heats less than that as the heat from it is directly transferred to the shell. The shell of the plug heats only slightly to 393 - 423 K for liquid cooling and 498 – 523 K for aircooling of the engine. High mechanical stress could result in the spark plug under high temperatures due to the difference of temperature linear expansion coefficients of neighbouring parts [7]. 11

Some rather active gases and substances are contained in the combustion products like ozone, oxygen, carbon oxide, sulphur and lead oxides that may cause corrosion on plug electrodes. During spark plug operation electrodes are subjected to the so-called electrical erosion – wear caused by the electrical spark [7]. The heavy duty operating conditions of the spark plug place high requirements for the construction and material of individual components and manufacturing techniques.

2.1.4 Electrodes The material selected for electrodes should be resistant to gas corrosion and electrical erosion under high temperature conditions. The heat expansion coefficient of the central electrode should be close to that of the insulator to avoid any local mechanical overstress. The side electrodes material should not be brittle so they do not break during adjustments of sparkling gap. Electrodes are usually manufactured of nickel-manganese alloys (97%-95% Ni, 3-5% Mn). This alloy has high melting temperature (1723 K), it is corrosion resistant when working with un-ethylized fuel and does not require specifically high breakdown voltage. Under high temperature nickel ionizes the spark gap and thus reduces necessary breakdown voltage [8]. Chrome-titanium steel could also be used to manufacture spark plug electrodes. Such electrodes have better corrosion resistance than nickel ones but they require higher breakdown voltage. The number of side electrodes could be one to four. When a higher number of side electrodes are adopted the spark passes through the smallest spark gap. When the given side electrode burns and the spark gap is thus increased, the spark shifts to another electrode. This way the spark moves around all electrodes in sequence and one does not need to adjust spark gap so often. The larger number of side electrodes facilitates spark plug scale deposition. Electrode polarity influences spark plug durability. The anode arch temperature is higher than cathode temperature. The side electrode cools better. When this is anode the operating conditions of the two electrodes are almost similar and their enrichment is reduced. The spark gap of spark plugs in ordinary engines is 0.6 – 0.7mm. For engines with very high degree of compression to reduce breakdown voltage this value is 0.4 – 0.6 [8]. In small spark gaps the ignition capabilities of the spark are reduced and also there is a risk of clogging it with deposited scale. When the spark gap is large the breakdown voltage is high and this creates harder operation conditions for the induction coil, high-voltage cables and spark plug insulator.

2.1.5 Insulator The insulator is the most heavily loaded component in the spark plug mechanically, thermally and electrically. The material chosen for the insulator should have high mechanical and electrical strength under both low and high temperatures; high heat conductibility; it should not react with the products of combustion and should preserve its crystal structure under high temperatures.

12

The insulator should be capable of withstanding a voltage of 15000 – 20000 V with no surface discharge rupture. Moreover, it should have high electrical resistance to allow only minimum current flow [8]. Spark plug insulators are usually manufactured of ceramic materials. These have very good heat conductance, high electrical and mechanical strength. For widely used engines operating under moderate temperature conditions spark plugs with ceramic material insulators are usually used containing 76% Al2O3, called uralite. For high-duty engines (with high degree of compression and heavy temperature conditions) spark plugs with ceramic insulators containing 90-98% Al2O3 are used (sinter corundum, crystal corundum, sintox, corundite, etc.)

2.1.6 Shell The shell is threaded and has a hex head provided for wrench, which allows the spark plug to be screwed to the cylinder head. The car engine spark plugs have M18x1.5 and M14x1.25 threads [9]. The smaller diameter spark plugs are smaller in size and it is easier to find a place for them when designing the engine it takes less time for the to heat up to operation temperature thus reducing the chance of engaging them at engine start up. But when the spark plug is smaller the walls of the insulator are thinner and higher requirements are placed for the material.

2.1.7 Shield Shielded ignition systems involve shielded spark plugs. The external part of the insulator of such plugs is positioned within a shield. Shielded cables should be used to connect to shielded spark plugs [9].

2.2 Spark Plug Thermal Characteristics It has been established through trials that carburettor engine could operate normally without interruption provided that the temperature of the bottom end of the insulator and the central electrode in the spark plug is within 850 – 1300K [9]. At temperatures lower than 850 K the oil getting into the insulator does not burn but only the light fractions evaporate leaving a thick resinous mass – scale, which is deposited on the spark plug. The scale thus shunts the spark gap in the plug, creates energy loss and reduces the voltage applied to the electrodes. At temperatures higher than 850K the oil getting into the spark plug burns out completely. The combustion products are dry and they sputter and are blown outside during release – the spark plug is self-cleaned. But at temperatures higher than 1130K the spark plug causes advance ignition of the mixture – the mixture is ignited by its contact with the strongly heated bottom insulator end and central electrode before the spark is applied. The engine overheats and is reduced in power due to advance ignition of the mixture [9]. A sign of advance ignition is the white colour of the bottom part of the insulator and the presence of melted material spots from the insulator and electrode. The temperature of the bottom end of the insulator depends on the heat flow of heated gases to the insulator and its release into the cooling medium and ambient air. The size and design of the insulator should be in correspondence with engine temperature conditions. The more an engine is accelerated (in degree of compression, average effective 13

pressure or frequency of rotation) the higher the heat released in the cylinder per unit time and the better should heat release in the spark plug be. The quantity of heat transferred to the insulator depends on the insulator –burnt gases contact surface and the distance between the insulator and the shell. Varying these values and using materials of various heat conductances to make the insulator, the central electrode, stem and washers, as well as varying the cross section of the latter could produce spark plugs of various heat characteristics. As the length of the bottom end of the insulator determines to a large extend the insulator and burnt gases contact surface area, it is also used to determine the heat characteristics of spark plugs. The longer the bottom parts of the insulator, the higher the heating of the spark plug would be at identical other conditions and the “warmer” it is going to be. The so-called heat number determines the thermal characteristics of spark plugs. The heat number is the time in hundreds of a minute after which the spark plug screwed to a special engine operating under certain conditions starts to apply advance ignition of the mixture. Spark plugs with heat numbers from 100 to 500 are available. The higher the heat number of a spark plug, the “colder” it is going to be [10]. The high heat number (225 – 500) spark plugs are intended for highly accelerated engines with high degree of compression. The mass used spark plugs in engines have 100 – 225 heat number. The correct choice of heat number is rather significant for the normal operation of spark plugs and engines. For new types for engines the spark plugs are selected after trials by installing various thermal characteristics spark plugs and measuring the temperature of the central electrode. If a given plug refuses to operate due to the scale deposited over it this means it is too “cold” and if it causes advance ignition – it is too “hot” for the selected engine. When the correct heat number has been selected the engine would operate under all conditions without interruptions and without any advance ignitions [10]. The correct spark plugs for a certain engines should be selected considering their thermal characteristics and thread length. When the spark plug is screwed in the face of its shell should be aligned with the combustion chamber surface – only the electrodes should show in the combustion chamber. The spark plugs should have the thermal characteristics given in the engine manufacturer’s leaflet. The spark plugs recommended by the manufacturer could be exchanged for “colder” or “warmer” plugs if needed for the operation conditions.

2.3

Manufacture

2.3.1 Body shell manufacture Manufacturing of certain products is determined by the selected materials, design requirements (precision, surface roughness, shape deviations, surface deviation, heat treatment, etc.) and last but not least by the scale of production.

Fig.2

Considering performance requirements for the body shell of 14

spark plugs, the scale of production and allowed expenses for production and materials we could make the following conclusions [10]: -

With respect to operating temperature conditions the body shell is subjected to 350°C.

-

No special precision requirements are claimed;

-

A production scale of 10000000 pieces per year is a fairly large volume, which determines the nature of our particular production as mass production;

-

The mass nature of production implies minimum waste technologies and maximum cut time of action. This immediately makes turning operation inefficient;

-

We determine production cycle for mass type of production by the following formula: F τ= N

, where F - is the actual annual working time fund N = 10 000 000 pieces – the annual production scale F = 359424 min for 260 working days, three-shift production and 4% time for scheduled maintenance. r = 0,0359 min = 2.16 sec Above cycle value shows that a ready spark plug should be produced every 2.16 seconds. When selecting materials for each spark plug component one should observe the linear expansion coefficient and the character of this expansion (how it would affect the distance between electrodes). The difference in heat accumulation of each component in various areas should also be considered. Considering the mass nature of production we could suggest to use the cold die forming (pressing) method for manufacturing the spark plug body shell. Thread cutting should better be made by cold rolling [10]. The advantages of forming methods described above are the following [11]: -

Lack of waste – complete usage of material

-

Provide higher production efficiency

-

Improve the structure of material

-

Surface quality is fairly good

-

Good dimension precision

-

Internal stress distribution in the material is more uniform and without any high concentration areas

Considering described methods of plastic deformation most suitable material is low-carbon steel with up to 0.08% carbon content (Ferritic steel). It is suitable for cold die forming and deep drawing. The material is also attractive in cost. This type of steel also satisfies all functional requirements for spark plug body shell.

2.3.2 Selecting materials and manufacturing spark plug insulator Various requirements are set for the insulator to comply with. These are [11]: 15

-

Withstand discharge voltages of up to 15000 – 20000V with no surface rupture;

-

Have high electrical resistance so the current flow through it is the minimum;

-

Withstand high mechanical loads;

-

Have high heat conductivity;

-

Not react with combustion products

-

Not change its crystal structure under high temperature.

Several ceramic materials comply with these requirements. The material, which could be used to manufacture the spark plug insulator is the ceramic material uralite containing 76% Al2O3. Ceramic materials containing 90-98% Al2O3 (sinter-corundum, crystal corundum, sintox, corundite, borrum -corundum, etc.). Suitable machines to be used for forming the insulator are isostatic presses [11]. The manufacture of spark plug insulator with its central electrode and terminal post could be performed in two ways [12]: -

manufacturing the insulator separate from the central electrode and terminal post;

-

manufacturing the insulator complete with the central electrode and terminal post.

The exact method to be applied would depend on the developed spark plug design and available know-how. The present matter does not make any commitment to the exactly point out the material trademark for producing the spark plug body shell and insulator. To be able to provide this information we will need to know design details, design [12].

References 1.

C.D. Rakopoulos, E.G. Giakoumis, Second-law analyses applied to internal combustion engines operation. Progress in Energy and Combustion Science, Volume 32, Issue 1, 2006, Pages 2-47.

2.

D. Steiner, H. Burtscher, H. Gross, Structure and disposition of particles from a sparkignition engine. Atmospheric Environment. Part A. General Topics, Volume 26, Issue 6, April 1992, Pages 997-1003.

3.

Epaminondas Mastorakos, Ignition of turbulent non-premixed flames. Progress in Energy and Combustion Science, Volume 35, Issue 1, February 2009, Pages 57-97.

4.

Seiichiro Kumagai, Tadami Sakai, Ignition of gases by high-energy sparks. Symposium (International) on Combustion, Volume 11, Issue 1, 1967, Pages 995-1001.

5.

J. D. Dale, M. D. Checkel, P. R. Smy, Application of high energy ignition systems to engines. Progress in Energy and Combustion Science, Volume 23, Issues 5-6, 1997, Pages 379-398.

6.

Michikata Kono, Seiichi Shiga, Seiichiro Kumagai, Kazuo Iinuma, Thermodynamic and experimental determinations of knock intensity by using a spark-ignited rapid compression machine. Combustion and Flame, Volume 54, Issues 1-3, December 1983, Pages 33-47. 16

7.

H.T. Lin, M.P. Brady, R.K. Richards, D.M. Layton, Characterization of erosion and failure processes of spark plugs after field service in natural gas engines. Wear, Volume 259, Issues 7-12, July-August 2005, Pages 1063-1067.

8.

Ignitability of spark plug — The consideration on leanburn condition: Hiroshi Ono, Masahiro Ishikawa, Yoshihiro Matsubara (NGK Spark Plug Co., Ltd.). JSAE Review, Volume 17, Issue 4, October 1996, Page 444.

9.

Henry S. Rawdon, A.J. Krynitzky, A study of the deterioration of nickel spark plug electrodes in service. Journal of the Franklin Institute, Volume 188, Issue 6, December 1919, Pages 812-813.

10.

Spark plug gasket sealing. Sealing Technology, Volume 2001, Issue 92, August 2001, Pages 12-13.

11.

L.A. Killick, The sparking plug Some design of considerations. Materials & Design, Volume 3, Issue 4, August 1982, Pages 511-514.

12.

N. Kawahara, E. Tomita, S. Takemoto, Y. Ikeda, Fuel concentration measurement of premixed mixture using spark-induced breakdown spectroscopy. Spectrochimica Acta Part B: Atomic Spectroscopy, Volume 64, Issue 10, October 2009, Pages 1085-1092.

17

CHAPTER 3 High Energy Rate (Her) Forming

Modern technological progress in the metal processing area is characterized by new progressive technological methods implemented in production and high mechanization and automation of existing ones. An important position in the raw of new technological processes in the plastic deformation metal processing area is occupied by the high-speed (impulse) methods of forming [1]. Stamping of large-size components made of high-strength alloys; creation of new composite materials and reinforcement of large products of complicated shape became possible thanks to the utilisation of high-pressure shock wave energy [1].

Fig. 1

Fig. 2 The most economically suitable and practically feasible means to create shock waves proved to be the use of various types of explosives. Considered for application in this area is the electro-magnetic field (Fig. 1), and the electric sparkling discharge in water medium (Fig. 2), (Fig. 3) [2]. The issue about the contribution of high-speed forming to the solution of manufacturing problems is rather important. This technique should be applied where conventional technological solutions prove to be complicated and expensive and sometimes – even impossible [2].

Fig. 3

18

Explosive forming (fig. 4) is performed in air or water medium. In some cases sand, oil or other liquid medium is applied. The most widely spread technique is explosive deformation in water medium (hydro-explosive deformation) [3].

3.1 Explosives and physical nature of explosions Explosives are materials featuring high speed of chemical interaction as a result of which a certain quantity of heat and gaseous products are released. When the blast wave is spread in a certain volume at a speed of several kilometres per second leaving heated gases under high pressure behind, the explosion process is called detonation [3]. The constant speed of detonation is a characteristic feature of explosives, which provides their efficient application. The maximum speed of spreading for the detonation wave of explosives used for engineering purposes is from 2000 to 9000 m/s. The maximum pressure of expanding gaseous products goes up to hundreds of thousands atmospheres. Explosives used for metal processing operations could be classified into four groups [4]:

Fig. 4 A. Slow-burning powders; B. Fragmentation – TNT, etc. C. Burning gaseous mixtures; D. Compressed gases, which under certain conditions undergo almost immediate transition from liquid into gaseous state. Fragmentation explosives find the widest application in forming operations. The time needed for the transition of a fragmentation explosive into a gaseous product is millions of a second at charge surface explosion pressure values of around 170.108 N/m2.

19

The energy of the explosion is transferred into the formed product via an intermediate conducting medium and the denser this medium is the higher the efficiency of the overall process. Air is the poorest conducting medium as it has very low density. Water provides for significantly higher efficiency with its density of 830 times the density of air. High-speed deformation is a result of the exceptionally fast spreading of the shock wave front (highpressure front). The shock wave amplitude is a decreasing function of time. The following relation expresses the pressure change [5]:

pt = pmax ⋅ e

−

t

θ

,

where θ is the time constant, which depends on the type, mass and location of the explosive. This is equal to the time needed for the pressure to be reduced by e number of times compared to pmax. The following relations are available to calculate the time constant [5]: -

for spherically shaped charge – TNT

⎛ ⎞ ⎜ R ⎟ −4 θ = 10 ⋅ Q ⋅ ⎜ 1 ⎟ ⎜ 3⎟ ⎝Q ⎠

0,24

1 3

-

for cylindrically shaped charge – TNT ⎛ ⎜ R −4 θ = 10 ⋅ q ⋅ ⎜ 1 ⎜ q2 ⎝ 1 3

⎞ ⎟ ⎟ ⎟ ⎠

0 , 45

, where

Q is the spherical-shaped charge mass, kg

q is the mass of a linear meter of cylindrically shaped charge, kg/m R is the distance from the centre of the charge to the sample, mm. It could be seen from the relation between θ and the weight of the charge and the distance (in the logarithmic scale) that the larger R is the larger would θ be. This shows that the wavelength increases. When R is maintained constant θ increases when Q is increased. The following relations determine the maximum pressure, impulse and energy [6]: D

pmax

⎛ 31 ⎞ ⎜Q ⎟ 2 = A⋅⎜ ⎟ ≈ 980,6MN / m ⎜ R ⎟ ⎠ ⎝

J = BQ

1 − 3

⎛ 13 ⎜Q ⋅⎜ ⎜ R ⎝

E

⎞ ⎟ 2 ⎟ ⋅ 980,6MNs / m ⎟ ⎠

20

⎛ 13 ⎜Q E = CQ ⋅ ⎜ ⎜ R ⎝ 1 3

F

⎞ ⎟ 2 ⎟ ⋅ 98,06kJ / m ⎟ ⎠

where A, B, C, D, E and F are constant. The progress of the detonation process in a water medium has a number of features, which are best manifested when exploding a spherically shaped charge. The powerful shock wave resulting from the detonation moves away from the centre of the explosion at a sonic speed. Resulting gaseous products form a gas bubble and expand at a constantly decreasing speed. This results in reduction of their pressure, which at a certain time becomes lower than the ambient pressure [6]. From this point the gaseous bubble begins to shrink until the pressure within it is higher than ambient pressure. As a result of the newly available super pressure the gaseous bubble again starts to expand, i.e. multiple pulsations result. If the gaseous bubble reaches the water surface before these pulsations have started a fountain is formed above it and anti-fountain mesh is used in this case positioned above water surface or explosion is performed at a depth of [7]: h = 9⋅3 Q

When the explosion is carried out under water the shock waves reverberating from the water surface would change direction and return as discharge waves. To avoid their strong effect the processed component should be positioned at a depth h where it would be first affected by the direct shock wave. The following relation determines this distance [7]:

⎛ ⎜ R 3 hmin = 3,5 ⋅ν ⋅10 ⋅ 0,11⋅ Q ⋅ ⎜ 1 ⎜Q2 ⎝ where v is the speed of sound under water. 1 2

3.2

⎞ ⎟ ⎟ ⎟ ⎠

0 , 24

m,

Characteristics & Technological Features Of Hydro-Explosive Deformation

Fig. 5 shows a scheme of hydro-explosive deformation: the flat sheet sample 1 is inserted between the die 2 and the clamp 3. When the charge 4 located at a distance R from the sample is blasted all abovementioned processes take place. When no special measures are taken (for example, installing a specifically shaped die) the component would have an approximately spherical shape with a depth h after the explosion. Some auxiliary devices include the pool 5, a crane mechanism, a vacuum system, etc. The shock wave emits part of its energy to form the sample. The rest of the energy is carried away by the reverberated wave. As a result of this action the metal of the sample is given a high initial acceleration and then continues to move at a constant speed (80-300 m/s). In the general case, transverse and longitudinal elastic waves result in the deforming body [8]. As a result of the reverberation of these waves some radial waves are formed from the circumference, which move towards the center and leave the metal behind them in a uniform plastic flow state. A transverse plastic wave is formed close to the edges, which also moves towards the inside but at a lower speed. This wave causes each ring-shaped element to bend as it goes through it [8]. The kinetic energy is thus transferred into the central area of the sample and is used for plastic elongation and thinning down. In such a process arrangement the 21

sample has the shape of a truncated cone in each deformation stage and the plastic forming section is ring-shaped. As a result of this the maximum deformation occurs in the centre of the sample.

Fig. 5 The following relation determines the speed of spread of the transverse plastic wave [8]:

ν = σS m/s The impulse load also causes some structural changes in the sample material – grain braking, etc. These changes alter metal properties – reduce plasticity, corrosion resistance, increase strength characteristics, etc. Metals behaviour under such deformation conditions has not been sufficiently studied yet. Impulse deformation also causes changes in metal elastic springing. Studies show that it exists and its value could be adjusted within certain limits by varying the size and location of the charge. The basic technological parameters determining the progress of the deformation process are explosive charge size and the distance from the sample. The mass of the explosion charge is determined by the relation between the energy needed for the deformation of the metal sample and the energy resulting from the explosive. Other analytical methods for determining the size of explosive charge are based on the theorem of preserving the momentum [8]. Having adopted a number of considerations and basing on the sonic field theory, R.B.Pichotovnikov recommends the following formulas for determining the mass of the explosive charge [8]: -

for spherically shaped charge 0 ,8

⎛ QsR1,8 ⎞ ⋅ N ⎟⎟ kg Q = ⎜⎜ 2 ⎝ 1 −ν ⎠ -

for linear charge

22

0 ,8

⎛ QsR 0,55 ⎞ ⎟⎟ kg / m , Q = ⎜⎜ M ⋅ 2 1 − ν ⎝ ⎠ where: a is the plastic deformation energy per unit sample surface (the specific work).;

ν=

ϕ 2

(

)

⋅ 1 − e − β - pressure and flow rate ratio in the reverberated and direct wave;

ϕ - reverberation coefficient (0.936 for steel; 0.824 for aluminium alloys; 0.813 for titanium alloys); s - material thickness;

β=

ρ o ⋅ν ⋅θ ρ ⋅s

ρo - water density ρ - material density; M and N - coefficients depending on the density of processed material: -

for aluminium alloys N = 0,494 ⋅10 −6 and M = 79.7 ⋅10 −6

-

for titanium alloys N = 0,813 ⋅10 −6 and M = 79.7 ⋅10 −6

The specific deformation work could be determined based on the diagram of summarized stress in degree approximation [9]:

σ i = β ⋅ ε ia , where

σi, εi are summarized stress and deformation, respectively; αi, β - approximation constants. The specific work would then be expressed by [9]: a=

β ⋅ ε 1+ a 1+ a

The deformed condition intensity should first be determined for each individual deformation and then determine specific work and charge size [7]. The shape of the charge could also influence the progress of the process. The best alternative is when the explosive charge has copied sample profile especially for flat samples. This could be accomplished using flat or ring-shaped charge and this could be located at a very small distance from the sample [9]. When a die is to be used provisions should be made to allow the air between the die and the sample to be released. This could either be accomplished by vacuum (for thinner components) or a groove system allowing the air to be released towards the walls of the die as the sample moves (for thicker components) [9].

23

References 1.

C.D. Rakopoulos, E.G. Giakoumis, Second-law analyses applied to internal combustion engines operation. Progress in Energy and Combustion Science, Volume 32, Issue 1, 2006, Pages 2-47.

2.

S.A. Tobias, The state of the art of high energy rate bulk forming. Journal of Mechanical Working Technology, Volume 9, Issue 3, May 1984, Pages 237-277.

3.

A.J. Organ, The calibration of high energy-rate impact forming machines. International Journal of Machine Tool Design and Research, Volume 7, Issue 4, December 1967, Pages 325-349.

4.

R.H. Brown, J.K. Russell, An experimental machine tool for cutting and high energy rate forming studies. International Journal of Machine Tool Design and Research, Volume 8, Issue 2, July 1968, Pages 73-82.

5.

V. P. Astakhov, S. V. Shvets, A novel approach to operating force evaluation in high strain rate metal-deforming technological processes. Journal of Materials Processing Technology, Volume 117, Issues 1-2, 2 November 2001, Pages 226-237.

6.

L.T. Chan, N.S. Ong, Design and development of an energy convertor for a mechanical press and its application to high speed forming. International Journal of Machine Tools and Manufacture, Volume 29, Issue 1, 1989, Pages 161-169.

7.

A.G. Mamalis, A. Szalay, N. Göbl, I. Vajda, B. Raveau, Near net-shape manufacturing of metal sheathed superconductors by high energy rate forming techniques. Materials Science and Engineering B, Volume 53, Issues 1-2, 1 May 1998, Pages 119-124.

8.

K. Ryttberg, M. Knutson Wedel, P. Dahlman, L. Nyborg, Microstructural evolution during fracture induced by high strain rate deformation of 100Cr6 steel. Journal of Materials Processing Technology, Volume 209, Issue 7, 1 April 2009, Pages 3325-3334.

9.

D.J. Mynors, B. Zhang, Applications and capabilities of explosive forming. Journal of Materials Processing Technology, Volumes 125-126, 9 September 2002, Pages 1-25.

24

CHAPTER 4. Gear Drive Assembly

4.1 Explanatory Epicyclical gearings are gear mechanisms where the gear rotates not only around its geometrical axis but along with it performs additional movement around the axis of the engaged gear, i.e. they provide complicated special movement [1]. The planet gears may be both internally and externally engaged with the so-called sun gears and their axes are supported in the planet carrier and together with the carrier are rotating around the geometrical axis of the sun gears [1]. When the sun gear is static, the mechanism is called planet-type. It is possible here to transfer movement from the sun gear to the planet carrier and vice versa. When it is possible to rotate the sun gear around its own axis, the mechanism is then called differential [1]. This mechanism allows rotating movement to be transferred from the sun gear to the planet carrier and to another sun gear or from the planet carrier to one or both sun gears, etc. These types of gear mechanisms find a very wide application. They can be used as summing (subtraction) mechanisms, mechanisms for co-ordination of two movements, as mechanisms for compensating for the difference in angular speeds of two independent movements.

4.2 Operation principle The sun gears 5 and 6 are seated in the body 1. They are the driving gears and receive their independent movement from the sprockets 8. The sun gears can either rotate in the same direction or in different directions at various angular speeds and are engaged with the planet gears 4 seated in the planet carrier. These are used to compensate for the difference in angular speeds and the directions of rotation of the sun gears [2]. The planet carrier is seated in the body 1. Its angular speed depends on the angular speeds of the sun gears and their direction of rotation. Its angular speed would be ω=0, provided that both sun gears have the same angular speed and opposite directions of rotation, and ω=max, when the sun gears have identical angular speed with identical sign [3]. In the first case, the planet carrier is static and the planet gears rotate and in the second case, the planet gears are static and the carrier rotates. Each difference in the angular speeds of the sun gears leads to a respective rotation of the carrier and planet gears regardless of the direction of rotation of the sun gears. The transmission ratios for the differential are determined by the equations in 4.3. The following are required for the seating of various parts due to the specificity of the differential gear [3]: -

provision of necessary kinematical accuracy (guaranteed side clearance);

-

provision of necessary geometrical precision (permanent center of engagement)

The nut 7 is used for the purpose, which eliminates and adjusts side clearance and interrelation of various components within the specified tolerance. The specified guaranteed side clearance should be provided to ensure proper mechanism operation.

25

Due to the fact that all gears are fixed and do not provide for axial shift except for the planet carrier, the clearance and their interrelation are ensured by carrier shift along its axis. The carrier is only fixed at the bearing inner diameter and is free at its outer diameter. This type of seating allows for some eventual temperature deformations to be compensated when the guaranteed side clearance has been ensured [4].

4.3

Design calculations

1. Gear transmission ratio [2]

u

4

2. Gear module [2]

m te

2

3. Total angle of shaft interposition [2]

Σ

90 . deg

4. Determining the angle of the pitch cone [3]

1 u

δ1

atan

δ2

atan ( u )

δ 1 = 14.036 deg δ 2 = 75.964 deg

5. Number of gear teeth [3]

z1

16

z2

z 1.u

z 2 = 64

6. Determining the tooth contour compensation [2]

x1

0.43

x τ1

a

x2

0.43

b. ( u

a 0.03 b 0.008 2.5 ) x τ 1 = 0.042 x τ1

x τ2

7. Determining the length of the pitch cone [2]

0.5 . m te . z 1 ψr . Rm Re 1 2 Re

2

z2

2

R e = 65.97 mm R m = 57.723 mm

8. Determining the width of the gear ring [2]

b

ψ r.R e

b = 16.492 mm

We assumed: 16.5 mm

26

9. Determining tooth height [2]

h e1 h e2

2 . h' a h e1

c' . m te

h e1 = 4.8 mm

10. Determining tooth head height [2]

h ae1 h ae2

x 1 . m te x 2 . m te

h' a h' a

h ae1 = 2.86 mm h ae2 = 2.86 mm

11. Determining tooth root height [3]

h fe1 h fe2

h' a h' a

c' c'

x 1 . m te h fe1 = 1.54 mm x 2 . m te h fe2 = 1.54 mm

12. Determining tooth thickness [3]

s e1

m te .

π 2

2 . x 1 . tan α t

x τ1

s e2

m te .

π 2

2 . x 2 . tan α t

x τ2

s e1 = 3.852 mm s e2 = 2.432 mm

13. Determining gear pitch diameter [3]

d e1 d e2

m te . z 1 m te . z 2

d e1 = 32 mm d e2 = 128 mm

14. Determining gear top diameter [3]

d ae1

m te . z 1

2 . h' a

x 1 . cos δ 1

d ae2

m te . z 2

2 . h' a

x 2 . cos δ 2

d ae1 = 37.549 mm d ae2 = 129.387 mm

15. Determining gear root diameter [4]

d fe1

m te . z 1

2 . h' a

x 1 cos δ 1

d fe2

m te . z 2

2 . h' a

x 2 cos δ 2

d fe1 = 29.788 mm d fe2 = 127.447 mm

27

16. Determining tooth head angle [4]

h fe1

ν a1

atan

ν a2

ν a1

Re

ν a1 = 1.337 deg ν a2 = 1.337 deg

17. Determining tooth root angle [4]

ν f1

atan

ν f2

ν f1

h ae1 Re

ν f1 = 2.482 deg ν f2 = 2.482 deg

18. Determining top cone angle [5]

δ a1 δ a2

δ1 δ2

ν a1 ν a2

δ a1 = 15.374 deg δ a2 = 77.301 deg

19. Determining root cone angle [5]

δ f1 δ f2

δ1 δ2

ν a1 ν a2

δ f1 = 12.699 deg δ f2 = 74.626 deg

20. Determining differential transmission ratios [5]

i 5.6 i 5.3 i 5.4 i 3.5 i 6.3 i 3.6

z1 z2 z1

1

z1 z2

z1 1 i 5.3 z1

z1

z1 1 i 6.3

i 5.6 = 0.25

when 3 is stopped

i 5.3 = 2

when 6 is stopped

i 5.4 = 4

when 3 is stopped

i 3.5 = 0.5

when 6 is stopped

i 6.3 = 2

when 5 is stopped

i 3.6 = 0.5

when 5 is stopped

28

21. Differential gear assembly condition [6]

q

4.4

2

z1

z2 q

= 40

Description of the Mechanism

The purpose of this mechanism is to enable movement transmission from one sprocket to the other and change the angular speed of one of the sprockets. The mechanism comprises two pairs of bevel gears, two shafts, two sprockets, casing and casing cover where bearing housings are enclosed [7]. Straight-tooth bevel gears were selected because of the features of the assignment, the speeds of up to 25 rads/sec and the lack of any special noise reduction requirements and load nature data. From the assigned gear ratio of 1:4 I select the number of teeth of the driven gear to be Z3, 4=20 and calculated from this ratio the number of teeth of the driven gears Z1, 2=80. I adopted m = 2mm as the gear modulus [7]. The drive gears are secured to the shafts by means of keys. The driving gears are made of C45 steel and subjected to thermal treatment /hardening/. The driven gears are made of 41Cr4 steel and are also subjected to thermal treatment /hardening/. The steel selected for the driven gears is of better strength characteristics as these gears are subjected to higher load. As shown on the sketch in the assignment, the bevel gears cross at an angle of 90°. The driving gears rotate along a pin with no bearings, as the rotation in respect to the driving bevel gears is insignificant [7]. Shafts are made of C45 steel. Journals are provided in them where the driving bevel gear, bearings, and the sprocket are seated and a journal for the sealing is also available. Key slots are provided in the journals where gears are to be mounted. An opening is also provided in one of the shafts, which is used for the carrier motion-limiting stop pin. The pin is made of C45 steel [8]. In view of the nature of the loads available during the operation of the bevel gears 33205 angle bearings were selected from the SKF catalogue [8]. Two bearings are mounted on each shaft and positioned so they can be secured to the shaft using the M25x1.5 nut (KM 5 from SKF catalogue) and at the same time secured in the bearing housing by means of two stop clip rings and thus be capable of bearing the loads. Bearings lubrication is by means of the oil used for the lubrication of the bevel gears. The pin where the driven bevel gears are seated is made of 41Cr4 steel. It is secured in the planet carrier by means of the head provided on one of its ends and a nut and a spring washer on the other end. The change in the planet carrier diameter is avoided by providing a smaller diameter at the thread end [8]. The planet carrier is used to secure the pin along which the driven bevel gears move, to fix them in the proper position and to restrict movement in accordance with the assignment requirements. The planet carrier is directly seated in the shaft because of the low relative movement and low rotation speeds. It is made of C50 steel. A slot is provided in its hub with a 90°shifted center with respect to the hub-opening center (to compensate for pin thickness), where the stop pin inserted. This enables restriction of the movement of the driven bevel gears in respect to the driving ones. Using the oil provides lubrication of the shaft contact surface. The body is made of Al Si11 aluminium alloy. This material was chosen to provide a lighter housing. A bearing seat having two key-slots is provided in the housing for the stop clip rings through which bearings are secured with respect to the housing. Holes are provided in the 29

walls for securing the cover – 8 off M6 and for securing the cap – 4off M6. The opening where the cover is to be mounted has been machined to be compatible with the bearing opening to provide necessary accuracy. The cover is made of Al Si11 aluminium alloy similar to the body. A bearing seat having two key-slots is provided in the cover for the stop clip rings through which bearings are secured with respect to the cover. A tooth is provided on the cover circumference, which has been machined along with the bearing seat and is used to center the cover in respect to the body which ensures normal functioning of the bevel gears [15]. An M12x1.5 opening is provided in the cover for the installation of a standard plug used for oil filling and checking oil level. 8 openings are provided along the circumference of the cover, where the heads of the bolts securing the cover to the body are seated. There are openings in the bearing seat hole, which are similar to the ones in the body and are used to secure the cap [14]. Bearing seats are closed by caps where 20x42x7 cup seals are installed to prevent oil flowing out of the body [16]. The caps for both bearing seats are identical and made of Al Si11 steel. Sprockets for the 08B chain are mounted on both shafts at Z=20. Sprockets transmit shaft movement by keys [15]. Assembling of the unit is in the following order [16]: The keys 16 are mounted on the shafts 1 and 18 and the sprockets 14 are then installed. The pin 17 is installed with the planet carrier installed before that. The stop clip rings 9 and bearings 8 are then mounted. The driven gears 13 and the pin 12 are installed securing them with the spacer 23 and nut 22. The shafts and external bearings are then mounted fastening them with the nuts 7 [16]. The cup seals 19 are installed in the caps 5 and the caps are then mounted in the body 15 and the cover 10, respectively. The keys 2 and the sprockets 3 are installed fastening them with the screws 4. The body and cover are assembled with the bolts 11. Oil is filled in the plug and the plug is screwed in [16].

4.5

Mechanism specification& design

№ Designation item 1 3EDM312-000-001

Name

No

Material

Note

Shaft

1

C45

DIN 1.0503

2

--

Key

2

C45

DIN 1.0503

3

3EDM312-000-003

Sprocket

2

C45

DIN 1.0503

4

--

М6х10 screw

2

5

3EDM312-000-005

Cap

2

6

--

М 6х16 bolt

8

7

--

Nut

2

8

--

33 205 bearing

4

9

--

Stop clip ring

4

10

3EDM312-000-010

Cover

1

11

--

М6х16 bolt

8

AlSi11

AlSi11

30

12

3EDM312-000-012

Pin

1

41Cr4

DIN 1.7035

13

3EDM312-000-013

Driven gear

2

41Cr4

DIN 1.7035

14

3EDM312-000-014

Driving gear

2

C45

DIN 1.0503

15

3EDM312-000-015

Body

1

AlSi11

16

--

Key

2

C45

DIN 1.0503

17

--

Pin

1

C45

DIN 1.0503

18

3EDM312-000-018

Shaft

1

C45

DIN 1.0503

19

--

Cup seal

2

20

--

Plug

1

21

3EDM312-000-021

Planet carrier

1

C50

DIN 1.0540

22 23

---

М8 nut M8 spring washer

1 1

31

32

33

34

35

36

37

38

39

40

41

42

43

44

References 1.

A. Bracci, M. Gabiccini, A. Artoni, M. Guiggiani, Geometric contact pattern estimation for gear drives. Computer Methods in Applied Mechanics and Engineering, Volume 198, Issues 17-20, 15 April 2009, Pages 1563-1571.

2.

R Keith Mobley, Gears and Gear Drives.Plant Engineer's Handbook, 2001, Pages 57/1029-57/1042.

3.

The generation principle and mathematical models of a novel cosine gear drive. Mechanism and Machine Theory, Volume 43, Issue 12, December 2008, Pages 15431556.Shanming Luo, Yue Wu, Jian Wang.

4.

Cheng-Kang Lee, Manufacturing process for a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission error. Journal of Materials Processing Technology, Volume 209, Issue 1, 1 January 2009, Pages 3-13.

5.

Szu-Han Wu, Shyi-Jeng Tsai, Contact stress analysis of skew conical involute gear drives in approximate line contact. Mechanism and Machine Theory, Volume 44, Issue 9, September 2009, Pages 1658-1676.

6.

Faydor L. Litvin, Ignacio Gonzalez-Perez, Kenji Yukishima, Alfonso Fuentes, Kenichi Hayasaka, Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mechanism and Machine Theory, Volume 42, Issue 8, August 2007, Pages 940-959.

7.

L.V. Mohan, M.S. Shunmugam, Geometrical aspects of double enveloping worm gear drive. Mechanism and Machine Theory, Volume 44, Issue 11, November 2009, Pages 2053-2065.

8.

Tengjiao Lin, H. Ou, Runfang Li, A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Computer Methods in Applied Mechanics and Engineering, Volume 196, Issues 9-12, 1 February 2007, Pages 1716-1728.

9.

D. Richards, D. J. Pines, Passive reduction of gear mesh vibration using a periodic drive shaft. Journal of Sound and Vibration, Volume 264, Issue 2, 3 July 2003, Pages 317342.

10. Li Ting, Pan Cunyun, On grinding manufacture technique and tooth contact and stress analysis of ring-involute spherical gears. Mechanism and Machine Theory, Volume 44, Issue 10, October 2009, Pages 1807-1825. 11. I. H. Seol, F. L. Litvin, Computerized design, generation and simulation of meshing and contact of worm-gear drives with improved geometry. Computer Methods in Applied Mechanics and Engineering, Volume 138, Issues 1-4, 1 December 1996, Pages 73-103. 12. F.L Litvin, M.De Donno, A Peng, A Vorontsov, R.F Handschuh, Integrated computer program for simulation of meshing and contact of gear drives. Computer Methods in Applied Mechanics and Engineering, Volume 181, Issues 1-3, 7 January 2000, Pages 71-85. 45

13. Biing-Wen Bair, Chung-Biau Tsay, Effects of profile shifted factor and pressure angle on the ZK-type dual-lead worm gear drives. Journal of Materials Processing Technology, Volume 112, Issue 1, 3 May 2001, Pages 29-36. 14. Biing-Wen Bair, Computer aided design of elliptical gears with circular-arc teeth. Mechanism and Machine Theory, Volume 39, Issue 2, February 2004, Pages 153-168. 15. Illés Dudás, Main operating charac teristics and quality assessment of worm gear drives. The Theory and Practice of Worm Gear Drives, 2004, Pages 260-288. 16. Faydor L. Litvin, Alfonso Fuentes, Matt Howkins, Design, generation and TCA of new type of asymmetric face-gear drive with modified geometry. Computer Methods in Applied Mechanics and Engineering, Volume 190, Issues 43-44, 17 August 2001, Pages 5837-5865.

46

CHAPTER 5 Local Bending Stresses in Axi-Symmetrical Thin Shells for Storing Pressure Vessels

5.1

Introduction

The engineering applications of thin shells include storage tanks for liquids or solids and pressure vessels for a variety of chemical processes. “Thin” is a relative term which indicates that the thickness of the material is small compared with the overall geometry, a ratio of 10:1 or greater being the usual criterion. Whenever there is a change in geometry of the shell, particularly for discontinuities in the meridian, the membrane stresses cause displacements which give rise to local bending in the wall. The resulting bending stresses may be significant in comparison with the membrane stresses (Calladine, 1989). This is the reason for introducing most of the times a reinforcing ring in the above problem. In most cases storage tanks for fluids equalise air pressure in compressor stations. Tanks are usually made with a cylindrical body and convex bottoms (Andrade, 1998). In some cases, the filler neck, the manometer reading the pressure within the tank and the outlet pipe flange are mounted on the cylindrical section. A safety valve (upper bottom section) and a release valve (lower bottom section) were mounted on the bottom sections of the tank. In current article cylindrical vessels with hemispherical ends of the same thickness, subjected to internal pressure will be considered in order to analyze the method of local bending. The design of thin shells depends primarily on the magnitude of the general system of membrane stresses. However, attention must also be given to the effect of local bending stresses at regions of discontinuity in the shell. These stresses are of the same order of magnitude as the membrane stresses, but they decay rapidly with distance from the discontinuity in thin walled shells (Khabakhpasteva, 2009). Surprisingly, reinforcement of a shell with rigid stiffeners increases the stress in a shell due to local bending. In practise continuum elements, which can model a quadratic variation in displacement or a linear variation in stress are usually preferred. These may be triangular or quadrilateral in shape for plane stress analysis (Opoka, 2004). A further advantage of this type of element is that it can have curved sides to approximate curved boundaries. Plane shell elements are being used such as the constant quadrilateral to allow the analysis of loading in the thin sheet curved material (Bathe, 1982).

5.2

Aluminium Small Capacity, Highly Pressurized Shell

5.2.1. Material selection Material’s chemical composition

To ensure minimum weight of the pressurised container being designed the high-strength aluminium alloy ALZN6MG2 has been selected having the chemical composition in Table 1 (Ashby, 1992):

47

Table 1 ALZN6MG2 chemical composition

Alloy

Al

AlZn6Mg2

Cu

Basic 1.4 - 2

Mg

Mn

Fe

Si

Zn

Cr

1.8 - 2.8

0.2- 0.6

0 D0.7 MPa and pressurised gas containers for pressure values above 1.5 Mpa.n = 4 for all other pressurised tanks. Above safety factor values relate to tanks operating at temperatures under 100°K. The allowable tensile strength can be determined using the formula:

[σ ] = σ B n

Where σB is the tensile strength of the basic material measured in MPa. Thus for Boiler steel and High-strength steel brands Table 5 allowable tensile strength data is obtained. 57

Table 5

Boiler steel brands: St 34-2 [σ ] = 82.5 MPa St 37-3 [σ ] = 92.5 MPa St 44-3 [σ ] = 105 MPa High-strength steel brands: 10Mn4 [σ ] = 122 MPa Determining the cylinder wall thickness.

The thickness of the wall of the cylinder is determined using the formula:

δ =

P.D .10 −3 ,m 2.ϕ .[σ ]

where p = 100 105 Pa is the pressure inside the tank; D is the internal diameter of the tank, mm. The thickness of the cylinder wall is dependent on [σ ] and the higher this value the smaller the wall thickness, turning the tank unstable. It is recommended that the wall thickness is increased by c = 1-3 mm, the material ageing factor, which accounts for corrosion, and deformations.(Li, et all., 2002)

δ =(

P.D + 1 ÷ 3).10 −3 m 2.ϕ .[σ ]

ϕ = 0.85 is the strength coefficient for butt weld seams. The obtained results for the tank wall thickness values are shown in Table 6. Table 6 Pressure vessel Thickness

Determining the bottom sections wall thickness

The wall thickness of the bottom sections of the tank is determined using the formula:

δ1 = [

P.D .y + 1 ÷ 3 ].10 −3 2.[σ ]

58

[σ ] = σ B n

is the allowed tensile stress for bottom sections operating at temperatures not less than 100° C; y – is the bottom section shape factor, which is dependent on the relation h/D; h – is the height of the convex section of the bottom, i.e.: h h = D 2R Buth = R, 1 h = = 0 .5 2R 2

According to the table h/D = 0.5 corresponds to y = 0.75 and h = 0.75.D The data for the bottom section wall thickness is shown in Table 6. Taking into account the transportation limitations, i.e. the max. height of the off-gauge load should not be larger than 3 meters, then the total tank length will be: L1 = L + 2R2 + C1 2R2 = D2 , Where, L is the length of the cylindrical section of the tank; D2 is the external diameter of the hemisphere; Based on the results presented in Fig. 8 and Table 6, several suitable tank alternatives could be selected to be made. From strength considerations (Tables 1 and 2) and results shown in Table 6, a tank to be manufactured of Steel 10Mn4 has been selected in Fig 9.

Fig. 9 The Steel 10Mn4 tank Determining the weight of the tank

All data presented so far could be used to calculate the weight of the tank when it is not under pressure. I shall consider it comprises 2 hemispheres and a cylindrical section: V = V1 + 2V2

59

Where, V1 is the volume capacity of the material in the cylindrical section [m3 ],V2 is the volume capacity of the material in the hemisphere section [m3 ].

V1 =

π 4

.l (D12 − D22 )

D1 = D +2δ is the outer diameter of the cylinder

V2 = V =

1 .π .( D23 − D 3 ) 12

π 4

.l.( D12 − D 2 ) + 2.

1 π ⎡ L.( D12 − D 2 ) D23 − D3 ⎤ .π .( D23 − D 3 ) = .⎢ + ⎥ 12 2 ⎣ 2 3 ⎦

G = V .ρ Where ρ = 7.85 . 103 kg/m3 is the specific gravity of steel.

Fig. 10. Length to Weight Conclusions can be drawn for the relation considering the tank weight and diameter: -

There are several curves, one for the alternative where the tank has uniform overall thickness and another one for the alternative where the tank has different thickness per section.

-

For the uniform thickness alternative the curve has a minimum, which is also a unique solution to the problem for a minimum weight requirement.

-

For the various thickness alternative the curve is rising, estimating a minimum weight of m = 478.88 kg available at D = 0.998 and L = 0.102 m.

When selecting the tank dimensions it has been taken into consideration that it is going to be transported, meaning that it should not be longer than 2.5 m. It should also be stable enough, in order to be protected against accidental shifting and occupy the smallest possible space. Finally, the following basic dimensions have been determined:

60

-

weight

-

internal diameter

0.600 m

-

length of cylindrical section

1.722 m

-

cylindrical section wall thickness

0.030 m

-

bottom sections wall thickness

0.020 m

1022.893 kg

Longitudinal section stress

The internal pressure tends to force the cylinder to break in two sections, the longitudinal and the cross section. When considering the stress occurring into the longitudinal, the assumption for the bottom sections being removed. The force ΔF is a radial force and is acting on an elementary small area ΔS. The force r r r ΔF = ΔFx + ΔFy

ΔF = P . ΔS. With the shear force obtained in .

Although, N=

P.D .l 2

The product P.D is the clamping area.The stress occurring at the longitudinal section is:

σ =

P.D ≤ [σ ] 2δ

From the above formula the larger the diameter of the cylinder, the higher will be the stress for identical pressure and cylinder thickness values. Consequently, tanks intended for highly pressurised fluids are made to have small diameters.

σ =

100.10 5.0,6 = 100.10 6 MPa < [σ ] = 122.10 6 Pa 2.0,030

The pressure applied on the bottom of the tank is calculated from equation: F = P.

π .D 2 4

This force subjects the hemisphere (the bottom section) to tension. The bottom section can be regarded as a ring having an interior diameter D and δ1 thickness. The area of the ring is S = π.D.δ1 . Hence the stress is obtained for:

σ =

P..D ≤ [σ ] 4.δ 1

100..10 5.0,6 σ = = 75.10 5 Pa < [σ ] = 122.10 6 Pa 4.0,020

From the strength calculations, the operational stress in the cylindrical and bottom sections of the tank are lower than the allowable ones. Therefore, the selected from the table data is suitable for the purpose. Also, the stress in the longitudinal section is higher than that in the

61

cross section. Thus, attention should be paid to the length of weld seams. Modern techniques provide opportunities to make seamless pipes of various diameters (Zhang, 2003).

Fig. 11 Design layout of the tank

Strength calculations of seams connecting the cylindrical tank section to the bottom sections

The strength of the weld seams is dependent on the interpenetration between the added melted material (the electrode) and the material of the elements being welded. Material melting should occur in a depth of 1,5 - 3mm. If the 3mm maximum depth is exceeded this results in material overheating, which reduces its toughness. According to material thickness tables (Mathon, 2006) materials thicker than 8 mm are recommended to be chamfered at an angle of 60° ± 5°.

Fig. 12 Weld seams connecting the cylindrical tank section to the bottom The strength of the weld seams is dependent on the type of electrodes employed, the material of the elements being welded together and the quality of the welding. The allowed stress in the weld seams is assumed to be lower than the stress for the materials being welded. For the 10Mn4 material a stress of [σ] = 1450.105 Pa and an electrode ∋42 are recommended. Weld seams are subjected to tension as a result of the internal pressure of the fluid within the tank. P σ = < [σ ] F P = 100 . 105 Pa is the pressure of the fluid contained in the tank F = π . D’ . h D’ = D + 1÷3 (from Figure 3) D’ = 600 + 2÷6 = 602 ÷ 606. I assume D’ = 606 mm. And h = 20 mm is the weld seam height (3 mm seam protrusion).

62

As there are two weld seams involved the pressure shall be uniformly distributed between them. Therefore, the stress formula will be expressed as:

σ=

100.10 5 P = = 1313,8.10 5 Pa < [σ ] = 1450.10 5 Pa 2.π .D'.[σ ] 2.3,14.0,606.0,02

The weld seam is strong enough to withstand the required load, it could either be made as a multi-layer seam or welding under a layer of flux.

5.4

Discussion

5.4.1. Aluminium small capacity, highly pressurized shell: finite element calculation results Node shifts The maximum increase of the cylindrical section radius resulting from the deformation in alternative V1 occurs in its middle section and is 0.9364 mm and the increase of its axial dimension is 1.008 mm. For alternative V2 the absolute variations of dimensions are lower. The maximum increase of the cylindrical section radius occurs close to the spherical section transition and is 0.2082 mm. Otherwise, this radius variation for locations away from the spherical section transition is almost constant and the axial dimension increase is 0.3684 mm. Figure 13a shows the non-deformed and deformed network for both alternatives discussed here, the comparison suggesting that the alternative V2 deformation is more uniform in nature.

63

a) Alternative V1

b) Alternative V2

Fig.13. a). Non-deformed (before the applied load) and b).deformed state(subsequent to the applied load). Shifts have been magnified 130 times.

Stress analysis Figures 14, 15 and 16 show the equivalent stress diagrams determined at the exterior, interior and middle surface planes in accordance with Von Misses energy theory for alternative V1. These are almost constant in the spherical section of the exterior surface (Fig. 14) increasing in the transition between the spherical and cylindrical section, and rissing to the maximum at the middle of the cylindrical section. Two local extremums (Fig. 15) were observed in the exterior surface of the transition area between the cylindrical and spherical sections. The equivalent stress at the middle surface plane (Fig. 16) of the spherical sections is constant and increases in the transition reaching its maximum in the cylindrical section middle. The maximum equivalent stress is acting on the cylindrical middle section at the exterior surface. Stress concentration is observed in the pipe connection opening area and this has a strictly local nature (in the interior surface) and does not represent any hazard for plastic materials.

64

Fig. 14. Equivalent stress distribution determined in accordance with Von Misses’s theory for the exterior surface of Alternative V1

Fig. 15. Equivalent stress distribution determined in accordance with Von Misses’s theory for the interior surface of Alternative V1

Fig. 16. Equivalent stress distribution determined in accordance with Von Misses’s theory for the middle surface of Alternative V1.

Fig. 17. Equivalent stress distribution determined in accordance with Von Misses’s theory for the exterior surface of Alternative V2. 65

Fig. 18. Equivalent stress distribution determined in accordance with Von Misses’s theory for the interior surface of Alternative V2

Fig. 19. Equivalent stress distribution determined in accordance with Von Misses’s theory for the middle surface of Alternative V2.

Figures 17, 18 and 19 show the equivalent stress diagrams determined at the exterior, interior and middle surfaces according to the energy theory of Von Misses for alternative V2. Two local extremums of equivalent stress can be observed in the exterior (Fig. 17), interior (Fig. 18) and middle surface (Fig. 19) in the area of transitions between the spherical and cylindrical section. The equivalent stress value decreases in the spherical sections and the cylindrical section is uniformly loaded. From the comparison between the two alternatives it is obvious that for the V2 alternative the larger material amount is uniformly loaded with stress, which is close to the allowed values. Stress concentration in the pipe opening area is also less in amount. Therefore, we can expect lower construction weight for longer cylindrical sections. Figures 20 through 23 show the directions of major stresses occurring in the meridian section for both alternatives both in the pipe opening area (Fig. 20 and 22) and the spherical to cylindrical transition area (Fig. 21 and 23). From these figures one of the three major stresses is in the radial direction and another one is in the tangential. The radial major stress is a pressure stress and the tangential one is a tension stress. The third major stress is in the circumferential direction and is a tension stress.

66

Fig. 20. Major stress directions in the meridian section in the pipe opening area for Alternative V1

Fig. 21. Major stress directions in the meridian section in the transition area between the spherical and cylindrical section for Alternative V1.

Fig. 22. Major stress directions in the meridian section in the pipe opening area for Alternative V2

Fig. 23. Major stress directions in the meridian section in the transition area between the spherical and cylindrical section for Alternative V2

5.4.2. HSS large capacity, low pressure loading tank: finite element calculation results Node shifts The maximum increase of the cylindrical section radius occurs close to the transition to the spherical section and is 0.1284 mm. Otherwise, this radius variation for locations away from the cylindrical section transition is almost constant and equal to 0.1272 mm and the axial dimension increase is 0.2877 mm. Figure 24 shows the non-deformed and deformed network. 67

Stress analysis Figures 25, 26 and 27 show the equivalent stress diagrams determined at the exterior, interior and middle surface planes in accordance with the energy theory of Von Misses. Two local maximums of the equivalent stress can be observed in the exterior surface in the area of transitions between the cylindrical and spherical sections, which is a result of the stress concentration from the transition between the two surfaces. Away from the transition locations the cylindrical and spherical sections are almost uniformly loaded and the equivalent stress value is higher in the cylindrical section. The maximum equivalent stress is observed in the locations on the interior surface plane. Stress concentration in the pipe union opening area is rather obvious, having a strictly local nature. Figures 28 and 29 show the directions of major stresses occurring in the meridian section both in the pipe opening area (Fig. 28) and the spherical to cylindrical transition area (Fig. 29). In these figures one of the three major stresses is in the radial direction and another one is in the tangential direction. The radial major stress is a pressure stress and the tangential one is a tension stress. The third major stress is in the circumferential direction and is a tension stress.

Fig. 24. Non-deformed (before the load is applied) and deformed (after the load is applied) state. Shifts have been magnified 130 times

Fig. 25. Equivalent stress distribution determined in accordance with von Mises’s theory for the exterior surface for Alternative V1

68

Fig. 26.. Equivalent stress distribution determined in accordance with von Mises’s theory for the interior surface for Alternative V1

Fig. 27. Equivalent stress distribution determined in accordance with von Mises’s theory for the middle surface for Alternative V1

Fig. 28. Major stress directions in the meridian section in the pipe opening area for Alternative V1.

69

Fig. 29. Major stress directions in the meridian section in the transition area between the spherical and cylindrical section for Alternative V1.

5.5. Selecting Acid-Resistant Materials 5.5.1 Introduction Accumulated statistics show that worldwide annually around 30% of all metal constructions become useless as a result of damages caused by corrosion. Corroded metal equipment is taken out of operation and subjected to processing in corresponding metallurgy plants. A certain part of metal equipment is subjected to electro chemical corrosion in electrolytic (socalled corrosive) medium. Included here are tanks designed for storage of acids, bases, salts, etc., which are subjected to electrolytic corrosion as they are surrounded by an electrolytic medium. Nowadays, there are multiple possibilities to fight corrosion effectively. There are some measures to protect metal constructions that should and must be taken from the very 70

design phase of the metal equipment by selecting the suitable material. Depending on the conditions and properties of the medium that the metal equipment is going to be subjected to various brands of steel and alloys having the appropriate corrosion resistance should be used to make it reliable and inexpensive. This task is covered by the present assignment of selecting materials for storing diluted sulphuric acid and hydrochloric acid (10 % w/w).

5.5.2 Anodic passivation It was M.V.Lomonosov (1738) and later Bertselius and M.Faraday that described the paradoxical fact that iron easily dissolves in diluted nitric acid solutions but this process continues only until acid concentration is increased. Faraday explained this by the formation of a protective oxide layer on the iron surface, which prevents the metal from dissolving further. The process of bringing metals to a condition of increased resistance when subjected to various oxidising agents is called passivation. With all the practical application possibilities that this phenomenon offers, namely for fighting metal corrosion, it has been the target of multiple and comprehensive studies ever since it was initially discovered. In addition to being subjected to oxidising agents metals could also be passivated by means of anodic polarization, i.e. by using electric current to divert the equilibrium potential of the electrode in the positive direction. In this case we talk about anodic passivation. Modern studies on anodic passivation of metals run basically in two main directions. On one side, the mechanics of the processes leading to changes in the condition of the metal surface and bringing the metal into stable (passive) state are investigated and the nature and morphology of oxidised layers thus formed are studied, on the other.

5.5.3 Mechanics of anodic passivation Dependent on the nature of the solution and the value of diversification of electrode potential in the positive direction metal passivation could take place in different ways. In active anodic dissolving of metals there may be a point of saturation of the electrolyte with respect to certain metal salts, thus forming a solid product that can be deposited on the surface of the metal. If the apparent current density is maintained constant then the actual current density in the areas accessible for the electrolyte will increase as a result of the shield formed on the electrode surface by the deposited non-conductive solid product. The potential in these areas strongly diverts into the positive direction, which makes it possible for a thermodynamic reaction to take place and formation of a hard metal oxide or hydroxide. The oxide layer thus formed on separate areas eventually spreads on the entire metal surface preventing it from dissolving further. Also outstanding are V.Muller’s (1933) trials that subjected iron, zinc, copper, etc. metal electrodes horizontally positioned in the electrolyte to anodic polarization in diluted sulphuric acid solutions. The polarized light studies have indicated that when there is no motion in the electrolyte hydrated sulphates of corresponding metals deposit on the surface of the electrodes. Once these salts are formed metals transform into their passive state. Anodic passivation of metals could also be carried out without the formation of the shielding solid products. If no anions are present in the electrolyte to precipitate the metal cations that have entered the solution and if the potential of the electrode has been sufficiently diverted into the positive direction to allow for a reaction to take place, then a new phase of metal oxide or hydroxide is directly deposited on the metal surface, which changes the properties of

71

the initial metal surface and the nature of the anodic reaction. Under such conditions the metal stops to dissolve measurably and transfers into passive state.

Theories of passivity of metals. Wide practical applications uncovered by metal passivation have enhanced not only applications studies in this area but also investigations involving the nature of the processes taking place in this phenomenon. A large number of hypothesis were made with regards to the mechanism of passivation and the nature of the passive state of metals. Various concepts of above issues could be classified into two basic groups. One of the groups, the smaller one, comprises the concepts according to which the passivation phenomenon is the result of a number of changes taking place in the physical properties of the metal itself (for example, the change in the electron state of the metal and its transformation into a specific, chemically inactive allotropic state). Another group of theoretical concepts links passivation to the formation of protective oxide layers on the metal surface. The metal does not become thermodynamically nobler during passivation but transfers into a stable state thanks to the protective layers formed on its surface, which significantly change the electrochemical properties of the metal-medium interface. And if the discussions on the issue of the passive state of metals still continue to be fierce they are mainly concentrated on the question: what is the nature of these protective layers? Are these two-dimensional layers of adsorbed oxygen that block the metal surface making it inactive (the adsorption theory) or these are three-dimensional oxide layers, which under the form of a separate phase cover the metal surface and purely mechanically prevent it from the actions of the corrosive medium (the phase theory). On the modern stage of development of our concepts of the mechanism of passivation and the nature of the passive state the widest popularity has the phase theory the basic ideas of which were stipulated by M.Faraday (1836). U.Evans gave direct experimental proof in support of these theoretical conceptions. He succeeded to separate from the surface of passivated iron some oxide layers and examined them directly under the microscope.

5.5.4 Experimental studies – anodic protection of mild steel in sulphuric acid solution Experimental setup. The apparatus consists of a simple support for suspending two electrodes made of mild steel strip into a 600 ml beaker containing approx. 400 ml acid. The current supply is from a stabilized power supply source. The current and voltage values could be measured using the power source devices and a multimeter. We increase the voltage in 0.1V intervals up to maximum 3.0V and we measure the current value for every voltage increase. Before we take down its value we wait for the current to stabilize. The current readings increase steadily up to the point where the passive section is reached when it suddenly drops. When 3.0V is reached we reduce the current through 0.1V intervals to see if there are some hysteresis effects. We repeat the experiment adding to the acid a small quantity of concentrated brine solution. We plot the voltage variation in relation to current density logarithm and we analyse the results.

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Fig. 30 Experimental setup diagram Analysis of resulting diagrams: The diagram shown in Appendix 1indicates that the curve consists of several characteristic sections, each corresponding to a specific metal state. We can note that when we increase the voltage current density suddenly increases from 1.5 to 3.0 log CD. This section corresponds to the active anodic dissolving of iron in sulphuric acid. For voltage values between 0.5V and 1.3V there is a section that characterizes by the fact that the current is independent of the potential of the electrode. A shielding solid product from basic iron sulphate is formed in this section, which has porous structure and dissolves in the electrolyte at a certain speed. When the speeds of formation and dissolving become equal the thickness of the sediment becomes constant and independent of the electrode potential. In the 1.3V section anode current suddenly drops and the electrode goes into passive state. In the section between 1.3V and around 2V iron is passivated. We could say the current is independent of electrode potential. Despite of the fact that the metal is in its passive state some very low anode current still flows through the electrode, which is due to the dissolving of passivated iron. This current is one of the most characteristic features of metals in passive state. The potential corresponding to this current could be regarded as the thermodynamic limit beyond which the metal goes in a state of active dissolving and above which conditions are created for forming protection oxide layers. After a voltage of 1.75V anodic deposition of oxygen starts on the passivated electrode as a result of which the current increases with every increase of electrode potential. The opposite processes take place when current density reduces. For voltage values of 1.75V electrode potential changes in the negative direction and anodic metal dissolving is resumed. In this process resumption the diagram indicates a hysteresis, which could be explained by the fact that the passive layer thus formed stays stable even at lower current densities than those when the layer was formed. It takes some time to cover the entire electrode with the oxide layer and this time would be smaller for higher anode current densities. When we repeat the experiment after adding a small quantity of concentrated brine solution to the acid the acid saturates with positive hydrated ions of hydrogen and negative ions of chlorine, which are directed to the electrodes and ensure increase and eventual flow of direct current as indicated by the diagrams shown in Appendix 2.

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Conclusions and practical applications. The results show that this experiment could be used for providing anodic protection of metals against corrosion. An oxidised layer covers metals when immersed into suitable oxidising medium (oxidation) or when used for a certain time as anodes in an electrolytic bath where their surface is oxidised by the oxide deposited on the anode (anodising).

5.5.5 Selecting materials for the tank Expensive special steels (£ 3 per kg). High-alloy steels are being produced for industrial, building and domestic applications, which are both corrosion resistant and fireproof. Corrosion resistant steels are capable of resisting the destructive chemical and electrochemical action of external environment. Considering steel’s ability to resist a certain aggressive corrosive medium it is classified as stainless, acid resistant and scale resistant. Acid resistant steel exhibits high corrosion resistance against the action of various aggressive mediums. Corrosion resistant steels are usually chrome- or chrome-nickel alloys containing above 12% chrome. Depending on its chemical composition steels microstructure could be ferrite, semiferrite and allowing structural transformations, i.e. that can be subjected to improvements (above 15% carbon, 10% to 18% chrome) having austenitic structure. High nickel and manganese steels feature extended areas of stable austenitic structure. When chrome-nickel steels are heated up to temperatures of 490 – 900 degrees or when being cooled down slowly in this interval chrome carbides are formed along the boundaries of the austenitic grains. This results in grains of rich in chrome and poor in carbon cores. As a result of this structural non-uniformity steel shows a tendency for inter-crystal corrosion. To avoid this drawback chrome-nickel steels have to be additionally alloyed using strong carbideforming elements such as titanium and niobium. The austenite structure of chrome-nickel and chrome-nickel-manganese steels renders these materials some very essential properties, such as non-magnetic characteristics, improved strength under high temperatures and good weldability. Chrome-nickel steels usually acquire satisfactory strength and good plastic characteristics after being hardened with austenite. Strength characteristics of such steels can be improved by cold-work hardening by means of cold rolling, cold drawing or stamping. Cold-work austenite steel maintains sufficient plastic properties. Semi-finished products made of such steel could be bended, shaped or even stamped.

Selecting a high-alloy steel brand. For our application I select X5CrNiMoCuNb18 18 steel, which exhibits highest sulphuric and other acids resistance and finds wide application in the chemical industry. I am going to give the following most essential mechanical characteristics for this steel: the strength σB, the yield strength σS, the percentage of specific elongation δ, the percentage reduction of area ψ and impact strength aK. I will also apply the chemical composition, approximate forging and temperature treatment temperatures. The data is presented in the following tables:

Steel brand

σS

σВ

δ

ψ

аK

ISO

DIN

МРа

МРа

%

%

KJ/m2

X5CrNiMoCuNb18 18

1.4505

230

750

40

35

650 74

Steel brand

Content of elements in %

ISO

DIN

C

Si

X5CrNiMoCuNb18 18

1.4505